Computational study of compounds with application in dye ...

Computational Study of Compounds with

Application in Dye Sensitized Solar Cells

Narges Mohammadi

Dissertation submitted in fulfilment of requirements for the degree of

Doctor of Philosophy

Faculty of Science, Engineering and Technology

Swinburne University of Technology

Australia

2014

Copyright © 2014

By Narges Mohammadi

i

Abstract

The global need for energy is estimated to double by 2050 and triple by the end of

this century. Currently, fossil fuels are the primary source for energy supply in the

world. However, the excessive use of fossil fuels has resulted in serious

environmental impact such as global warming. Another major problem is the

limited resources of fossil fuels. As a result of these problems associated with

fossil fuels, the demand for replacing them with clean, renewable and

sustainable energy sources is increasing.

Solar energy is the largest source of clean energy readily available. Nevertheless,

it is not the main source of electricity power generation yet; mainly because of the

high price of the current conventional silicon-based solar cells. Dye sensitized

solar cells (DSSC) are a newer type of solar cells. They have gained considerable

attention in the last two decades, as potentially inexpensive alternative to

conventional costly silicon solar cells. However, their efficiencies are still lower

than the traditional solar cells. DSSC is a complex device composed of several

components. That is, the conversion of solar radiation into electrical energy in this

device relies on the interplay of several key components. The unique architecture

of DSSC provides numerous possibilities to alter its components. As a result, over

the past twenty years a considerable and increasing amount of research efforts

have been devoted to design and synthesis new materials such as dye sensitizers

as a route to improve DSSC’s power conversion efficiency. However, most of

such efforts have been based on the costly and time-consuming synthesis

procedures. This drawback calls for applying new methods such as computational

modelling and rational designing of new materials.

This thesis has focused on the state-of-the-art computational methods to study,

model and rationally design compounds for application in DSSC. Two main

components of DSSC, i.e. the dye sensitizer and the redox mediator have been the

subject of this thesis. The density functional theory (DFT) and time dependent

DFT (TD-DFT) methods have been employed. The electronic structures of two

already well-performing reference dyes, TA-St-CA and Carbz-PAHTDDT, have

ii

been studied quantum mechanically. New dyes have been rationally designed by

chemically modifying these reference dyes. In order to improve the light

harvesting efficiency of the cell, the rational design of the dyes have been aimed

at producing new sensitizers with reduced energy gap between the highest

occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital

(LUMO), as well as enhanced red-shifted electronic absorption spectra, with

respect to the reference dyes.

Computational methods are powerful tools to study and design new materials for

DSSC. Dewar's rules which are based on perturbational molecular orbital theory

have been applied to design a number of new dyes based on the reference TA-St-

CA dye. Dewar's rules have been found to serve as a good indicator for

determination of the appropriate substitution positions on the π-conjugated bridge

of the reference dye. Two new dyes have also been designed by modifying the

donor group of the TA-St-CA dye. This thesis reveals that for this reference dye,

the donor modifications have more profound impact on the absorption spectra

compared to the linker alternations.

Two new carbazole-based organic dye sensitizers have also been designed

through chemical modifications of the π-conjugated bridge of the Carbz-

PAHTDDT (S9) dye. Reduced HOMO-LUMO gap and red-shifted absorption

spectra have been achieved for both new dyes. It is also found that the long-range

correction to the theoretical model in the TD-DFT simulation is important to

produce accurate absorption wavelengths for this reference dye and its derivatives.

This thesis has further studied the electronic structure, molecular properties and

conformers of ferrocene (Fc) as an important candidate for the redox mediator of

DSSC. This thesis has found a fingerprint in the infrared (IR) spectral region of

450–500 cm−1 of ferrocene as a key to differentiate its eclipsed and staggered

conformers. It is shown that the basis set plays an important role in the accuracy

of DFT calculations of ferrocene and the B3LYP/m6-31G(d) model provides

excellent agreement with experiments on the simulated IR spectra of Fc. The

B3LYP/m6-31G(d) model is also found to be a very efficient and accurate model

for calculations of the redox potential of the Fc/Fc+ redox couple.

iii

To my beloved Alireza, Mom and Dad

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Acknowledgment

I take this opportunity to express my profound gratitude and deep regards to my

supervisor, Professor Feng Wang, for the continuous support of my PhD study

and research. I would like to thank her for encouraging my research and for

allowing me to grow as an independent research scientist. I would also like to

thank my other supervisor, Dr. Peter J Mahon, for the assistance he provided at all

levels of the research project.

I am grateful for the funding sources and high-tech facilities that made this

research project possible. I would like to acknowledge the Swinburne University

of Technology for the Vice-Chancellors’ Postgraduate Research Award and also

the Australian Government for the International Postgraduate Research

Scholarship (IPRS), that provided the necessary financial support for this

research. The library facilities and the high performance supercomputing facilities

of the Swinburne University have been indispensable. I also acknowledge the

Victorian Partnership for Advanced Computing (VPAC) for supercomputing

facilities. I acknowledge the THz/Far-IR beamline at the Australian Synchrotron,

Victoria, Australia. I also thank the Australian Synchrotron for travel funding

under the International Synchrotron Access Program (ISAP) to access the

GasPhase beamline at the Elettra Sincrotrone Trieste, Italy.

I have been very privileged to get to know and to collaborate with many great

people. I thank Professor Christopher T. Chantler (School of Physics, The

University of Melbourne, Australia) for the motivation of the ferrocene study, as

well as his continuous collaboration and support for this research work.

Appreciation also goes out to Dr. Stephen Best (School of Chemistry, The

University of Melbourne, Australia) for his collaboration and support in this work

and for providing the experimental FTIR data of ferrocene. He has patiently

taught me many new things and helped me get confidence to do experimental

work at Australian Synchrotron. Thank you Dr. Stephen Best. A very special

thanks goes out to Professor Kevin C. Prince (Elettra Sincrotrone Trieste, Italy)

v

for his kind support and hospitality during my visit. I also thank Dr. Dominique

Appadoo (THz/Far-IR beamline, Australian Synchrotron) for his technical support

to measure the experimental IR data of ferrocene in gas-phase. I would also like to

thank Dr. Bob Laslett for kindly letting me work as a lab demonstrator under his

guidance.

I owe my deepest gratitude to Dr. François Malherbe and Dr. Karen Farquharson.

I can’t say thank you enough for your tremendous support and help when I needed

it most.

I would like to show my gratitude to Professor Richard Sadus, Professor Billy

Todd, Ms. Jennifer Lim, Ms. Alyssa Wormald, Ms. Robyn Watson and Ms.

Hayley Mowat. Thank you for your smile, positiveness and the assistance you

provided to me in the past four years.

My sincere thanks goes to all my friends in Swinburne University. We have

shared many smiles and many tears, and you became a part of my life. Thank you

Lalitha, Fangfang, Anoja, Aravindhan, Marawan, Bita, Azadeh, Sanjida, Ronit

and Qudsia for your friendship.

I would like to thank my loved ones, who have supported me throughout entire

life. Mom and Dad, it's impossible to thank you adequately for everything you've

done, for your love, encouragement, support, and patience. Thank you for

everything. Thank you my dear Parisa, Najmeh, Javad, and my always little cute

ones, Kosar, Mohammad, Yasmin, and Orkideh. You enlighten my life.

I have saved the last words of acknowledgment for my better half and beloved

Alireza. Thank you for your unconditional love and endless support. You have

been by my side throughout this journey, living every single minute of it. I love

you.

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Declaration

I hereby declare that the thesis entitled “Computational study of compounds with

application in dye sensitized solar cells”, which is submitted in fulfilment of the

requirements for the degree of Doctor of Philosophy in the Swinburne University

of Technology, is my own work. To the best of my knowledge and belief, it

contains no material previously published or written by another person, except

where due references are made in the text of the thesis. Any contribution made to

the research by colleagues, with whom I have worked at Swinburne or elsewhere,

during my candidature, is fully acknowledged. I affirm that this thesis contains no

material, which has been accepted for the award to the candidate of any other

degree or diploma.

Narges Mohammadi

April 2014

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Refereed Publications

• Mohammadi, N., & Wang, F. (2014). First-principles study of Carbz-PAHTDDT dye sensitizer and two Carbz-derived dyes for dye sensitized solar cells. Journal of Molecular Modeling, 20(3), 2177.

• Ganesan, A., Mohammadi, N., & Wang, F. (2014). From building blocks of proteins to drugs: A quantum chemical study on structure-property relationships of phenylalanine, tyrosine and dopa. RSC Advances, 4 (17), 8617–8626.

• Mohammadi, N., Mahon, P. J., & Wang, F. (2013). Toward rational design of organic dye sensitized solar cells (DSSCs): an application to the TA-St-CA dye. Journal of Molecular Graphics and Modelling, 40, 64-71.

• Mohammadi, N., Ganesan, A., Chantler, C. T., & Wang, F. (2012). Differentiation of ferrocene D5d and D5h conformers using IR spectroscopy. Journal of Organometallic Chemistry, 713(0), 51-59.

• Chantler, C. T., Rae, N. A., Islam, M. T., Best, S. P., Yeo, J., Smale, L. F., Hester, J., Mohammadi, N., & Wang. F. (2012). Stereochemical analysis of ferrocene and the uncertainty of fluorescence XAFS data. Journal of Synchrotron Radiation, 19, 145-158.

• Ivanova, E. P., Truong, V. K., Webb, H. K., Baulin, V. A., Wang, J. Y., Mohammodi, N., Wang, F., Fluke, C., & Crawford, R. J. (2011). Differential attraction and repulsion of Staphylococcus aureus and Pseudomonas aeruginosa on molecularly smooth titanium films. Scientific Reports, 1, 165.

• Mohammadi, N., Wang, F. (Accepted, to be published in April 2015). Application of Computational Methods to the Rational Design of Photoactive Materials for Solar Cells. In Computational Chemistry Methodology in Structural Biology and Material Sciences. Apple Academic Press (USA and Canada).

viii

Conference Presentations

• Mohammadi, N., Wang, F., Best, S., Appadoo, D., Islam, T. M., & Chantler, C. T. (2013). Use of IR spectra and isotope label to probe ferrocene conformers: theory and experiment. Australian Synchrotron User Meeting 2013, Melbourne, Australia, December 2013 (Poster Presentation).

• Mohammadi, N., Arooj, Q. & Wang, F. (2013). XPS studies of (S)-α-(Z-Amino)-γ-butyrolactone, a signaling molecule in bacterial cell communication. Australian Synchrotron User Meeting 2013, Melbourne, Australia, December 2013 (Poster Presentation).

• Mohammadi, N., & Wang, F. (2013). TD-DFT Simulation of the UV-Vis Spectra of Ferrocene. 38th International conference on Vacuum Ultraviolet and X-ray Physics, Hefei, Anhui Province, China, 12-19 July, 2013. (Poster Presentation).

• Wang, F., & Mohammadi, N. (2013). Use of IR spectra to probe ferrocene conformers: theory and experiment. 4th Asian Spectroscopy Conference, Singapore, December 15-18, 2013. (Oral Presentation).

• Mohammadi, N., & Wang, F. (2012). Bathochromic shift in photoabsorption spectra of organic dye sensitizers through structural modifications for better solar cells. 20th Australian institute of physics congress, University of New South Wales, Australia, 9-13 December 2012 (Oral Presentation).

• Mohammadi, N., & Wang, F. (2012). Toward rational design of organic dye sensitized solar cells through chemical modifications: an application to the TA-St-CA dye, Melbourne Meeting of Molecular Modellers, University of Melbourne, Australia, 25 September 2012 (Poster Presentation).

• Uppiah, O. J., Mohammadi, N., & Wang, F. (2012). Sugar saturation of nucleoside antibiotics revealed by simulated IR spectra: Thymidine and Stavudine. Melbourne Meeting of Molecular Modellers, University of Melbourne, Australia, 25 September 2012 (Poster Presentation).

• Mohammadi, N., & Wang, F. (2011). A computational study of the HOMO-LUMO gap reduction through modifications of the π –conjugated bridge of TA-St-CA organic dye. Australian Synchrotron User Meeting 2011, Melbourne, Australia, December 2011 (Poster Presentation).

• Mohammadi, N., & Wang, F. (2010). A study of phenothiazine using quantum mechanical modeling. MM2010 - Molecular modelling for the life and materials sciences, Melbourne, Australia, 28th November-1st December 2010 (Poster Presentation).

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Contents

List of figures xii

List of tables xvi

List of abbreviations xviii

1. Introduction 1

1.1. Background 1

1.2. Dye sensitized solar cells 4

1.3. Device structure and working principles 6

1.3.1. The semiconducting photoanode 7

1.3.2. Redox shuttles 8

1.3.3. Dye sensitizers 10

1.3.3.1. Features of ideal dye sensitizers 12

1.4. Motivation of this thesis 15

1.4.1. Rational design of organic dyes 17

1.5. The aim, focus and overview of this thesis 21

References 24

2. Methods and theoretical details 35

2.1. Introduction 35

2.2. Background 36

2.3. The time-independent Schrödinger equation 37

2.4. The Born-Oppenheimer approximation 39

2.5. Hartree-Fock theory 41

2.6. Molecular orbital theory and basis set 46

2.7. Density functional theory 48

2.7.1. Hohenberg–Kohn theorems 50

2.7.2. Kohn–Sham approach 51

2.7.3. Approximate exchange-correlation functionals 52

2.8. Time-dependent density functional theory 54

2.9. Potential energy surface and geometry optimization 56

x

2.10. Vibrational frequency calculation 57

2.11. UV-Vis spectroscopy 58

2.12. Solvent effects 60

References 62

3. Rational design of new dyes based on TA-St-CA sensitizer 70


3.2. Dewar’s rules and design of new dyes 73

3.3. Computational details 77

3.4. Molecular properties 78

3.5. Frontier molecular orbital analysis 82

3.6. UV-Vis absorption spectra 86

3.7. Summary and conclusions 95

References 96

4. Novel annulene-based dyes 101


4.2. Design of the new dyes 102

4.3. Computational details 107

4.4. Geometrical details 108

4.5. Frontier molecular orbital analysis 115

4.6. UV-Vis absorption spectra 117

4.7. Molecular orbital spatial distribution 121


References 126

5. Carbz-PAHTDDT dye and its derivatives 130


5.2. Methods and computational details 132

5.3. Molecular structures and design of the new dyes 135

5.4. Frontier molecular orbitals 142

5.5. Nonlinear optical properties 147

5.6. Excitation energies and UV-Vis spectra 150


References 156

xi

6. Ferrocene 162


6.2. Computational methods and experimental details 163

6.3. Ferrocene structure 166

6.3.1. Geometries and potential energy scan 170

6.3.2. Molecular electrostatic potential 178

6.3.3. Infrared spectroscopy of ferrocene in isolation 180

6.3.4. Differentiation of the D5h and D5d conformers 186

6.3.5. Influence of deuteration on the IR spectra 189

6.3.6. Infrared spectroscopy of ferrocene in solution 195

6.4. Ferrocene-based electrolyte 205

6.4.1. Ferrocene/ferrocenium redox potential 205

6.5. Conclusions 209

References 211

7. Summary, conclusions and outlook 220

Appendix 226

xii

List of Figures

Fig.1.1: Schematic illustration of DSSC structure and components and

working principle of a typical DSSC.

6

Fig.1.2: Structure of the representative members of the Ru-based dyes:

N3, N719 and black dye.

10

Fig.1.3: The photon flux density of solar radiation. 13

Fig.1.4: A scheme of D-π-A dye configuration. 19

Fig.1.5: The cyanoacrylic acid acceptor/anchoring group. 20

Fig.2.1: Various transitions between the bonding and anti-bonding

electronic states of a molecule, when light energy is absorbed.

59

Fig.3.1: Molecular structure of the reference TA-St-CA dye. 71

Fig.3.2: A scheme Dewar’s rules. 74

Fig.3.3: The structure of reference dye TA-St-CA. 78

Fig.3.4: The calculated frontier MO energy levels using PBE0/6-31G*

in vacuum.

83

Fig.3.5: Comparison of the charge density of HOMOs and LUMOs of

the new dye, ED-I and EW-I with respect to those of the

reference TA-St-CA dye.

86

Fig.3.6: The simulated UV–Vis absorption spectra of TA-St-CA dye in

gas-phase and ethanol solution, compared with the

experimental spectra in ethanol solution.

87

Fig.3.7: The simulated UV–Vis absorption spectra of TA-ST-CA dye

and its substituted new dyes generated from the substitutions

of –NH2, and (b) from –N(CH3)2 ED groups.

89

xiii

Fig.3.8: The simulated UV–Vis absorption spectra of TA-ST-CA dye

and its substituted new dyes generated from the substitutions

of the electron withdrawing group (–CN).

90

Fig.4.1: Molecular structure of different annulenes. 102

Fig.4.2: Molecular structure of the reference TA-St-CA sensitizer and

new dyes AN-14 and AN-18.

106

Fig.4.3: Optimized 3D structures of the new dyes AN-14 and AN-18. 109

Fig.4.4: Optimized 3D structure and labelling of the [14]-annulene

ring.

110

Fig.4.5: Optimized 3D structure and labelling of the [18]-annulene

ring.

113

Fig.4.6: The calculated frontier MO energy levels using PBE0/6-31G*

model in vacuum.

115

Fig.4.7: The simulated UV–Vis absorption spectra of the TA-ST-CA,

AN-14 and AN-18 in ethanol solution.

119

Fig.4.8: Comparison of the HOMOs and LUMOs of the new dye, AN-

14 and AN-14 with respect to those of the reference dye.

122

Fig.5.1: Optimized 3D structures of the reference Carbz-PAHTDTT

(S9) dye sensitizer.

135

Fig.5.2: Optimized 3D structures of S9, S9-D1 and S9-D2. 138

Fig.5.3: Sketch of the reference S9 dye and the structure of the bridge

of S9, S9-D and S9-D2 dyes showing NBO charge of atoms.

140

Fig.5.4: Calculated frontier MO energy levels using B3LYP/6-

311G(d)// PBE0/6-311G(d) model in DCM solution.

144

Fig.5.5: Comparison of the charge density of HOMOs and LUMOs of

the reference S9 dye, and the new S9-D1 and S9-D2 dyes.

146

Fig.5.6: The simulated UV-Vis spectra of three dyes, S9, S9-D1 and

S9-D2 using TD-BHandH/6-311G(d) model in DCM solution.

154

xiv

Fig.6.1: Proposed structures for ferrocene: stretched, sandwich and

double cone.

167

Fig.6.2: Optimized molecular structures of the eclipsed (D5h) and

staggered (D5d) conformers of ferrocene in (3D) space.

168

Fig.6.3: Optimized molecular structures of the eclipsed conformer of

ferrocene in 3D space, visualized by different GUI tools.

171

Fig.6.4: Molecular orbital diagrams of ferrocene conformers. 174

Fig.6.5: The highest occupied molecular orbitals (HOMOs) and the

lowest unoccupied molecular orbitals (LUMOs) of D5h and D5d

conformers of ferrocene.

176

Fig.6.6: Potential energy scan (PES) of the dihedral angle rotating the

axis connecting the middle Fe atom as well as the centres of

two Cp rings.

177

Fig.6.7: Two-dimensional (2D) cross sections of the molecular

electrostatic potential (MEP) of ferrocene

179

Fig.6.8: Comparison of the simulated and the experimental IR spectra

of ferrocene in the region of 400-1200 cm-1.

181

Fig.6.9: Comparison of simulated IR spectra of ferrocene, D5h and D5d

in vacuum in the region of 400-4000 cm-1.

183

Fig.6.10: Comparison of high resolution (FWHM =5 cm-1) IR spectra of

D5h and D5d ferrocene based on in the region of 400-650 cm-1.

186

Fig.6.11: The IR spectra of the eclipsed (D5h) and staggered (D5d)

ferrocene in the fingerprint region.

188

Fig.6.12: The IR spectra of the eclipsed (D5h) and staggered (D5d)

ferrocene (Fc-h-10) and deuterated ferrocene (Fc-d-10).

190

Fig.6.13: The IR spectra of ferrocene (Fc-h-10) and deuterated ferrocene

(Fc-d-10) in the fingerprint region.

194

xv

Fig.6.14: Measured FTIR spectra of ferrocene in the region of 400-1200

cm-1 in a number of solvents at room temperature.

196

Fig.6.15: The measured IR spectrum of Fc in acetonitrile solution with

the simulated infrared spectra inthe region of 400-1200 cm-1.

198

Fig.6.16: The simulated IR spectra of eclipsed Fc in the DOX solution

using PCM, CPCM and SMD solvation models with the FTIR

spectral measurement.

202

Fig.6.17: Comparison of the simulated IR spectra of the eclipsed Fc in

the region of 400-600 cm-1 with the FTIR measurement in

various solvents.

204

xvi

List of Tables

Table.3.1: Molecular structure of the TA-ST-CA dye and new dyes. 75

Table.3.2: Molecular properties of the new dyes and the reference TA-

ST-CA dye.

81

Table.3.3: Calculated excited energy (in nm), transition configuration,

and oscillator strengths (f) for the two most intense peaks of

TA-ST-CA dye and the new dyes in ethanol solution.

91

Table.3.4: Comparison of the substitution effects on the energies of the

HOMOs, LUMOs, the HOMO-LUMO energy gap, shift of

the spectral peaks and spectral widths in ethanol solution.

94

Table.4.1: Compression of the optimized geometries of the [14]-

annulene ring of the present work with data reported in

literature.

112

Table.4.2: Compression of the optimized geometries of the [18]-

annulene ring of the present work with data reported in

literature.

114

Table.4.3: Calculated excited energy (in nm), transition configuration,

and oscillator strengths (f) for the two most intense peaks of

TA-ST-CA dye and the new dyes in ethanol solution.

120

Table.5.1: The selected bond length, dihedrals, π-lengths and dipole

moment of the S9, S9-D1 and S9-D2 dyes.

142

Table.5.2: Energy levels of HOMO, LUMO and HOMO-LUMO gap

calculated by different functionals.

143

xvii

Table.5.3: The first total hyperpolarizability (βtot), isotropic

polarizability (α) and polarizability anisotropy (Δα) of S9,

S9-D1 and S9-D2 dyes.

149

Table.5.4: Calculated excited energy (in nm), oscillator strengths (f),

and transition configurations for the three most intense peaks

of S9, S9-D1 and S9-D2 dyes in DCM solution.

151

Table.6.1: Comparison of the optimized geometries of eclipsed and

staggered conformers of ferrocene.

172

Table.6.2: Calculated IR frequencies and their assignment for the D5h

and D5d conformers of ferrocene using the B3LYP/m6-

31G(d) model.

185

Table.6.3: Calculated IR frequencies and their assignment for the D5h

and D5d conformers of Fc-h-10 and Fc-d-10 and their

corresponding spectral shifts.

191

Table.6.4: Comparison of the measured Fc spectral peak positions in

various solvents and available experiment and calculations.

197

Table.6.5: Comparison of the measured and simulated Fc IR spectral

peak positions in various solvents in the region of 400-1200.

cm-1.

200

Table.6.6: Calculated values required to obtain the redox potential of

Fc/Fc+ in DSMO solution.

208

xviii

List of Abbreviations

ACN Acetonitrile

BO Born-Oppenheimer approximation

Cp Cyclopentadiene

CT Charge-Transfer

DCM Dichloromethane

DFT Density Functional Theory

DMSO Dimethyl Sulfoxide

DOX Dioxane

D-PCM Dielectric Polarized Continuum Model

DSSC Dye Sensitized Solar Cells

D-π-A Donor-π linker-Acceptor

ED Electron-Donating

EDS Electron Donating Substitution

EDS Electron Donating Substitutions

EW Electron-Withdrawing

Fc Ferrocene

Fc/Fc+ Ferrocene/Ferrocenium

FTIR Fourier Transform Infrared Spectroscopy

GED Gas phase Electron Diffraction

GUI Graphical User Interface

HF Hartree-Fock

HK Hohenberg-Kohn

HOMO Highest Occupied Molecular Orbital

I−/I3− Iodide/Triiodide

ICT Intra-molecular Charge Transfer

IR Infrared

IUPAC International Union of Applied Chemistry

LUMO Lowest Unoccupied Molecular Orbital

xix

MEP Molecular Electrostatic Potential

MO Molecular Orbitals

NBO Natural Bond Orbital

NLO Nonlinear Optical

PCM Polarizable Continuum Model

PES Potential Energy Scan

PES Potential Energy Surface

PMO Perturbation Molecular Orbital Theory

PV Photovoltaics

SCE Saturated Calomel Electrode

SMD Solute Molecule Density

SS-DSSC Solid State DSSC

TD-DFT Time Dependent Density Functional Theory

THF Tetrahydrofuran

TiO2 Titanium Dioxade

TPA Triphenylamine

1

Chapter 1

Introduction “When the sun is shining I can do anything; No mountain is too high,

no trouble too difficult to overcome.” Wilma Rudolph

1.1. Background As the world’s population increases and lifestyles becomes more dependent on

new technologies and machines, the world energy consumption increases. The

global need for energy is estimated to double by 2050 [1]. Currently, carbon-

based fossil fuels such as oil, coal, and natural gas provide the majority of our

primary energy needs which is about 14 terawatts (TW). There are a couple of

major problems with this sort of energy: the limited reserves of fossil fuels and the

environmental impact. As an example, generating electricity in Australia relies

mainly on coal. The coal industry is the largest contributor to Australia's total

greenhouse gas emissions (approximately 38%) [2]. Other air pollutants, such as

nitrogen oxides, sulphur dioxide, volatile organic compounds and heavy metals

are the other consequences of the combustion of fossil fuels. As a result of these

major problems, clean and sustainable energy sources become of dramatic

importance.

Introduction Chapter 1

2

There are several renewable alternatives for energy existing today such as:

hydropower, wind, biomass, geothermal and solar sources. Among them, solar

energy is the most abundant source of clean energy which is readily available. The

sun radiates about 100,000 TW of energy to the surface of the earth [3, 4].

Conversion of only a fraction of this abundant energy to other usable energy

forms, such as heat or electricity, can meet most of our energy needs. Today,

electricity production from solar radiation, which is known as photovoltaics (PV),

is in the frontline of the research and development of solar-based renewable

energy. Photovoltaics technology is capable of generating direct current (DC)

electricity from the semiconductors that are illuminated by photons [5].

The discovery of photovoltaic effect dates back to 1839 by a French physicist

named Edmond Becquerel [6]. He observed an electric current by illuminating

two metal sheets (electrodes) which were dipped into an electrolyte solution [7].

However, it wasn’t until 1905 when Albert Einstein explained these observations

in terms of “photoelectric effects” being the result from the “light quanta”, which

means that light energy is carried in discrete quantized packets [8]. As a result of

this work, the 1921 Nobel Prize in Physics was awarded to Einstein “especially

for his discovery of the law of the photoelectric effect” [9]. Moreover, this

revolutionary discovery by Einstein was central to the early development of

quantum theory.

Photovoltaic cells, also known as solar cells, are the electric devices which can

directly generate electricity when they are illuminated by the sun. The most

conventional type of solar cells (also known as first generation) are based on

crystalline silicon wafers [10]. Today, most of the commercially produced

residential solar panels belong to this generation. In spite of showing a high

efficiency of up to 25% [11], the high cost of the energy-intensive manufacturing

processes of this type of solar cells have limited this technology and stimulated

the development of other technologies such as “thin-film” solar cells (also known

as the second generation). The most commonly used materials for thin-film

photovoltaics are cadmium telluride (CdTe), copper indium gallium selenide


3

(CIGS) and amorphous silicon. The costs associated with their productions are

far less than the first generation, as they require less material to be produced.

However, the efficiencies of thin-film cells are also lower than the first

generation. Their wide-spread production and application is also limited by the

scarcity of their materials (e.g. indium, selenium and tellurium), as well as the

high toxicity of cadmium [12]. Finally, the third generation of solar cells

encompasses all emerging technologies, based on various new materials, to

develop new PV devices. The focal point of the third generation is producing

more cost-effective and more efficient solar cells for different types of

applications.

The dye sensitized solar cell (DSSC) is a representative member of the third

generation of the PV devices. The DSSC differs from the conventional solar cells

in design and working principles. In conventional solar cells, the semiconductor is

responsible for both absorbing the light and transporting the charge. In contrast, a

DSSC separates these two tasks. That is, light is absorbed by a dye, with charge

separation and electron transport taking place at a semiconductor electrode (e.g.

titanium dioxide).

In the past twenty years, researchers have shown an increased interest in the

development and investigation of this type of solar cell. DSSCs are attractive

because they are economically viable, owing to cost-effective materials and

fabrication processes associated with them. The main focus of this thesis is on the

DSSC. As a result, the rest of the present chapter is aimed at introducing this type

of solar cell and the rationale behind this thesis.


4

1.2. Dye sensitized solar cells Dye sensitized solar cells are developed by inspiration from the nature. These

cells are able to mimic the charge separation process which takes place during

photosynthesis in plants. The stacked structure of titanium dioxide semiconductor

in DSSC also resembles the piled thylakoid membrane in green leaves [13]. Such

unique structure and process of electron generation and charge separation in

DSSC differentiates it from all other solar cells.

Dye sensitization of wide band gap semiconductors, such as titanium dioxide

(TiO2), forms the basic idea of dye sensitized solar cells. The electronic band gap

of TiO2 is about 3.2 eV [14], which is much greater than that of the commonly

used silicon semiconductor (1.1 eV) in conventional solar cells. As a result, wide

band gap semiconductors are not able to absorb most of the solar emission

themselves and need to become sensitive to the visible light by means of dye

sensitizers. However, wide band gap semiconductors have several important

advantages over the silicon-based semiconductor. They are very inexpensive,

abundant and stable.

Prior to the invention of DSSC, this concept (i.e. dye sensitization of wide band

gap semiconductors) had been employed in technologies such as colour

photography and xerography [15]. Application of this concept to the

photoelectrochemical (PEC) processes had been reported since late 1960s. For

example, Gerischer and Tributsch [16] and Hauffe et al. [17] first investigated the

sensitization of wide band gap semiconductor zinc oxide (ZnO) by organic dyes.

A photo conversion efficiency of 1% was achieved by Tsubomura et al. in 1976

for a dye sensitized zinc oxide photo cell [18]. Dye sensitization of titanium

dioxide (TiO2) can be traced back to Chen et al. who reported such usage in a US

patent issued in late 1978 [19].

The real breakthrough in the field of dye-sensitized solar cell (DSSC) research

resulted from the work of Grätzel and O’Regan which was published in 1991 [20].


5

In their modern version of DSSC, they employed ruthenium-based dye sensitizer

and achieved an efficiency of 7.1% in a solar cell made of TiO2 nanocrystalline

particles [20]. This conversion efficiency was high enough to stimulate worldwide

research interest in DSSC “as a serious competitor to other solar cell

technologies” [21]. Three years later, the Grätzel group achieved an efficiency of

10% [22]. Until recently, the highest solar to electricity energy conversion

efficiencies exceeding 11% belonged to cells using ruthenium-based dye photo-

sensitizers N3 [22, 23] , N719 [24, 25] and black dye [26-28], together with

titanium dioxide semiconductor and iodide/triiodide redox couple [23, 25, 28, 29].

To achieve this efficiency, internal energy levels of all of the three main

components of DSSC (i.e. semiconductor, dye sensitizer, and redox shuttle) have

been well-tuned [30]. In 2011, Yella et al. reported an efficiency exceeding 12%

[31]. This efficiency was gained by incorporating a cobalt-based redox mediator

replacing the iodide/triiodide redox couple in conjugation with a porphyrin-based

dye which was specifically designed to retard interfacial back electron transfer.

Furthermore, this porphyrin-based dye was co-sensitized with another organic dye

sensitizer to improve the light-harvesting efficiency.

Over the past two decades there has been a dramatic increase in research interest

in DSSC. However, the immense research effort to enhance efficiency of DSSC,

which is still lower than that of silicon-based solar cells [32], has not been paired

with proportional increase of the energy conversion efficiency of this device for

commercialization until 2013. The past year (2013) has seen increasingly rapid

advances in the field of DSSC with an unexpected breakthrough and spectacular

results achieved in solid-state DSSC (SS-DSSC) based on perovskite absorbers

[32-35].

DSSCs can broadly be categorized into solid state and liquid state cells, based on

the electrolyte employed in their production. The new solid-state embodiment of

the DSSC, in which a perovskite material is used as light harvester and the cell's

electrolyte is replaced by an organic hole transport material, raised DSSC power-

conversion efficiency up to a record 15% [32] . This new record efficiency will


6

open a new era of DSSC development. However, the focus of this thesis is only

on the liquid state DSSC, as this “game changing breakthrough” in SS-DSSC was

introduced just towards the completion of this thesis.

1.3. Device structure and working principles

Dye sensitized solar cell is composed of several components. These components

include a wide band gap mesoporous semiconductor, a dye sensitizer, an

electrolyte containing a redox couple, a counter electrode and a conducting glass

substrate. From these components, the first three ones (i.e. the wide band gap

semiconductor, dye sensitizer and the redox couple also known as redox shuttle)

are usually referred to as the main components. Fig. 1.1 gives a schematic

structure of DSSC. This figure also illustrates the main processes that occur in this

photovoltaic device (Fig. 1.1(b)).

Fig. 1.1: a) Schematic illustration of DSSC structure and components, adopted from [36]. b) Working principle of a typical DSSC, adopted from [37].


7

As shown in Fig 1.1(a), the working electrode or photoanode of DSSC is

constructed from a mesoporous oxide layer of TiO2 nanoparticles (or other wide

band gap mesoporous semiconductor networks), which are deposited on a

transparent conducting substrate. This substrate is usually a glass coated with

fluorine-doped tin oxide (FTO). A monolayer of the charge-transfer dye sensitizer

is attached to the surface of the nanocrystalline film (TiO2) by chemical bonding.

The mesoporous oxide layer provides a high internal surface area to adsorb as

many dye sensitizer molecules as possible. By employing a high surface area, the

light harvesting efficiency (LHE) of the cell is increased. The electrolyte (or hole

conductor) of a conventional DSSC (liquid state DSSC as mentioned previously)

is usually an organic solvent containing the iodide/triiodide (I−/I3−) redox system.

This component is responsible for the regeneration of the sensitizer. The counter

electrode of a conventional DSSC consists of a thin catalytic layer of platinum

which is deposited onto a conducting glass substrate.

1.3.1. The semiconducting photoanode

In a DSSC, light is absorbed by a dye sensitizer which is grafted onto the

semiconductor surface through a suitable anchoring group. Incident photons, with

enough energy to be absorbed, create an excited state of the dye (Fig. 1.1(b)).

TiO2|S + ℎ𝑣 → TiO2|S∗ (1.1)

where TiO2 is the semiconductor and, S*, represents the excited sensitizer. Please

note that titanium dioxide (TiO2) is by far the most employed oxide

semiconductor and we will use it to represent the semiconductor.

The excited dye rapidly injects an electron into the conduction band of the TiO2

resulting in an oxidized state of the photo sensitizer.

TiO2|S∗ → TiO2|S+ + 𝑒𝑐𝑏 − (1.2)


8

where, 𝑒𝑐𝑏− , stands for an electron in conduction band of semiconductor and, S+, is

the oxidized dye.

Electrons that are injected into the conduction band of the TiO2 are then

transported between TiO2 nanoparticles by diffusion and will be collected at the

front-side transparent conducting oxide (TCO) electrode and reach the counter

electrode through the external load and wiring. A plethora of materials is available

for different components of dye sensitized solar cells. For example, alternative

metal oxides to the standard TiO2 semiconductor include SnO2 [38-42], ZnO [43-

46], and Nb2O5 [47-50].

1.3.2. Redox shuttles

The oxidized dye is regenerated by accepting an electron from a redox shuttle

such as iodide/triiodide (I3-/I-

) dissolved in an organic solvent.

S+ +32

I− → S +12

I3− (1.3)

The oxidized form of the shuttle, I3-, diffuses to the counter electrode to be

reduced to I- ions to complete the circuit.

12

I3− + 𝑒𝑝𝑡

− →32

I− (1.4)

where, ept-, stands for the electron from the Pt-coated counter electrode.

Many attempts have been made to employ alternative redox couples to the

conventional iodide/triiodide (I−/I3−) redox mediator. The alternative redox

shuttles include organic redox systems (e.g. halogens [51-53], nitroxide radicals

[54-56] and sulphur-based [57, 58] mediators) and transition-metal redox couples

(e.g. ferrocene [59-61], copper (I/II) [62], cobalt (II/III) [31, 63-67] and nickel


9

(III/IV) [68, 69] –based complexes) to name a few. Recent reviews have

summarized progress in electrolyte development [36, 59, 70, 71].

Until recently, the iodide/triiodide couple was the unsurpassed redox shuttle in

almost all high-efficiency DSSCs (η > 10%) [21, 72-74]. Its efficient dye

regeneration capability combined with its exceedingly slow interception of

injected electrons at the TiO2, which prevents loss of generated electrons, has

made it the most commonly used redox mediator [30, 61, 72, 75]. However, the

iodide/triiodide redox shuttle has several drawbacks, such as: (a) corrosiveness,

(b) limitations on the achievable open-circuit voltage and (c) incapability to

regenerate far-red-absorbing dyes at acceptable rates, which limits achievable

photocurrent and thus efficiency of the cell, to name a few [30, 59, 61, 63, 72, 75,

76]. As a result, many alternative redox couples have been reported [61, 75].

Among them are “one electron outer-sphere transition-metal” redox couples, such

as ferrocene/ferricinium (Fc/Fc+).

The ferrocene/ferricinium redox couple is a kinetically fast mediator which can

work under low driving force conditions. As a result, it is possible, in principle, to

reduce the redox potential difference between the dye and the electrolyte to

enhance the efficiency by employing ferrocene or its derivatives as the redox

shuttle in DSSC. However, due to the low efficiency of the cells in which Fc/Fc+

couple were employed, this redox mediator was not considered as a viable

alternate to iodide/triodide until 2012, when Daeneke et al. reported a promising

efficiency by coupling the Fc/Fc+ mediator with a novel dye sensitizer called

Carbz-PAHTDDT [59]. This impressive efficiency stimulated two chapters of this

thesis that will be discussed later.


10

1.3.3. Dye sensitizers

As for the dye sensitizers, there are numerous classes of dyes available for

semiconductor sensitization [36, 77, 78]. Dye sensitizers can broadly be classified

into metal complexes and metal-free organic dyes. The former class of

compounds are typically functional ruthenium (II)–polypyridyl complexes. The

N3 [22], N719 [25] and black dye [26] (Fig. 1.2) are perhaps the most renowned

members of the ruthenium-based sensitizers for their superior performances over

other dyes. The good performances of these dyes are attributed to their broad

absorption through metal-to-ligand charge transfer (MLCT), the longer exciton

lifetime and their long-term chemical stability [79]. Several reviews have

summarized development of ruthenium (II)–polypyridyl complexes [80-83].

Metal-free all-organic dye sensitizers have several advantages over the metal

complexes (Ru) that can be listed as follows:

• High molar extinction coefficients. The molar absorption coefficient or molar

extinction coefficient is a measurement of how strongly a chemical species

absorbs light at a given wavelength. The high absorption coefficient feature of

organic dyes allows thinner layers of semiconductor nanoparticles to be

Fig. 1.2: Structure of the representative members of the Ru-based dyes: N3, N719 and black dye.


11

exploited compared to metal-based dyes without a loss of comparable light-

harvesting efficiency [84-86].

• Relatively easy and low cost preparation process [84-86].

• Elimination of environmental issues as they don’t contain any rare materials

such as ruthenium [79].

• Their optical properties are easily tuneable [86].

• Organic dyes are suitable to construct semitransparent and/or multicolour

solar cells. This feature is useful in their application in power producing

windows as an example [85].

• Last but not the least, new organic dyes can be developed by rational design

methods [87]. This feature is central to the present thesis and will be explained

shortly in Section 1.4.1.

As a result of these attractive features, various metal-free dyes have been

developed and investigated intensively. These dyes may contain different

functional groups, such as indoline, triphenylamine, carbazole, coumarin,

merocyanine or fluorene moieties in their structures.

However, organic dyes are usually less efficient and practical compared to their

metal-based counterparts. The major factors hindering the efficiency of organic

sensitizers are: (a) relatively narrow absorption in the visible region; (b) shorter

exciton lifetimes in their excited states; (c) chemical and photochemical

degradation; and (d) aggregation.

This thesis will address the first disadvantage of metal-free organic dye

sensitizers, which is their absorption profile. One of the objectives of this research

is to design new dye sensitizers with better absorption properties. More

specifically, the new dyes should absorb the near infrared region of the spectrum,

as will be explained shortly. As a result, the following section gives a brief

overview of an ideal dye sensitizer which should be considered to design new

dyes.


12

1.3.3.1. Features of ideal dye sensitizers

The ideal sensitizer should have several characteristics. It should absorb all light

below a threshold wavelength of about 920 nm (i.e. visible and near infra-red

spectrum) [36, 88, 89]. Up to now, no dye has been found that injects in the whole

visible and the near infra-red region (NIR) with the same efficiency. Most of the

well-performing dyes such as N3 ruthenium-based dye lack the absorption in the

NIR region (e.g. 750-900 nm).

The short-circuit current density of DSSC, Jsc, can be increased by extending the

absorption region of the dye sensitizer into near infra-red region. To better

understand how this happens, the photon flux density of solar radiation needs to

be considered. The photon flux is an important factor which influences the

number of electrons that can be generated and consequently determines the

electrical current produced from a solar cell. Fig. 1.3 (a) illustrates the photon flux

density of solar radiation on earth against the corresponding wavelength of the

photons and Fig. 1.3 (b) lists the expected current density by different harvesting

degrees. As seen in the figure, the photon flux exhibits a non-uniform distribution,

with the highest photon flux density observed in ca. 600-800 nm [79].

From Fig. 1.3 (b) it can be interpreted that if a dye sensitizer absorbs all solar

radiation from 280-500 nm, then in principle, it can generates a maximum current

density of 5.1 mA cm-2 [79]. However, if it covers a smaller region of the

spectrum, but a region that has higher photon flux density, it can generate more

current density. For example, if the dye only covers the region of 600 nm to 700

nm (which is smaller than the 280-500 nm region), in theory it can generate a

maximum current density of 6.5 mA cm-2 (calculated as 17.6−11.1= 6.5 mA cm-2).

This example clearly shows how absorption range of a dye can influence the

corresponding expected current. Therefore, the unique distribution of the photon

flux needs to be considered when designing new dye sensitizers. It is therefore

suggested to alter the optical band gap of a dye, so that its absorption range

matches the high photon flux region of the solar spectrum [79].


13

Fig. 1.3: a) Flux of photons per area and time and wavelength interval. b) The dependence of the

current density, the degree of harvested light and the harvested wavelengths. This figure is

reproduced based on ref. [79].


14

The increase of the short-circuit current density, Jsc, can increase the overall solar

conversion efficiency of the cell, η, which is calculated according to the following

equation:

𝜂 =

𝐽sc × 𝑉oc × 𝐹𝐹𝑃in

(1.5)

where Voc is the open-circuit voltage, FF is fill factor and Pin is the total solar

power incident on the cell. A comprehensive review of improving efficiency

based on the above equation for DSSC is given in reference [30].

Another aspect of the dye structure is related to the physical stability of the DSSC

as the dye sensitizer must also carry attachment groups such as carboxylate or

phosphonate to firmly graft it to the semiconductor oxide surface [36, 90]. To

produce a photocurrent density, the energy of the dye excited-state (manifested as

the energy of the lowest unoccupied molecular orbital (LUMO)) necessarily must

be higher than the conduction band edge of the n-type semiconductor (e.g. TiO2).

High quantum efficiency for injection is achieved when the LUMO of the dye is

both energetically matched and reasonably strongly coupled to the underlying

semiconductor [5-7].

In order to be rapidly regenerated via donation of electrons from a redox shuttle or

hole-conductor, the highest occupied molecular orbital (HOMO) of the dye

sensitizer should lie below the energy level of the redox shuttle [3-5, 8, 9]. The

dye should not have significant degradation for at least 20 years (108 turnover

cycles) of operation and should sustain natural light for this period of time. In

other words, it should satisfy long term stability [5].


15

1.4. Motivation of this thesis

With a boom in research effort to develop cost-effective renewable energy

devices, dye sensitized solar cells [20] have been the topic of more than a

thousand published papers just in 2010 [91]. However, the bottleneck of the

design and testing of the new materials (e.g. dye sensitizer) for DSSCs, which is

dominated by the often costly and time-consuming synthesis procedures [78], has

prevented the rapid increase of their efficiencies. As in the case of new dye

sensitizer materials development, it is difficult for synthetic chemists to generate

high-performance dyes with the desirable properties prior to the experiments on

the assembled cell, without any support on the information of the new dyes [92].

For example, the energy conversion efficiencies of the recently constructed

DSSCs based on two chemically similar dyes were very different [93]. One is

η=6.79% and the other is η=4.92%. And interestingly, the two dyes only differ in

their π-spacers: one takes thiophene (η=6.79%) and the other is thiazole

(η=4.92%). Both spacers have a sulphur embeded in the pentagon ring, but the

former contains two C=C bonds and the latter has one C=C bond and one C=N

bond.

Unfortunately, the structure and property relationship of the new dyes would

hardly be obtained from “chemical intuition” without the use of quantum

mechanical calculations. In some cases, disappointing results from final stage

testing of the synthesized dye indicate an urgent need to understand the physical

behaviour of dyes at the molecular level, prior to experiments taking place. To

overcome this bottleneck in the development of new DCCSs with better

efficiency, state-of-art computational methods need to be utilised.

Today, first-principle quantum chemical calculations are made available on

supercomputing facilities accessible to more research groups. Such calculations

are a powerful and reliable tool to probe the already existing materials, as well as

to design, study and screen new materials prior to synthesis.


16

It should be kept in mind that a holistic theoretical and computational simulation

of DSSC is very challenging and difficult as it is a very complex device composed

of many different components with complex interatomic interactions. A

comprehensive model, which can simulate the entire working-cell, is still very

ambitious given the dimensions of DSSC system. The need to study the system

not only in the ground state but at excited state which also includes different

phases (gas, solution and interface) is another hurdle. Then there is the common

problem when applying computational methods, which is finding the balance

between accuracy of the computational methods and the required computational

power. However, such a model is perhaps the ultimate goal of computational

simulations [94].

Nevertheless, computational simulations have proven to be efficient in many

aspects of DSSC materials and processes studies. A very recent review of the

first-principles computational simulations of DSSC is reported by Pastore and De

Angelis [95]. Pastore and co-workers have also reported another comprehensive

review of how state-of-the-art computational methodologies can be applied to

model and probe DSSCs [94]. A very significant overview of the main

applications of computational investigations to the simulation of DSSC is given

by De Angelis and Fantacci [96]. Labat et al. have designed and tested their

computational framework based on density functional theory (DFT) to model,

reproduce and predict the spectroscopic properties of the isolated components of

the DSSC [97]. According to above references, quantum mechanical calculations

based on DFT and time dependent DFT (TD-DFT), are suitable tools to

computationally model and study DSSC (DFT and TD-DFT will be explained in

details in Chapter 2). Such studies can be categorized into two main areas, the

computational simulation of individual components of DSSC (e.g. the dye

sensitizer, the TiO2 semiconductor and the redox couple) in isolation, and the

computational study of the interactions between two or more components.

As for the investigations of individual components in isolation, numerous studies

have been performed on the ground and excited state properties of the dye


17

sensitizers through DFT and TD-DFT calculations. For example, the molecular

geometry, the shape and the energy levels of the frontier molecular orbitals (e.g.

HOMO and LUMO), polarizability and hyperpolarizability, and UV-Vis

absorption spectra of dye sensitizers can be studied by DFT and TD-DFT

approaches [95]. Similarly, due to its wide range of applications, many

computational modelling studies have been conducted on the surface and

nanoparticles of TiO2 by employing either cluster-based approaches or periodic

boundary conditions (PBC). The PBC model is capable of modelling an infinite

periodic solid. This model is usually applied on a periodic slab of 3-4 layers of

TiO2 [96]. The most studied type of the interactions between two components is

the computational modelling of the dye adsorption on TiO2 semiconductor

surfaces. For example, binding modes, aggregation, the UV-Vis spectra of the

dye-TiO2 system, and electron injection have been computationally studied [95].

Returning to the issue of expensive and time-consuming laboratory development

of dyes, computer-aided rational design of new dye sensitizers is a promising

approach to reduce the cost and to discover new dyes more efficiently. The

systematic chemical modifications of the dye structures to produce new dyes has

recently drawn the attention of several groups, including ours [87, 98-106], and

motivated the current thesis. In addition to the in silico rational design of new dye

sensitizers, computational studies can be employed to probe other components of

DSSC such as redox couples (e.g. ferrocene/ferrocenium), which has motivated

another significant part of this thesis.

1.4.1. Rational design of organic dyes

The term ‘rational design’ is generally understood to mean a design strategy to get

a well-defined goal or target [107]. This goal is usually achieving a desired

behaviour for the object under design. Rational design can be applied to any

system; however its application in chemical biology is well-established. In the

context of chemical biology, rational design can be defined as generating new


18

molecules with a desired functionality, based on the biological principle that states

“structure determines function”. Here, new molecules are designed by predicting

their behaviour through physical modelling or calculations on their structure.

Applications of this type of rational design include protein design, nucleic acid

design and drug design. As mentioned in Section 1.3.3, an advantage of metal-free

organic dyes is the possibility of applying rational design on them. To understand

this feature, the typical configuration of a metal-free organic dye needs to be

considered.

Central to the structure of organic dye sensitizers is the concept of D-π-A

configuration, shown in Fig. 1.4 (a), where ‘D’ stands for a donor group, ‘π’ for a

π-conjugated bridge (also known as spacer or linker) and ‘A’ for an acceptor

moiety [36, 78, 108-114]. For each moiety (i.e. donor, bridge and acceptor), some

examples of chemical groups, which have been reported in literature [36], are also

shown in Fig. 1.4 (b). The D-π-A structure is an effective and flexible approach to

adjust the properties of dye sensitizers and to accommodate rational design of

dyes with desirable properties. For example, the highest occupied molecular

orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy

levels of a dye sensitizer can be tuned by independent modification of individual

moieties [115]. This feature is employed in this thesis to rationally design new

dyes as will be explained shortly.

In this thesis, the rational design is applied on a couple of already well-performing

dyes with D-π-A configurations. These dyes are designated as “the reference”,

“the original” or “the parent” dyes throughout this thesis. They are selected based

on their overall performance in an assembled working solar cell from the

literature. By modifying the chemical structure of the reference dyes, new dye

sensitizers are designed. The main target is producing new dyes with reduced

HOMO-LUMO energy gap and red-shifted absorption spectra in comparison to

their parent dyes. A variety of approaches can be adopted to red-shift the

absorption spectra of a particular D-π-A dye, such as: (1) increasing the length of

the π-conjugated bridge, (2) employing stronger electron-donating groups, (3)


19

increasing the electron-withdrawing character of the acceptor group, and (4)

making modifications into the structure of the π-conjugated bridge [116].

Fig. 1.4: a) A scheme of D-π-A dye configuration. b) Some example of chemical groups employed for different moieties of the metal-free organic dye sensitizers.


20

The first approach, i.e. the extension of the conjugating bridge has several

disadvantages. For example, it is applicable only on certain types of dyes.

Moreover, it makes the molecules unstable to heat and light, which restricts its

application [116]. As a result, this approach will not be employed in the present

thesis.

As for the third approach, although alternative acceptor moieties have been

reported in literature, the “cyanoacrylic acid” acceptor group is the most dominant

one, employed in most of the dyes designed for DSSC. This group (shown in Fig.

1.5) acts as both electron withdrawing unit (through the cyano-part) and as the

anchoring unit (through the carboxylic group) to attach it onto the surface of the

semiconductor. As a result of its good performance and wide-application, the

cyanoacrylic acid would remain unchanged in all rationally designed dyes in this

thesis. That is, the first approach of red-shifting the absorption spectra above is

not employed in the present work. This thesis applies the second and the fourth

approaches (i.e. employing stronger electron-donating groups and making

modifications into the structure of the π-conjugated bridge) to the rational design

of the new dyes. Details of each approach and how it is applied will be given in

the related chapters.

Fig. 1.5: The cyanoacrylic acid acceptor/anchoring group.


21

The new dyes are rationally designed in silico. As a result, their properties need to

be predicted. In this thesis, computational methods based on quantum mechanical

calculations are employed to model and calculate properties of the new dyes. The

most important properties of the new dyes that will be studied in this thesis are the

energy level of the HOMO and the LUMO, as well as the UV-Vis absorption

spectra. The quantum mechanical calculations in this thesis are based on density

functional theory (DFT) and time-dependent density functional theory (TD-DFT).

The DFT and TD-DFT models (here model means a combination of DFT

functionals and basis set, which will be explained in Chapter 2) employed in this

thesis vary and are validated based on the agreement of the calculations with

available experimental data for each reference dye. That is, for each parent dye,

the computational calculations are performed and the results are compared with

available experimental data for that parent dye. Models which provide the best

agreement with experiment for the reference dye are then selected to study the

corresponding new rationally designed dyes. The initial decision to employ which

model for the parent dye is made by consulting with literature.

1.5. The aim, focus and overview of this thesis

This thesis addresses two important components of DSSC, the dye sensitizer and

the redox couple by first-principle quantum chemical calculations, with more

weight given to the study of dyes.

The aim is to rationally design well-performing organic dyes, with enhanced

spectral response, through “chemical modification” and “computational

modelling”. This thesis studies how rational and in silico design can be exploited

in the design of new organic dye sensitizers with red-shifted (also known as

bathochromic) absorption spectra. Such bathochromic shifts can be obtained by

reducing the HOMO-LUMO energy gap of the dye sensitizers. Because of this,

the relationship between the molecular structure and the HOMO-LUMO gap, as


22

well as the UV-Vis absorption spectra of organic dyes is the main focus of this

project. Investigation of other features, such as long-term stability, adsorption to

the semiconductor surface, kinetics of electron injection, transfer, etc. are beyond

the scope of the current thesis.

As for the study of the redox couple, the aim is to probe the electronic properties

of ferrocene, CpFeCp, a sandwich organometallic compound and its Fc/Fc+ redox

couple, quantum mechanically.

This thesis has been organised in the following way.

Chapter 2 provides a general overview of the theory behind the quantum

chemical calculations. But the specific computational methods and details for the

investigation of each compound that are studied in this thesis are given separately

in their related chapters.

Chapter 3 reports a computer aided rational design which is performed on a

reference dye sensitizer with D-π-A structure, known as TA-St-CA. This dye

sensitizer is among good performing dyes in experimental settings. Rational

design of new dyes in this chapter is based on the chemical modifications of the

“π-bridge” moiety of the parent TA-St-CA dye. A number of electron-donating

(ED) and electron-withdrawing (EW) units based on Dewar’s rules are substituted

into the π-conjugated bridge of the reference TA-St-CA dye to produce new dyes.

The effects of these alterations on the molecular structures, HOMO-LUMO

energy gap, and the electron absorption spectra of the new dyes are calculated and

compared to those of the reference dye [87].

Chapter 4 describes new designs for the “donor” moiety of the same parent, TA-

St-CA. Two novel dyes are designed by substitution of different aromatic

annulenes, [14]- and [18]- annulene, as the building blocks of the donor moiety.

As a result, this chapter investigates the influence of increasing the number of sp2


23

hybridized atoms (in the donor moiety) on the reduction of the HOMO-LUMO

energy gap and enhancing the absorption spectra of organic dye sensitizers.

Chapter 5 investigates geometric and electronic structure of the Carbz-

PAHTDDT (S9) organic dye sensitizer, quantum mechanically [106]. This dye

has a reported promising efficiency when coupled with ferrocene-based

electrolyte composition [59]. As there is no computational study available on the

structure of the S9 dye, this chapter begins by probing different DFT and TD-DFT

models to calculate features of the reference dye. Based on the agreement with the

experimental values available, the best model is then selected to study the new

dyes in this chapter. New dyes are produced by altering the chemical structure of

the original Carbz-PAHTDDT dye on the π-conjugated bridge. The effects of

these structural alterations on the molecular structures, HOMO-LUMO energy

gap, and the electron absorption spectra of the new dyes are calculated for

comparision to those of the reference dye.

Chapter 6 is devoted to the study of ferrocene (Fc) as an important compound for

alternative redox mediator preparation in liquid state DSSC. The correct structure

of this compound has been a disputed subject within the field of organometallic

chemistry. As a result, a substantial part of this chapter is concentrated on the

study of the ferrocene structure and its conformers, i.e. eclipsed and staggered.

This chapter begins by studying different properties of Fc to find the ones which

can differentiate the eclipsed and staggered conformers. Different properties

including geometry, molecular electrostatic map, infrared spectra in the gas and

solvent phase are discussed [117, 118]. This chapter further investigates the

molecular properties of this compound that are related to its application as a redox

mediator in dye sensitized solar cells. These properties include UV-Vis absorption

spectra and Fc/Fc+ redox potential. A very accurate DFT model for the calculation

of the redox potential of Fc/Fc+ couple will be presented in this chapter.

Finally, Chapter 7 gives a summary and some important conclusions drawn from

the thesis. Furthermore, this chapter outlines the prospects for future research.


24

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107. D.L. Parnas and P.C. Clements, A Rational Design Process - How and Why to Fake It. Ieee Transactions on Software Engineering, 1986. 12(2): p. 251-257.

108. M. Velusamy, Y.C. Hsu, J.T. Lin, C.W. Chang and C.P. Hsu, 1-Alkyl-1H-imidazole-Based Dipolar Organic Compounds for Dye-Sensitized Solar Cells. Chemistry-An Asian Journal, 2010. 5(1): p. 87-96.

109. K. Srinivas, C.R. Kumar, M.A. Reddy, K. Bhanuprakash, V.J. Rao and L. Giribabu, D-pi-A organic dyes with carbazole as donor for dye-sensitized solar cells. Synthetic Metals, 2011. 161(1-2): p. 96-105.

110. M.K.R. Fischer, S. Wenger, M. Wang, A. Mishra, S.M. Zakeeruddin, M. Grätzel and P. Bäuerle, D-π-A Sensitizers for Dye-Sensitized Solar Cells: Linear vs Branched Oligothiophenes. Chemistry of Materials, 2010. 22(5): p. 1836-1845.

111. M. Marszalek, S. Nagane, A. Ichake, R. Humphry-Baker, V. Paul, S.M. Zakeeruddin and M. Gratzel, Structural variations of D-π-A dyes influence on the photovoltaic performance of dye-sensitized solar cells. RSC Advances, 2013. 3(21): p. 7921-7927.

112. Y. Ooyama, N. Yamaguchi, I. Imae, K. Komaguchi, J. Ohshita and Y. Harima, Dye-sensitized solar cells based on D-[small pi]-A fluorescent dyes with two pyridyl groups as an electron-withdrawing-injecting anchoring group. Chemical Communications, 2013. 49(25): p. 2548-2550.

113. H. Li, T.M. Koh, A. Hagfeldt, M. Gratzel, S.G. Mhaisalkar and A.C. Grimsdale, New donor-[small pi]-acceptor sensitizers containing 5H-[1,2,5]thiadiazolo [3,4-f]isoindole-5,7(6H)-dione and 6H-pyrrolo[3,4-g]quinoxaline-6,8(7H)-dione units. Chemical Communications, 2013. 49(24): p. 2409-2411.


34

114. Z.-S. Wang and F. Liu, Structure-property relationships of organic dyes with D-π-A structure in dye-sensitized solar cells. Frontiers of Chemistry in China, 2010. 5(2): p. 150-161.

115. D.P. Hagberg, T. Marinado, K.M. Karlsson, K. Nonomura, P. Qin, G. Boschloo, T. Brinck, A. Hagfeldt and L. Sun, Tuning the HOMO and LUMO energy levels of organic chromophores for dye sensitized solar cells. Journal of Organic Chemistry, 2007. 72(25): p. 9550-9556.

116. A.T. Peters and H.S. Freeman, Modern Colorants: Synthesis and Structures. 1995: Blackie Academic & Professional.

117. N. Mohammadi, A. Ganesan, C.T. Chantler and F. Wang, Differentiation of ferrocene D5d and D5h conformers using IR spectroscopy. Journal of Organometallic Chemistry, 2012. 713(0): p. 51-59.

118. C.T. Chantler, N.A. Rae, M.T. Islam, S.P. Best, J. Yeo, L.F. Smale, J. Hester, N. Mohammadi and F. Wang, Stereochemical analysis of ferrocene and the uncertainty of fluorescence XAFS data. Journal of Synchrotron Radiation, 2012. 19: p. 145-158.

35

Chapter 2

Methods and Theoretical Details “Everything should be made as simple as possible, but not simpler.”

Albert Einstein

2.1. Introduction

Advances in computational science in the 20th century flourished many emerging

scientific fields dealing with complex problems such as computational chemistry.

Computational chemistry, also known as molecular modelling or molecular

simulation, is an interdisciplinary field that exploits computational science

techniques to develop codes and software programs which can solve chemical

problems. These computer codes implement the results of theoretical chemistry.

As a result, the fundamental principle upon which computational chemistry is

built is theoretical chemistry. Theoretical chemistry itself combines mathematical

methods with fundamental laws of physics to formulate the behaviour of matter

on an atomistic scale.

This chapter will provide a brief introduction and background to the theoretical

foundation of the computational chemistry methods applied to this study,

followed by a number of general important molecular properties and the

computational methods employed to calculate them. However, the more specific

Methods and theoretical details Chapter 2

36

methods and justification of the models applied to study each molecule

throughout this thesis are given separately in the related chapters.

2.2. Background

It is well-known that properties of compounds are derived as a function of their

molecular structure [1-4]. The molecular structure or molecular geometry is

nothing but a set of three dimensional coordinates which describe the position of

atoms within the molecule. Therefore, the type and the geometrical position of

atoms are the key to the differences between molecules. One can think of a

molecule as positively charged nuclei surrounded by electrons which stay together

by Columbic attraction. However, the classical Newtonian equation of motion (i.e.

F=ma) fails to describe the behaviour of electrons and nuclei. That is because

electrons which are very light elementary particles show both wave and particle

characteristics. Therefore, quantum mechanics approaches which provide

mathematical description for dual wave-particle behaviour should be employed.

The mathematical formulations of quantum mechanics were postulated in the

early 20th century, based on the experimental observations to describe those

phenomena which could not be explained by classical physics (e.g. wave-like

behaviour of matter). A fundamental postulate of quantum mechanics specifies

that the state of a quantum system can be described completely by a wavefunction

[5, 6]. This means that all the experimentally measurable information about the

system is contained in the wavefunction and thus wavefunction becomes central

to quantum mechanics.

The wavefunction which is represented by the Greek letter ψ (or the capital letter

Ψ) is a function of position and time for a single particle (i.e. Ψ (position, time))

whose values can be complex numbers which does not have any physical

interpretation. However, the square of the absolute value of the wavefunction (i.e.

complex square or |ψ|2) is a real number. It can be related to the probability of


37

finding the particle at a given position in a given time based on the statistical

interpretation of Max Born [7]. Even though the wavefunction is not an

experimentally measurable entity itself, it contains all the information about

observable properties which can be determined experimentally. Quantum

mechanics postulates that it is possible to obtain experimental measurements of

physical properties as the expectation (average) values by averaging an

appropriate operator acting on the wavefunction [8, 9].

To obtain wavefunctions, one needs to solve the Schrödinger’s equation. An

Austrian physicist called Erwin Schrödinger formulated this equation in 1925 and

published it in 1926 [10]. There are two types of Schrödinger’s equation, a time-

dependent one (which is the most general form) and a time-independent one. The

time-dependent equation describes the behaviour of a dynamic system which

evolves with time and is analogous to the Newton’s second law (i.e. equation of

motion) in classical mechanics. Although time-dependent equation is the most

general form of the Schrödinger’s equation, it is quite complicated and

challenging to be solved. Moreover, the majority of theoretical chemistry

problems deal with stationary states which do not change over time, which means

that the wavefunction for stationary states is a standing wave which is a function

of the position only (and is not a function of the time). For that reason, the time-

independent Schrödinger equation is sufficient to find the wavefunctions for such

states.

2.3. The time-independent Schrödinger equation

The time-independent Schrödinger equation, which will be called simply as

Schrödinger equation hereafter, is the fundamental equation employed to obtain

the wavefunctions of atomic particles and is given in the form of

𝐻�Ψ = 𝐸Ψ (2.1)


38

where 𝐻� stands for the Hamiltonian operator, Ψ represents the wavefunction and

E is the energy eigenvalue for the system.

In Schrödinger equation, the total energy of a system is represented by the

Hamiltonian operator, after William Rowan Hamilton (1805 –1865), and is given

as the sum of kinetic and potential energy operators,

𝐻� = 𝑇� + 𝑉� (2.2)

where 𝑇� is the kinetic energy operator and 𝑉� is the potential energy operator.

For a system of M nuclei and N electrons, let R and r be the set of nuclear

coordinates and electronic coordinates, respectively. The kinetic energy operator

consists of the nuclei and the electrons kinetic energy terms, whereas the potential

energy operator contains three terms, i.e., nuclear-nuclear repulsion, nuclear-

electron attraction and electron-electron repulsion as follows:

𝐻� = − �12

𝑁

𝑖=1

∇𝑖2 − �

𝑀

𝐴=1

12𝑀𝐴

∇𝐴2 − � �

𝑍𝐴

𝑅𝑖𝐴

𝑀

𝐴=1

𝑁

𝑖=1

+ � �1

𝑟𝑖𝑗

𝑁

𝑗>𝑖

𝑁−1

𝑖=1

+ � �𝑍𝐴 𝑍𝐵

𝑅𝐴𝐵

𝑀

𝐵>𝐴

𝑀−1

𝐴=1

(2.3)

𝑇�e(r) 𝑇�N(R) 𝑉� eN(r,R) 𝑉� ee(r) 𝑉� NN(R)

where:

i, j are used to index electrons and A, B are indices for nuclei.

𝑇�e(r): is the kinetic energy operator for the electrons and is a function of r.

𝑇�N(R): is the kinetic energy operator for the nuclei and is a function of R.

𝑉� eN(r,R): is the potential energy operator for the Coulomb attraction between

electrons and nuclei and is a function of both r and R.

𝑉� ee(r): is the potential energy operator for the Coulomb repulsion between

electrons and is a function of r.

𝑉� NN(R): is the potential energy operator for the Coulomb repulsion between

nuclei and is a function of R.

𝑀𝐴: is the ratio of the mass of nucleus A to the mass of an electron.

𝑟𝑖𝑗: is the distance between electron i and electron j.


39

𝑅𝐴𝐵 : is the distance between nucleus A and nucleus B.

𝑅𝑖𝐴 : is the distance between electron i and nucleus A.

𝑍𝐴: is the atomic number of nucleus A.

∇𝑖2 and ∇𝐴

2 : are the laplacian operator acting on ri and RA, respectively (∇𝑖2= 𝜕2

𝜕𝑥𝑖2 +

𝜕2

𝜕𝑦𝑖2 + 𝜕2

𝜕𝑧𝑖2).

And ri = (xi, yi, zi) is the coordinates of the electron i and RA = (xA, yA, zA) is the

coordinates of the nucleus A.

To obtain the energy and wavefunction, the Hamiltonian in Eq. (2.3) should be

inserted into the Eq. (2.1). The resultant Schrödinger equation is a partial

differential eigenvalue equation (PDE) with a large number of variables (i.e.

variables of the spatial coordinates of the electrons and the nuclei). In other

words, the wavefunction of a many-electron molecule (Ψ (R,r)) is a function of

the coordinates of all the nuclei (R) and all the electrons (r).

In fact, such equation is intractable [11] and cannot be solved exactly for most of

the molecular systems (i.e. molecules with more than one electrons, also known as

many-body systems) [12, 13] and several approximations are required to simplify

this equation as will be outlined in the following sections.

2.4. The Born-Oppenheimer approximation

The fundamental Born-Oppenheimer approximation (BO) was proposed by Max

Born and J. Robert Oppenheimer in early days of quantum mechanics (1927) [14],

only a year after the publication of the Schrödinger equation. The term 𝑉� eN(r,R) in

Eq. (2.3) prevents us from seprating the wavefunction into a product of an

electronic part and a nuclear part. But the BO makes it possible to break the

electronic and nuclear components of the wavefunction as will be explained


40

shortly. As a result, the computation of the wavefunction becomes less

complicated.

The BO relies on the high ratio between nuclear and electronic masses. It is well-

known that the nuclei are much heavier than the electrons (mproton≈ 1836 melectron),

so they move much more slowly than the electrons. As a result, the nuclei can be

considered stationary to electrons and the electrons can adapt their positions

instantaneously as the nuclei change positions. This implies that the electrons are

moving in the field of the fixed nuclei within a molecule. As a result, it is possible

to “fix” the nuclear configuration at some value Ra, and then the wavefunction

depends only parametrically on the nuclear positions (R).

On the basis of the BO, the following total wavefunction is approximately correct:

Ψ𝑡𝑜𝑡𝑎𝑙 = Φ𝑒𝑙(𝒓; 𝑹) × Φ𝑁(𝑹) (2.4)

The BO consists of two steps. In the first step, for a fixed nuclear configuration,

the 𝑇�N(R) term in Eq. (2.3) can be neglected and VNN becomes a constant. The

electronic Hamiltonian (𝐻�𝑒𝑙) becomes:

𝐻�𝑒𝑙 = − �12

𝑁

𝑖=1

∇𝑖2 − � �

𝑍𝐴

𝑟𝑖𝐴

𝑀

𝐴=1

𝑁

𝑖=1

+ � �1

𝑟𝑖𝑗

𝑁

𝑗>𝑖

𝑁−1

𝑖=1

(2.5)

which describes the motion of N electrons in the field of M fixed point charges,

such that the electronic Schrödinger equation becomes:

𝐻�𝑒𝑙Φ𝑒𝑙(𝒓; 𝑹) = 𝐸𝑒𝑙Φ𝑒𝑙(𝒓; 𝑹) (2.6)

Eq.(2.6) is often reffered to as the “clamped-nuclei” Schrödinger equation. That is

because in Eq. (2.5), the 𝑉� eN (electron-nucleus interaction) is not removed and

electrons can still feel the Coloumb potential of the nuclei which are clamped

(fixed) at certain positions in space (nuclear configuration).


41

The solutions of the electronic Hamiltonian (𝐻�𝑒𝑙) are the electronic wavefunctions

(Φ𝑒𝑙). It describes the motion of the electrons for a fixed nuclear configuration. It

should be noted that the electronic energy eigenvalue (𝐸𝑒𝑙) in Eq. (2.6) is not a

constant and depends parametrically on the chosen nuclear configuration. By

repedatly varying the nuclear configurations in small steps for a range of R (one at

a time) and solving the electronic Schrödinger equation, 𝐸𝑒𝑙(𝑅) is obtained as a

function of R, and is generally termed as potential energy surface (PES). That is

because the dependance of the electronic energy on the position of the nuclei

(nuclear configuration) plays the role of the “potential energy” in the Schrödinger

equation for the nuclear motion. This implies that the nuclei move on a potential

energy surface (𝑈(𝑹)).

𝑈(𝑹) = 𝐸𝑒𝑙 + 𝑉� NN (2.7)

Once the PES is obtained, it is possible to solve the second step of BO which is to

solve the Schrödinger equation for the motion of nuclei,

𝐻�𝑁 = − �

𝑀

𝐴=1

12𝑀𝐴

∇𝐴2 + 𝑈(𝑹) (2.8)

𝐻�𝑁Φ𝑁(𝑹) = 𝐸𝑁Φ𝑁(𝑹) (2.9)

As seen in Eq. (2.8), the nuclear kinetic energy term, 𝑇�N(R), which contains

partial derivatives with respect to the components of R is reintroduced. Next,

Schrödinger equation for the nuclear motion, Eq. (2.9) is solved to yeild the the

nuclear wavefunction Φ𝑁(𝑹) which contains all the information about vibration,

rotation and translation of the molecule.

2.5. Hartree-Fock theory

Although Hartree-Fock (HF) method is not directly employed in the calculations

of this work, it is important to briefly introduce this theory as it is fundamental to

the quantum mechanics. The HF theory is also the predecessor of density


42

functional theory (DFT) [15]. Furthermore, DFT shares some concepts in

common with HF which will be introduced in this section.

As mentioned earlier in section 2.3, exact solutions to Schrödinger equation can

only be found for one-electron systems. Although BO simplifies the solution, it

doesn’t prescribe any solution for the electronic Schrödinger equation. In other

words, the main hurdle with many-body systems is the electron-electron repulsion

interaction (𝑉� ee(r)), which still remains unsolved and intractable for electronic

Schrödinger equation. The Hartree-Fock method is employed to tackle this

problem using a number of assumptions and simplifications. HF method

approximates the true many-body wavefunction by a single Slater determinant of

N spin-orbitals where each electron is occupying an orbital.

In HF method, the electron-electron repulsion interaction is not considered

explicitly. Instead, the average effect of repulsion is taken into account. As a

result, HF method makes it possible to break the many-electron Schrödinger

equation into a number of one-electron equations which are simpler to resolve.

The first assumption of the HF method is that the wavefunction can be written as

a Hartree product (HP) such that:

Ψ𝐻𝑃(𝐫1, 𝐫2, … , 𝐫𝑁) = 𝜓1(𝐫1)𝜓2(𝐫2) … 𝜓3(𝐫𝑁) (2.10)

where the individual one-electron wavefunctions, 𝜓𝑖, are called molecular

orbitals.

In Eq. (2.10), 𝜓𝑖(𝐫i) is a spatial orbital. It is a function of a single electron's

spatial coordinates only. However, an electron is a fermion having not only three

spatial coordinates, but also one spin coordinate, ω. By including the full set of

“space-spin” coordinates, the HP becomes:

Ψ𝐻𝑃(𝐱1, 𝐱2, … , 𝐱𝑁) = 𝜒1(𝐱1)𝜒2(𝐱2) … 𝜒𝑁(𝐱𝑁) (2.11)

where:


43

x={r,ω} is the set of space-spin coordinates and ω is the spin variable (which can

take the values of either α (spin up, ↑) or β(spin down, ↓) ).

𝜒(x) : is a spin orbital and is a function of the space and the spin coordinates of a

single electron. A spin orbital can be written as a product of a spatial orbital and

one of the two spin functions, i.e., 𝜒↑(x)= 𝜓(r)α(ω) or 𝜒↓(x)= 𝜓(r)β(ω).

So far we have introduced and discussed some of the postulates of quantum

mechanics. Another postulate of quantum mechanics applied to fermions is

realted to the antisymmetry principle. This principle states that “for a system of

fermions, the wavefunction must be antisymmetric with respect to the interchange

of all (space and spin) coordinates of one fermion with those of another” [6]. A

direct consequent of this principle is the Pauli exclusion principle which states

that identical fermonions (two or more) cannot occupy the same quantum state

simultaneously [8]. The mathematical description of an antisymmetric

wavefunction is

Ψ(𝐱1, … 𝐱𝑘, … 𝐱𝑙 , … 𝐱𝑁) = −Ψ(𝐱1, … 𝐱𝑙, … 𝐱𝑘, … 𝐱𝑁) (2.12)

which does not hold for the general HP wavefunction given in Eq. (2.11).

To satisfy the antisymmetry requirement, an antisymmetric solution can be built

by introducing the following determinant of spin orbitals also known as Slater

determinant, after John Slater [16]:

Ψ𝑆𝐷(𝐱1, … 𝐱𝑁) = 𝟏

√𝑁! �

�

𝜒1(𝐱1) 𝜒2(𝐱1) … 𝜒𝑁(𝐱1)

𝜒1(𝐱2) 𝜒2(𝐱2) … 𝜒𝑁(𝐱2)

⋮ ⋮ ⋱ ⋮

𝜒1(𝐱𝑁) 𝜒2(𝐱𝑁) … 𝜒𝑁(𝐱𝑁)

�

�

(2.13)

The outcomes of this functional form are:


44

• 𝜒𝑖s are normalized single-particle wave functions for each respective

particle. All 𝜒𝑖 ’s must be different, otherwise the determinant becomes

zero. This feature clearly show the Pauli’s exclusion principle.

• The interchange of two columns or rows, which are equivalent to the

exhchange of two fermions , results in a change of sign and thereby satisfy

Eq. (2.12).

• Since each electron is associated with every orbital (each column is a

function of all ( 𝐱1, 𝐱2, … , 𝐱𝑁)), electrons are all indistinguishable. This is

in agreement with other results of quantum mechanics [17, 18].

The electronic energy of a Slater determinant wavefunction, i.e. ESD, can be

derived in terms of spatial orbitals by integrating out the spin variable (by making

the assumption that there are even number of electrons which doubly occupy each

spatial orbitals, i.e. closed-shell system ):

𝐸𝑆𝐷 = 2 � ℎ𝑖

𝑁/2

𝑖=1

+ � �

𝑁2

𝑗=1

𝑁2

𝑖=1

�2𝐽𝑖𝑗 − 𝐾𝑖𝑗 � (2.14)

where ℎ𝑖 is the the kinetic and nuclear attraction energy of an electron in orbital

𝜓𝑖, and is given by the below equation.

ℎ𝑖 = � 𝜓𝑖∗ (𝒓)ℎ�𝜓𝑖(𝒓)𝑑𝒓

ℎ� = −12

∇2 − �𝑍𝐴

|𝒓 − 𝑹𝑨|

𝑀

𝐴=1

(2.15)

In Eq. (2.14), 𝐽𝑖𝑗>0 is the Columb or electrostatic interaction energy of the

electron in orbital 𝜓𝑖 with an electron in orbital 𝜓𝑗.

𝐽𝑖𝑗 = �

|𝜓𝑖(𝒓𝟏)|2|𝜓𝑗(𝒓𝟐)|2

𝑟12𝑑𝒓𝟏𝑑𝒓𝟐 (2.16)

𝐾𝑖𝑗>0 is the Exchange interaction energy of the electron in orbital 𝜓𝑖 only with

the electrons of the same spin in orbital 𝜓𝑗. The exchange interaction is a

consequence of antisymmetry and is a purely quantum effect.


45

𝐾𝑖𝑗 = �

�𝜓𝑖∗(𝒓𝟏)𝜓𝑗(𝒓𝟏)��𝜓𝑖

∗(𝒓𝟏𝟐)𝜓𝑗(𝒓𝟐)�∗

𝑟1𝑑𝒓𝟏𝑑𝒓𝟐 (2.17)

It should be noted that a single instance of Slater determinant ( or Φ𝑖) only

represents a single eigenstate of the overall system. A system is thus described by

a complete set of slater determinants as:

𝜓𝑒𝑙 = ∑ 𝑑𝑖Φ𝑖 = 𝑑0Φ0𝑖 + 𝑑1Φ1+… (2.18)

However, it is not feasible to have the set of all possible Slater determinants.

Hartree-Fock approach then assumes the system to be in the ground electronic

state in terms of a single Slater determinant (Φ0) of the N lowest spin-orbitals as a

suitable ansatz for applying the variational principle. Based on the variational

theorem, the energy obtained from any approximate wavefunction is always

greater than (or equal to) the energy of the exact (true) wavefunction. As a result,

HF method tries to find the best Slater determinant, which is the one giving the

lowest possible HF energy. For the energy of a Slater determinant to be

minimised, the molecular orbitals should be the solution of an eigenvalue equation

(HF eigenvalue equation) involving Fock operator. This operator itself depends

on the molecular orbitals that are being seeked (i.e. its own eigenfunctions). As a

result, an iterative procedure should be employed to find the optimal set of

molecular orbitals, representing a single determinant for Φ0. Such an iterative

approach is also known as self consistance field (SCF) calculation.

Hartree-Fock results are obtained based on the initial approximation that electrons

are indipendent from each other. As a result, HF theory only considers the

electron exchange part of the electron-electron interaction, whereas the electron

correlation interaction is completely neglected. However, neglecting the electron

correlation results in a poor description of the electronic structure. It can result in

large deviations from experimental results. A number of approaches, known as

post Hartree-Fock methods, try to improve the HF results by incorporating the

electron correlation.


46

2.6. Molecular orbital theory and basis set

Molecular orbital (MO) theory was developed by two pioneers of theoretical

chemistry, Friedrich Hund [19-24] and Robert S. Mulliken [25, 26] in 1927 and

1928, respectively. A molecular orbital can be considered as a mathematical

function which can describe the quantum behaviour of an electron in a molecule.

Assuming that the electronic Schrödinger equation is to be solved for a molecule,

the one-electron functions expressed in the form of Slater determinants in the

previous section are conceptually the same as the molecular orbitals [27]. A

molecular orbital is often expressed as a linear combination of atomic orbitals

(LCAO).

Mathematically speaking, it is possible to expand an unknown function, in a set of

known functions (also known as basis). An expansion in a basis is a generalization

of the Fourier series [28]. Such an expansion is exact if the basis set is complete

(i.e. infinite number of basis functions are employed). This concept can be applied

to define an unknown molecular function in terms of known atomic functions. In

order to find a numerical solution for an unknown molecular orbital 𝜓𝑖 , it is

approximated as a linear combination of a set of some fixed known functions,

called basis set

𝜓𝑖(𝐫) = � 𝐺𝛼(𝒓)𝐶𝛼𝑖

𝑁𝐵𝐹

𝛼=1

(2.19)

where 𝐶𝛼𝑖 is the expansion coefficient and should be determined by the SCF

calculations, and 𝐺𝛼 is called basis function, which is approximated by atomic

orbitals. The introduction of a basis set to quantum mechanical methods is another

approximation made in computational chemistry [27]. However, using a complete

basis set (i.e. infinite number of known functions) is impossible in real

calculations. Finite basis sets are usually used, however, a small basis set usually

leads to poor description of the MO. Apart from the size of the basis set, the type

of basis functions employed also determine the accuracy of the results. Generally


47

two types of functions are employed to describe atomic orbitals in MO

calculations: Slater type orbitals (STOs) and Gaussian type orbitals (GTOs).

STO functions were introduced by John C. Slater in 1930 [29]. Their similarity to

the correct shape of the hydrogen atomic orbitals and their accuracy made STO an

appealing choice for basis functions. However, STOs are mathematically difficult

to compute. In 1950, Frank Boy [30] proposed the use of Gaussian type functions,

(i.e. GTOs, although the term GTO is a misnomer) which are computationally

more efficient. GTOs simulate the shape of STOs by summing up a number of

GTOs with different exponents and coefficients. In other words, STOs can be

approximated as a linear combination of Gaussian functions (also known as

Gaussian primitives). A primitive GTO has the polar functional form of:

𝑔𝜁,𝑛,𝑙,𝑚(𝑟, 𝜃, 𝜑 ) = 𝑁𝑌𝑙,𝑚(𝜃, 𝜑)𝑟2𝑛−2−𝑙𝑒−𝜁𝑟2 (2.20)

where N is normalization constant, Yl,m are spherical harmonic functions, ζ (zeta)

controls width of orbital and l=lx+ly+lz determines type of orbital (e.g. l=1 is a p

orbital).

Basis sets are usually classified based on the number of functions used to describe

orbitals. For example, a minimum basis set is the one in which only sufficient

functions are used to contain all the electrons (core through valence) of the neutral

atoms. Based on the fact that the valence electrons are chemically more important

(e.g. bonding take place between valence electrons), it is sensible to treat core and

valence basis functions differently. Such a method where core electrons are

handled with a minimal basis set while the valence electrons are treated with a

larger basis set is called split-valence. The split-valence basis sets of Pople and

coworkers [31] are among the most widely used families of basis sets [32]. The

general notation of Pople basis sets is “M-ijk…G”. Here, M specifies the number

of Gaussian functions which are summed (contracted) to describe the inner shell

(core) orbitals. The number of digits (i.e. ijk…) after the hyphen is variable

(usually 2 or 3) and denotes the number of basis functions per valence atomic


48

orbital. The value of each digit denotes the degree of contraction to be used for the

given valence basis function.

Other improvements made to basis sets are the addition of polarization and diffuse

functions. Polarization is an effect taking place when atoms approach each other

to form chemical bonds which changes the charge distribution and distorts the

shape of the atomic orbitals. In order to account for the required flexibility to

atomic orbitals to shift to one side or the other when forming chemical bonds,

polarization functions can be added into the Pople basis sets. In Pople’s notation,

polarization functions are denoted by one or two asterisk (* or **) after the basis

set name. Another common addition to basis sets is diffuse functions to represent

electrons far away from the nucleus (i.e. the "tail" portion of the atomic orbitals).

Addition of diffuse functions is necessary for calculation on anions or neutral

molecules with lone pair electrons and very electronegative atoms (e.g. fluorine).

Diffuse functions are indicated by + or ++ in Pople basis set notation.

2.7. Density functional theory

The Hartree-Fock ab initio method which was discussed in the section 2.5 is

based on the electronic wavefunction. Although wavefunction encompasses all the

information of a system in a certain state, its complexity is overwhelming. A

wavefunction for a system of Nel electrons is dependent on all three spatial and

one spin coordinate of each electron and its complexity increases exponentially

with the number of the electrons. Density functional theory (DFT) is another

approach to the electronic structure of matter, in which the properties of interest

are calculated based on the ground state electron density, rather than the

wavefunction. The advantage of electron density (denoted by ρ(r) given in Eq.

(2.21)) is that it is independent of the number of electrons (i.e. it is a function of

only 3 variables) and thus less complicated.


49

ρ(𝐫) =

Nel � … � Ψ*�r,ω1,r2,ω2,…,rNel ,ωNel �Ψ �r,ω1,r2,ω2,…,rNel,ωNel �dω1dr2ω2…drNelωNel

(2.21)

Apart from being simpler to calculate, the electron density is an experimental

observable, thus unlike the wavefunction, electron density can be measured by X-

ray diffraction or electron diffraction experiments [33]. The term functional in

DFT exists from the use of functionals of the electron density to determine the

properties of a many-electron system in this method. A functional is a

mathematical rule which acts on a function as the input, and transform it into a

number as the output, i.e. function of functions.

Employing electron density distribution to find the electronic energy was first

introduced in Thomas-Fermi (TF) theory [34, 35], shortly after the introduction of

the Schrödinger equation. However, TF method could not describe molecular

bonding and remained inappropriate for most applications of chemistry and

material science. Density functional theory, as known today, was established on

the basis of firm theoretical footing by the Hohenberg-Kohn (HK) theorems,

which prove that an exact method based on electron density exists in principle.

Based on HK theorems, “there exist a one-to-one correspondence between the

electron density and the energy of the system” [36]. Since early attempts to design

DFT models were focused on expressing all the energy components as a

functional of the electron density, with poor performances, DFT was not

considered practical and the wave function-based methods were preferred [37].

The popularity of modern DFT originates from the approach of Kohn and Sham

(KS) proposed in 1965 [38]. Within the framework of Kohn–Sham DFT, the

intractable many-body problem of interacting electrons in a static external

potential is replaced by an auxiliary system of traceable independent particles in

an interacting density. Applying KS approach, a rather small fraction of the total

energy, i.e. the exchange–correlation energy, remains the only unknown

functional and must be approximated.


50

The vast majority of the modern quantum chemistry calculations are based on

density functional theory (DFT) because of its relatively low computational costs

with good accuracy. In the following subsections, this method will be presented in

more details.

2.7.1. Hohenberg–Kohn theorems

DFT is based on a firm theoretical foundation of two Hohenberg–Kohn theorems

(HK) [39] . The first theorem states that:

“For any system of interacting particles in an external potential Vext(r), the

potential Vext(r) is determined uniquely, except for a constant, by the ground state

particle density ρ0(r).”[37]

The corollary of this theorem is that all the properties of the system such as the

total electronic energy (Eel) are completely determined, given only the ground

state density (ρ0(r)) [37, 40]. The external potential Vext(r) is the nuclear attraction

energy part of the electronic Hamiltonian. It is called external due to the Born-

Oppenheim approximation which assumes nuclei are fixed objects which exert

their Coulomb potential to the electrons. As a result, the total electronic energy

can be written as [40]

𝐸𝑒𝑙[𝜌] = 𝑇[𝜌] + 𝑉𝑒𝑒[𝜌] + 𝑉𝑁𝑒[𝜌] = 𝐹𝐻𝐾[𝜌] + � 𝑉𝑒𝑥𝑡 (𝒓)𝜌(𝒓)𝑑𝒓 (2.22)

where 𝐹𝐻𝐾[𝜌] is a universal functional (i.e. does not depend on the external

potential), which contains the electron kinetic energy, 𝑇[𝜌], and the electron-

electron repulsion potential energy 𝑉𝑒𝑒[𝜌]. The nuclei-electron attraction 𝑉𝑁𝑒[𝜌] is

expressed in terms of external potential. Furthermore, with reference to Hartree–

Fock theory, the 𝑉𝑒𝑒[𝜌] term can be divided into two parts: a classical Coulomb

energy of a charge distribution with itself, 𝐽[𝜌] given by


51

𝐽[𝜌] =12

�𝜌(𝒓1)𝜌(𝒓2)

𝑟12𝑑𝒓1𝑑𝒓2 (2.23)

and a non-classical exchange-correlation energy term, 𝐸𝑥𝑐′ [𝜌]. The later part,

arising from the antisymmetrization, is a correction that should be made to

Coulomb energy to take into account the effect of spin correlation [27, 36].

According to the second theorem, “a universal functional for the total energy

E[ρ] in terms of the density ρ(r) can be defined, valid for any external potential

Vext(r). For any particular Vext(r), the exact ground state of the system is the

global minimum value of this functional, and the density ρ(r) that minimizes the

functional is the exact ground state density ρ0(r);”[37].

The second theorem establishes a variational principle for density functional

theory. Based on this theorem, any trial electron density function will result in an

energy higher than (or equal to) the true ground state energy.

Although in principle correct, attempts to deduct density functionals for all terms

of Eq. (2.16), also known as “orbital free” approaches, are not very accurate

mainly because of the lack of good approximations for the kinetic energy

functional [41, 42]. The Kohn-Sham approach to DFT was proposed to overcome

this problem [38].

2.7.2. Kohn–Sham approach

The major breakthrough in developing the modern density functional theory

resulted from Kohn and Sham in 1965 [38]. They assumed that the original many-

body interacting system would be replaced by constructing a fictitious set of non-

interacting electrons which have the same density as the original system by

definition [43]. There exists an exact expression for the kinetic energy of non-

interacting electrons in terms of molecular orbitals, 𝜓𝑖 rather than density. In KS


52

approach, the single particle orbitals (which is a special type of wavefunctions

describing the non-interacting particles), are reintroduced. As a result, the KS

model is closely related to the HF method.

The 𝐹𝐻𝐾[𝜌] functional in Eq. (2.22) can then be written as

𝐹𝐻𝐾[𝜌] = 2 � � 𝜓𝑖∗(𝒓) �−

12

∇2� 𝜓𝑖(𝒓)𝑑𝒓𝑁𝑒𝑙 2⁄

𝑖=1

+ 𝐽[𝜌] + 𝐸𝑥𝑐[𝜌] (2.24)

where 𝐸𝑥𝑐[𝜌] contains all non-classical effects (i.e.𝐸𝑥𝑐′ [𝜌]) as well as the

difference in kinetic energy between the real (interacting) and the reference (non-

interacting) system.

The initial problem of finding the kinetic energy functional for the system of

interacting particles is now shifted to finding the molecular orbitals of non-

interacting electrons. By applying the variational principle, Kohn-Sham equations

are derived which are formally very similar to Hartree-Fock (HF) equations.

Kohn-Sham (KS) method uses an initial guess of the electron density in the KS

equations to calculate the KS orbitals. It is a very similar approach to that of HF

method to solve for molecular orbitals (i.e. basis set expansion of KS orbitals and

SCF method) [13, 40].

2.7.3. Approximate exchange-correlation functionals

The key problem with DFT is that no functional is known for the exchange-

correlation, 𝐸𝑥𝑐[𝜌], term in Eq. (2.24) and approximations should be sought for

this energy term. Several approximations have been made for this entity such as

local-density approximation (LDA), generalized gradient approximations (GGA),

meta–GGA (MGGA) and hybrid functionals. Exchange-correlation functionals

can be written in the form of:


53

𝐸𝑥𝑐[𝜌] = � 𝜌(𝒓)𝜖𝑥𝑐 [𝜌(𝒓)]𝑑𝒓 (2.25)

where 𝜖𝑥𝑐[𝜌(𝒓)] is the exchange-correlation energy density which represents the

energy per electron, whereas the density, i.e. 𝜌(𝒓) shows the number of electrons

per unit volume.

The simplest approximation is LDA which is based on the assumption of a

uniform electron gas model. The exchange-correlation energy in LDA can simply

be decomposed into exchange and correlation terms, linearly (i.e. Exc=Ex+Ec). The

correlation energy (Ec) is not analytically known and should be approximated. For

example, it can be approximated based on fitting the results of accurate quantum

Monte Carlo simulations). The exchange energy (Ex) is known analytically and

can be expressed as

𝐸𝑥

𝐿𝐷𝐴[𝜌] = 𝐶 � 𝜌43(𝒓) 𝑑𝒓 (2.26)

which only depends on the value of the density at a point. Results of the LDA can

be improved by also incorporating the gradient of density. Such an approach is

known as generalised gradient approximation (GGA):

𝐸𝑥𝑐

𝐺𝐺𝐴[𝜌] = � 𝜌(𝒓)𝜖𝑥𝑐 (𝜌(𝒓), |∇𝜌(𝒓)|)𝑑𝒓 (2.27)

Consequently, in Meta-GGA approach, the Laplacian (the second derivative) of

the density is also incorporated to improve the results.

The most important and widely used class of functionals, which are mainly used

throughout this thesis, is known as hybrid functionals. This approach was first

introduced by Axel D. Becke in 1992 [44]. The main idea of hybridization is to

combine Hartree–Fock (HF) theory with local density‐functional theory. In this

manner, hybrid functionals incorporate a portion of exact exchange from the HF

theory, calculated as a functional of Kohn-Sham molecular orbitals rather than the

density, with exchange and correlation from other sources (ab initio or empirical).

The HF exchange energy can be written as:


54

𝐸𝑥𝐻𝐹[{𝜓𝑖 }] = − � � �

𝜓𝑖∗(𝒓)𝜓𝑗(𝒓)𝜓𝑗

∗(𝒓′)𝜓𝑖(𝒓′)|𝒓 − 𝒓′|

𝑑𝒓𝑑𝒓′𝑁𝑒𝑙 2⁄

𝑗=1

𝑁𝑒𝑙 2⁄

𝑖=1

(2.28)

The general form of hybrid functionals can be written as a weighted sum of HF

part and DFT part in the form of:

𝐸𝑥𝑐 = (1 − a)𝐸𝑥𝑐

𝐷𝐹𝑇 + 𝑎𝐸𝑥𝐻𝐹 (2.29)

One of the most successful and popular hybrid functionals to this date is B3LYP

(Becke, three-parameter, Lee-Yang-Parr) [44-47]. Another functional which has

recently become very popular is PBE0 functional [48]. These two functionals are

widely used for most of the calculations in this thesis. However, long range

corrected functionals are also investigated in Chapter 5 in time-dependent DFT

calculations (TD-DFT) which will be discussed in that chapter.

2.8. Time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) is an extension to the

density functional theory (DFT) to study the molecular properties arising from

time-dependent domains such as electric or magnetic potential fields. The fact that

DFT is a ground state theory for investigating properties of a system at

equilibrium makes it inappropriate for studying properties such as excitation

energies or photo-absorption spectra. However, the efficiency of DFT, i.e.

exploiting the density variable which is less complex than wavefunction, has been

employed to develop TD-DFT. In principle, TD-DFT can be viewed as a

reformulation of time-dependent quantum mechanics, where the fundamental

variable is the density instead of the complex wavefunction [49].

The formal foundation for TD-DFT is provided by the Runge-Gross theorem [50],

which is analogue of the Hohenberg-Kohn (HK) [39] theorem for the time-

dependent version of the Schrödinger equation, given (in atomic units) as


55

𝐻�Ψ = i

∂∂𝑡

Ψ (2.30)

where the Hamiltonian and the wavefunction are a function of both the spatial

coordinates and the time, i.e., 𝐻�(𝒓, 𝑡) and Ψ(𝒓, 𝑡). Given the quantum state of the

system at an initial time, t0 , the wavefunction at any other time, t, can be

calculated from Eq. (2.30) [49].

The Runge-Gross theorem proves that for a time-dependent system evolving from

a given fixed initial many-body state, Ψ0, there exist a one-to-one correspondence

(i.e. an invertible mapping, modulo c(t)) between the external potential, Vext(r,t),

and the electron density, ρ(r,t) [49-53]. It follows that the time-dependent density

is sufficient to obtain all observable of a time-dependent many-body system [52].

Similar to the static DFT approach, the next step for developing a practical TD-

DFT method is to replace the interacting system with an auxiliary non-interacting

system (Kohn-Sham system) that reproduces the same density. This becomes

possible by Van Leeuwen theorem [54]. It shows that (under some restrictions and

assumptions) for every interacting time-dependent probability density ρ(r,t), there

exists a non-interacting (i.e. one-body) Kohn-Sham potential which reproduces

the same density of the interacting-system [49].

One of the most popular applications of TD-DFT is the calculation of excited-

state properties and optical spectra using linear response theory [49, 52, 55-57]. In

fact, the primary application of TD-DFT to this date is in the linear response

regime [58]. Linear-response theory can be used if the time-dependent potential is

weak so that it does not completely destruct the ground-state structure of the

system. This is the case with the weak perturbation of the molecular arrangement

as a response to rather weak long-wavelengths optical field (e.g. the UV-Vis

range) [58]. Within the linear response regime, the system is assumed to be in the

ground state initially, and then a weak time-dependent external perturbation is

applied. The linear response of the density (i.e. the induced change in the density

as a result of the perturbation) will be obtained from a “response function”, which


56

is the central quantity of linear response theory. A linear response treatment of

TD-DFT is therefore the application of the linear response theory to a time-

dependent Kohn-Sham framework (i.e. a fictitious system of non-interacting

electrons). The application of TD-DFT to UV-Vis absorption spectroscopy will be

explained shortly in section 2.11.

2.9. Potential energy surface and geometry optimization

Most of the computational studies of chemical processes and molecular properties

begin with geometry optimization. The reason is that the most stable structure of a

system is the minimum energy structure. There is an established relationship

between the molecular properties and molecular geometry. As a result, it is

important to obtain accurate molecular geometry before any other calculations

take place. This starting step, i.e. geometry optimization, aims at exploring the

potential energy surface (PES) to locate the minimum energy structure. In other

words, the geometry optimization, also known as energy minimization, is a search

to find the minima structures on the PES.

Potential energy surface is perhaps the most fundamental and central concept to

computational study of the molecular structure [33, 59, 60]. A PES, which was

introduced in section 2.4, can be defined as the relationship between the energy of

a molecule and its geometry. This relationship naturally arises from the fact that

the energy of a molecular system varies even with small changes in its structure

(as shown in Born–Oppenheimer approximation).

Geometry optimization calculations usually begin with providing an initial guess

of the structure for the molecule to a computer algorithm that systematically

changes the geometry until a stationary point on the potential surface is found.

Each molecular structure (i.e. geometric set) corresponds to an energy value and

the collection of such points is called potential energy (super) surface. The

minimum energy structure determines the molecular bond lengths, bond angles


57

and dihedral angles. A number of algorithms are available for geometry

optimization, such as Berny algorithm using GEDIIS [61] in Gaussian 09

computational package [62], which is employed in this thesis.

Once a stationary point on the PES is found by the geometry optimization

procedure, the nature of the stationary point, which can be either a minimum, or a

transition state, or a hilltop needs to be identified. In order to check the character

of a stationary point, it is necessary to determine the curvature of the PES at the

stationary point, i.e. the second derivatives of the energy with respect to the

geometric parameters. This can be done by calculating the vibrational frequencies

on the optimized geometry [33]. A frequency value less than zero is known as

imaginary frequency and mathematically, any stationary point containing

imaginary frequency is not an energy minimum.

2.10. Vibrational frequency calculation

Vibrational frequency calculations can be employed to characterize stationary

points, to obtain infrared (IR) spectrum, to obtain zero point energies and to

realize various thermo-chemical properties. Such calculations usually involve

finding the normal-mode frequencies which are the simplest vibrations of the

molecule. For a nonlinear molecule with n atoms there exist 3n-6 normal modes

which are the simplest type of vibrations of a molecule (3n -5 normal modes in

case of a linear molecule). In fact, calculation of normal-modes yields the IR

spectrum of the molecule [33].

Infrared spectroscopy is among the most important and powerful spectroscopy

techniques employed for analytical study of molecules [63-65]. Any spectroscopy

techniques conceptually study the interaction between the matter and a different

region of the electromagnetic spectrum. In case of the IR spectroscopy, photons of

lower energies and frequencies (and longer wavelengths) in the infrared region are

used to excite vibrations of chemical bonds and functional groups within a sample


58

molecule. The excitation of a molecular vibration occurs when the molecule

absorbs a quantum of energy, E, from the infrared radiation that corresponds to

the vibration's frequency, ν, according to the relation:

𝐸 = ℎ𝜈 (2.30)

where h is Planck's constant. Such a vibration should lead to a change of the

dipole moment of the molecule to be called IR active.

Vibrational frequency calculations are utilized to identify the nature of all

optimized geometries throughout this work (Chapters 3-7), as well as to

differentiate the conformers of ferrocene (Chapter 7). Furthermore, such

calculations are employed to obtain the zero point energies as well as the thermo-

chemical features of ferrocene/ferrocenium couple in order to study its redox

potential (Chapter 7).

2.11. UV-Vis spectroscopy

While interaction with infrared light causes molecules to undergo vibrational

transitions which can be captured by IR spectroscopy, the higher energy radiation

in the ultraviolet (UV) and visible (Vis) range of the electromagnetic spectrum

leads many molecules to undergo electronic transitions. This means that

absorption of the energy from UV or Vis light by the molecule gives rise to one of

its electrons to jump from a lower energy to a higher energy molecular orbital. As

a result, absorption spectroscopy performed in this region is also called "electronic

spectroscopy" or “UV-Vis spectroscopy”. The feature of absorbing in the UV-Vis

part of electromagnetic spectrum, is the characteristic of a class of molecules

called “dyes” [66]. The functional or elementary group of the compound

responsible for the absorbance is called chromophore [67-70].

Fig. 2.1 shows a diagram of the various kinds of electronic excitation that may

occur in organic molecules which are the subject of this thesis. This figure shows


59

three types of electrons in a molecule, namely σ (single bond, having the lowest

energy level and being the most stable electrons), π (multiple-bond, relatively

unstable and can be excited more easily), or non-bonding (n- caused by lone pairs,

possessing higher energy levels than π-electrons). Among the various transitions

outlined in Fig. 2.1, only the transitions with the lowest energy, i.e. n and (the left-

most, blue colour transitions in Fig. 2.1) can occur by the energies available in the

UV-Vis region.

Experimentally, an optical spectrometer is employed to record the transition

wavelengths and their absorption. A graph of the resulting spectrum is then

plotted illustrating absorbance (A) versus wavelength. Accurate computational

calculation of the UV-Vis spectra can also be obtained, but for large molecules it

is a very challenging task.

Computational study of the electronic (UV-Vis) spectrum of a molecule involves

obtaining its excited states properties: the excitation energies and oscillator

strengths. There are several quantum-chemical methods for calculating excited

states. Some examples of these methods include: configuration interaction singles

Fig. 2.1: Various transitions between the bonding and anti-bonding electronic states of a molecule, when light energy is absorbed in UV-Visible spectroscopy.


60

(CIS), random-phase approximation (RPA), approaches based on coupled-cluster

(CC-based methods), time-dependent density functional theory (TD-DFT), and a

more recently proposed multi reference configuration interaction DFT method

(DFT/MRCI). Because of its simplicity, low computational cost and reasonable

accuracy, TD-DFT is presently very popular and has become the most widely

used theory for modelling excited states of medium-sized to large molecules [55,

71-74]. Today’s popularity of TD-DFT was predicted in a major review in 2005

as, “Most probably, excited-state calculations will be carried out in near future by

using the TD-DFT (Time-Dependent Density Functional Theory) approach, which

is becoming more and more popular because of their simplicity and apparent

black-box behaviour” [75]. As a result, calculations of the UV-Vis absorption

spectra and excited-state properties of dye sensitizers have been dominated by

TD-DFT method in a number of theoretical studies [76-91], and it is also

employed in this thesis.

2.12. Solvent effects

It is important to include the effects of solvation on the calculations of molecular

properties, because many experimental measurements take place in solutions. For

example, the experimental measurements of the absorption spectra of dye

sensitizers or the infrared spectra of ferrocene are usually measured in the

presence of a solution. Another reason for including the solvent effects is to study

the redox potential of ferrocene/ferrocenium (Fc/Fc+) as liquid electrolyte in this

study.

Ideally, the solvation effects should be calculated by explicit inclusion of solvent

molecules. However, this approach is a computationally demanding task and is

limited to very small solutes [92, 93]. Alternatively, implicit solvation methods

can be employed in which the solute is placed into a cavity of the solvent reaction

field. Here, the solvent is treated as a structure-less dielectric medium with surface


61

tension at the solute-solvent boundary. Such an approach to the simulation of

solvation is called “continuum” approximation.

In this thesis, continuum solvation methods such as PCM (or D-PCM) [94], C-

PCM [95, 96] and SMD [97] are employed to simulate the molecular properties in

solutions. In all of the above methods, the solvation effect is considered implicitly

as the solvent is modelled in the form of a polarizable continuum rather than

individual molecules. The conventional PCM model, treats the continuum as a

polarizable dielectric, while C-PCM treats the continuum as a conductor-like

media. PCM is also called as D-PCM in recent years [98]. Finally, the SMD

method, models the quantum mechanical charge density (i.e. the full electron

density without defining partial atomic charges) of the solute molecule which

interacts with a continuum description of the solvent [97].


62

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Chapter 3

Rational design of new dyes based on TA-St-

CA sensitizer “If you wish to make an apple pie from scratch, you must first invent the

universe.” Carl Sagan

3.1. Introduction This chapter presents rational design of new dyes based on making modifications

to the linker of a reference D-π-A compound known as TA-St-CA dye [1]. The

molecular structure of this compound is given in Fig. 3.1. The donor, acceptor and

spacer moieties of the reference dye are also marked in the figure. As was pointed

out in Chapter 1, a variety of approaches can be adopted to red-shift the

absorption spectra of a particular D-π-A dye, such as making modifications into

the structure of the π-conjugated bridge [2], which is a very efficient strategy [3].

As a result, we concentrate on this approach, i.e. structural modifications of the

linker of the reference dye, to design new dyes in the present chapter.

The reference TA-St-CA dye [1] (Fig. 3.1) belongs to a class of organic

sensitizers known as “TPA-based” dyes. TPA-based dyes are among the most

successful classes of organic dyes. They are based on triphenylamine (TPA)

Rational design of new dyes based on TA-St-CA sensitizer Chapter 3

71

donating group (D) and its derivatives. The exceptional electron-donation nature

of the TPA group, its chemical stability and structural ability to suppress the dye

aggregation has made it an attractive electron-donating candidate for the design of

organic dyes in DSCSs [4-16]. Perhaps the significance and popularity of the TPA

donating group is best realized by a literature search under the keywords

“triphenylamine AND dye”. It brings more than 4000 results in the Scopus

database (as in August 2013). TA-St-CA is a very successful sensitizer based on

TPA which is designed and synthesized by Hwang et al. [1]. DSSC based on this

dye has shown the overall solar-to-energy conversion efficiency of 9.1% [1],

which is very high for a cell with organic dye sensitizer. As a result, this push–

pull dye is selected as the backbone reference structure for the π-bridge

modifications to produce new dyes in the present chapter.

The new dyes [17] in this chapter are rationally designed based on a theory known

as Dewar’s rules. In 1952, Dewar published a series of six famous papers on the

“molecular orbital theory of organic chemistry” in journal of the American

Fig. 3.1: Molecular structure of the reference TA-St-CA dye.


72

chemical society, in which he developed a qualitative/semi-quantitative treatment

of organic chemistry by employing perturbation molecular orbital theory (PMO)

[18-23].

According to Dewar’s rules, the π-conjugated spacer in a D-π-A molecule (dye)

exhibits alternative electronegativity along the charge transfer direction.

Furthermore, based on Dewar’s rules the relationships between substituent groups

(and their positions) on the π-spacer and the molecular energy levels is

predictable. Although more accurate quantitative calculations are possible today,

Dewar’s rules can still serve as a prediction tool to rationally design organic dyes

with desired molecular energy levels. For these reasons, Dewar’s guidelines have

been applied for the engineering of molecular structures of several stable and

efficient nonlinear optical chromophores with enhanced hyperpolarizability [24,

25]. To the best of our knowledge, Dewar’s rules have not been employed in the

rational design of new organic dyes for the application in solar cells. In this

chapter, we apply Dewar’s rules to rationally design new dye sensitizers, based on

the modifications of the linker of the existing and well-performing TA-St-CA dye

[1].

In this chapter, a number of electron-donating (ED) and electron-withdrawing

(EW) units will be considered. The new dyes are obtained by substituting the ED

and EW units onto the π-conjugated oligo-phenylenevinylene bridge of the

reference TA-St-CA dye, based on Dewar’s rules [17]. The molecular structures,

frontier molecular energy levels and the electron absorption spectra of the new

dyes are calculated using density functional theory (DFT) and time-dependant

density functional theory (TD-DFT).


73

3.2. Dewar’s rules and design of new dyes

Fig. 3.2 shows a general graphical scheme of Dewar’s rules employed in this

chapter. According to Dewar’s rules, atoms on the π-conjugated bridge of a

chromophore with D–π–A structure can alternately be indexed as “starred” and

“unstarred”. According to perturbational molecular orbital theory, substituting

electron donating groups on the starred positions results in an increase in the

energy of highest occupied molecular orbital (HOMO). Substituting an EW group

on unstarred positions in the bridge is expected to decrease the energy of the

lowest unoccupied molecular orbital (LUMO). Both of these substitutions reduces

the ∆E between HOMO and LUMO and cause a bathochromic shift [25] .

To improve the original TA-St-CA dye, it is required to red-shift (bathochromic

shift) the absorption spectrum and to reduce the HOMO-LUMO energy gap (∆E)

of the new dyes. Based on Dewar’s rules (i.e., PMO theory) illustrated in Fig. 3.2,

to move up the energy of the HOMO, an electron-donating group (ED) needs to

substitute on the starred positions of the π-conjugated bridge to form a new dye.

Alternatively, to move down the energy of the LUMO, an electron-withdrawing

group (EW) needs to substitute on the unstarred positions of the π-conjugated

bridge to form a new dye. Therefore, the new dyes can rationally be designed by

replacing an ED group on the starred positions or an EW group on one of the

unstarred positions of the π-conjugated bridge of the original dye.

Following Dewar’s rules as a guideline, the present study designed new dye

structures by the substitutions of a couple of electron-donating groups such as

−NH2 and −N(CH3)2 and an electron-withdrawing (−CN) group at various

possible positions along the π–conjugated bridge of the original TA-St-CA dye

(Fig. 3.2). Note that no substitution is possible on position 3 and 6* as the C(3) and

C(6*) carbon atoms are saturated. Table 3.1 lists the reference TA-St-CA dye,

which is labelled as starred and unstarred alternately on its linker, as well as all

rationally designed new dyes.


74

Fig. 3.2: A scheme Dewar’s rules. a) Labelling the π-bridge. b) Effect of substitutions on the frontier MO energy levels. Adopted from [25].


75

Table 3.1: Molecular structure of the TA-ST-CA dye and new dyes.

Name Type Group Position Picture

TA-St-CA

−

−

−

ED-I

Electron Donating

−NH2

2*

ED-II

Electron Donating

−NH2

4*

ED-III

Electron Donating

−NH2

8*


76

Name Type Group Position Picture

ED-IV

Electron Donating

−N(CH3)2

2*

ED-V

Electron Donating

−N(CH3)2

4*

ED-VI

Electron Donating

−N(CH3)2

8*

EW-I

Electron Withdrawing

−CN

1

EW-II


−CN

5

EW-III


−CN

7


77

3.3. Computational details

All quantum mechanical calculations are performed using density functional

theory (DFT) based PBE0 hybrid density functionals [26] and polarized split-

valence triple-zeta 6-311G(d) basis set, without any constraints. The DFT based

PBE0 functional (a hybrid of PBE with 25% HF exchange term contribution) is

found to be a reliable functional to estimate the excitation energies of dye

molecules [27, 28]. As a result, it has been widely employed to study the colours

of most industrial organic dyes. In an assessment on a set of more than 100

organic dyes, the PBE0 functional outperformed all other functionals in the study

for reproducing the experimental UV-Vis π→ π* absorption wavelengths [29]. As

a result, the present study employs this functional to study the dye molecules. All

calculations are based on Gaussian 09 computational chemistry package [30].

The optimized geometry of the TA-St-CA dye is obtained using the PBE0/6-

311G(d) model. To verify that the optimized structure is a true minimum,

frequency calculations are performed on the optimized geometry and no

imaginary frequencies are found for the optimized structure. Single point

calculations on the optimized structures in vacuum using the same computational

model are employed to construct the molecular energy levels and isodensity plots.

The experimental UV–Vis spectrum of the reference TA-St-CA dye was

measured in ethanol solution [1]. In order to make comparisions, the present

study has been performed in vaccum and in ethanol solution using the

conductor-like polarizable continuum model (CPCM) [31, 32]. The UV-Vis

spectra of the dyes are calculated using singlet-singlet transitions up to the 30th

lowest spin-allowed excited state of each dye. These lowest-energy electronic

transitions are then transformed into simulated UV-Vis spectra by GaussView 5

visualization software [33], using Gaussian functions with half-widths of 2500

cm–1.


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3.4. Molecular properties

Fig. 3.3 gives the optimized structure of the reference TA-St-CA dye. It is

composed of three moieties, an electron rich “triphenylamine” group (TPA) acting

as electron donor (D-section), an “oligo-phenylenevinylene” group (π-conjugated

bridge, or linker) and a “cyanoacrylic acid” group which works as electron

acceptor/anchoring moiety (A-section). Between the D-section and the A-section,

there is a π-conjugated bridge (π-bridge section) which connects the electron

donor and acceptor moieties to conduct the excited electrons of the dye sensitizer.

Fig. 3.3: The structure of reference dye TA-St-CA (red: oxygen; blue: nitrogen; grey: carbon). Atoms on conjugated bridge (indicated by brackets) are marked alternatively by asterisks. Note that structure is saturated by hydrogen atoms which are not displayed on the structure [17].


79

As seen in Fig. 3.3, the A-section contains a carboxyl group as an anchoring unit

to attach the dye onto TiO2 semiconductor. The optimized structure of the TA-St-

CA dye in the ground electronic state indicates that the π-conjugated oligo-

phenylenevinylene bridge is almost planar, which is nearly coplanar with the

cyanoacrylic acid group. Such a coplanar structure leads to the conjugation

effects. Chemically modifying the conjugation bridge of the TA-St-CA dye

produces a number of new dyes (structures ED-I to EW-III in Table 3.1) which

slightly deviate from the planarity.

The four benzene rings in the molecular structure of the TA-St-CA dye are

labelled as R1-R4 as seen in Fig. 3.3. Perimeters [34] of the terminal benzene rings

R3 and R4 are slightly longer than the benzene rings inside the molecule, i.e., R1

and R2. For example, R3 and R4 are given by 8.38 and 8.37 Å, respectively,

whereas both R1 and R2 are the same at 8.35 Å, which is the same as an isolated

benzene ring [34]. Other geometrical parameters of the studied dyes vary,

depending on the chemical structure of the molecule. Table 3.2 summarizes

related properties such as geometric, dipole moments, and size of the dyes.

The length of the π -bridge, Lπ, are also listed in Table 3.2. Here, we define the

length of the π -bridge, Lπ, as the direct distance between C(18) and C(23) as

indicated in Fig. 3.3 [17]. For the TA-St-CA dye, Lπ is calculated as 5.23 Å. In the

table, the new dyes produced by the substitutions of the EW group (i.e. −CN) on

1, 5, and 7 positions of the π-conjugated bridge (i.e. dyes “EW-I” to “EW-III” in

last three columns of Table 3.2) exhibit equal or larger Lπ with respect to the

reference dye. For example, Lπ is calculated as 5.33 Å and 5.24 Å for EW-I and

EW-II, respectively. The influence of the electron donating substitutions (EDS) is

not as systematic as the new dyes produced by the EWS. Instead, the ED dyes

have either shorter or longer Lπ with respect to the TA-St-CA dye. However, it is

noted that the new dyes ED-I and ED-IV possess the shortest π-conjugated bridge

lengths of 5.13 and 5.10 Å, respectively, in this table.


80

The molecular size, i.e., electronic spatial extent <R2> (in a.u.), is calculated as

34612.20 a.u for the parent TA-St-CA dye. All new dyes except for ED-I have

larger molecular sizes with respect to the parent dye. The molecular size of ED-I

is calculated as 34474.2 a.u. The dipole moments (μ) of the dyes exhibit a similar

trend to the π-conjugated bridge length (Lπ) in general. That is, the substitutions of

the EW group polarize the molecules and therefore produce a larger than the

reference (6.58 Debye) dipole moment. For example, the new dyes “EW-I”, “EW-

II” and “EW-III” result in a noticeable increase in dipole moment of 8.38, 8.41

and 8.81 Debye, respectively. However, in general, EDS reduce the dipole

moment from the reference dye. For example the new dyes ED-I and ED-IV

possess smaller dipole moments of 4.63 and 4.64 Debye, respectively.


81

Table 3.2: Molecular properties of the new dyes and the reference TA-ST-CA dye*[17].

TA-St-CA

ED-I ED-II ED-III ED-IV ED-V ED-VI EW-I EW-II EW-III

Lπ (a) (Å) 5.23 5.13 5.19 5.26 5.10 5.20 5.27 5.33 5.24 5.23

8-7-14 (°) 120.40 119.99 120.47 120.35 120.07 120.56 120.41 120.61 120.62 120.43

6-7-14 (°) 120.32 120.07 120.29 120.47 120.12 120.27 120.46 120.47 120.52 120.67

18-19-20 (°) 126.53 120.55 128.23 125.31 118.74 128.70 125.76 131.85 126.29 126.19

23-24-25 (°) 132.20 132.11 132.21 132.18 132.16 132.12 132.17 132.07 128.72 131.39

15-16-17-18 (°) -179.67 -179.25 -178.95 -179.03 -176.46 -179.14 -179.10 -178.40 -178.89 179.97

18-19-20-21 (°) -178.70 -146.00 153.77 151.42 -37.68 161.72 157.58 172.85 173.69 -177.33

18-19-20-32 (°) 1.34 34.99 -27.08 -30.47 141.57 -14.86 -26.33 -7.73 -7.67 2.70

22-23-24-25 (°) -179.73 -179.11 177.78 -179.95 -179.91 -177.73 -179.09 179.46 -136.43 -179.76

<R2> ( a.u) 34612.20 34474.2 35088.40 35182.90 35646.00 36605.00 36285.80 35192.60 36808.20 36088.30

μ (Debye) 6.58 4.63 5.82 6.82 4.64 5.68 6.55 8.38 8.41 8.81

*The PBE0/6-311G(d) model.

(a) The length of the π-bridge, Lπ =direct distance between C(18) and C(23) [17].


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3.5. Frontier molecular orbital analysis

Frontier molecular orbitals (MOs) are sensitive to the changes in the π-spacer of

the dye. The effect of modified π-spacer on the energy levels of the frontier

molecular orbitals (e.g. HOMO and LUMO) of new dyes provides feedback to the

design of the new dyes. As stated in Chapter 1, an important goal of our rational

design is to reduce the HOMO-LUMO energy gap of the new dyes with respect to

the reference dye. The energy level diagrams of the dyes are illustrated in Fig. 3.4.

The orbital energies of the HOMO and the LUMO of the parent TA-St-CA dye in

vacuum are calculated at -5.51 and -2.69 eV, respectively, and the corresponding

energy gap between its HOMO and LUMO is given by 2.82 eV.

As seen in Fig 3.4 the HOMO and LUMO energy levels of the new dyes generally

follow the Dewar’s prediction (refer to Fig. 3.2 (b) for Dewar’s rule). For

example, new dyes “ED-I” to “ED-VI”, generated by the ED substitutions, exhibit

elevated HOMO energies, with respect to the reference dye. A closer look reveals

that the new dyes produced by the ED substitutions on the position “2*” lead to a

noticeable decrease of the HOMO-LUMO gaps. For example, the energy gap for

ED-I (obtained by substitution of –NH2 on 2*) is calculated as 2.60 eV, which is

0.22 eV less than that of the reference dye. Similarly, ED-IV (produced by

substitution of –N(CH3)2 on 2*) gives an energy gap of 2.61 eV, which is 0.21 eV

less than that of the parent dye. As seen in Fig 3.4, both dyes “ED-I” and “ED-IV”

reduce the HOMO-LUMO gap by lifting up the HOMO energies without

apparently lifting up the LUMO energies. As for the ED substitution on position

“4*” (i.e. ED-II and ED-V), the resultant gap is increased with respect to the

reference dye. Such increase is attributed to an apparent increase of their LUMO

energies. As a result, these two positions are not appropriate for the design of new

dyes. New dyes “ED-III” and “ED-VI” are designed by ED substitutions on

position 8* of the reference dye. Both dyes exhibit slightly smaller HOMO-

LUMO gap compared to that of the reference dye.


83

Fig. 3.4: The calculated frontier MO energy levels using PBE0/6-31G* in vacuum [17].

Unoccupied M

Os

Occupied M

Os


84

On the contrary to the ED dyes, the EW dyes exhibit lowered LUMO energy

levels, in agreement with the Dewar’s rules. As can be predicted by the Dewar’s

rules [25, 35, 36], the EW substitutions results in a decrease of the HOMO-

LUMO gap with larger energy drops of the LUMOs than the energy drops in the

HOMOs. As seen in Fig 3.4, all three EW dyes follow this pattern. For example,

in comparison with the reference dye, the HOMO and the LUMO energies of EW-

I are lowered by 0.20 eV and 0.39 eV, respectively. This has resulted in a gap of

2.63 eV for EW-II dye, which is about 0.20 eV less than that of the reference dye.

Fig. 3.4 also provides information about the suitability of the new dyes for the

application in DSSC. As mentioned earlier in Chapter 1, alignment of the LUMO

energy level above the conduction band edge of semiconductor (e.g. TiO2) and the

HOMO energy level below the redox potential of redox couple (e.g.

iodide/triodide) should be considered, when deciding about the suitability of the

newly designed dyes. That is, the HOMO-LUMO gap of a new dye should be

outside of the green parallel dash lines in Fig. 3.4. As seen in this figure, the

LUMO energies of all dyes are well located above the conduction band of the

TiO2 semiconductor, therefore enough energy potential is provided for electron

injection. It is also observed that the HOMO energies of all dyes are located

below the energy level of iodide/triodide for efficient regeneration of the oxidized

dye. As a result, all new dyes meet this criterion. The calculated frontier MO

energy levels in ethanol solution also show the same trend and results. Please refer

to Appendix A-I for the MO energy levels in solution.

To further explore the different behaviours of the ED and EW impact on the

reference (TA-St-CA) dye, Fig. 3.5 provides the charge density information of the

HOMOs and the LUMOs of the reference (TA-St-CA) dye, a new dye produced

by an ED modifications (new dye “ED-I”) and an EW modifications (new dye

“EW-I”). As seen in Fig. 3.5, the HOMO of TA-St-CA is a π orbital, which is

dominated by p electrons from the backbone atoms. It populates over the entire

triphenylamine donor group including R2, R3 and R4 (refer to D-section of the D–

π–A dye in Fig. 3.3). It partially populates the oligo-phenylenevinylene π-


85

conjugated bridge and the R1 ring, as shown in the green box in this figure. The

HOMO is located far away from the A-section and therefore TiO2 surface.

Significant contribution of the triphenylamine donor group into the HOMO

minimizes the probability of charge recombination between the injected electrons

and the resulting oxidized dye [37]. Charge recombination is a determinant factor

of the efficiency of DSSC. Therefore, the present distribution of the HOMO of

TA-St-CA, which minimizes this factor, is desirable.

The LUMO of the reference dye is a singlet π* orbital which largely populates the

cyanoacrylic acid acceptor group (the A-section of the D–π–A dye). The LUMO

also spreads into the π-spacer and into the triphenylamine donor group of R2 ring

in the D-section. As a result, the HOMO to LUMO transition ensures an intra-

molecular charge transfer from the donor end to the acceptor end of the dye,

through the conjugated spacer. The LUMO of a dye is the final state in the charge

transition from HOMO to LUMO. Significant contribution of cyanoacrylic acid

group (A-section) to the LUMO ensures a strong electronic coupling between the

dye's lowest excited state and conduction band of the semiconductor (TiO2). It

facilitates an efficient electron injection as the dye sensitizer is anchored into TiO2

through the A-section.

It is important that the new dyes follow the same pattern of HOMO and LUMO

charge density distribution of the parent TA-St-CA dye. In other words, the

charge distribution of the HOMO should mainly populate the donor (D) end,

whereas the LUMO should be distributed largely on the acceptor (A) end of the

new dyes. This requirement is met for the new dyes, such as ED-I and EW-I.

Please refer to Appendix A-II for the information of all other dyes, which show

the same trend of charge density distribution. Fig. 3.5 further shows that the

modifications made in new dyes changes the charge distribution over the π-spacer,

rather than the donor and acceptor ends. That is, the HOMO and LUMO of the

new dyes “ED-I” and “EW-I” are very similar to those of the reference TA-St-CA

dye in the D and A ends (i.e. outside the green box in the figure).


86

3.6. UV-Vis absorption spectra

Electronic absorption spectroscopy (also known as UV-Vis spectroscopy) is

the most appropriate technique to indicate the presence of chromophores in a

molecule. Chromophores are π-electrons or lone pair electrons in a molecule,

which are likely to absorb light in the UV-Vis region (200 to 800 nm). As a

result, conjugated π-electrons in a molecule becomes the major structural

feature identified by this UV-Vis spectroscopic technique. Time-dependent

density functional theory (TD-DFT) is employed to simulate electronic

absorption spectra with PBE0 hybrid functionals in this chapter.

Fig. 3.5: Comparison of the charge density of HOMOs (left) and LUMOs (right) of the new dye, ED-I and EW-I with respect to those of the reference TA-St-CA dye [17].


87

Fig. 3.6 compares the simulated UV-Vis spectra of the reference TA-St-CA

dye in ethanol solution and in gas-phase with available experiment (in ethanol

solution) [1]. It is seen that the calculated spectra agree reasonably well with the

experiment which is only measured in the region of λ< 450 nm, i.e., the first

absorption spectral peak region. The simulated UV-Vis spectrum of the

reference TA-St-CA dye in ethanol solution closely reproduce the majour

spectral peak at λI= 374.52 nm with respect to the experiment at λI= 386 nm

(I). In the spectral region of λ> 450 nm, the present simulation in ethanol

produces a major peak at λII=545.03 nm in the green region (II), which is in

agreement with an early computational study [38]. In addition, it is observed

that the ethanol solvent causes the simulated spectral peaks of the reference dye to

red-shift from their positions in vacuum. The good agreement with experiment

and literature indicates that the present computational model employed is a

good model.

Fig. 3.6: The simulated UV–Vis absorption spectra of TA-St-CA dye in gas-phase and ethanol solution, compared with the experimental spectra in ethanol solution [17].


88

Fig. 3.7 compares the simulated spectra of the new dyes obtained from electron

donating substitutions (EDS) with the reference dye in ethanol solution. The

absorption spectra of the new dyes which are designed from –NH2 (EDS) group

are plotted in Fig. 3.7(a), and those of the –N(CH3) substitution are illustrated in

Fig. 3.7(b). As seen in this figure, modifications of the reference dye results in

shifts of the spectral peaks, either bathochromic shift (i.e. to the longer

wavelength) or hypsochromic shift (i.e. to the shorter wavelength) from positions

of the reference dye.

Chemical modifications by EDS with respect to the reference dye lead to

bathochromic shift of peak II, but hypsochromic shift of peak I (λI) in the new

dyes “ED-I” to “ED-VI”. For example, the –NH2 (EDS) group on the position

“2*”of the reference dye (i.e. “ED-I”) results in a bathochromic shift of ~44

nm on peak II, whereas a ~31 nm hypsochromic shift on peak I of the TA-St-CA

spectrum (in ethanol solution).

Although the position of the peak I is blue-shifted in new EDS dyes, the intensity

of this peak is increased in all new dyes, with respect to the reference TA-St-CA

dye. On the other hand, the position of peak II is red-shifted in almost all new

dyes but either with the same or less intensity, compared to the reference dye. For

example, peak II of ED-I and ED-IV are both red-shifted and less intense in

comparison to that of TA-St-CA. On the other hand, the intensity of this peak in

all other dyes in Fig. 3.7 is comparable to the parent TA-St-CA dye.


89

a.

b.

Fig. 3.7: The simulated UV–Vis absorption spectra of TA-ST-CA dye and its substituted new dyes in ethanol solution using the (CPCM) TD-DFT calculations [17]. (a) New dyes generated from the substitutions of –NH2, and (b) from –N(CH3)2 ED groups.

I II

I II


90

Fig. 3.8 compares the new dyes obtained from electron withdrawing substitutions

with the original dye. As seen in Fig. 3.8, the EW substituations result in

bathochromic shift in both peak I and II in new dyes “EW-I” to “EW-III” with

enhanced intensity of the peak.

Table 3.3 collects the calculated spectral properties, such as maximum absorption

wavelengths (λ), oscillator strengths (f), and dominant transitions responsible for

the two most intense peaks (λI , λII) of the dyes in this chapter (in ethanol

solution).

Fig. 3.8: The simulated UV–Vis absorption spectra of TA-ST-CA dye and its substituted new dyes in ethanol solution using the (CPCM) TD-DFT calculations [17]. New dyes are generated from the substitutions of the electron withdrawing group (–CN).

I II


91

Table 3.3: Calculated(a) excited energy (in nm), transition configuration, and oscillator strengths (f) for the two most intense peaks of TA-ST-CA dye and the new dyes in ethanol solution. λI (ca. 360 nm) λII (ca. 500 nm)

Structure λ (nm) f Transitions λ (nm) f Transitions

TA-St-CA 374.53 0.77 H-1→LUMO (91%) HOMO→L+1 (7%)

545.03 1.22 HOMO→LUMO (99%)

ED-I 343.43 0.78 HOMO→L+1 (90%) H-4→LUMO (4%) H-2→LUMO (2%)

588.97 0.59 HOMO→LUMO (99%)

ED-II 355.83 0.85 HOMO→L+1 (63%) H-2→LUMO (32%)

545.36 1.04 HOMO→LUMO (98%)

ED-III 358.32 0.75 H-2→LUMO (73%) HOMO→L+1 (18%)

550.33 1.10 HOMO→LUMO (98%)

ED-IV 353.92 1.19 HOMO→L+1 (73%) H-2→LUMO (24%)

608.45 0.50 HOMO→LUMO (97%)

ED-V 362.31 0.85 H-2→LUMO (76%) HOMO→L+1 (17%) H-1→LUMO (5%)

551.43 1.05 HOMO→LUMO (97%)

ED-VI 368.57 0.69 H-2→LUMO (81%) HOMO→L+1 (9%) H-1→LUMO (8%)

559.82 1.15 HOMO→LUMO (97%)

EW-I 380.14 0.89 H-1→LUMO (83%) HOMO→L+1 (15%)

586.65 0.87 HOMO→LUMO (99%)

EW-II 393.67 0.68 H-1→LUMO (93%) HOMO→L+2 (4%)

605.92 1.09 HOMO→LUMO (99%)

EW-III 381.80 0.70 HOMO→L+1 (83%) H-1→LUMO (13%)

560.58 0.92 HOMO→LUMO (99%)

(a) Calculated using TD-DFT based PBE0/6-311G(d) model in ethanol solution (CPCM).


92

It is found from the simulated spectra of the reference TA-St-Ca dye in ethanol

solution that the most intensive absorption band observed at λII=545.03 nm

(f=1.22) corresponds to a transition (excitation) from the HOMO to the LUMO

of the reference dye, as seen in Table 3.3. Since the HOMO-LUMO gap

requires the least energy to excite an electron from an occupied orbital onto a

virtual (unuccupied) orbital, there is no doubt that the HOMO-LUMO

transition is almost always the favourite transition in energy. The second

strongest absorption band near λI=374 nm (f=0.77) is a combination of two major

transitions. One is dominated by the transition from HOMO-1 to LUMO (~91%)

and the other is a minor transition from HOMO to LUMO+1 (~7%). The HOMO-

1→LUMO and/or HOMO→LUMO+1 transition are usually the second

energetically favourite transitions.

The red/blue shifts of the main peaks in new dyes can be rationalised by looking

at the underlying electronic transition orbitals listed in Table 3.3. As explained

earlier, peak II is mainly (i.e. 99%) a HOMO→LUMO transition which are

brought closer to each other in new dye “ED-I”; therefore, this peak is red-

shifted in ED-I compared to TA-St-CA dye. On the other hand, an excitation

transition from HOMO-1→LUMO (∆E=3.76 eV) is mainly (i.e. 91%)

responsible for peak I in TA-St-CA structure, while a HOMO→LUMO+1

(∆E=4.29 eV) exciation contributes 90% to this peak in ED-I. It is seen that

the first peak (I) in ED-I needs more energy compared to that of TA-St-CA dye

because of its bigger energy gap. Therefore, this peak shifted to longer

wavelenghths. Similar justification and reasoning hold for all other

substitutions.

It should also be noted that for a more precise study of the absorption spectra, the

influence of the dye adsorption onto TiO2 nanocrystals should also be taken into

account. A number of TD-DFT calculations on the dyes adsorbed onto TiO2 have

been reported [39-44]. Although such calculations are beyond the scope of the

current thesis, it is important to have a glimpse of the effect of adsorption on the

electronic structure and absorption spectra of dye-TiO2 system. In addition to


93

altering the conduction band of the semiconductor [45], adsorption of dye

sensitizer onto TiO2 will change the electronic properties and absorption spectra

of dye sensitizer. For example, it can change the stabilization of the LUMO of the

dye sensitizer, leading to a red-shift of the absorption spectra of adsorbed dye

compared to isolated dye.

Sánchez-de-Armas et al. studied the optical properties of five coumarin-based

dyes and observed a widening of the first band and small bathochromic shift in the

absorption spectra of adsorbed coumarin dyes compared to free dye molecules

[46]. Another study by Wen et al. shows that morphology and size of TiO2

nanocrystals can influence the UV-Vis spectra of N17 sensitizer [47]. Another

example is the absorption spectra of free and bounded (onto TiO2) catechol and

aliazarin molecules. Although these two molecules have similar binding patterns,

upon binding onto TiO2 an entirely new band is observed in the absorption spectra

along with exactly the same bands of the free catechol spectra, whereas no new

band appears and only red-shifting is observed for alizarin bound onto TiO2

semiconductor [48]. Although adsorption can change the electronic absorption

spectra, the above examples show that such influences are usually positive. That

is, the absorption spectra of the dyes attached onto the surface of semiconductor

are usually enhanced, compared to those of the free molecules. In this study we

only compared the absorption spectra of free dye molecules (which is in the scope

of the current thesis).

Table 3.4 summarises the effects of chemical substitutions on a number of

important properties of organic dyes, such as the energies of the HOMOs (εHOMO),

the LUMOs (εLUMO), the HOMO-LUMO energy gap (∆ε), shift of the spectral

peaks (∆λI and ∆λII ) as well as changes in their spectral widths (∆γ). From Table

3.4, it can be seen that the new dye “ED-I” almost meets all the requirements of

the preferred properties of an improved dye, except for the slight decrease in the

wavelength of its first absorption peak. The EW substituted dyes, “EW-I” to

“EW-III”, enable the bathochromic shift of both absorption peaks, for functionally

enhanced dyes.


94

Table 3.4: Comparison of the substitution effects on the energies of the HOMOs (εHOMO), the LUMOs (εLUMO), the HOMO-LUMO energy gap (∆ε), shift of the spectral peaks (∆λI and ∆λII) and spectral widths (∆γI and ∆γII) in ethanol solution* [17].

Dyes ∆ε (a) εHOMO(b) εLUMO(c) ∆(∆ε)(d) ∆λI (360 nm)(e) ∆λII (500 nm)(e) ∆γI (360 nm)(f) ∆γII (500 nm)(f)

TA-St-CA 2.82 NA(g) NA(g) NA(g) NA(g) NA(g) NA(g) NA(g)

ED-I 2.60 + + – – + + –

ED-II 2.87 + + + – NC(h) – +

ED-III 2.81 + + – – + – +

ED-IV 2.61 + + – – + + –

ED-V 2.83 + + – – + – +

ED-VI 2.76 + + – – + NC(i) NC(i)

EW-I 2.63 – – – + + + –

EW-II 2.59 – – – + + + –

ED-III 2.79 – – – + + + –

(a) HOMO-LUMO gap (eV). (b) Indicates whether HOMO level is shifted up (+) or down (–) compared to TA-St-CA base structure. (c) Indicates whether LUMO level is shifted up (+) or down (–) compared to TA-St-CA base structure. (d) Indicates whether HOMO-LUMO gap is decreased (–) or increased (+) compared to TA-St-CA base structure. (e) Indicates a bathochromic shift (+) or hypsochromic shift (–) of this peak compared to TA-St-CA base structure. (f) Indicates an increase of peak width (+) or a decrease of peak width (–) of this peak compared to TA-St-CA base structure. (g) NA=Not applicable. (h) NC= Not changed.


95

3.7. Summary and conclusions

The present chapter aimed to enhance appropriate properties, such as HOMO-

LUMO gap and red-shift the spectral absorption through rational chemical

modifications. Chemical modifications were made on the π-spacer of a well-

performing organic dye sensitizer (the TA-St-CA dye) for the development of

new and more efficient organic dyes. Perturbational molecular orbital theory (e.g.

Dewar’s rule) has been found to serve as a good indicator for determination of the

appropriate substitution positions on the π-conjugated bridge of the reference dye,

and for selection of electron donating/withdrawing building blocks for new dyes.

It is found that the electron donating groups (ED substitutions) on position 2* of

the reference dye, which is close to the donor section of the reference structure,

exhibit advantages over the electron withdrawing group (EW substitutes) to

reduce the HOMO-LUMO energy gap, as well as to redistribute the electron

density of the frontier orbitals (i.e., HOMO and LUMO) of the new dyes. The

impact on the optical spectra of new dyes are, however, less significant and

warrants further studies in this direction.

To the best of my knowledge, this study demonstrated for the first time that

Dewar’s rule can be employed to rationally design new dye sensitizers for the

application in DSSC. The present study might have an important practical

application. It provides a systematic way (based on Dewar’s rules) to modify an

existing well performing dye. A systematic method of modifying dye structure

provides the possibility to design a software program to automatically design new

dye sensitizers. Therefore, it is recommended that further effort be undertaken to

design and code such software program.


96

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101

Chapter 4

Novel annulene-based dyes “Imagination is everything. It is the preview of life's coming attractions.”

Albert Einstein

4.1. Introduction

The previous chapter was mainly focused on the design of new dye sensitizers

through chemical modifications of the π-conjugated bridge (linker) of a good-

performing dye. As seen in that chapter, the linker of a reference dye called TA-

St-CA, was subject to the modifications by substitutions of small electronegative/

electropositive groups based on Dewar’s rules. The present chapter takes a new

approach to the design of new dye sensitizers. That is, to employ new chemical

groups in the donor (D) moiety of an existing promising organic dye sensitizer.

Design of the new dyes in this chapter is based on the backbone structure of the

TA-St-CA dye. This chapter is designed to examine how modifications on the

donor moiety of the reference dye affect the properties and absorption spectra of

the new dyes.

Electron donating groups (EDG) (also known as electron releasing group (ERG)

or activating group) may be broadly defined as groups of atoms which can

contribute electron density to a system. This chapter investigates the influence of

Novel annulene-based dyes Chapter 4

102

increasing the number of sp2 hybridized atoms (in the D moiety) on the reduction

of the HOMO-LUMO energy gap and enhancing the absorption spectra of organic

dye sensitizers.

4.2. Design of the new dyes

The central concept for the design of new dye sensitizers in this chapter is to

utilize two different aromatic annulenes as building blocks to reconstruct the

donor (D) moiety of D-π-A structure. Annulenes are conjugated monocyclic

hydrocarbon rings without side chains, such as benzene. They have the general

formula of CnHn (if n is an even number) or CnHn+1 (when n is an odd number) [1].

Fig. 4.1 gives examples of annulenes.

Fig. 4.1: Molecular structure of different annulenes.


103

Aromaticity of annulenes can be studied by the famous Hückel's rule of

aromaticity formulated in 1931 [2]. Hückel's rule states that a planar (or almost

planar) cyclic ring with a continuous system of π-orbitals is aromatic, if these π-

orbitals are occupied by 4m+2 electrons (where m is a non-negative integer). The

most well-known aromatic member of annulenes is benzene (i.e. C6H6 or [6]-

annulene, n=6, m=1).

Cyclodecapentaene or [10]-annulene (i.e. C10H10, n=10, m=2) should display

aromaticity as it exhibits 10 π–electrons and satisfies the 4m+2 rule (m=2). But

this annulene is not aromatic, due to a combination of steric strain and angular

strain. If the planar all cis-configuration is assumed for it (see Fig. 4.1), there

would be bond angles of as large as 144° between the carbon atoms (instead of the

120° angles required for sp2 hybridized carbon). This creates large amounts of

considerable angle strain, which destabilizes the planar all cis-configuration. Such

destabilization (owing to angle strain) apparently exceeds the stabilization

associated with aromaticity. As a result the planar all cis-cyclodecapentaene is a

highly reactive substance. Another possible planar configuration is 1,5-trans

cyclodecapentaene (i.e. the configuration in which two of the double bonds are

trans, see Fig. 4.1). This isomer is free of angle strain. However the repulsive

force between two hydrogen atoms that are forced together in the interior of the

ring destabilizes this planar structure. As a result, this isomer is also relatively

reactive.

The next two aromatic annulenes, based on Hückel's rule of aromaticity, are [14]-

annulene (also known as Cyclotetradecaheptaene, i.e. C14H14, n=14, m=3) and

[18]-annulene (i.e. C18H18, also known as cyclooctadecanonaene, n=18, m=3). All

of these ring structures (i.e. [6]-annulene, [14]-annulene and [18]-annulene) are

completely conjugated, monocyclic hydrocarbons, which follow the Hückel's rule

of aromaticity (see Fig. 4.1).

The molecular structure and aromaticity of [14]- and [18]- annulenes have been

thoroughly studied in several articles such as Wannere et al. [3, 4], Jug et al. [5] ,


104

Kennedy et al [6] and Gellini et al. [7]. Such studies confirm that both of these

annulenes indeed show aromatic character. However, [14]-annulene tends to be

less planar, because of the steric interactions among the four inner-rings hydrogen

atoms in its structure. Such ring strain might destabilize this compound and make

it quite reactive. Nevertheless, there have been no dye sensitizer designed based

on [14]-annulene to the best of our knowledge. If our novel design based on this

group shows promising results, at least in theory, future studies can be directed to

finding strategies for designing and synthesizing more stable dyes based on [14]-

annulene rings (such as bridged [14]-annulenes).

Several properties of annulenes draw our attention to employ these compounds in

the structure of new dye sensitizers. The existence of n delocalized π-electrons in

their rings (n refers to the number of carbon atoms in annulene formula) makes

annulenes electron-rich compounds, which is ideal for the donor moiety of a push-

pull dye. Moreover, the aromatic annulenes (i.e. [6]-, [14]- and [18]- annulenes)

are able to enhance chemical stability of the new dyes. Stability is an important

requirement for the commercialization of the dye sensitizers. Annulenes are also

conjugated structures. Conjugation increases the electron delocalisation, and

therefore reduces the energy gap between the bonding (π) and anti-bonding

orbitals (π*). As a result, by employing larger conjugated groups, the HOMO-

LUMO energy gap should decrease, and the maximum absorption should move to

longer wavelengths. As mentioned previously, our aim is to design dye

sensitizers, which can absorb in longer wavelengths (i.e. red-shifting the

absorption spectra). As a result, annulenes are suitable candidates for our rational

design.

In this chapter two new dyes are rationally designed by altering the donor (D)

moiety of the parent TA-St-CA dye. These dyes inherit the same π-linker and

acceptor (A) moieties of the parent dye, and only differ in the donor (D) section.

Fig. 4.2 shows structure of these molecules. The D section of the parent dye

consists of a triphenylamine (TPA) moiety. Three phenyl rings of the TPA group

are labelled as R1-R3, as shown in Fig. 4.2(a)). Phenyl groups are derived from


105

benzene ring (i.e. C6H6 or [6]-annulene). In the first rationally designed dye, AN-

14, all three rings (R1-R3) are replaced with [14]-annulene rings (Fig. 4.2(b)). In

the second new dye, AN-18, two of these ring, i.e. R1 and R2 remain unchanged,

while R3 is substituted with [18]-annulene ring. Fig. 4.2(c) shows structure of AN-

18 dye.

As seen in Fig. 4.2, the “oligo-phenylenevinylene” group (π-linker) and the

“cyanoacrylic acid” group which works as electron acceptor/anchoring moiety (A-

section) remains unchanged in all three molecules. A purple box in Fig. 4.2

encompasses the identical sections of the dyes in this study. Theoretical

calculations are performed on AN-14 and AN-18 dye structures to investigate

how modifying the donor moiety affects the HOMO-LUMO energy gap as well as

the UV-Vis absorption spectra.


106

Fig. 4.2: Molecular structure of the reference TA-St-CA sensitizer and new dyes AN-14 and AN-18.


107

4.3. Computational details

Density functional theory (DFT) based PBE0 hybrid density functionals [8] and

polarized split-valence triple-zeta 6-311G(d) basis set are exploited without any

constraints. This computational model is employed to allow comparisons of the

newly designed dyes with the reference TA-St-CA dye, which was studied in

previous chapter. As seen in chapter 3, this computational model (i.e. PBE0/6-

311G(d)) provides good agreement with the experiment for the reference dye. All

quantum mechanical calculations are performed with Gaussian 09 computational

chemistry package [9].

For each of the newly designed dyes, the geometries are optimized followed by

frequency calculations to ensure that the structures are true minimal energy ones.

Single point energy calculations on the optimized structures in vacuum are

conducted by the same PBE0/6-311G(d) computational model to construct the

molecular energy levels and isodensity plots.

In order to make comparisions, the present study simulates the absorption

spectra of the reference TA-St-CA sensitizer and the new dyes in ethanol

solution using the conductor-like polarizable continuum model (CPCM) [10,

11]. The UV-Vis spectra in ethanol solution are simulated using singlet-singlet

transitions up to the 30th lowest spin-allowed excited states of each dye based

on time dependant density functional (TD-DFT) calculations by employing the

PBE0/6-311G(d) model. These lowest-energy electronic transitions are then

transformed into simulated UV-Vis spectra by GaussView 5 visualization

software [12], using Gaussian functions with half-widths of 3000 cm–1.

To address the issue of charge-transfer (CT) excitations [13], a TD-DFT

calculation using CAM-B3LYP functional is also performed on the reference and

new dyes in this chapter. The CAM-B3LYP functional proposed by Yanai et al.

[14] is a long-range corrected density functional. This functional has been found

to be successful in overcoming the problem with CT bands in many different


108

studies [14, 15], including theoretical studies of dye sensitizers [16-18].

Consequently, this long-range corrected functional (i.e. CAM-B3LYP) has been

employed in recent in silico design of new dye sensitizers [19, 20]. As a result, the

UV-Vis spectra in ethanol solution are also simulated using singlet-singlet

transitions up to the 30 lowest spin-allowed excited states of each dye based on

TD-DFT calculations using CAM-B3LYP/6-311G(d) model.

4.4. Geometrical details

Fig. 4.3 gives the optimized 3D structures of the new AN-14 and AN-18 dye

sensitizers. These dyes are rationally designed in silico. No experimental

geometry measurements of the entire structures are available for comparison.

However, the theoretical model employed to optimize the structures of new dyes

has been validated using TA-St-CA dye in Chapter3.

A reverse multi-fragment approach [21] is adopted in this study to validate our

model. That is, the optimized structure is obtained first. The geometry features of

the main fragments of the compounds are then compared with the available

experimental data. For AN-14 molecule, a [14]-annulene ring is selected to be

compared with data from literature. This fragment is labelled as R1 in Fig. 4.3 (a).

In a similar way, the [18]-annulene ring of the AN-18 dye (R3 in Fig. 4.3 (b)) is

investigated in this section.


109

Table 4.1 compares selected bond lengths, bond angles, and dihedrals of the [14]-

annulene ring with available theoretical and experimental data. For better

visualization, this ring is given separately in Fig. 4.4. In the figure, this ring (i.e.

R1) is re-oriented and its atoms are labelled. Table 4.1 is closely related to Fig.

4.4.

Fig. 4.3: Optimized 3D structures of the new dyes AN-14 (a) and AN-18 (b), (red: oxygen; blue: nitrogen; grey: carbon).


110

[14]-annulene was first synthesized by Sondheimer and Gaoni in 1960 [22]. Based

on Hückel's rule of aromaticity, [14]-annulene should be aromatic and likely to be

planar. The photoelectron spectrum of [14]-annulene identifies a vertical

ionization energy which is consistent with an aromatic system [23, 24]. The

structure of [14]-annulene was investigated experimentally by X-ray study [25].

There are also several theoretical studies reported on the structure of this aromatic

ring, employing a variety of theoretical levels. For example, Allinger and Sprague

performed molecular mechanics (MM) calculations on C2h and D2 conformations

of this molecule [26]. Jug and Fasold investigated D2, C2h and Cs symmetries for

[14]-annulene by employing a semi-empirical self-consistent field molecular

orbital method, called SINDO1 [5]. Density functional theory (DFT) approaches

have also been applied to probe the D2, C2h and Cs symmetries of this annulene

ring. Selected results of such studies are listed in Table 4.1.

The potential energy surface of [14]-annulene exhibits multiple minimum

structures. According to the X-ray studies on the crystal structure, [14]-annulene

is centrosymmetric and non-planar, but with approximate C2h symmetry [25].

Arrangement of the inner hydrogen atoms (i.e. H17, H21, H24 and H27 in Fig. 4.4)

Fig. 4.4: Optimized 3D structure and labelling of the [14]-annulene ring (R1).


111

determines the symmetry. From these four atoms, two are above the plane of

carbon rings and two are below this plane. For example, if H17 and H27 in Fig. 4.4

are above the plane, the molecule has C2h symmetry. According to the DFT study

of Wannere et al., [14]-annulene may exhibit C2h or Cs structures [3]. That is, the

C2h symmetry is a local minimum at B3LYP level, whereas a transition state when

functionals such as BHLYP and KMLYP are employed [3]. The latter functionals,

having larger Hartree-Fock component, lead to a more stable Cs structure due to

an imaginary frequency if the C2h symmetry is assumed [3, 7]. Nevertheless, all

investigated DFT levels in Ref. [3] have shown that the C2h symmetry is slightly

more stable (i.e. 2.5 kcal.mol-1) than the D2 form. The [14]-annulene adopts a D2

symmetry if two opposite inner hydrogen atoms (e.g. H17 and H24) are above the

plane of the carbon ring, and the other two are below this plane [5]. It should be

noted that the highest possible symmetry for this annulene ring could be D2h, if

this annulene ring was planar [3]. However, the X-ray structure determines that

this molecule is “clearly and significantly non-planar” [25]. The non-planarity is

attributed to the steric interactions between the four internal hydrogen atoms (e.g.

H17, H21, H24 and H27 in Fig. 4.4) [3, 5, 7, 27]. Since our optimization is performed

on the AN-14 dye structure, not an isolated [14]-annulene ring, a detailed

symmetry analysis of our results is irrelevant. As a result, no point group

assignment is listed in Table 4.1 for this work.

Table 4.1 reports the optimized structure of AN-14 dye. As listed in the table, the

C-C bond lengths range from 1.384 to 1.412 Å, with an average of 1.397 Å. This

leads to a moderate C-C bond alternation (Δr) of 0.053 Å, which indicates the

aromaticity of the conjugated molecular system. From the table, it can be seen that

this bond alternation is very similar to that of the experiment. Other theoretical

studies reported bond alternations that are either substantially smaller [5, 26] or

greater [3] than the experimental measurements. For the angles reported in the

table, our results are on the average in better agreement with the experimental

data, compared to those of the SINDO1 simulations. Results based on the

SINDO1 simulations are larger than the MM calculations, the experimental

measurements and our DFT calculations.


112

Table 4.1: Compression of the optimized geometries of the [14]-annulene ring of the present work with data reported in iterature.

This Work Ref.a Ref.b Ref.c Model PBE0/6-

311G* B3LYP/6-311+G**

SINDO1 MM expt

Point group − C2h D2 C2h CS D2 C2h Ci(C2h) C1-C2(Å) 1.412 1.410 1.420 1.422 1.509 1.407 1.410 1.395 C2-C3(Å) 1.384 1.395 1.423 1.424 1.368 1.409 1.408 1.382 C3-C4(Å) 1.400 1.395 1.418 1.418 1.484 1.403 1.405 1.350 C4-C5(Å) 1.391 1.407 1.426 1.423 1.368 1.413 1.411 1.407 H21…H24(Å) 2.04 H21…H27(Å) 2.91 H24…H27(Å) 2.02 ∡C1-C2-C3(°) 120.3 − 122.7 127.5 127.0 120.4 124.2 123.3 ∡C2-C3-C4(°) 130.1 − 137.7 133.6 132.5 130.3 126.9 130.3 ∡C3-C4-C5(°) 125.4 − 127.1 126.4 125.5 125.2 123.7 125.5 ∡C4-C5-C6(°) 129.1 − 132.0 130.0 128.5 129.7 126.9 128.4 ∡C1-C2-C3-C4 (°) -167.6 − 174.3 158.6 161.1 158.2 158.5 162.5 ∡C2-C3-C4-C5 (°) 174.4 − 177.9 -156.5 -139.6 174.5 163.4 -162.7 ∡C3-C4-C5-C6 (°) -14.0 − 14.7 15.2 -2.5 15.1 18.7 13.1 ∡C4-C5-C6-C7 (°) -10.1 − − − 39.1 − − 15.4 ∡C14-C1-C2-C3 (°) 18.6 − -21.0 − − 23.5 − − Δrd (Å) 0.053 0.015 0.008 0.005 0.141 0.01 0.006 0.057e a. Ref.[3]. b. Ref.[5] c. Ref. [25] d. Δr is the difference between the shortest and the longest C-C bond length. e. For C2h point group, from Ref. [28].


113

Table 4.2 compares selected bond lengths, bond angles, and dihedrals of the [18]-

annulene ring with available theoretical and experimental data. For better

visualization, this ring is given separately in Fig. 4.5. In the figure, atoms of this

ring (R3) are labelled. Table 4.2 is closely related to Fig. 4.5.

The C-C bond lengths of R3 are in the range of 1.379 Å to 1.422 Å, with an

average of 1.397 Å. This corresponds to a C-C bond alternation (Δr) of 0.043 Å.

The difference between the shortest and the longest C-C bond is denoted by Δr

here. The X-ray study of the [18]-annulene by Bregman et al. identifies C-C bond

lengths that range from 1.371 Å to 1.429 Å. This corresponds to a Δr of 0.058 Å

[29]. As seen, this experimental bond alternation (i.e. 0.058 Å) is slightly larger

than the present work (i.e. 0.043 Å). However, other experimental works have

reported [3, 28, 30] Δr value of 0.042 Å which is almost equal to the one obtained

in the present theoretical calculations (i.e. 0.043 Å).

Fig. 4.5: Optimized 3D structure and labelling of the [18]-annulene ring (R3).


114

Values listed in Tables 4.1 and 4.2 suggest that the calculated geometry

parameters in the present work are in good agreement with experiment. This

ensures that our computational model is sufficiently acceptable for the

calculations of the new dyes designed in this chapter.

Table 4.2: Compression of the optimized geometries of the [18]-annulene ring of the

present work with data reported in literature.

This Work Ref.b Ref.c Ref.d

Model PBE0/6-311G*

SINDO1 MM expt

Point group − D3h C6h D3 Ci(D6h)

C1-C2(Å) 1.407 1.358 1.423 1.357 1.412

C2-C3(Å) 1.385 1.495 1.418 1.465 1.377

C3-C4(Å) 1.406 1.361 1.418 1.361 1.380

C4-C5(Å) 1.422 1.502 1.423 1.465 1.429

∡C1-C2-C3(°) 124.0 125.5 126.7 126.0 123.6

∡C2-C3-C4(°) 130.2 130.6 133.4 123.2 127.8

∡C3-C4-C5(°) 119.8 125.1 126.7 123.2 122.9

∡C4-C5-C6(°) 125.6 125.1 126.7 126.0 124.0

Δre (Å) 0.043 0.058

a. Ref.[3]. b. Ref.[5]. c. Ref.[26]. d. Ref.[29] e. Δr is the difference between the shortest and the longest C-C bond length.


115

4.5. Frontier molecular orbital analysis

An important aim of designing new dyes in this thesis is to obtain a reduced

HOMO-LUMO energy gap (in comparison to a reference dye).To investigate the

influence of the donor moiety variation on the energy levels of the frontier

molecular orbitals (e.g. HOMO and LUMO) of new dyes, the calculated energy

diagram is illustrated in Fig. 4.6. The orbital energies of the HOMO and the

LUMO of the original TA-St-CA dye in vacuum are calculated at -5.51 eV and -

2.69 eV, respectively, and the corresponding energy gap between the HOMO and

the LUMO is given by 2.82 eV. The new designs for the donor moiety of AN-14

and AN-18 lead to a reduction of of their HOMO-LUMO gap by apparently

lifting up the HOMO energies and shifting down the LUMO energies.

Fig. 4.6: The calculated frontier MO energy levels using PBE0/6-31G* model in vacuum.

TiO2 conduction band

Iodide/Triiodide redox level


116

Significant HOMO-LUMO gap energy reduction is in fact obtained for new dyes.

For example, the HOMO and LUMO energy levels of AN-14 are calculated at -

5.00 eV and -2.92 eV, corresponding to a HOMO-LUMO gap of 2.08 eV. In a

similar way, by the variation of the donor moiety of the reference dye, AN-18 can

achieve an increased HOMO energy (-5.11 eV) and decreased LUMO energy (-

2.95 eV), corresponding to a reduced gap of 2.16 eV.

From Fig. 4.6, it can also be seen that the LUMO energies of the new dyes are

very similar, whereas the HOMO energy of AN-14 is about 0.11 eV larger than

that of the AN-18. These findings suggest that in general, the mechanism of the

energy changes on the molecular orbitals of AN-14 and AN-18 are very similar.

However, the influences of the donor modifications are more profound on the

AN-14 dye. In other words, replacing all three [6]-annulene rings of the reference

dye with three [14]-annulene rings results in noticeable increase of the HOMO

energy level.

Fig 4.6 also gives positions of the conduction band of the TiO2 semiconductor

(dotted red line), as well as the redox potential of the iodide/triiodide redox

mediator (dotted green line). As seen in the figure, the HOMO energy levels of

both new dyes are well located below the redox energy level of the

iodide/triiodide redox couple. This implies that sufficient driving force is

available for the regeneration of AN-14 and AN-18. In fact, the HOMO level of

the new AN-14 sensitizer is very close to that of N3 sensitizer. The N3 (i.e.

Ru(4,4-dicarboxylate-2,2-bipyridine)2-(NCS)2)) dye sensitizer [31], is believed to

be one of the the best dyes from the ruthenium–polypyridyl sensitizer family [32].

Yang et al. calculated the HOMO level of the N3 dye sensitizer

(B3LYP/LANL2DZ level of theory) at -5.08 eV [32]. It is suggested that “the

sensitizer candidates with HOMO level close to that of the N3 dye would be

promising for the regeneration since the N3 dye can be regenerated very well”

[32]. As a result, the HOMO energy of the AN-14 dye is in favour of a very

promissing dye for functional DSSC. In general, the increased HOMO energies of

the new dyes suggest that AN-14 and AN-18 are more efficient than the reference


117

TA-St-CA dye in being regenarted fast and effectively by the iodide/triiodide

redox mediator.

Fig. 4.6 also compares the LUMO levels of the investigated dyes with the

conduction band edge of the semiconductor located at -4.0 eV for anatase TiO2

[33] (dotted red line). Although the new dyes exhibit a downshifted LUMO levels

compared to that of the reference dye, their LUMO energies are still well above

the CBE of TiO2. That is, the LUMO levels of both AN-14 and AN-18 are higher

than the conduction band edge of TiO2 by at least 1.0 eV. This means that upon

excitation, the photoexcited electrons posess enough driving force to be rapidly

injected to the conduction band of the semiconductor. As a result, these two new

dye senzitizers, i.e. AN-14 and AN-18, can operate functionally in working

DSSC.

4.6. UV-Vis absorption spectra

The main purpose of designing the new dyes, AN-14 and AN-18, in this chapter

was to broaden and to red-shift the absorption spectra of the reference TA-St-CA

dye by the variation of the donor moiety. To investigate the light absorption

properties of the new dyes, their electronic spectra are simulated in Fig. 4.7. This

figure also gives the simulated UV-Vis spectrum of the parent TA-St-CA dye for

comparison. In the figure, the absorption spectra of the reference TA-St-CA dye is

shown in black line, whereas the spectra of the AN-14 and AN-18 dyes are

illustrated in red and blue lines, respectively. The related electronic and optical

data predicted from time dependent density functional calculations of the

investigated dyes are given in Table 4.3. All spectra reported in Fig. 4.7 and Table

4.3 are simulated at PBE0/6-311G(d) level of theory in ethanol solution. In

Chapter 3, it was shown that this model closely reproduces the experimental

electronic absorption spectra of the reference TA-St-CA dye.


118

Significant enhancement in UV-Vis spectra is achieved in the new AN-14 and

AN-18 dyes over the reference dye. Fig. 4.7 shows that the modifications of the

reference dye resulted in bathochromic shift (i.e. to the longer wavelength or red-

shift) of the spectral peaks from positions of the reference dye. For example, the

two most intense peaks of the reference dye are calculated at λI=374 nm and

λII=545 nm. In new dye “AN-14”, these peaks are significantly red-shifted to

λI=418 nm and λII=763, respectively. For λI, a relatively small red-shift of ca. 44

nm is calculated, whereas a very significant red-shift of ca. 218 nm is seen on the

position of λII in AN-14, when compared to the reference dye.

The effects of structural modifications on the electronic absorption spectra of AN-

18 are similar to those of AN-14. For instance, in AN-18, the positions of both

Peaks I at λI and Peaks II at λII are shifted to longer wavelengths, compared to

those of the TA-St-CA dye. The simulations on AN-18 produce a sharp intense

peak at λI=439 nm and a broader peak at λII=722 nm. As a result, the rational

donor design of AN-18 leads to a bathochromic shift of ca. 65 nm and ca. 177 nm

on the positions of the spectral peaks λI and λII, compared to those of the

reference dye, respectively.


119

As listed in Table 4.3, new dyes exhibit more or less enhancement in the oscillator

strengths (f) of their absorption Peak I and Peak II. For example, the Peak II of the

reference dye exhibits an oscillator strength of 1.22, which is increased to 1.53

and 1.27 in AN-14 and AN-18, respectively. For this peak the oscillator strengths

follow a trend of fTA-St-CA <fAN-18<fAN-14. For the other main absorption peak, the

trend is quite different, that is, fAN-14< fTA-St-CA < fAN-18.

Fig. 4.7: The simulated UV–Vis absorption spectra of the TA-ST-CA, AN-14 and AN-18 in ethanol solution using the (PBE0/6-311G*) TD-DFT calculations.

λI

λII

λI

λII


120

The calculated expansion of the absorption spectra of AN-14 and AN-18 dyes

with respect to the reference dye can be attributed to the reduction of the HOMO-

LUMO energy gap of these dyes. As listed in Table 4.3, Peak II is a charge-

transfer (CT) band corresponding to a HOMO→LUMO transition. As seen in

the table, the contribution of such transition is 99%, 96% and 95% in Ta-St-

CA, AN-14 and AN-18, respectively. As explained in section 4.5 of this

chapter, the HOMO and the LUMO energy levels are brought closer to each

other in new dyes AN-14 and AN-18, compared to the reference dye;

Table 4.3: Calculated (a) excited energy (in nm), transition configuration, and oscillator strengths (f) for the two most intense peaks of TA-ST-CA dye and the new dyes in ethanol solution. I II

Structure λ (nm) f Transition Orbital

λ (nm) f Transition Orbital

TA-St-CA

374.53

0.77

H-1→L (91%) H→L+1 (7%)

545.03

1.22

H→L (99%)

AN-14

418.38

0.61

H-2→L+1 (35%) H-2→L+2 (23%) H-1→L+1 (19%) H-1→L+2 (14%)

763.30

1.53

H→L (96%)

AN-18

439.74

2.10

H-1→L+1 (48%) H-3→L (17%) H→L+2 (13%) H-1→L+2 (7%) H-2→L (5%) H-2→L+2 (5%)

722.76

1.27

H→L (95%) H-1→L+1 (3%)

(a) Calculated using TD-DFT based PBE0/6-311G(d) model in ethanol solution (CPCM).


121

therefore, this CT band (i.e. Peak II) is red-shifted in both new candidates

compared to TA-St-CA. Such justification can also be considered for Peak I.

In short, the results, as shown in Fig. 4.7 and Table 4.3, indicate that the

replacement of [6]-annulene rings in the reference dye by the electron-rich [14]-

annulene rings in AN-14 and [18]-annulene ring in AN-18, leads to significant

improved absorption spectra. New absorption spectra are red-shifted, more

intense, and broadened compared to that of the reference TA-St-CA dye. In

addition, the light absorption spectrum of the AN-14 dyes seems to be superior to

that of the AN-18.

The UV-Vis absorption spectra of the dyes in the present chapter are also

simulated by long-range corrected CAM-B3LYP functional. Results and

discussions of such simulations, as well as their comparison with the PBE0

simulations are provided in Appendix A-III. Regardless of the functional

employed in the TD-DFT calculations, results presented in this chapter clearly

show that both new AN-14 and AN-18 dyes exhibit an enhanced and expanded

absorption spectra, compared to the parent dye. As a result, the new AN-14 and

AN-18 dyes are potentially promising dye candidates for better DSSCs with

enhanced efficiencies. It is therefore recommended that the new dyes to be

synthesized. More information on the experimental absorption spectra of these

dyes and their performances in a working DSSC would help us to establish a

greater degree of accuracy on this matter. Such information can only be obtained

by experimentalists and only after these compounds are synthesized.

4.7. Molecular orbital spatial distribution

To further investigate the influence of modifications on the electronic properties

of the rationally-designed dyes, Fig. 4.8 plots the electron density distribution of

their frontier molecular orbitals.


122

HOMO LUMO

TA-St-CA

AN-14

AN-18

This figure (Fig. 4.8) compares the highest occupied molecular orbital (HOMO)

and the lowest unoccupied molecular orbital (LUMO) of the reference TA-St-CA

dye as well as the AN-14 and AN-18 sensitizers. These molecular orbitals

represent the dominant components of the main band (i.e. Peak II, see Table 4.3).

This band corresponds to a strong transition from the ground state (S0) to the first

Fig. 4.8: Comparison of the HOMOs (left) and LUMOs (right) of the new dye, AN-14 and AN-14 with respect to those of the reference TA-St-CA dye.


123

excited electronic state (S1) in the visible region of the spectrum (Refer to Table

4.3).

It is apparent from this figure that for the three dyes, the HOMOs are spread

mainly over the entire donor (D) moieties (i.e. left hand side of the dyes in the

figure). Moreover, the HOMOs are extended to the conjugated bridge (spacer) of

all three dyes. For example, the HOMOs of AN-14 and AN-18 are π orbitals

(dominated by p electrons from the backbone atoms) and populate over the entire

donor group (R1, R2 and R3, refer to D-section of the D–π–A dye in Fig. 4.2) and

partially populates the oligo-phenylenevinylene π-conjugated bridge and the R4

ring. Similar HOMO distribution is observed on the TA-St-CA dye. The most

noticeable difference between the HOMOs of the reference and the new dyes is a

reduced contribution from the R4 ring (the boxes in Fig. 4.8) of the π-conjugated

bridge on the HOMO of AN-14 and AN-18.

The LUMOs, on the other hand, are mainly localized on the cyanoacrylic acid

group which works as electron acceptor/anchoring moiety (A-section) for all three

dyes. Similar to the HOMOs, the LUMOs are also spread over the entire π-

conjugated bridges. For example, the LUMOs of AN-14 and AN-18 are singlet π*

orbitals which largely populates the cyanoacrylic acid acceptor group and also

spread into the π-conjugated bridge and into the R3 ring in the D-section. For AN-

14, negligible contributions of the R1 and R2 rings in the D section to the LUMO

are also observed. But R1 and R2 do not contribute to the LUMOs of the TA-St-

CA and AN-18 dyes.

Such distribution of the HOMOs and the LUMOs demonstrates that the HOMO-

LUMO excitation has an intra-molecular charge transfer (CT) character. As

mentioned in Chapter 3, such distribution pattern for the HOMOs and the LUMOs

is beneficial to a functional solar cell. This is because: (a) significant contribution

of cyanoacrylic acid group (A-section) to the LUMO ensures a strong electronic

coupling between the dye's excited state and conduction band of the

semiconductor (TiO2), which facilities the ultrafast electron injection, and (b)


124

significant localization of the HOMO on the donor end (left-side of the dyes in the

figure) minimizes the probability of charge recombination between the injected

electrons and the resulting oxidized dye.


This chapter has investigated new designs for the donor moiety of organic dyes

with D-π-A structure. Two new dyes, AN-14 and AN-18, have been designed by

variation of the donor moity of the backbone structure of the well-performing TA-

St-CA sensitizer. New dyes have been rationally designed with the aim of

reducing the HOMO-LUMO energy gap and producing panchromatic sensitizers.

The broadened and red-shifted absorption spectra compared to that of the

reference dye have been indeed achieved.

It is found that both new dyes exhibit reduced HOMO-LUMO energy gap

compared to that of the reference dye. The new dye AN-14 has a smaller HOMO-

LUMO energy gap than that of AN-18. More importantly, the HOMO-LUMO

energy gap of the new AN-14 dye is very similar to that of the N3 dye. It is well

known that this dye (i.e. N3) is one of the most efficient ruthenium-based

sensitizers for DSSC and is usually used as a benchmark for the evaluation of

other dyes [34]. Based the alignment of the energy levels of HOMOs and

LUMOs, both new dyes from this chapter are also suitable for the application in

DSSCs with conventional settings (i.e. nanocrystalline-TiO2 electrode and

iodide/triiodide redox-based electrolyte).

The UV-Vis absorption spectra of the new dyes have also been simulated by the

TD-DFT calculations. The results of this investigation showed that the absorption

spectra of both new dyes are in general red-shifted and broadened compared to the

reference dye, regardless of the functional employed to simulate them. As a matter

of fact, the absorption spectrum of the new dye AN-14 is much more superior to


125

that of the reference dye in terms of the strengths of the peaks and the coverage of

the visible absorption region.

In summary, these results suggest that the new dye AN-14 is a promising

sensitizer for the application in DSSC. However, determining whether or not these

rationally designed dyes become new dyes in industrial DSSCs also depends on

others properties, such as stability and costs of synthesis. The present chapter has

gone some way towards enhancing our knowledge towards rational dye design.

The findings of this chapter have opened many new questions in need of further

investigation. For example, the stability of the AN-14 dye structure needs to be

addressed by experimental chemists. Of the same importance is how this dye

performs in an assembled cell. The interaction of this dye sensitizer with the other

components of the cell as well as the dynamic processes, which take place for

electron generation and transfer, in the cell should be assessed in a working cell.

In conclusion, further investigation and experimentation into the application of

these novel dyes (and especially AN-14 dye) in DSSC is strongly recommended.


126

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12. Roy Dennington, Todd Keith and J. Millam, GaussView, Version 5. 2009, Semichem Inc. Shawnee Mission KS.

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14. T. Yanai, D.P. Tew and N.C. Handy, A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chemical Physics Letters, 2004. 393(1–3): p. 51-57.

15. A.D. Laurent and D. Jacquemin, TD-DFT benchmarks: A review. International Journal of Quantum Chemistry, 2013. 113(17): p. 2019-2039.

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17. M. Pastore, E. Mosconi, F. De Angelis and M. Grätzel, A Computational Investigation of Organic Dyes for Dye-Sensitized Solar Cells: Benchmark, Strategies, and Open Issues. The Journal of Physical Chemistry C, 2010. 114(15): p. 7205-7212.

18. P. Dev, S. Agrawal and N.J. English, Functional Assessment for Predicting Charge-Transfer Excitations of Dyes in Complexed State: A Study of Triphenylamine–Donor Dyes on Titania for Dye-Sensitized Solar Cells. The Journal of Physical Chemistry A, 2012. 117(10): p. 2114-2124.

19. M.I. Abdullah, M.R.S.A. Janjua, A. Mahmood, S. Ali and M. Ali, Quantum Chemical Designing of Efficient Sensitizers for Dye Sensitized Solar Cells. Bulletin of the Korean Chemical Society (Print), 2013. 34(7): p. 2093-2098.

20. R. Tarsang, V. Promarak, T. Sudyoadsuk, S. Namuangruk and S. Jungsuttiwong, Tuning the electron donating ability in the triphenylamine-based D-π-A architecture for highly efficient dye-sensitized solar cells. Journal of Photochemistry and Photobiology A: Chemistry, 2014. 273(0): p. 8-16.

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130

Chapter 5

Carbz-PAHTDDT dye and its derivatives “Research is to see what everybody else has seen,

and to think what nobody else has thought.” Albert Szent-Gyorgyi

5.1. Introduction Rational design of the new dyes in Chapter 3 and Chapter 4 were based on the

TA-St-CA reference dye. This chapter investigates a rational design based on a

new reference dye, known as Carbz-PAHTDTT (S9) dye. Daeneke et al. [1]

reported a highly efficient DSSC in early 2011. In their study, a novel organic dye

sensitizer called Carbz-PAHTDTT (S9) dye was utilized. In addition, the

conventional iodide/triiodide redox mediator was replaced with

ferrocene/ferrocenium (Fc/Fc+) redox couple. This was a noticeable study as the

previous attempts to replace the conventional iodide/triiodide with ferrocene-

based redox couples led to very low efficiencies (η<0.4%) [2, 3], where changes

have only been made on a single component (i.e. redox couple); whereas the dye

sensitizer, i.e. conventional N3 dye remained unchanged.

The recent breakthrough of the DSSC based on Fc/Fc+ redox couple and the

Carbz-PAHTDTT (S9) dye sensitizer, stimulated the present chapter [4] with

more theoretical insight to probe the structure of the S9 dye sensitizer as well as

Carbz-PAHTDDT dye and its derivatives Chapter 5

131

ferrocene compound. To the best of our knowledge, no detailed computational

study on the S9 dye is available. Computational study gives insight into the

geometric and electronic structure of the dye sensitizer and serves as the starting

point for rational design of new dyes with desirable properties such as improved

spectral coverage. As a result, the current chapter will focus primarily on the

study of the Carbz-PAHTDTT dye (See Fig. 5.1). This chapter will also

investigate rational design through chemical modifications on the structure of this

dye sensitizer aiming at red-shifting and broadening the absorption spectra of the

S9 dye that might enhance the efficiency of DSSC by utilising a greater fraction

of the solar spectrum. Chapter 6 will be dedicated to the study of ferrocene

compound.

The present chapter further studies the nonlinear optical properties (NLO) of the

dye sensitizers, in addition to other properties such as the HOMO-LUMO energy

gap and the UV-Vis absorption spectra. It is known that nonlinear optical (NLO)

properties of a push-pull organic dye such as its polarizability (α) and first

hyperpolarizability (β) are associated with its intra-molecular charge transfer

(ICT) character [5-7]. The intra-molecular charge transfer character is a very

important feature of organic D-π-A dye sensitizers. The ICT character of the

push-pull dye sensitizer can affect the short-circuit charge transfer, 𝐽sc , and

therefore the efficiency, 𝜂, of the cell [8]. Edvinsson et al. [9] studied some

perylene-based sensitizers for the relationship between ICT character of the

molecules and their performance in DSSC. It was found that the photocurrent and

the overall solar-to-electrical energy conversion efficiency improve remarkably

with increasing ICT character of the dyes. A later study of Tian and co-workers

on triphenylamine dyes [10] suggests that an effective ICT has a positive effect on

the performance of DSSC. As a result we will study the NLO properties of the

Carbz-PAHTDTT dye and the rationally designed dyes in this chapter.


132

5.2. Methods and computational details

The structure of the Carbz-PAHTDDT (S9) dye in three dimensional (3D) space

is obtained through geometry optimizations in vacuum and in dichloromethane

(DCM, CH2Cl2) solution, respectively. The DCM solution was used in

experimental study of the reference dye [1]. Density functional theory (DFT)

based PBE0 hybrid density functionals [11] and polarized split-valence triple-zeta

6-311G(d) basis set, that is, the PBE0/6-311G(d) model, is employed in the

calculations without any symmetry restrictions. No imaginary frequencies are

found for the optimized structure, which ensures that optimized structure of S9

dye is a true minimum structure. All ab initio calculations are performed in

Gaussian09 package [12].

To analyse the charge population of the dye sensitizer, natural bond orbital (NBO)

analysis is performed on the optimized structure in vacuum using the NBO 3.1

program [13] embedded into Gaussian09 package.

The solvent effects (i.e. DCM) on the absorption spectra and molecular energy

levels are calculated using the polarizable conductor calculation method (CPCM)

[14, 15]. The CPCM model can effectively and accurately compute the influence

of solute-solvent interactions on molecular energies, structures, and properties and

is a particularly good model for large systems such as S9 dye. The model “has

spread in the scientific community due to its accuracy and the relative simplicity

of the expressions involved in the definition of the solvent reaction field” [15]. As

a result, this model is employed to account for the solvent effects (i.e. DCM) on

the absorption spectra and molecular energy levels in the present chapter.

Several hybrid DFT functionals, namely, B3LYP [16], PBE0 [11], and BHandH

(as implemented in Gaussian 09, i.e. BHandH: 0.5*EXHF + 0.5*EX

LSDA + ECLYP)

[17] with the same basis set (6-311G(d)) were employed for the calculations in


133

DCM solution, in order to identify the most appropriate DFT functionals to

calculate the S9 energy gap.

The calculations of the nonlinear optical (NLO) properties such as polarizability

and hyperpolarizability are done by exploiting the same PBE0/6-311G(d) model

using static frequencies in vacuum. It is necessary to briefly explain the NLO

properties such as hyperpolarizability, before explaining the computational

methods employed to calculate them. When a molecule is exposed to an external

electric field such as that of the electromagnetic radiation (e.g. visible light), a

force is exerted on its electric charges (i.e. electron cloud of the molecule). As a

result, in the presence of an static electric field, the energy of a molecule “can be

expanded as:

E = E0 − μi Fi – 1/2 αij FiFj – 1/6 βijk Fi Fj Fk – 1/24 γijkl Fi Fj Fk Fl −… , (5.1)

where E0 is the unperturbed energy, Fi is the component of the field in the i

direction, μi is the permanent dipole moment, αij is the polarizability tensor, and

βijk and γijkl are the first and second hyperpolarizability tensors, respectively. β is a

third order symmetric tensor that measures the second order response of the

molecular electric dipole moment to the action of an external electric field and is

thus often referred to as dipole hyperpolarizability” [18].

By employing the “POLAR” keyword in Gaussian 09, the tensor components of

polarizability and hyperpolarizability are obtained in the lower triangular and

lower tetrahedral order, i.e. αxx, αxy, αyy, αxz, αyz, αzz and βxxx, βxxy, βxyy, βyyy, βxxz,

βxyz, βyyz, βxzz, βyzz, and βzzz, respectively. From these results, the mean molecular

isotropic polarizability, α, which is defined as the mean value of three diagonal

elements of the polarizability tensor is calculated as

𝛼 = 13

�𝛼xx + 𝛼yy + 𝛼zz �, (5.2)

and the anisotropy of polarizability is calculated as [8]


134

∆𝛼 = �(𝛼xx−𝛼yy)2+( 𝛼xx−𝛼zz)2+(𝛼yy−𝛼zz )2

2 (5.3)

The following equation also gives the total hyperpolarizability (βtot) [19]

𝛽𝑡𝑜𝑡 = �(𝛽xxx + 𝛽xyy + 𝛽xzz)2 + (𝛽yyy + 𝛽yzz + 𝛽yxx)2 + (𝛽zzz + 𝛽zxx + 𝛽zyy)2 (5.4)

The UV-Vis spectra in ethanol solution are simulated using singlet-singlet

transitions up to the 30th lowest spin-allowed excited states of each dye based

on time dependant density functional (TD-DFT) calculations by employing

several density functionals as explained below. These lowest-energy electronic

transitions are then transformed into simulated UV-Vis spectra by GaussView 5

visualization software [20], using Gaussian functions with half-widths of 3000

cm–1.

To accurately reproduce the experimental λmax, several standard hybrid (B3LYP

[16] , PBE0 [11] and BHandH [17]) and long-range corrected (LC) functionals

(CAM-B3LYP [21], ωB97XD [22] and LC-ωPBE [23-25]) are employed for TD-

DFT calculations. The standard hybrid functionals, which include a mixture of

Hartree-Fock (HF) exchange with DFT exchange-correlation, exploited in this

study featured a gradual increasing fraction of HF (exact) exchange as: B3LYP

(20% HF), PBE0 (25% HF) and BHandH (implemented in Gaussian 09 with 50%

HF) [26]. The CAM-B3LYP functional consists of 65% of HF and 35% of B88 at

long-range and 19% of HF and 81% of B88 exchange at short-range and uses ω=

0.33. In ωB97XD functional, the short-range HF (exact) exchange is 22.20% and

ω= 0.2. Finally, LC-ωPBE functional uses ω= 0.4 and no short-range exchange.

The ω (in bohr-1) is a damping parameter which controls the range of the inter-

electronic separation between the short-range and the long-range terms of the

Coulomb energy.


135

Two new dyes are also designed and investigated in the current chapter. These

dyes are rationally designed by structural changes in the π-conjugated bridge of

the reference Carbz-PAHTDDT (S9) dye. These derivatives are designed with the

aim of extending the absorption spectra to the near infrared (NIR) region by

reducing the HOMO-LUMO energy gap of the dye sensitizer. Both new dyes are

computationally studied using the same method in the S9 dye study.

5.3. Molecular structures and design of the new dyes

The optimized three dimensional (3D) structure of the Carbz-PAHTDTT dye (S9)

is given in Fig. 5.1. This dye exhibits an electron-rich donor group (D), a π-

conjugated bridge or linker and an acceptor moiety (A) as marked in the figure by

three boxes. As a result, S9 has a D-π-A configuration, which is a common

structure for organic dye sensitizers [27-33].

Fig. 5.1: Optimized 3D structures of the reference Carbz-PAHTDTT (S9) dye sensitizer (red: oxygen; blue: nitrogen; grey: carbon; yellow: sulphur). Note that hydrogen atoms and hexanyl chains are not explicitly displayed.

Lπ


136

A two-carbazole-unit substituted triphenylamine group is employed as the

electron donor unit (D) of the dye. It has been previously shown that this donor

structure suppresses the close π-stacked aggregation between the donor moieties

of dye sensitizers adsorbed onto the surface of TiO2 semiconductor [34].

Aggregation can result in intermolecular quenching and also leads to dye

molecules which are not functionally attached to the semiconductor’s surface and

work like filters [35]. This phenomenon is known to be a detrimental factor of the

efficiency for DSSC which should be avoided either by structural design or by

employing co-adsorbents [36]. The non-coplanar structure of the electron

donating moiety (D) can enhance thermal stability of dye sensitizer molecules by

decreasing the contact between them. Thermal stability of dye sensitizer is an

important factor for long term stability of functional solar cells [34].

The π-bridge (linker, the middle box in Fig. 5.1) consists of five pentagon rings

which are labelled as I, II, III, IV and V in the figure. A dithienothiophene (DTT)

unit forms central part of the π-conjugated bridge of the S9 dye. This moiety leads

to a better stability of the dye sensitizer in high polarity electrolytes used in

DSSC.

To provide additional double conjugation into the linker moiety [37], two hexanyl

(C6H13) chain-substituted thiophene rings (i.e. 3-hexylthiophene or rings I and V

in Fig. 5.1) exist in the π-conjugated bridge of the S9 dye which can form either

trans or cis isomers. A cis-S9 is formed when both of the hexanyl chains (C6H13)

are in the same side of the π-bridge, or a trans-S9 isomer is formed if the hexanyl

chain (C6H13) groups locate on different sides of the π-bridge. The long hexanyl

chains suppress the aggregation of the dye molecules, and also enable longer

electron life time (τ) [38].

The present calculations indicate that the cis-S9 isomer possesses a total energy of

approximately 4.6 kJ⋅mol-1 less than the total energy of the trans conformer,

indicating that the S9 dye slightly favours the cis conformation. Therefore, only

cis conformation will be studied in this chapter (results and discussion of the trans


137

conformation are given in the Appendix A-IV). On the acceptor side of this dye

(A), the conventional acceptor moiety is employed. It contains the cyano group as

an electron withdrawing group and the carboxyl group as an anchoring unit to

attach the dye onto the TiO2 semiconductor.

As was mentioned in Chapter 3, all three moieties of a dye, i.e., the donor, the π-

bridge and the acceptor can be modified to produce new dyes. As mentioned

earlier, in the π-bridge of the S9 dye, a dithienothiophene unit (DTT) is employed.

Kwon et al. who synthesized the S9 dye, have also reported another DTT-based

dye sensitizer (DAHTDTT 13) with a similar structure to the S9 dye, which only

differs in its D group [37]. The absorption spectra of these two dye sensitizers are

very similar for the visible portion of the spectrum, i.e., λ>400 nm (please refer to

Appendix A-V to see the similarity of their absorption spectra). As a result, in the

present chapter, instead of making changes in the D-group and A-group (which is

a standard and commonly used group), the linker (i.e., the π-bridge) of the S9 dye

is modified to produce new dyes. Fig 5.2 shows the 3D structure of the reference

S9 dye and the new dyes S9-D1 and S9-D2.

An aim of the design of the new dyes is to shift the absorption spectra to near

infrared (NIR) region by reducing the HOMO-LUMO energy gap of the new dye

sensitizers. As a result, two new derivatives dyes (S9-D1 and S9-D2) are designed

from the original (cis-) Carbz-PAHTDTT (S9) dye through the modification of

the π-bridge linker. The optimized 3D structures of S9-D1 and S9-D2 are given in

Fig. 5.2(b) and 5.2(c), respectively. In S9-D1, the X1 and X2 groups in S9 dye are

replaced by the −N groups, but in S9-D2 dye, the X1 and X2 groups are substituted

by the −NH groups, respectively.


138

Fig. 5.2: Optimized 3D structures of S9 (a), S9-D1 (b) and S9-D2(c), (red: oxygen; blue: nitrogen; grey: carbon; yellow: sulphur).Note that hydrogen atoms and hexanyl chains are not explicitly displayed. The orange dotted ovals mark where modifications take place.


139

The rationale behind the modifications is the concept of atom’s electronegativity

(χ). Electronegativity is a quantitative measure of how tightly an atom holds onto

its electrons. The concept of electronegativity was first introduced by Pauling in

1932 [39] as the power (tendency) of an atom to attract electrons toward itself

[18]. In Pauling scale, nitrogen (χ= 3.04) has greater electronegativity than

sulphur (χ= 2.58). It is known that electronegativity is not strictly an atomic

property. It is affected by the molecular environment of an atom. In other words,

electronegativity is a property of an atom in a molecule [40]. Although

electronegativity is a quantitative property, it influences other properties of a

molecule such as its HOMO-LUMO gap [41]. As a result, this chapter

investigates how such concept (i.e. the ability of atom to pull electron density

towards itself) can affect the electronic structure of different compounds.

The new dyes will exhibit differences in their atomic charges as they consist of

atoms with different electronegativity. To study how atomic charges are changed

upon rational modifications, atomic charges according to the natural bond orbital

(NBO) is employed. Fig. 5.3(b)-(d) gives the NBO charge of the π-conjugated

bridges of the three dyes S9, S9-D1 and S9-D2, respectively. As predicted using

electronegativity, the nitrogen atoms (which are more electronegative than the

sulphur) are predicted by NBO to have negative charges, while the sulphur atoms

exhibit positive charges. For example, in S9, the sulphur atoms at X1 and X2 show

a positive NBO charge of 0.411 a.u. and 0.433 a.u., respectively. In S9-D1, the X1

and X2 atoms are replaced by nitrogen atoms, which exhibit negative charges of

-0.449 a.u. and -0.442 a.u., respectively. The nitrogen atoms of S9-D2 exhibit

even more negative charges, as each of them bond with one hydrogen (−NH).

Nitrogen is much more electronegative than hydrogen (χ= 3.04 for nitrogen

compared to χ= 2.20 for hydrogen). As a result, the nitrogen atoms of S9-D2

attract the electrons of the bonded hydrogen so that the nitrogen atoms become

more negative in S9-D2 compared to S9-D1. It is also obvious that the atomic

charges change more apparently at the positions local to the X1 and X2 atoms in

the new dyes, with respect to the reference dye; whereas only small changes in

atoms away from X1 and X2 are observed.


140

Fig. 5.3: Sketch of the reference S9 dye (a), and the structure of the bridge of S9 (b), S9-D1 (c) and S9-D2 (d) dyes showing NBO charge of atoms in the linker. Note that hexanyl chains are not included.

Lπ


141

The total NBO charges of the π-bridge (linker) in the D-π-A dyes can be either

negative or positive. However, the overall net charge for the donor section (D) of

the dyes is always positive, whereas the acceptor section (A) of the dyes is always

negative [42, 43]. Although new dyes show similar trend in their individual NBO

atomic charges, the total NBO charges (over the linker of the dyes) are not the

same. The total NBO charges over the π-linker of the dyes are calculated at

+0.062 a.u., -0.029 a.u. and +0.118 a.u., for S9, S9-D1 and S9-D2, respectively.

The fact that the original S9 dye and the new dye S9-D2 possess positive charges

of the linker suggests that the π-conjugated bridges of these dyes exhibit electron-

donating character. On the contrary, the negatively charged linker of the S9-D1

dye suggests that the chemical modifications with the –NH group alter the

electron-donating character of the linker in the original dye (S9), to an electron-

withdrawing character in the S9-D1 dye. In following sections, it will be seen that

such a change would affect other properties of the new dyes such as the HOMO-

LUMO energy levels and the UV-Vis absorption spectra of the dyes. It will

shortly be seen that when the total NBO charge decreases from +0.062 a.u in S9

to -0.029 in S9-D1, the LUMO energy level will also be reduced in S9-D1.

Whereas, when the total NBO charges increases from +0.062 a.u in S9 to +0.118

a.u in S9-D2, the HOMO energy level of the S9-D2 dye also increases. Such

results suggest that there might be a correlation between the total NBO charge of

the linker and energy level of the HOMO and the LUMO of dyes.

Table 5.1 lists the important molecular properties of the Carbz-PAHTDTT (S9)

dye (cis isomer) and the new S9-D1 and S9-D2 dyes calculated in vacuum. As all

the dyes are either new dyes (S9-D1 and S9-D2) or recently synthesised dye (S9),

only very limited information is available for comparison. However, the PBE0/6-

311G(d) model has been shown to be reliable in previous studies [11, 44, 45]. The

π-conjugated bridge length (Lπ) of the D-π-A dye is defined as the direct distance

between C(43) and C(61) as shown in Fig. 5.3 (a). It is calculated at 17.14 Å for S9

dye which is shortened in S9-D1 (16.33 Å) and S9-D2 (16.52 Å) as the N atoms

(S9-D1 and S9-D2) have smaller radius than the S atoms (S9). This is also


142

reflected by the calculated molecular sizes (i.e., the electronic spatial extent <R2>)

of the dyes. The dipole moments (μ) of the S9-D2 dye (µ=5.12 Debye) exhibit

very similar values to the original S9 dye (µ=5.10 Debye), whereas the dipole

moment of S9-D1 (6.72 Debye) exhibits larger changes.

5.4. Frontier molecular orbitals

The experimental energy values for the HOMO, LUMO and HOMO-LUMO gap

of the Carbz-PAHTDTT (cis-S9) dye in CH2Cl2 (DCM) solution are estimated at -

5.08 eV, -2.97 eV and 2.11 eV, respectively [1] (Please refer to Appendix A-VI

for more details). The present study employs a number of different DFT

functionals with various levels of exchange energy in order to understand how

exchange energy affects the frontier orbitals. In order to find the most appropriate

functional, the present study exploits three hybrid functionals (B3LYP, PBE0, and

BHandH) calculate the frontier molecular orbital energies of the S9 dye in DCM

solution. These three functionals have an increasing trend in the percentage of HF

(exact) exchange as B3LYP (20%) < PBE0 (25%) < BHandH (50%).

Table 5.1: The selected bond length, dihedrals, π-lengths(a) and dipole moment of the S9, S9-D1 and S9-D2 dyes*[4].

S9 S9-D1 S9-D2

Lπ (a) (Å) 17.14 16.33 16.52

C48-C49 (Å) 1.44 1.37 1.44

X1-C48-C49-X2 (°) -144.91 -179.09 -157.07

X2-C52-C53-S4 (°) 0.93 -0.79 -0.10

S4-C56-C57-S5 (°) 150.10 157.57 148.19

<R2> ( a.u) 275867.82 256546.52 260606.50

μ (Debye) 5.10 6.72 5.12

*Optimized at PBE0/6-311G(d) level. (a) Direct distance of C(43)-C(61).


143

Table 5.2 lists results of the calculated values DFT functionals in DCM solution.

As seen in the first row of this table (Carbz- PAHTDTT results), the B3LYP

functional provides the best agreement with the experiment by less than 0.02 eV

deviations from the experimental values, indicating that the exchange energy in

this case is less important than correlation energy. Results listed in this table

suggest that the same trend exists for the HOMO-LUMO energy gap (Δ) of the

dyes, regardless of the functionals employed to calculate them. That is, ΔS9-D1<

ΔS9-D2< ΔS9. Another result emerged from this table is that for all three dyes, the

Δ values calculated by the BHandH functional are the highest, followed by those

of the PBE0 functional and finally by the B3LYP functional. Since the B3LYP/6-

311G(d) model provides the best agreement with the experimental value, this

model is employed to construct the molecular energy levels graph and isodensity

plots.

Table 5.2: Energy levels of HOMO, LUMO and HOMO-LUMO gap calculated by different functionals in DCM solution.

Structure Model(a) HOMO (eV) LUMO( eV) Δε (eV)

Carbz- PAHTDTT (S9)

Exp. -5.08 -2.97 2.11

B3LYP -5.08 -2.99 2.08

PBE0 -5.31 -2.94 2.37

BHandH -5.90 -2.17 3.72

S9-D1

B3LYP -5.32 -3.66 1.66

PBE0 -5.54 -3.65 1.89

BHandH -6.12 -2.98 3.14

S9-SD2

B3LYP -4.79 -2.91 1.88

PBE0 -5.01 -2.86 2.15

BHandH -5.53 -2.10 3.43

(a) All calculations are performed on the geometries optimized using PBE0 functional in DCM solution. The CPCM model and 6-311G* basis set is employed in all calculations.


144

Fig. 5.4 compares the calculated frontier molecular orbital energy levels of the S9

dye and the new dyes S9-D1 and S9-D2 in DCM solution, focusing on the

HOMO–LUMO energy gap. As seen in this figure, the HOMO-LUMO gap of the

dyes reduces from 2.08 eV in S9 to 1.66 eV in S9-D1 and to 1.88 eV in S9-D2.

Although the energy gaps of both new dyes are reduced with respect to the

reference dye, the mechanism of HOMO-LUMO gap reductions in S9-D1 and S9-

D2 are different. For example, in S9-D1, the most significant change is the

reduction of the LUMO energy, from -2.99 eV in S9 to -3.66 eV in S9-D1. The

energy of the HOMO of S9-D1 also exhibits a small reduction, from -5.08 eV

(S9) to -5.32 eV (S9-D1). On the other hand, the HOMO-LUMO gap reduction in

S9-D2 dye is achieved by shifting up the energy level of the HOMO, from -5.08

eV to -4.79 eV, whereas the energy of the LUMO almost remains the same as -

2.99 eV in S9 and -2.91 eV in S9-D2. From Fig. 5.4, it is noticeable that

modifying the π-conjugated bridge of the reference S9 dye doesn’t produce

sizable impact on the LUMO energy level of S9-D2, while the impact on that of

S9-D1 is very prodigious.

Fig. 5.4: Calculated frontier MO energy levels using B3LYP/6-311G(d) // PBE0/6-311G(d) model in DCM solution.


145

The position of the conduction band minimum (CBM) of TiO2 (i.e. -4.2 eV, taken

from ref. [46]) is also illustrated in this figure. The CBM of TiO2 lies below the

LUMO of the S9 dye and the new dyes S9-D1 and S9-D2. This indicates that

sufficient driving force is provided for ultrafast excited state electron injection as

a main criterion of an effective dye sensitizer. It should also be noted that even

though the LUMO of S9-D1 is closer to the CBM of TiO2 compared to the other

two dyes, it is still above the CBM. This provides enough driving force for the

excited electrons of the S9-D1 to be injected effectively into the conduction band

of TiO2. Moreover, it is well known that adsorption of dye molecules onto the

surface of semiconductor material will change the band energies and is likely to

downshift TiO2 conduction band [47], which can lead to providing even more

driving force for electron injection. The influence of sensitizer adsorption on TiO2

band energies was beyond the scope of the current thesis and warrant further

studies in this direction.

It is worth noting that S9-D1 appears to be a good candidate for the sensitization

of SnO2 semiconductor, too. This is because the conduction band edge of SnO2 is

about 0.5 eV lower than that of TiO2 [31]. This suggests that SnO2 can be a

suitable semiconductor material coupled with S9-D1 dye sensitizer, which is

another advantage of this new dye.

To examine the molecular charge distribution of the dyes, the frontier molecular

orbitals of the reference S9 dye and new dyes “S9-D1” and “S9-D2” are compared

in Fig. 5.5. It is seen that the HOMO and LUMO of S9 exhibit little overlap. That

is, the HOMO dominates the D-region, whereas the LUMO locates in the A-

region. For example, the HOMO of the S9 dye is distributed over the entire

triphenylamine group and mainly nitrogen atoms of the carbazole-units in the D

moiety, and is extended into the π-conjugated bridge over the first hexanyl chain -

substituted thiophene ring and next three fused thiophene rings. For this dye

structure (S9), the LUMO populates the entire cyanoacrylic group in the acceptor

moiety of the dye sensitizer as well as the second hexanyl chain-substituted

thiophene ring in the linker moiety and partially populates the rest of the π-


146

conjugated bridge. This type of orbital distribution confirms the perfect D-π-A

character of the Carbz-PAHTDTT dye and leads to an ICT from the HOMO (i.e.

donor end) to the LUMO (i.e. acceptor end) via the linker upon excitation. This is

the favourite behaviour for a dye sensitizer employed in DSSC, where electron-

hole separation needs to take place on the surface of the semiconductor (e.g.

TiO2).

Fig. 5.5: Comparison of the charge density of HOMOs (left) and LUMOs (right) of the reference S9 dye, and the new S9-D1 and S9-D2 dyes.


147

The new dyes, S9-D1 and S9-D2, show some differences from their parent S9

dye. The new dye S9-D1 has similar HOMO distribution to the reference structure

but with more contribution from the carbazole-units in the donor moiety and the

second hexanyl chain-substituted thiophene ring (i.e. ring V) in the linker moiety.

However, the LUMO of S9-D1 populates the linker significantly, and is extended

into a phenyl group in the donor moiety of the dye structure. A small density

decrement is observed on the carboxyl group (A section) which might lead to a

weaker electron coupling with semiconductor surface compared to the reference

S9 structure. Also, S9-D2 dye shows very similar HOMO and LUMO distribution

to the reference S9 dye with the HOMO being slightly shifted from the donor

section toward the π-conjugated bridge. The HOMO-LUMO energy gap

reductions of the new dyes in Fig. 5.4 are also seen in the corresponding orbitals

of the dyes in Fig. 5.5. When the orbitals are more localised, the energies increase,

whereas when the orbitals are more delocalised, the energies decrease.

Fig. 5.4 further shows that the electronic structures of these dyes are in favour of

the high overall efficiency of the solar cells, as explained in previous chapters.

That is, the HOMOs are distributed far away from the acceptor moiety, to prevent

charge recombination (i.e. recombination of the injected electron with oxidized

dye). The LUMOs on the other hand are well located over the acceptor end of the

dye to enhance the electronic coupling between the dye and semiconductor (e.g.

TiO2) and expedite electron injection.

5.5. Nonlinear optical properties

Table 5.3 collects the NLO properties, such as the isotropic polarizability (α),

polarizability anisotropy (Δα) and the first-order hyperpolarizability (βtot) of the

reference S9 dye, as well as the new designed dyes, S9-D1 and S9-S2 dyes. The

full tensor components for α and β are given in Appendix A-VII. As listed in

Table 5.3, the total hyperpolarizabilities, βtot, are calculated as 805 esu for S9,


148

2190 esu for S9-D1 and 856 esu for S9-D2. The βtot values of both new dyes, S9-

D1 and S9-D2, are significantly higher than the reference dye. However, a

dramatic increase of almost 2.7 times is calculated for the magnitude of the βtot of

the new S9-D1 dye.

The molecular hyperpolarizabilities of the dyes are dominated by the βxxx tensor

component, which is listed in Table 5.3 (please refer to Appendix A-VII for the

list of all components). The S9-D1 exhibits the highest magnitude of the βxxx (i.e.

|βxxx|=252,260 au), when compared to S9-D2 (|βxxx|=94,044 au) and S9

(|βxxx|=89,930 au). For all three dyes, the calculated x component of the total

hyperpolarizability, βx= (βxxx + βxyy + βxzz)2, is dramatically higher in magnitude

than the y component of the total hyperpolarizability, βy= (βyyy + βyzz + βyxx)2,

which is significantly higher in magnitude than the z component of the total

hyperpolarizability, βz= ( βzzz + βzxx + βzyy)2, i.e., , βx > βy > βz.

The results listed in Table 5.3 also show that S9-D1 has higher polarizability

properties compared to those of the reference S9 as well as S9-D2 dyes. Both the

isotropic polarizability (α) and the polarizability anisotropy (Δα) of the molecules

under study follow a trend as S9-D1>S9>S9-D2. The higher polarizability values

of S9-D1 suggest that electrons can transfer easier from the donor to the acceptor

ends of this dye sensitizer. This is because polarizability indicates the response of

electrons to an external electric field [8].

The enhanced NLO properties of the S9-D1 are attributed to the planarity of the π-

conjugated bridge of this dye compared to both S9 and S9-D2 dyes. The non-

planarity in S9 and S9-D2 is resulted from the sigma (σ) bond between the

pentagon rings I and II, which reduces the overlap of the interacting orbitals and

consequently will reduce the ICT from donor to acceptor ends of these dyes. On

the other hand, because of the chemical modifications made in S9-D2 dye, the

aforementioned sigma bond becomes a double bond in S9-D2, which prevents the

free rotation around this bond (please refer to Fig. 5.2 (b) and 5.3 (c)). As a result,

the overlap of the interacting orbitals is enhanced in S9-D2 and its ICT character


149

is increased which will be manifested through the dramatic increase of the

hyperpolarizability of this sensitizer.

Table 5.3: The first total hyperpolarizability (βtot), isotropic polarizability (α) and polarizability anisotropy (Δα) of S9, S9-D1 and S9-D2 dyes.(a)

S9 S9-D1 S9-D2

βtot*10-30 (esu)(b) 805 2190 856

βxxx (au) -89930.67 252260.26 94044.55

α (au) 1350.78 1577.39 1334.81

Δα (au) 1145.31 1857.12 878.41

(a) All calculations are performed using PBE0/6-311G(d) model on the geometries optimized by the same model in vacuum. (b) The atomic units (au) can be converted into electrostatic units (esu) using the following conversion factors: α (1 au = 1.48176 × 10−25 esu) and β (1 au = 8.63993 × 10−33 esu) [48].

Our results together with other studies show that HOMO-LUMO gap is a critical

factor in determining the βtot value [6, 19]. That is, the highest βtot is observed for

the molecule with the smallest energy gap (i.e. S9-D2). The higher βtot values of

S9-D1 suggests that this molecule possesses better push-pull properties which can

enhance the electron charge transfer capability of this dye sensitizer and

consequently the efficiency (η) of the solar cell. In brief, the S9-D1 dye exhibits

significantly larger NLO properties such as βtot, α and Δα values as well as

reduced HOMO-LUMO gap which are desirable properties for good performing

dye sensitizers for the application in DSSC.


150

5.6. Excitation energies and UV-Vis spectra

The experimental absorption spectrum of the S9 dye was measured in the

dichloromethane (DCM) solution [1]. The three main absorption bands in the UV-

Vis spectral region of 300-800 nm of the S9 dye are reported at λ1=491 nm,

λ2=426 nm, and λ3=330 nm [1]. Table 5.4 compares the experimental

measurement with theoretical results using TD-DFT with respect to different DFT

models indicated in the previous section for the original S9 dye. To assess the

overall performance of TD-DFT functionals with reference to the experimental

values in this table, the mean absolute error (MAE) criterion is employed. The

MAE is defined as,

MAE= 1n

� �λicalc. − λi

expt.�n

i=1 , (n=3). (5.5)

The MAEs of the DFT functionals are given in the last row of Table 5.4. In the

table, the CAM-B3LYP model and the BHandH are compatible with MAEs being

14 nm and 18 nm, respectively. Next comes the ωB97XD (MAE=23 nm) and the

LC-ωPBE (MAE=52 nm) models. The PBE0 (MAE=108 nm) and B3LYP

(MAE=149 nm) models exhibit the least accurate performance on prediction of

the spectral line positions. Three long-range (LC) corrected DFT functionals,

namely CAM-B3LYP, ωB97XD and LC-ωPBE show a good general performance

in reproducing the experimental main bands.

Non-LC hybrid functionals are not usually suitable and accurate at large distances

for electron excitations to high orbitals. That is because the non-Coulomb fraction

of exchange functionals usually diminishes very fast. In the range-separated (or

LC) hybrid DFT functionals, the Coulomb energy is divided into long-range and

short-range energies. The HF exchange interaction is included in the long-range

part and the DFT exchange interaction is included in the short-range part [49].

The ω (in bohr-1) parameter is a damping parameter which controls the range of

the inter-electronic separation between these two terms.


151

Table 5.4: Calculated excited energy (in nm), oscillator strengths (f), and transition configurations for the 3 most intense peaks of S9, S9-D1 and S9-D2 dyes in DCM solution*.

Carbz-PAHTDTT(S9) S9-D1 S9-D2

Method TD-B3LYP TD-PBE0 TD-LC-ωPBE TD-ωB97XD TD-CAM-B3LYP

TD-BHandH Exp.(a) TD-BHandH ∆λ(b) TD-BHandH ∆λ(c)

λ1 668 (1.12) 611 (1.48) 420 (2.83) 460 (2.87) 479 (2.74) 490 (2.71) 491 (3.0) 662 (2.55)

172 535 (2.17) 45

H→L (97%) H-1→L (2%)

H→L (90%) H-1→L (6%) H→L+1 (3%)

H-1→L (29%) H→L (25%) H→L+1 (12%) H-3→L (10%) H-6→L (6%) H-6→L+1 (3%) H-1→L+2 (2%)

H→L (32%) H-1→L (28%) H→L+1 (15%) H-3→L (9%) H-6→L (4%) H-6→L+1 (2%)

H-1→L (28%) H→L (40%) H→L+1 (13%) H-3→L (8%) H-6→L (3%)

H→L (52%) H-1→L (23%) H→L+1 (12%) H-3→L (6%)

H→L (78%) H-1→L (14%) H-7→L (2%)

H→L (76%) H-1→L (9%) H→L+1 (5%) H-3→L (5%)

λ2 540 (0.80)

498 (0.71) 365 (0.43)

391 (0.40) 401 (0.40)

402 (0.39)

426 (2.7) 528 (0.13) 126 394 (0.84) -8

H-1→L (91%) H→L+1 (4%) H→L (3%)

H-1→L (82%) H→L (8%) H-3→L (5%) H→L+1 (4%)

H→L+1 (48%) H-6→L (10%) H-3→L (10%) H-1→L (6%) H→L+2 (4%) H-8→L (3%) H-1→L+1 (3%) H-1→L+7 (2%) H-3→L+1 (2%)

H→L+1 (53%) H-3→L (11%) H-6→L (9%) H-1→L (9%) H→L+2 (4%) H-1→L+7 (2%) H-8→L (2%)

H→L+1 (57%) H-1→L (11%) H-3→L(10%) H-6→L (7%) H→L+2 (4%)

H→L+1 (60%) H-1→L (14%) H-3→L (10%) H-6→L (5%) H→L+2 (3%)

H-3→L (45%) H-6→L (26%) H-1→L (17%) H→L (4%)

H→L+1 (72%) H-1→L (7%) H-3→L (6%) H-6-→L (2%)

λ3 488 (1.10)

463 (0.94)

306 (0.29)

325 (0.29) 335 (0.33)

360 (0.29) 330 (2.5) 440 (0.21)

80 374 (0.52)

14

H→L+1(88%) H-1→L (5%) H-3→L (3%)

H→L+1 (89%) H-1→L (6%)

H→L+2 (27%) H-1→L+1(21%) H-8→L (12%) H-3→L+1 (7%) H-6→L (6%) H→L+7 (5%) H-1→L+2 (2%)

H-1→L+1(26%) H→L+2 (26%) H-8→L (11%) H-6→L (9%) H-3→L+1 (6%) H→L+7 (5%)

H→L (38%) H-6→L (15%) H-3→L (11%) H→L+2 (10%) H→L+1 (9%) H-8→L (8%) H-1→L (3%)

H→L (44%) H-1→L (20%) H→L+1 (13%) H-3→L (9%) H-6→L (5%) H-1→L+1(3%)

H-1→L (45%) H-6→L (30%) H→L (8%) H-8→L (4%) H→L+1 (4%) H-3→L+1 (2%) H-7→L+1 (2%)

H-6→L (10%) H-3→L (22%) H-1→L (29%) H→L (22%) H→L+1 (11%) H-8→L (4%)

MAE 149 108 52 23 14 18 * All TD-DFT calculations are performed in DCM solution using CPCM solvation model on geometries optimized at CPCM-PBE0/6-311G(d). (a)See supplementary information of [1]. (b)∆λ= λ(S9-D1)-λ(S9), method= TD-BHandH. (c)∆λ= λ(S9-D2)-λ(S9), method= TD-BHandH.


152

The results in Table 5.4 also suggest that without long-range corrections, the

inclusion of the Hartree-Fock (HF) exchange energy is important to reproduce the

major band, λ1. The TD-BHandH DFT model gives the major absorption peaks of

the S9 dye the most accurate results and the TD-B3LYP DFT model produces the

least accurate results in the table. For example, the TD-BHandH DFT model

almost reproduces the spectral line position of the major absorption band at λ1=

490 nm with respect to the experiment at λ1=491 nm. This model also closely

reproduces the other minor bands at λ2=402 nm (expt. 426 nm) and λ2=360 nm

(expt. 330 nm).Without sufficient inclusion of the exchange energy in the DFT

functionals, the B3LYP and PBE0 hybrid functionals are unable to produce

spectral band positions with sufficient accuracy as seen previously [50, 51].

Table 5.4 also collects the excitation energies, oscillator strengths, and transition

configurations for the three main absorption bands of all three dyes (i.e. S9, S9-

D1 and S9-D2) and the corresponding UV-Vis absorption spectra of these dyes

are plotted in Fig. 5.6. From Table 5.4, it is also noticeable that the calculated

vertical electronic transitions obtained by the best performing functionals for TD-

DFT calculations in this study, i.e. BHandH and CAM-B3LYP, have very similar

assignments. On the other hand, the assignments resulted from other functionals

are different in terms of both the molecular orbitals involved and the percentage

(weight) of the contributions.

The BHandH functional is employed for the TD-DFT calculations of the new

dyes. As mentioned in Chapter 1, the most important absorption region of dye

sensitizers for the application in DSSC is the one close to infra-red region. This

means that the absorption bands at λ1 followed by λ2 are more important than λ3in

the present study. From the MAE results over all three bands, it can be seen that

both CAM-B3LYP and BHandH functional outperformed other functionals in this

study. However, BHandH functional gives the most accurate band positions for

the most important bands, λ1 and λ2, compared to all other functionals. The

accuracy of the calculations at this region is more important, which justify the use


153

of BHandH functional in the TD-DFT calculations of the new rationally designed

dyes.

The effect of modifications on shifting the spectral peaks is also reflected in Table

5.4 and Fig. 5.6. For S9-D1, a remarkable bathochromic shift (i.e. to the longer

wavelengths or red-shift) of 172 nm on λ1 compared to the reference S9 dye is

observed. Based on the results of TD-DFT calculations, this band is mainly

composed of an excitation transition from HOMO → LUMO both for the

reference S9 dye (i.e. 52% contribution from H→L transition) and for the new S9-

D1 dye (i.e. 78% contribution from H→L transition). As discussed earlier, the

energy gap between HOMO and LUMO of S9-D1 is significantly reduced

compared to that of the S9 dye, which in turn results in the red-shift of λ1 as seen

in Fig. 5.6. Very large red-shifts of λ2 and λ3 are also observed for S9-D1

compared to the S9 dye.

The λ1 band of the new dye S9-D1 indeed outperforms the original Carbz-

PAHTDTT (S9) dye with not only a significant preferred spectral shift on the

position of this band, but also this band covers a broader region with nearly

doubled full width at half maximum (FWHM) than the original S9 dye. The

significant bathochromic shift and broadening of the UV-Vis spectra of S9-D1

structure indicates its enhanced light harvesting capability which is an important

criterion for a well-performing dye sensitizer employed in DSSC. In the S9-D2

dye, the λ1 and λ3 spectral bands both show a preferred bathochromic shift of 44

nm compared to the S9 dye. However, an unwanted hypsochromic shift (i.e. to the

shorter wavelengths or blue-shift) of -32 nm on the λ2 spectral band was

calculated for this (S9-D2) dye.


154


The present chapter was to study the Carbz-PAHTDTT (S9) organic dye

sensitizer and its rationally-designed derivatives, theoretically. An investigation to

search for the accurate and reliable first-principles quantum-mechanical models

for this large-sized dye sensitizer was performed. On the basis of the agreement

with available experimental data, the B3LYP/6-311G(d)// PBE0/6-311G(d) model

Fig. 5.6: The simulated UV-Vis spectra of three dyes, S9, S9-D1 and S9-D2 using TD-BHandH/6-311G(d) model in DCM solution. The electronic transitions are transformed into simulated UV-Vis spectra using Gaussian functions with half-widths of 3000 cm–1[4].


155

in DCM solution reproduced the energy levels of HOMO and LUMO more

accurately. However, to accurately produce the UV-Vis spectra of the dyes, it is

found that the long-range corrected functionals yielded better agreement with the

experiment in general.

By utilizing the mean average error (MAE) criterion over all three bands, the

functionals used for TD-DFT calculations were ranked. The CAM-B3LYP

followed by BHandH functionals gave the least deviation from experiment over

the three main absorption bands of the S9 dye. However, the half and half

BHandH functional, which outperformed all other functionals to reproduce the

spectral region of our interest (i.e. λ1 and λ2), was chosen to predict the absorption

spectra of the rationally designed new dyes S9-D1 and S9-D2. These new dyes

were rationally designed by modifying the π-conjugated bridge of the reference

S9 dye. The modifications were made by substituting two of the sulphur atoms of

the reference dye with −N (in S9-D1) or −NH group (in S9-D2).

Both new dyes showed red-shifted and broadened absorption spectra, reduced

HOMO-LUMO gap, better NLO properties as well as noticeable redistribution of

the electron density compared to the reference dye. However, such improvements

were much more noticeable and significant in new S9-D1 dye compared to S9-

D2. A correlation was observed between the total NBO of the linker of the dyes

with their corresponding HOMO or LUMO energy levels. Furthermore, based on

the LUMO energy level of the new dye S9-D1, it was also suggested that this dye

sensitizer is a suitable candidate for the effective sensitization of both TiO2 and

SnO2 semiconductors. The present study explored a useful direction of rational

design for new dyes in DSSC.


156

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162

Chapter 6

Ferrocene “The measure of greatness in a scientific idea is the extent to which it stimulates

thought and opens up new lines of research.” Paul Dirac

6.1. Introduction

In recent years, there has been an increasing interest in developing and employing

new materials (e.g. redox mediators based on ferrocene-derivatives [1]), as a route

to improve the conversion efficiency of dye sensitized solar cells (DSSC). As

aforementioned in chapter five of this thesis, the recently-reported impressive

results obtained by using ferrocene-based redox shuttle in combination with

Carbz-PAHTDTT (S9) organic dye sensitizer [2] stimulated the theoretical

investigation of the structure of the S9 dye sensitizer as well as the ferrocene

compound. While chapter five had focussed on the S9 dye sensitizer, the present

chapter will probe an accurate description of the electronic structure of the

ferrocene complex.

Ferrocene was first discovered unintentionally a few decades ago. Two

independent groups reported the preparation of an orange colour substance from

cyclopentadiene (Cp) and iron with C10H10Fe formula, which showed a

Ferrocene Chapter 6

163

remarkable stability [3, 4]. The correct structure of this compound has been a

disputed subject within the field of organometallic chemistry [5, 6]. As a result, a

substantial part of this chapter is devoted to the study of the ferrocene structure

and its conformers. Apart from the methods section (6.2), this chapter is divided

into two main sections. Section 6.3 investigates the structure of the ferrocene

conformers. The main issues addressed in this section are: a) geometries and

potential energy scan (PES), b) molecular electrostatic potential (MEP) and c)

infrared (IR) spectroscopy of ferrocene both in vacuum and solution. The second

section of this chapter (i.e. section 6.4) focuses on the molecular properties of this

compound that are related to its application as a redox mediator in dye sensitized

solar cells (DSSC). A very accurate DFT model for the calculation of the redox

potential of Fc/Fc+ couple will be presented in this section.

6.2. Computational methods and experimental details

All calculations are performed using Gaussian 09 computational chemistry

package [7], unless stated otherwise. Geometry optimizations of the ferrocene

conformers are carried out using the B3LYP/m6-31G(d) model. The basis set m6-

31G(d), a modified version of the 6-31G(d), is employed in the calculations [8].

This basis set incorporates necessary diffuse d-type functions for the first-row

transition metals such as Fe. It exhibits a better performance than the conventional

6-31G(d) basis set for the iron atom in ferrocene by providing a more appropriate

description for the important energy difference between the atomic 3dn4s1 and

3dn-14s2 states [9].

A potential energy scan (PES) is performed by rotating the central

cyclopentadienyl axis which is defined by a dihedral angle δ (C(1)−X(2)−Fe(3)−C(4))

which connects the centres (X(1)−X(2)) of each cyclopentadienyl planes through

Ferrocene Chapter 6

164

the middle Fe atom. The PES produced from the calculations starts from an

eclipsed (D5h) conformer (δ = 0°) at a step size of ∆δ = 4°. Due to the pentagonal

structure of the Cp ring, every 36° that the dihedral angle rotates will result in an

alternative staggered-eclipsed (D5d-D5h) conformation periodically.

The infrared (IR) spectra of the ferrocene conformers are simulated on the

optimized structure using the same B3LYP/m6-31G(d) model, both in vacuum

and in a number of solvents. As the simulated IR spectra of Fc will be compared

with several FTIR spectra measured in solutions, a number of implicit solvent

models are employed in the simulations to account for solvation effects on the

simulated IR spectra. Continuum solvation methods such as polarizable

continuum model (PCM) or dielectric polarized continuum model (D-PCM which

neglects the volume polarization) [10], the conductor PCM (C-PCM, which

approximates the volume polarization) [11, 12] and the solute molecule density

(SMD) model [13] are employed in the IR spectral simulations. Geometry

optimization calculations of Fc are performed for each of such simulations in

solutions, respectively, followed by vibrational frequency calculations.

The experimental FTIR data are provided by Dr. Stephen Best (School of

Chemistry, The University of Melbourne, Australia). Infrared spectra of ferrocene

dissolved in non-polar solvents such as acetonitrile (ACN, ε=35.69),

dichloromethane (DCM, ε=8.93), tetrahydrofuran (THF, ε=7.43) and dioxane

(DOX, ε=2.21) are obtained using a Bruker Tensor 27 FTIR and a conventional

solution cell fitted with KBr windows and a 100 µm spacer. A resolution of 1 cm-1

is used for all measurements. Concentrated solutions are prepared in each case and

these spectra are compared with those obtained from the corresponding solutions

diluted by factors ranging between 2 and 4. No significant concentration-

dependent variation in the band profile is observed.

Ferrocene Chapter 6

165

Calculations of the redox potential of ferrocene/ferrocenium (Fc/Fc+) couple is

performed based on the procedure given in Ref. [14]. To calculate redox

potentials from first principles, computational thermodynamics approaches should

be employed. Computational thermodynamics is a free energy approach which

can be used to model electrochemical processes [15].

To compute Fc/Fc+ absolute redox potential, Gibbs free energy change (∆Gox(sol))

of the following redox reaction should be calculated:

𝐹𝑐(𝑠𝑜𝑙)

0 → 𝐹𝑐(𝑠𝑜𝑙)+ + 𝑒−

In this reaction, one electron is transferred from ferrocene (𝐹𝑐(𝑠𝑜𝑙)0 ) to ferrocenium

(𝐹𝑐(𝑠𝑜𝑙)+ ). Total change of Gibbs free energy, ∆Gox(sol), can be calculated from

Born-Haber thermodynamic cycle as follows:

which is an application of Hess's law, where ∆Gsolv(Fc0) and ∆Gsolv(Fc+) are the

solvation free energies of [Fc]0 and [Fc]+, respectively, and ∆Gox(g) is the free

Fc0(g)

Fc0(sol) Fc+

(sol)

Fc+(g)

∆Gox(g)

∆Gox(sol)

∆Gsolv(Fc+) ∆Gsolv(Fc0)

Scheme 6.1: The thermodynamic cycle used to calculate Gibbs free energy of Fc/Fc+ redo reaction.

Ferrocene Chapter 6

166

energy change due to oxidation reaction of [Fc]0 to [Fc]+ in the gas phase. PCM

solvation model and dimethyl sulfoxide (DMSO) solvent are employed in this

study.

Redox potential is calculated from the following equation:

𝐸(𝑚)

(0/+) =𝛥𝐺𝑜𝑥(𝑠𝑜𝑙)

−𝑛𝐹 , (6.1)

where F is the Faraday constant (23.061 kcal.mol-1V-1) and n is the number of

electrons transferred (n=1 for Fc/Fc+ redox reaction). The outputs of frequency

calculations on the optimized structures of both Fc0 and Fc+ are needed to gain

thermodynamics values required to solve eq. (6.1).

6.3. Ferrocene structure

A new era in organometallic chemistry began by the unintentional discovery of

ferrocene (Fc) by two independent groups reported in late 1951 [3] and early 1952

[4]. The “renaissance of inorganic chemistry”, as called by Sir Ron Nyholm in his

inaugural lecture in 1956 delivered at University College London [16], originated

from attempts to find the true structure of the ferrocene compound [6], as the

“stretched” structure (Fig 1.(a)) proposed by Pauson and Kealy in their seminal

paper [3] was not convincing. In 1952 Wilkinson et al. proposed a “sandwich”

structure (Fig 1.(b)), having a symmetry point group of D5d (staggered) for this

compound. However, they also suggested that a D5h structure in which “split d3p2

plane pentagon bonding” exists between iron to carbons, is not unlikely [17].

Fischer and co-workers were also studying the structure of ferrocene at the same

time. Based on their preliminary X-ray crystallography data and coordination

chemistry knowledge, they concluded that in ferrocene molecule, the iron (II)

atom is confined in between the two cyclopentadienyl rings similar to ligands

[18]. Later on in 1952 they assigned a “double cone” structure (Fig 1.(c)) to

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ferrocene [19]. Several follow-up X-ray analyses confirmed the true structure (i.e.

sandwich structure) of ferrocene [20-22]. The revolutionary discovery of the

unusual sandwich structure of ferrocene as the prototype of other metallocenes

was a great breakthrough for organometallic chemistry and spurred the growth of

this field [5].

Most of the early experiments in 1950s were focused on the discovery of the

novel “sandwich” structure for Fc and were performed on the crystalline form of

this compound, which demonstrated an staggered (D5d) conformation. It wasn’t

until 1966 when Bohn and Halland [23] carried out a diffraction studies on the

ferrocene vapour at 140°C and found out that the equilibrium configuration of the

free Fc molecule is indeed eclipsed (D5h), having a small barrier for internal

rotation. The development of ferrocene study since its discovery in 1951 [3] has

Fig. 6.1: Proposed structures for ferrocene. (a): stretched, (b): sandwich and (c): double cone.

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been well documented in recent articles such as Coriani et al. [24], Roy et al. [25],

Gryaznova et al. [26] and Bean et al. [27].

Fig. 6.2 gives the optimised geometries of the eclipsed (D5h) and staggered (D5d)

conformers of ferrocene as three-dimensional (3D) structures [28]. In the figure,

(a1) and (b1) are the side views, whereas the bottom panel (a2) and (b2) gives the

top views of the eclipsed and staggered conformers, respectively. One of the

cyclopentadienyl rings of ferrocene is also labelled as Cp in Fig. 6.2(a1).

Fig. 6.2: Optimized molecular structures of the eclipsed (D5h) and staggered (D5d) conformers of ferrocene in three-dimensional (3D) space.

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As a prototypical metallocene with a sandwich structure, ferrocene exhibits only a

small energy barrier separating the staggered (D5d symmetry) and eclipsed (D5h

symmetry) rotational orientations of the parallel cyclopentadienyl rings [29]. The

fact that the barrier to the internal rotation of ferrocene is very small and that the

cyclopentadienyl rings (Cp) in Fc can easily rotate between eclipsed/staggered

conformations makes it difficult to find properties which can differentiate these

two conformers. It has been stated [26] that a staggered ferrocene structure (i.e.

D5d point group symmetry) dominates experiments in the condensed phase [21,

22, 30, 31], whereas the eclipsed structure (D5h) is found in the gas phase [23, 32,

33]. The eclipsed conformation was also observed at 90 K in the solid [34] and at

room temperature in solutions [20]. As most of the theoretical studies of ferrocene

are based on the gas phase or solutions, the eclipsed (D5h) structure of ferrocene

has been more extensively studied than the D5d conformer.

Study of ferrocene conformers will help our understanding of other metallocenes

and their derivatives with applications in biotechnology, nanotechnology and solar

technology [35]. For example, Cooper et al. [36] recently developed a class of

ferrocene synthons which may add to the number for organometallics with useful

medicinal properties [37]. The rotational energy barriers with respect to the metal-

cyclopentadienyl axis between the eclipsed and staggered conformers are only a

few kJ.mol-1 [35, 38]; as a result, it is possible that the ground electron state

structures of ferrocene may contain both of the conformations.

The fact that electronic structures and properties of the ferrocene conformers are

strikingly similar is a key hurdle to differentiate or separate the configurations

from one another. However, detailed studies of D5h and D5d of ferrocene are

important as ferrocene derivatives may inherit particular properties which only

exist in one conformer [38]. For example, additional ligands coordinating to the

metal and the Cp rings while maintaining certain symmetry, can be a geometric

requirement for the D5h conformer [36]. In addition, the understanding of

synthesis pathways, mechanics and reaction dynamics of the ferrocene derivatives

Ferrocene Chapter 6

170

will require the understanding of the structure, symmetry and properties of the

ferrocene conformers.

In the following section (6.3), we use simulated IR spectra and a number of other

properties of D5h and D5d conformers of ferrocene, combined with available

experiments [23], [32], [33] and [39] and other theoretical calculations [24], [40]

and [26] to confirm that the eclipsed conformer dominates the ferrocene in the

vapour phase and to find properties that differentiate these two conformers.

6.3.1. Geometries and potential energy scan

Based on the vibrational frequency calculations on the optimized structures in this

thesis (B3LYP/m6-31G(d) model), the eclipsed conformer is a true global

minimum structure of ferrocene without imaginary frequencies in isolation. The

staggered conformer is the saddle point in the gas phase due to an imaginary

frequency [28]. This is in good agreement with other theoretical studies [24, 25,

41].

Fig. 6.3 compares the visualization of the optimized structures generated by the

default settings of three different graphical user interface (GUI) tools for

computational chemistry: Gaussview [42], Molden [43] and Gabedit [44]. From

this figure, it is noticeable that tools such as Gabedit and Molden almost always

indicate the ten localised Fe−C bonds existing in both D5h and D5d conformers of

ferrocene in display, when their default settings (e.g. the default bond cut-off) is

employed. However, the graphics generated by Gaussview GUI are more realistic.

That is, the Cp-iron-Cp alignments are likely to adopt stacking structures due to

the ligand π-orbitals and aromaticity as noted by Bean et al. [27]. Infrared (IR)

discussion herein will also provide evidences of the stacking structures rather than

the conventional Fe-C bonds for ferrocene.

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Table 6.1 compares selected characteristic geometric and electronic properties of

D5h and D5d conformers of ferrocene with other theoretical and experimental

results [28]. The optimized geometric parameters for the conformer pairs are

almost identical using the same model as shown in Table 6.1. For example, all

C−C bonds are given by 1.428Å, which is between a C−C single bond and a C=C

double bond. Also, all C−H bonds are reported as 1.082Å.

The results in Table 6.1 also indicate that the hydrogen atoms of Cp are not in the

same plane with the C5 pentagon ring. The hydrogen atoms slightly bend towards

their counterpart in the opposite Cp ring, again in agreement with experimental

findings [32] that the conformer bond angle involving the hydrogen atoms in D5h

is ∡C5−H = 3.7 ± 0.9°. However, calculations indicated that this angle is much

smaller than the crystalline structure of D5h of Fc, from ∡C5−H = 0.66° in

B3LYP/m6-31(d) to ∡C5−H = 1.03 in CCSD(T)/ TZV2P+f [9].

Theory also indicates that this angle, ∡C5−H, for D5d (0.92° in B3LYP/m6-31(d)

and 1.344° in CCSD(T)/6-31G** [9]) is slightly larger than that of D5h. Small

differences of the distances between Fe and the Cp rings in D5h and D5d are also

observed. The Fe−Cp distance of the latter (D5d) is slightly longer than the Fe−Cp

Fig. 6.3: Optimized molecular structures of the eclipsed conformer of ferrocene in 3D space, visualized by three GUI tools: Gaussview, Molden and Gabedit.

Ferrocene Chapter 6

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distance in D5h, i.e., 1.674 Å in D5d whereas in D5h this distance is given by

1.670Å.

Table 6.1: Comparison of the optimized geometries of eclipsed and staggered conformers of ferrocene. Bond/angle This worka HFb MP2c CCSD(T)c B3LYP/Type-Id Expte

Eclipsed (D5h) Fe-C5 (Å) f 1.670 1.865 1.464 1.655 1.687 - 1.688 1.660 Fe-C (Å) 2.065 2.219 1.910 2.056 2.079 - 2.080 2.064 ± 0.003 C-C(Å) 1.428 1.413 1.441 1.433 1.428 1.440 ± 0.002

C-H(Å) 1.082 1.074 1.076 1.077 - 1.104 ± 0.006 ∡C5-H (°) 0.66 0.58 0.33 1.03 3.7± 0.9 g

Etotal(Eh) -1650.662

Etotal+ZPE(Eh) -1650.492

<R2> ( a.u) 1358.84

μ (Debye) 0.0

Electronic State

1A1’

∆ HOMO-LUMO(eV)

5.30

A,B,C (GHz) A: 2.19453 B: 1.05862 C: 1.05862

Staggered (D5d) Fe-C5(Å) 1.674 1.866 1.487 1.659 Fe-C(Å) 2.068 2.220 1.925 2.058 C-C(Å) 1.428 1.413 1.437 1.432 C-H(Å) 1.082 1.074 1.076 1.077 ∡C5-H(°) 0.92 0.55 1.39 1.34 Etotal(Eh) -1650.661 Etotal+ZPE(Eh) -1650.491 <R2> ( a.u) 1361.78 μ (Debye) 0.0 Electronic State

1A1g

∆ HOMO-LUMO(eV)

5.26

A,B,C (GHz) A: 2.19455 B: 1.05503 C: 1.05503

a This work with the B3LYP/m6-31G(d) model. The basis set is a modified version of 6-31G(d) basis set [8]. b See [45]. c See [24]. d See [26]. e See [32]. f Denotes the distance from Fe atom to the centre of cyclopentadienyl ring. g See [33]. From an ND experiment (not corrected for thermal motion) the value is 1.7 ± 0.2 [46]. h Energy difference between D5h ,and D5d is : ∆ E= 0.0272 eV = 0.62kcal⋅mol-1 (0.9 kcal⋅mol-

1, expt [32]).

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Due to their high symmetries, both D5h and D5d conformers do not possess

permanent dipole moments. As a result, the IR spectroscopy of ferrocene will be

due to induced dipole moments during vibration. The calculated molecule size

(i.e., the electronic spatial extent <R2> as given in Table 6.1) of the D5d conformer

is slightly larger than the D5h conformer. The former (D5d) is 1361.80 a.u. but the

latter (D5h) is 1358.84 a.u. The size of D5d is slightly larger but was found in

condensed phase, whereas the smaller size ferrocene D5h is found in gas phase,

solid and solution. The energy gap between the HOMO and the LUMO, i.e.,

∆ε(HOMO-LUMO), is given by 5.30 eV and 5.26 eV for D5h and D5d,

respectively.

The ground electronic state of ferrocene is a low-spin state as indicated by

Gryaznova et al. [26]. Calculations in this thesis using B3LYP/m6-31G(d) model

gives the configurations as [28]:

D5h, X1A2: (core)… (e1”)4(a1’)2(e1’)4(e2’)4(e2”)4(a2”)2(e1”)4(e1’)4(a1’)2(e2’)4(e1”)0

D5d, X1A1g: (core)…(e1g)4(a1g)2(e1u)4(e2u)4(e2g)4(a2u)2(e1g)4(e1u)4(a1g)2(e2g)4(e1g)0

The major difference between the conformers is due to a symmetric plane for D5h

but a symmetric centre for D5d in their point group character tables. As a result,

the orbital irreducible representations which are correlated as ’ and ” in D5h

become g and u in D5d. The highest occupied molecular orbital (HOMO) of D5h

conformer is a doubly degenerate e2’ state and the next HOMO (HOMO-1) is a1’

but the lowest unoccupied molecular orbital (LUMO) is e1”. On the other hand,

the HOMO for D5d is a doubly degenerate e2g state, the HOMO-1 is a1g and

LUMO is e1g.

In this study, a molecular orbital diagram is also constructed by fragmenting

ferrocene into metal (i.e. Fe+2) and ligand (i.e. (Cp)2-2 ) sections and constructing

the molecular orbital diagrams of the D5h and D5d symmetries of ferrocene (in

ADF package using SAOP/et-pvqz model). The result is shown in Fig. 6.4.

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Fig. 6.4: Molecular orbital diagrams of ferrocene conformers. Red dots indicate electron pairs.

Ferrocene Chapter 6

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In metallocenes such as ferrocene, the primary orbital interactions, that form the

metal‐ligand bonds, occur between the metal orbitals (e.g. d orbitals of Fe in

ferrocene) and the carbon-carbon π‐orbitals of the cyclopentadienyl (Cp) ligand.

Several studies have reported various qualitative molecular orbital diagrams of

ferrocene [47-50]. The present work is, however, more quantitative and

calculational. For each of the fragments (i.e. metal and ligand), a molecular orbital

diagram is calculated separately. The resultant molecular orbital diagram of

ferrocene is constructed by connecting the metal and ligand orbitals which match

both in energy and in symmetry as shown in Fig. 6.4. Another significance of this

figure is that it includes the diagrams of both eclipsed and staggered conformers,

whereas the previous works have just considered the staggered (D5d) form.

Fig. 6.5 gives the orbitals of the doubly degenerate HOMOs for D5h (e2’) and for

D5d (e2g), as well as the doubly degenerate LUMOs for D5h (e1”) and for D5d (e1g),

based on our B3LYP/m6-31G(d) calculations [28]. As can be seen from this

figure, the HOMO-LUMO gaps of the eclipsed and the staggered conformers

exhibit a small difference in energy (0.04 eV).

The HOMOs and LUMOs of the eclipsed and staggered exhibit major similarities

to their corresponding partners, except the bottom Cp of the eclipsed ferrocene

orbitals which are not mirror reflection of the top part as in the staggered. The

HOMOs and LUMOs are dominated by both the iron atom and the carbon atoms

of ferrocene. As a result, the differences between the HOMOs and LUMOs are

not significant enough to differentiate the conformers.

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Fig. 6.6(a) reports the potential energy scan (PES) of ferrocene. The PES is

constructed by rotating the central cyclopentadienyl axis, i.e., the dihedral angle, δ

(∡C(1)-X(2)-Fe(3)-C(4)) [28]. In this dihedral angle, X(2) is a dummy atom (purple

colour in the figure) which is located at the centre of the top Cp pentagon plane,

as shown in Fig. 6.6(b). Due to the pentagonal structure of the Cp fragment,

rotation of the dihedral angle δ from 0° to 2π will reproduce D5h and D5d

symmetries five times periodically as the period is 2π/5.

The energy difference, ∆E, between eclipsed (D5h) and staggered (D5d)

conformers of ferrocene is given by 0.62 kcal⋅mol-1 using the B3LYP/m6-31G(d)

Fig. 6.5: The highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) of the eclipsed (D5h) and the staggered (D5d) conformers of ferrocene.

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model, comparing to approximately 0.9(3) kcal⋅mol-1 as measured by gas phase

electron diffraction (GED) [32]. This result is in agreement with other DFT

calculations [24]. For example, Coriani et al. [24] calculated ∆E values of 0.39

kcal⋅mol-1, 0.75 kcal⋅mol-1, 0.99 kcal⋅mol-1, and 1.13 kcal⋅mol-1 by employing

BHLYP, B3LYP, BLYP, and BP86 density functionals, respectively. However,

such small differences in the properties are not sufficient to warrant meaningful

investigation for such differences in most measurements. Other properties which

can differentiate the conformers sensitively ought to be disclosed.

Fig. 6.6: (a) Potential energy scan (PES) of the dihedral angle rotating the axis connecting the middle Fe atom as well as the centres of two Cp rings. Due to the

pentagon structure of Cp, every 36° rotation of the dihedral angle will produce either the D5h or the D5d structure once. This figure only presents one period of the PES.

(b) The definition of the dihedral angle.

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6.3.2. Molecular electrostatic potential

Fig. 6.7 gives cross sections of the molecular electrostatic potentials (MEPs) of

D5h and D5d conformers. In this figure, the upper panels, (a1) and (a2), are the

cross sections through one of the pentagon Cp rings of the conformers. As seen in

the figure, (a1) and (a2) are virtually identical in D5h and D5d conformers. That is

because only one of the Cp rings is presented in the MEP which is independent of

the other Cp ring and their orientation. Perhaps the noticeable difference between

(a1) and (a2) is that the projection of the opposite Cp ring overlaps with the

working Cp ring in D5h, whereas the same projection in the D5d case does not

overlap with the working Cp ring due to its reflection centre, i.

In the middle panel of Fig. 6.7, (b1) and (b2) are the MEP cross sections with an

oblique cut through the centre Fe atom. The MEP cross sections in (b1) and (b2)

are very different for D5h and D5d. Such dissimilarity reflects the unique symmetry

of σh for D5h and i for D5d. For example, staggered conformer (D5d) gives a

symmetric 2D MEP showing the character of the symmetric centre, i, whereas the

eclipsed conformer (D5h) provides a butterfly shaped 2D MEP exhibiting a single

σh plane. Furthermore, the bottom panel, (c1) and (c3) gives cross sections through

the centre Fe atom parallel to the Cp rings, which clearly indicate that the electron

densities at the Fe centre and its vicinity are very different in D5h and D5d

conformers. As shown in (c1), the electron density map of the eclipsed Fc presents

a pentagonal MEP, whereas (c2) reports an electron disk centred at the Fe atom in

the staggered Fc. The observation suggests that any properties of ferrocene

reflecting such different σh and i symmetries may be able to differentiate the

conformers. This information provides a clue to concentrate on the investigation

of Fe-centred properties in the next sections.

Ferrocene Chapter 6

179

Fig. 6.7: Two-dimensional (2D) cross sections of the molecular electrostatic potential (MEP) of ferrocene.

(a1) and (a2): the cross section through the Cp plane; (b1) and (b2): the cross section through the oblique plane (via Fe) and the Cp ring plane;

(c1) and (c3): cross sections through the Fe atom and parallel to the Cp planes.

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6.3.3. Infrared spectroscopy of ferrocene in isolation

Ferrocene is a highly symmetric compound with no permanent dipole moment. As

a result, the IR spectra of ferrocene are relatively simple with only a few transition

peaks (I≠0) caused by vibrations which lead to induced dipole moments. Fig 6.8

compares the simulated and the experimental IR spectra of ferrocene in the region

of 400-1200 cm-1. In this figure, two experimental IR measurements and three

simulated ones are presented. The first spectrum (Fig 6.8(a)) belongs to a recent

gas-phase infrared spectrum of Fc measured at 1 cm-1 resolution in the region of

400-1200 cm-1 at the Far-IR beamline of the Australian Synchrotron [51]. Fig

6.8(b) shows an earlier experimental measurement of Lippincott and Nelson [39]

in vapour state. Fig 6.8(c) gives a recent simulated IR spectrum of the D5h

conformer using B3LYP/Type-I model [26]. The IR frequencies simulated by the

B3LYP/m6-31G(d) in the present study are also given in Fig 6.8(d) and Fig 6.8(e)

for D5h and D5d conformers of ferrocene, respectively.

As seen in Fig. 6.8, the simulated IR spectra agree well with the major peaks in

the experiment, except that the entire IR band in the region of 600-750 cm-1

shown in the earlier experiment [39] is missing in theoretical results, including the

present study and a previous one [26]. It suggests that this medium strong IR band

in the experiment [39] might be stemmed by vibrations other than ferrocene, such

as impurities and the environment etc.

The agreement between the present results and recent theoretical results (D5h

conformer) [26] is good. However, it is noted that in Ref. [26] the Type-I basis set

in the B3LYP/Type-I model uses the 6-31G* basis set for the ligand atoms, such

as H and C, but the ECP LanL2DZ basis set for the Fe atom. In this reference

[26], the calculated IR frequencies of the eclipsed ferrocene have been scaled by a

number of scaling factors (see Table 1S in the supplementary materials in Ref.

[26]). For example, the calculated Fe−C stretching vibrations need a scale factor

as large as 1.25 in order to fit the corresponding experimental vibrational

Ferrocene Chapter 6

181

frequencies of Lippincott and Nelson [39], also one of the scale factors for the

C−H stretch vibrations is given as 0.889 [26]. Exploiting a number of scaling

factors with respect to the experiment in Ref. [26], leads to loss of the prediction

power of theoretical studies.

Fig. 6.8: Comparison of the simulated and the experimental IR spectra of ferrocene in the region of 400-1200 cm-1. (a) and (b): experimental, (c) simulated for D5h conformer, from Ref. [27],

(d) and (e): simulated for D5h and D5d, respectively in the present study.

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In the present study, the IR frequencies for both D5h and D5d conformers of

ferrocene using the B3LYP/m6-31G(d) model are the direct results, without any

scaling and manipulation [28]. The modified m6-31G(d) basis set [8], which

incorporates necessary diffuse d-type functions for the first-row transition metals

such as Fe, exhibits a more accurate description than the ECP LanL2DZ basis set

(Type-I) for the iron atom in ferrocene. To be more specific, the m6-31G(d) basis

set provides a more appropriate description for the important energy difference

between the atomic 3dn4s1 and 3dn-14s2 states [8, 9]. As a result, the present IR

frequencies agree well with experiment without any scaling.

The present simulation only differ in the basis set with Ref. [26], where scaling

were applied. From the agreement of the present IR frequencies with experiment

without any scaling, it can be concluded that basis set plays an important role in

the accuracy of DFT calculations of ferrocene. Such results also support the

previous finding that the centre Fe atom plays a significant role in determining

properties of ferrocene, as the two basis sets discussed here only differ in their

description of the transition Fe metal.

Fig. 6.9 compares the simulated infrared spectra of D5h and D5d conformers of

ferrocene in the region of 400-4000 cm-1 using the B3LYP/m6-31G(d) model. The

spectrum for D5d is in red colour, and for D5h is in black. As mentioned earlier, the

IR spectra of ferrocene are relatively simple with only a few transitions due to

induced dipole moments. The spectra consist of six major peaks in this region.

The IR spectra are very similar in eclipsed (D5h) and staggered (D5d) conformers,

with only small blue shift in the spectra of the D5h ferrocene. For example, the

clustered IR peaks of the eclipsed conformer in the region < 500 cm-1 (i.e. Band

A, highlighted in a blue box) show a small blue shift of ca. 12 cm-1. To further

understand the IR spectra of Fc, more detailed analysis is needed.

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Table 6.2 [28] reports the IR spectral analysis in the region of 400-4000 cm-1 for

the six major non-zero intensity (I≠0) transitions in Fig. 6.9. In this table, the IR

frequencies of conformer D5h compare with a recent theoretical study of the same

conformer of Fc (D5h) [26] and an earlier experimental study (D5d) of Lippincott

and Nelson [39].

Based on point group theory, there are eight irreducible representations (modes)

for each of the D5h and D5d [39] ferrocene conformers. According to the selection

Fig. 6.9: Comparison of simulated IR spectra of ferrocene, D5h and D5d in vacuum in the region of

400-4000 cm-1 using the B3LYP/m6-31G(d) model without any scaling.

Ferrocene Chapter 6

184

rules, five of the modes are IR active modes but three of them are IR inactive.

Among the five IR active modes, only two modes will show strong IR transitions,

as indicated by their character table. That is,

D5h: a1’, a2’, e1’, e2’, a1”, a2”, e1”, and e2”;

IR active: a1’, e1’, e2’, a2”, e1”; where e1’ and a2” are strong IR active

modes;

IR inactive: a1”, a2’, and e2”;

D5d: a1g, a2g, e1g, e2g, a1u, a2u, e1u, e2u;

IR active: a1g, e1g, e2g, a2u, e1u; where e1u and a2u are strong IR active

modes;

IR inactive: a2g, a1u, e2u;

The two modes, i.e., e1u and a2u for D5d and e1’ and a2” for D5h produce strong IR

spectral lines. As a result, the major IR spectral peaks in Fig. 6.9 are assigned to

e1u and a2u for D5d and e1’ and a2” for D5h in Table 6.2. It is found that the IR

frequencies of the D5h and D5d conformers are indeed very similar, the

discrepancies are within 5 cm-1 for the vibrations in the region above 800 cm-1 (i.e.

Bands B, C, D, E and F). For example, the largest frequency mode, a2’ for D5h and

a2u for D5d are given by 3268 cm-1 and 3267 cm-1, respectively (Band F). Larger

differences in the IR spectra are shown in the region of 400-500 (Band A) cm-1.

For example, the second smallest mode in this region is given as 488 cm-1 for e1’

(D5h) which corresponds to the first (smallest frequency) IR F peak at 459 cm-1 for

e1u (D5d).

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185

Table 6.2: Calculated IR frequencies and their assignment for the D5h and D5d conformers of ferrocene using the B3LYP/m6-31G(d) model. D5h Ref.a D5d Exp.b Assignment

Band Mode No.

υ(cm-1) (I(km.mol-1)) , Symmetry Type

υ(cm-1) (I(km.mol-1)) , Symmetry Type, Int

Mode No.

υ(cm-1) (I(km.mol-1)) , Symmetry Type

υ(cm-1), I c

A 7 471 (17.75), a2” 470 (13), a2” 11 7,8d 459 (25.54), e1u 480, s ν FeCp

A 8,9 488 (22.30), e1’ 473 (48), e1’, 16 9e 461 (17.39), a2u 496, s Ring tilt

B 18 844(60.31), a2” 825 (79), a2” 10 18 848 (60.85), a2u 816, s γ CH

B 22,23 870 (1.58), e1’ 841 (10), e1’ 15 22,23 871 (1.92), e1u 840, w Asymmetric γCH(2 CH upward, 2 CH downward)

C 30,31 1035 (17.04), e1’ 1017 (34), e1’, 14 30,31 1035 (16.29), e1u 1012, s δ CCH

D 37 1141(20.23), a2” 1141 (15), a2”, 9 36 1139 (20.46), a2u 1112, s Breathing(one Cp shrinks, one Cp expands)

E 46,47 1470 (1.55), e1’ 1441 (4), e1’ 13 44,45 1469 (1.37), e1u 1416, w Asymmetric ν CC: Cp, in plane δ CCH

F 54,55 3257 (23.63), e1’ 3123 (46), e1’, 12 54,55 3256 (23.88), e1u 3106, m ν CH

F 56 3268 (2.75), a2” 3134 (3), a2”, 8 57 3267 (2.54), a2u ν CH

ν= Stretch γ= Out of plane δ=Bend a See [26]. b See [39]. c w=weak, m=medium, s=strong . d Assignment differs from D5h and is ν FeCp here. e Assignment differs from D5h and is ring tilt here.

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6.3.4. Differentiation of the D5h and D5d conformers

Experimental IR measurement [39] in the 400-500 cm-1 region is indeed

reproduced by the present simulation [28]. In order to reveal more details, Fig.

6.10 reports the expanded IR spectra of the ferrocene conformers in the region of

400-650 cm-1. The splitting of the first IR spectral peak of the eclipsed ferrocene

agrees well with the simulated one (Figure 2, S=0) in Ref. [26]. For example, for

the eclipsed Fc, the present calculation gives the IR frequency splitting of ∆υ as

large as 17 cm-1, which is in excellent agreement with the measured one of 16 cm-

1 [39] .

A closer inspection of the vibration modes of D5h reveals that the mode at 471.23

cm-1 (17.75 km⋅mol-1) is a strong vibration being assigned to a2”, whereas the

second spectral line at 488.70 cm-1 (22.30 km⋅mol-1) is a stronger vibration with

Fig. 6.10: Comparison of high resolution (FWHM =5 cm-1) IR spectra of the eclipsed (D5h, black) and staggered (D5d, red) conformers of ferrocene based on B3LYP/m6-31G(d) model in vacuum in

the region of 400-650 cm-1 without any scaling.

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187

doubly degenerate states being assigned to e1’, a splitting of ∆υ is as large as 17

cm-1 between first two IR spectral peaks as shown in Fig. 6.10 (D5h). Although

Gryanova et al. [26] show only a small splitting of 3 cm-1 between 470 cm-1 (13

km⋅mol-1) and 473 cm-1 (48 km⋅mol-1), respectively, using the B3LYP/Type-I

model, their IR spectra simulated using the OPBE/Type-I model indeed indicate

that the higher vibration mode is the stronger vibration being assigned to e1’, is

consistent with simulated spectra in the present study for the eclipsed ferrocene.

Although the IR experiment in Ref. [39] assigned the structure of ferrocene to the

staggered D5d Fc, the split intensity pattern at ca. 470 cm-1 suggests the opposite,

i.e., being the eclipsed D5h conformer. If the Fc sample were dominated by the D5d

conformer in the experiment, the two spectral lines in the 400-500 cm-1 region

should be as close as 2 cm-1 (B3LYP/m6-31G*) or 3 cm-1 (B3LYP/Type-I) [26].

In addition, the observed first IR spectral peak for D5d in the region of 400-500

cm-1 must be a single and symmetric peak as shown in Fig. 6.10. If the sample is

dominated by the D5h conformer of Fc, however, the first IR spectral peak in the

same region is asymmetric and split into two peaks using a spectrometer with

higher resolution.

The vibrations in the IR spectral region near 500 cm-1 are dominated by vibrations

involving the centre Fe atom. As noted in previous sections (e.g., the MEP), the

eclipsed and staggered structures start to show differences when Fe is involved.

Fig. 6.11 gives the vibrations representing the IR peak clusters at ca. 460-470 cm-1

to demonstrate the Fe centred vibrations. In the eclipsed Fc (D5h), the first IR peak

at υ1 = 471.23 cm-1 which is assigned to a2” is not as strong as the second peak at

υ2(1), υ2

(2) = 488.70 cm-1 which is assigned to the doubly degenerate state of e1’.

The υ1 peak at 471.23 cm-1 of the IR spectrum of eclipsed ferrocene exhibits the

vibration in which the Fe atom moves up and down against the flipping directions

of the Cp rings. That is, if both the Cp rings flip down, the centre Fe atom moves

up and vice versa. The doubly degenerate vibrations of υ2(1) and υ2

(2) of the same

conformer (D5h) at 488.70 cm-1 engage with the centre Fe atom wobbling left and

right, as shown in Fig. 6.11. The Fe atom plays a central role in these vibrations.

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188

Due to the orientation differences of the Cp rings in the eclipsed ferrocene, the

three vibrations present two IR spectral peaks in a 1:2 ratio and a ca. 17 cm-1 split.

The vibrations of D5d exhibit a single spectral peak at ca. 460 cm-1. This peak in

fact consists of two vibrational lines of one doubly degenerate vibrations of υ1(1),

υ1(2) = 459.23 cm-1 and a less intensive transition at υ2 = 461.27 cm-1. The theory

predicts that the transitions are ∆υ = 1.74 cm-1 apart which is insufficient to be

measured by experiment even with state-of-the-arts high resolution IR technique.

The more intensive transition υ1 of D5d is associated with a doubly degenerate Cp

rings flips up and down which leads to the middle Fe atom vibration apparently.

The less intensive transition υ2 at 461.27 cm-1 reveals the pentagonal Cp ring

waging vibration which is similar to sugar puckering of tetrahydrofuran [52-54]

(THF). As seen in Fig. 6.11 the centre Fe atom of D5d exhibits a left and right

wagging vibration.

Fig. 6.11: The IR spectra of the eclipsed (D5h) and staggered (D5d) ferrocene in the fingerprint region.

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189

6.3.5. Influence of deuteration on the IR spectra

Deuteration can be defined as the change of more common isotope of hydrogen

(i.e. protium or light hydrogen, 1H) with deuterium (D or 2H). The nucleus of

deuterium contains one proton and one neutron, while the nucleus of protium

contains no neutron. As a result, deuterium or 2H is heavier than the normal

hydrogen (1H). Such differences in atomic mass have considerable impact on

many physical and chemical properties of deuterated compounds compared to the

hydrogen analogues. For example, vibrational spectra of the molecules will

change upon deuteration. For a fixed vibrational force constant, the transition

energy decreases as the mass of the oscillator increase. Because of this, the

vibrational spectrum of a sample is different than its deuterated analogue. In fact,

selective manipulation of a sample by deutration is a well-known experimental

method for the identification of vibrations involving hydrogen atoms [55].

Lippincott and Nelson employed the vibrational spectrum of fully deuterated

ferrocene (Fc-d-10) to assist in the band assignments of ferrocene spectrum [39].

In their experimental study, the spectrum of Fc-d-10 was exploited for

distinguishing between the CC and CH modes. These days, one can easily

visualize the simulated vibrations and easily realize the band assignments. Tools

such as Gaussview [42] easily allow calculated vibrational data to be displayed as

dynamic screen motions. However, simulation of Fc-d-10 may still reveal useful

information such as differences between ferrocene conformers. As a result, we

have simulated the infrared spectra of fully deuterated ferrocene (Fc-d-10) both

for eclipsed and staggered conformers in isolation (gas-phase). Results are given

in Fig. 6.12 and Table 6.3.

Fig. 6.12 compares the simulated infrared spectra of D5h and D5d conformers of

ferrocene (Fc-h-10) with those of Fc-d-10 in the region of 400-4000 cm-1

simulated using the B3LYP/m6-31G(d) model. The two bottom spectra are for Fc-

d-10 and the upper ones are for Fc-h-10. There is not any scaling or manipulation

in the present simulation.

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190

It can be seen from Fig. 6.12 that the spectra of both D5h and D5d Fc-d-10

conformers exhibit apparent red-shifts compared to those of Fc-h-10, except for

Band A. However, such red-shifts are more apparent for bands involving

hydrogen vibrations, resulting from large differences in masses between Fc-h-10

and Fc-d-10. For example, the IR peak at 3257 cm-1 (Band F) for D5h conformer of

Fc-h-10 is shifted to 2413 cm-1 in its deuterated analogue. This represents a shift

by factor of 1.35, in agreement with factor of 1.34 which is reported in Ref. [39].

This band is due to the CH stretch mode. It is also apparent that the intensities of

all bands are decreased more or less for all Fc-d-10 bands compared to those of

Fc-h-10 analogue. Table 6.3 reports the IR spectral frequencies in the region of

400-4000 cm-1 for the major non-zero intensity (I≠0) transitions for D5h and D5d

conformers of ferrocene and their deuterated analogues.

Fig. 6.12: The IR spectra of the eclipsed (D5h) and staggered (D5d) ferrocene (Fc-h-10) and deuterated ferrocene Fc-d-10.

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Table 6.3: Calculated IR frequencies and their assignment for the D5h and D5d conformers of Fc-h-10 and Fc-d-10 and their corresponding spectral shifts.

D5h a D5d

a Exp. b Assignment Band υ(Fc-h-10)c

(cm-1) υ(Fc-d-10)d

(cm-1) Δυh-d

e (cm-1)

υ(Fc-h-10)

(cm-1)

υ(Fc-d-10)

(cm-1)

Δυh-d

(cm-1) υ(Fc-h-

10) (cm-1)

υ(Fc-d-10)

(cm-1)

Δυh-d

(cm-1)

A 471 443 28 459 436 23 480 452 28 ν FeCp

A 488 477 11 461 450 11 496 476 20 Ring tilt

B 844 652 192 848 652 196 816 638 178 γ CH

B 870 674 196 871 673 198 840 671 169 Asymmetric γCH (2 CH upward, 2 CH downward)

C 1035 797 238 1035 797 238 1012 775 237 δ CCH

D 1141 1083 58 1139 1083 56 1112 1070 42 Breathing(one Cp shrinks, one Cp expands)

E 1470 1350 120 1469 1350 119 1416 1358 58 Asymmetric ν CC: Cp, in plane δ CCH

F 3257 2413 844 3256 2413 843 3106 2354 752 ν CH

ν= Stretch γ= Out of plane δ=Bend a Simulated in vacuum using B3LYP/m6-31G(d) model. b Ferrocene IR vapour, See [39]. c Ferrocene having ten 1H hydrogen. c Ferrocene having ten 2H hydrogen (fully deuterated). d Δυh-d=υ( Fc-h-10)-υ( Fc-d-10).

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192

In Table 6.3, the simulated IR frequencies of Fc-h-10 and Fc-d-10 are compared

to the experimental data from Lippincott and Nelson study [39]. This table also

compares the results obtained from the preliminary analysis of spectral shifts upon

deutration. In the table, Δυ indicates the difference between frequencies of Fc-h-

10 major bands and their corresponding Fc-d-10 bands.

As seen in Table 6.3, vibrations involving hydrogen motions change more from

Fc-h-10 to Fc-d-10. For example, the frequencies due to CH stretch (νCH, Band

F) show a significant redshift as large as 844 cm-1 for both D5h and D5d

conformers, respectively (experimental value is 752 cm-1 [39]). Another

significant red-shift is observed for vibrations related to CCH bending (i.e. Band

C, δ CCH in Table 6.3). For both D5h and D5d conformers, this band is shifted by a

factor of 1.30 in Fc-d-10, which is in excellent agreement with experimental

factor of 1.30 for the same band [39]. The out of plane CH vibration (i.e. Band B,

γ CH in Table 6.3) is shifted from 844 cm-1 to 652 cm-1 in Fc-d-10 (D5h). This

means that this band is shifted by a factor of 1.30. This band is shifted by the

same factor (i.e. 1.30) for D5d conformer. The frequencies due to the asymmetric

out of plane CH motions (i.e. asymmetric γCH in the table) are observed at 870

cm-1 and 871 cm-1 in D5h and D5d conformers of Fc-h-10, respectively. These

frequencies are shifted by a factor of 1.29 to 674 cm-1 and 673 cm-1 in eclipsed

(D5h) and staggered (D5d) conformers of Fc-d-10, respectively. Analysis of the

results in Table 6.3 indicates that D5h and D5d conformers exhibit very similar

ferrocene (Fc-h-10) and Fc-d-10 bands for modes due to CH vibrations.

Fig 6.12 clearly shows that Band A does not exhibit significant shift, irrespective

of conformer and isotopes. Further analysis of the vibrations in the IR spectral

region near 500 cm-1 reveals interesting results. As mentioned earlier, the

vibrations in this region are dominated by vibrations involving the centre Fe atom.

It was discussed in section 6.3.3 that for eclipsed ferrocene (D5h, Fc-h-10), the

first IR peak at υ1 = 471.23 cm-1 is assigned to a2”, whereas the second peak at

υ2(1), υ2

(2) = 488.70 cm-1 is assigned to the doubly degenerate state of e1’. For the

deuterated analogue of eclipsed ferrocene (D5h, Fc-d-10), the υ1 peak is shifted by

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193

a factor of 1.06 to 443.14 cm-1 and υ2 peak is shifted by a factor of 1.02 to 477.14

cm-1. This means that the splitting (Δυ) between υ1 and υ2 is 17 cm-1 for eclipsed

ferrocene (Fc-h-10), whereas 34 cm-1 for eclipsed Fc-d-10. As a result, this

splitting has increased by the deutration of ferrocene.

As explained earlier in section 6.3.3, for the staggered conformer of ferrocene

(D5d, Fc-h-10), the first IR peak at υ1(1), υ1

(2) = 459.52 cm-1 is assigned to a doubly

degenerate state of e1u, whereas the second peak at υ2 = 461.23 cm-1 is assigned to

a2u. The splitting between υ1 and υ1 is very tiny, i.e. ca. 2 cm-1. However, for the

deuterated analogue of D5d ferrocene (Fc-d-10), υ1 is assigned to a2u, but υ2 is a

doubly degenerate states being assigned to e1u. Therefore, the degeneracy and the

symmetry assignment of the D5d conformer of ferrocene in this region (ca. 500

cm-1) are swapped compared to its deuterated analogue, while no such swapping

is observed for D5h conformer.

Examination of the positions of υ1 and υ2 in staggered Fc-d-10 reveals that υ1 is

shifted by a factor of 1.05 to 435.76 cm-1 in Fc-d-10, while υ2 is shifted by a factor

of 1.02 to 449.82 cm-1. This corresponds to a splitting of 14.06 cm-1 between υ1

and υ2 in staggered Fc-d-10. As was seen in Fig. 6.10, the splitting (Δυ) between

υ1 and υ2 in staggered conformer of ferrocene was so tiny that it couldn’t appear as

two peaks in its IR spectrum. However, Δυ is large enough for its deuterated

counterpart to appear in the IR spectra.

By comparing the splitting (Δυ) of the IR spectra of ferrocene and Fc-d-10 (in the

fingerprint region, ca. 500 cm-1), it is observed that the splitting between spectra

has been enhanced in Fc-d-10. For example, Δυ has increased from 17 cm-1 → 34

cm-1, 2 cm-1 → 14 cm-1 and 16 cm-1 → 24 cm-1 for simulated D5h, simulated D5d

and experimental ferrocene upon deutration, respectively.

Fig. 6.13 gives the IR peaks at ca. 460-470 cm-1 for ferrocene eclipsed (D5h) and

staggered (D5d) conformers and their deuterated analogues. This figure clearly

shows the widening of the splitting (Δυ) of the IR spectra of ferrocene upon

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194

deutration. It can also be seen from this figure than deutration of ferrocene results

in the red-shift of the IR spectral peaks.

Fig. 6.13: The IR spectra of the eclipsed (D5h) and staggered (D5d) ferrocene (Fc-h-10) and deuterated ferrocene (Fc-d-10) in the fingerprint region.

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195

6.3.6. Infrared spectroscopy of ferrocene in solution

As seen previously in section 6.3.3, the B3LYP/m6-31G(d) model accurately

simulated the IR spectra of Fc without scaling in gas phase, as the basis set [8] for

the central Fe atom of the sandwich compound plays a significant role [28]. For

the Fe atom, the modified 6-31G(d) basis set, i.e., m6-31G(d) is an appropriate

basis set for accurately modelling the IR spectra of the complexes containing Fe.

In the present section, we provide a combined study of DFT calculations with

high-resolution FTIR experimental measurements in various solvents, in order to

validate the earlier theoretical prediction of the Fc conformers.

Fig. 6.14 compares the FTIR spectral region of 400-1200 cm-1 in a number of

different solvents at room temperature. The FTIR spectra were recorded in non-

polar solvents such as acetonitrile (ACN, ε=35.69), dichloromethane (DCM,

ε=8.93) and tetrahydrofuran (THF, ε=7.43). As seen in this figure, all spectra

exhibit four major bands at ca. 480-500 cm-1 (Band A), 820 cm-1 (Band B), 1010

cm-1 (Band C) and 1100 cm-1 (Band D). Band A at ca. 480-500 cm-1 consists of

two peaks: a peak of lower intensity at 479.5 cm-1 and another one at 495.0 cm-1.

The latter has a higher intensity. Band B at ca. 820 cm-1 presents two small

shoulders. One of these shoulders is located on the right side, and the other one is

located on the left side of the main peak. From FTIR spectra illustrated in Fig.

6.14, it is apparent that the positions and the intensities of these shoulders slightly

vary in different solutions.

Fig. 6.14 also shows that the Band C at ca. 1010 cm-1 exhibits slightly different

intensity when measured in different solutions. For example, the intensity of this

peak is higher in DCM compared to that of ACN and THF solutions. There are no

significant differences associated with these three solvents for Band D at ca. 1100

cm-1. Perhaps the most noticeable difference is a slightly lower intensity of this

peak in THF solution compared to that of ACN and DCM. The present FTIR

spectra in solutions consistently show excellent agreement with the experimental

IR spectrum of ferrocene reported by Duhovic and Diaconescu in the DCM

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196

solution [56] as well as the early IR spectrum of Fc published by Lippincott and

Nelson [39] in chloroform solution (CCl4) at room temperature.

Fig. 6.14: Measured FTIR spectra of ferrocene in the region of 400-1200 cm-1 in a number of solvents at room temperature.

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197

To further validate the measured FTIR data, Table 6.4 reports the Fc IR spectral

peak positions in the solutions and compares with other experimental

measurements and calculations in 400-1200 cm-1. It can be seen from the data in

Table 6.4 that the present experimental measurements in different non-polar

solvents consistently agree with the available IR measurements in solutions in this

region. For example, the IR spectral peak positions in the dichloromethane

(DCM) solution were measured as 478 cm-1 and 494 cm-1, 822 cm-1, 1004 cm-1

and 1106 cm-1 in a recent study [56]. The present FTIR measurement reports these

peaks at 478 cm-1 and 495 cm-1, 820 cm-1, 1005 cm-1 and 1107 cm-1. As a result,

the present experimental measurement in DCM solution almost exactly

reproduced all IR spectral peak positions in the region of 400-1200 cm-1. The

experimental results, as shown in Table 6.4, indicate that the positions of the

spectral peaks measured in the non-polar solvents are almost identical, which

are consistently reported within ±3 cm-1 of accuracy. This reveals that the

influence of the solvent on the IR spectra of Fc is small and negligible.

Table 6.4: Comparison of the measured Fc spectral peak positions in various solvents and available experiment and calculations.

This Worka Ref.[56] Ref.[26] Ref.[39]

Expt. B3LYP/m6-31G(d)

Expt. B3LYP/ 6-31G*b

B3LYP/ Type-I

Expt.

ACN DCM THF DOX DOXa Gas[28] DCM Gas Gas CCl4 Gas

υ1 480 478 479 479 471 471 478 480 470 478 480

υ2 496 495 495 495 489 488 494 510 473 492 496

υ3 823 820 820 821 845 844 822 844 825 811 816

υ4 1006 1005 1005 1006 1033 1035 1004 1036 1017 1002 1012

υ5 1107 1107 1108 -c 1141 1141 1106 1140 1141 1108 1112

a DFT model: SMD-B3LYP/m6-31G(d). b A scaling factor of 0.95 was employed in the calculations in Ref. [56] and private communications (2013). c The spectrum cut off in this solution was after 1100 cm-1 as the measurement in this solution concentrated in the region under 1000 cm-1.

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198

Comparisons between the theoretical and the experimental IR spectra of ferrocene

are made using Fig 6.15. This figure compares the measured FTIR spectrum

(middle panel) of Fc in the acetonitrile (ACN) solution with the simulated infrared

spectra of the eclipsed (D5h, top panel) and the staggered (D5d, bottom panel)

conformers of ferrocene in the region of 400-1200 cm-1. In the simulations

reported in Fig. 6.15, the implicit solute molecular density (SMD) model [13] is

applied.

Fig. 6.15: The measured IR spectrum (middle panel) of Fc in acetonitrile (ACN) solution with

the simulated infrared spectra of the eclipsed (D5h, top panel) and the staggered (D5d, bottom panel) conformers of Fc in the region of 400-1200 cm-1. The spectrum clearly indicates the

dominance of eclipsed Fc in this solution.

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199

It can be seen from Fig. 6.15 that the overall agreement between simulations and

experiment (FTIR) is excellent. For example, the major FTIR spectral peaks in the

measurement (middle panel) are reproduced by the simulations of both Fc

conformers. For instance, the measured peak positions are given at 480 cm-1,496

cm-1, 823 cm-1, 1006 cm-1 and 1107 cm-1 in the ACN solution. In the simulated IR

spectrum of the eclipsed Fc conformer in the same solution, these spectral peaks

are calculated as 467 cm-1/484 cm-1, 852 cm-1, 1027 cm-1 and 1133 cm-1,

respectively, without any scaling and shifting. These IR peaks of the staggered Fc

conformer, on the other hand, are given by 458 cm-1 (only one peak), 854 cm-1,

1029 cm-1 and 1134 cm-1, accordingly, under the same conditions.

From Fig. 6.15 it can be seen that only the IR spectral peak(s) of the eclipsed Fc

conformer in the region less than 500 cm-1 splits into two peaks. For the simulated

IR spectrum of D5h conformer, a more intensive peak at a larger frequency (i.e.

495 cm-1) and a less intensive peak at a smaller frequency (i.e. 479 cm-1) are

observed. The staggered Fc conformer, however, does not show such the splitting,

in agreement with our previous study in gas phase [28] (discussed in section 6.3.3

of this chapter).

In addition to the present experimental FTIR measurement, such IR spectral

splitting of Fc has also been observed by a number of earlier experiments

including the ones reported by Lippincott and Nelson [39] and Duhovic and

Diaconescu [56]. Therefore, the most striking result to emerge from comparing

the simulated and the measured IR spectra presented in Fig. 6.15 is that the

measured IR spectra is more likely related to dominance of eclipsed ferrocene

conformer in solution. As explained earlier in section 6.3.3, this particular spectral

feature in the IR fingerprint region of 400-500 cm-1 can be considered as the

signature of the eclipsed Fc conformer.

From Fig 6.15 it is also noticeable that the calculated spectral peaks red-shift (i.e.

shift to smaller wavenumbers) in the region below 500 cm-1 but blue shift (i.e.

shift to larger wavenumbers) in the spectral region above 500 cm-1 compared to

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200

the measurements (Expt.). Further investigation into the related vibrations reveals

that the spectral peak(s) in the region below 500 cm-1 are associated with Fe-C

stretches, whereas the vibrations at 845 cm-1, 1032 cm-1 and 1141 cm-1 are

assigned to C-H out of plane, C-C-H bend and Cp breathing (one Cp shrinks, one

Cp expands) vibrations, respectively. This is in agreement with the gas-phase

studies of ferrocene (discussed in section 6.3.3 ) [26, 28, 39]. Previous studies [26,

57, 58] indicated that the scaling factors of simulated IR spectra (force field) of

compounds are usually smaller than 1.0 [59-61]. That is, the calculated vibrational

frequencies are usually larger than the measurement, except for the Fe-C stretch

vibration which needs a scaling factor as large as 1.25 [26] (1.02 in the present

study due to the more suitable m6-31G(d) basis set), i.e., the calculated

frequencies of Fe-C related vibrations are smaller than the measured ones.

Table 6.5 compares the measurement and calculations for the spectral peaks of the

eclipsed Fc in different solutions. The largest error is within 4% between the

measurements and calculations in the region of 400-1200 cm-1, indicating that the

theoretical model is sufficiently accurate for the Fc conformers. The red shift (by

colour) for the Fe related vibrations and the blue shift for other vibrations are

apparently shown in this table.

Table 6.5: Comparison of the measured and simulated Fc IR spectral peak positions in various solvents in the region of 400-1200 cm-1.

ACN (ε=35.69) DCM(ε=8.93) THF(ε=7.43) DOX(ε=2.21)

Expt Calca ∆υb Expt Calca ∆υb Expt Calca ∆υb Expt Calca ∆υb

υ1 480 467 -13 478 466 -12 479 467 -12 479 471 -8

υ2 496 484 -12 495 484 -11 495 485 -10 495 489 -6

υ3 823 852 29 820 850 30 820 851 31 821 845 24

υ4 1006 1027 21 1005 1029 24 1005 1029 24 1006 1033 27

υ5 1107 1133 26 1107 1134 27 1108 1134 26 - 1141 -

(a) Simulation DFT model: SMD-B3LYP/m6-31G(d). (b) Spectral shift: ∆υ = υcalc.-υexpt.

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201

The present study will concentrate on the IR spectra of the eclipsed Fc in the

region of 400-500 cm-1, as the most noticeable feature of the FTIR spectra in Fig.

6.14 and Fig. 6.15 is the spectral peak splitting in the region of approximately

480-500 cm-1 in all solutions. The major peak locates at 495 cm-1, whereas the

minor peak locates at 479 cm-1 (note that the resolution of the Bruker Tensor

FTIR spectrometer is 1 cm-1), with a measured spectral splitting of approximately

16 cm-1 in the ACN solution. The splitting of the twin peak agrees well with the

earlier IR measurement of Lippincott and Nelson [39], in which the spectral peaks

located at 492 cm-1 and 478 cm-1 in chloroform solution with a spectral splitting of

14 cm-1, and with the recent FTIR measurement at 478 cm-1 and 494 cm-1 in DCM

solution with a splitting of 16 cm-1 of Duhovic and Diaconescu [56]. Note that the

present IR calculations do not use any scaling, whereas the calculated IR spectra

of Ref. [56] employed a scaling factor of 0.95.

In order to simulate solvation effects on the simulated infrared (IR) spectra of

ferrocene, implicit continuum solvation methods are employed in this thesis. Of

the implicit solvent models, some are able to reproduce the experiment

measurements better than other solvent models. Figure 6.16 compares the

simulated IR spectra of eclipsed (D5h) Fc in dioxane (DOX) solution using three

different models including polarizable continuum model (PCM) [26], C-PCM

(conductor PCM) [27, 28] and SMD (solute molecule density) [29], with the

present FTIR spectral measurement.

The solute molecule density (SMD) model seems to achieve a slightly more

accurate agreement with the measurement over the PCM and C-PCM models. As

shown in Fig. 6.16, PCM and CPCM model produce almost exactly the same

result for the peaks in the spectral region below 500 cm-1. For instance both

models predict the frequency of the first peak (i.e. the one with lower-intensity) at

469 cm-1 and the that of the second peak at 487 cm-1 (i.e. the one with higher-

intensity). This means that the deviation from the experimental values, as

presented in the figure, is 10 cm-1 for the first peak and 8 cm-1 for second peak.

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202

The PCM and C-PCM solvent models only implicitly consider the solvation

effects in the form of a polarizable continuum model rather than individual

molecules. For example, the conventional PCM model (also called dielectric PCM

or D-PCM [36]) treats the solvent as a polarizable dielectric continuum medium.

For non-polar solvents the PCM and C-PCM models do not show apparent

differences over the IR spectra of Fc.

Fig. 6.16: The simulated IR spectra of eclipsed Fc in the DOX solution using three different solvation models (PCM, CPCM and SMD) with the FTIR spectral measurement. The SMD

model show slightly more accurate spectrum.

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203

Fig. 6.16 also shows that SMD model predicts the frequencies of the first and the

second peak at 471 cm-1 and 489 cm-1, respectively. As a result, the deviations

from the experimental values in the figure are 6 cm-1 for the first peak and 8 cm-1

for the second peak. The solute molecule density (SMD) model is a continuum

solvation model based on the quantum mechanical charge density of a solute

molecule interacting with a continuum description of the solvent. From the

deviation data, it can be concluded that the SMD model simulates the IR spectra

of Fc in solutions more accurately and therefore, it is employed to simulate the

solvent effects on the IR spectra of ferrocene in this thesis.

From the previous figure (Fig. 6.16), it can be seen that the simulated (D5h, SMD)

and the measured (FTIR) spectra of ferrocene in the fingerprint region in dioxan

(DOX) solution are in excellent agreement. To investigate solvent effects, Fig.

6.17 compares the simulated IR spectra of the eclipsed Fc in the region of 400-

600 cm-1 with the FTIR measurements in several solvents. The theory (simulation)

employs the DFT based B3LYP/m6-31G(d) model in conjunction with the SMD

continuum solvent model to simulate the IR spectra of the eclipsed Fc in THF,

DCM, ACN and DOX solvents. The theoretical spectra of the eclipsed Fc (D5h)

are produced in the present study without any scaling. However, the simulated

spectra in Fig. 6.17 are presented with a blue shift of 6 cm-1 and 10 cm-1 for

DOX and THF solvents, respectively, and of 11 cm-1 for DCM and ACN solvents.

As seen from this figure, after small shifts, the simulated spectra agree well with

the measurements including the twin peak splitting of the eclipsed Fc.

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Fig. 6.17: Comparison of the simulated IR spectra of the eclipsed Fc in the region of 400-600 cm-1 with the FTIR measurement in various solvents. Small shift to align the larger peak is

applied.

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205

6.4. Ferrocene-based electrolyte

So far chapter has focussed on the structure and properties of the ferrocene

conformers. The following section will discuss some of the properties of ferrocene

which needs to be investigated when considering ferrocene application in dye

sensitized solar cells.

6.4.1. Ferrocene/ferrocenium redox potential

Rational approach can be taken to design not only new dye sensitizers, but also

new redox mediators. In chapters 3-5 of this thesis, several rational design

strategies for the development of new dyes have been discussed. The aim of the

current chapter was to study the ferrocene compound as an important candidate

for the redox system. So far this chapter has focussed on the structure of the

ferrocene compound. Turning now to the application of ferrocene in dye

sensitized solar cells (DSSC), the electrochemical characterization of

ferrocene/ferrocenium (Fc/Fc+) redox couple will be discussed hereafter. In

addition, an accurate model for computing the redox potential of Fc/Fc+ redox

couple will be given. This model is particularly important for the rational design

of ferrocene derivatives as new redox couples.

The redox couple, as its name suggests, contains two parts, an oxidizing agent

(oxidant) and a reducing agent (reductant). For example, ferrocene (Fc) is the

reducing part in the Fc/Fc+ redox couple. It means that Fc reduces the dye cation.

This reaction is known as “dye regeneration”. The ferrocenium (Fc+) cation

should be reduced to ferrocene at the counter electrode of the cell. This step is

known as the diffusion of the oxidized form of the redox shuttle (e.g. Fc+ in this

example) to the counter electrode, which completes the electrochemical circuit in

DSSC [62]. As seen, the redox couple functions as one of the key components in

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the DSSC. In addition, the open circuit voltage of the cell depends on the redox

couple in the electrolyte [63] (as well as the semiconductor (TiO2)).

There is a large volume of published studies on the redox properties of the

ferrocene/ferrocenium (Fc/Fc+) couple [64-76]. Such considerable attention in

electrochemistry of ferrocene stems from the recommendation of the international

union of applied chemistry (IUPAC) for employing Fc/Fc+ as the reference redox

system in non-aqueous solutions [77]. In addition, derivatives of ferrocene can be

prepared relatively easy by modifications of the cyclopentadienyl rings [78-83].

This allows tuning the redox behaviour of the redox mediator. Such feature also

facilitates rational design of new redox couples based on ferrocene and its

derivatives for the application in DSSC [1].

Ferrocene-based redox couples were not considered as serious alternative to the

conventional iodide/triiodide redox couple until recently. That is because the

previous attempts to replace the iodide/triiodide with ferrocene-based redox

couples led to very low efficiencies (η<0.4%) [84, 85], where changes have only

been made on a single component (i.e. redox couple); whereas the dye sensitizer,

i.e. conventional N3 dye remained unchanged. In 2011, a high-efficiency DSSC

was reported by Daeneke et al., in which Fc/Fc+ redox couple was employed in

combination with a novel organic dye sensitizer (i.e. Carbz-PAHTDTT) [2]. This

cell could achieve energy conversion efficiency (η) of 7.5% under simulated one

sun irradiation (AM1.5, 1000 Wm-2). In a follow-up study published in 2012, the

same authors investigated ferrocene derivatives as redox mediator [1]. The focus

of this latter work was “to examine the effect of the redox potential on charge

transfer process” [1]. Here, the authors chose six already-available (synthesized)

ferrocene derivatives which could cover a redox potential range of 0.09-0.94 V vs.

normal hydrogen electrode (NHE). Such investigation heightens the need for the

“rational design” of alternative redox mediators such as ferrocene derivatives

with desirable redox potential.

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207

A feasible and applicable direction for rational design of ferrocene derivatives

should focus on the modifications of the cyclopentadienyl rings with the aim of

achieving an specific target redox potential (i.e. tuning the redox-potential).

Density functional theory (DFT) has been proven a reliable tool to calculate the

redox potential of couples based on ferrocene [64, 86, 87], ferrocene derivatives

[87], other transition metal complexes [86, 88-95], actinide systems [96] and

organic compounds [97]. As a result, DFT model can be employed for the rational

design of ferrocene derivatives. Here, we probe the performance of the

B3LYP/m6-31G(d) model to accurately reproduce the absolute redox potential of

Fc/Fc+ couple in dimethyl sulfoxide (DMSO) solution. To the best of our

knowledge, this model has not been employed for such calculations on ferrocene.

If this model reproduces the experimental redox potential accurately, it is

anticipated to reproduce the redox potential of ferrocene derivatives, and thus

facilitates the rational design of alternative ferrocene-based electrolyte for DSSC.

The previous results in this chapter showed that D5h is the dominant conformation

of gas-phase ferrocene. Therefore only the eclipsed form is considered to calculate

redox potential. The required values to calculate the redox potential from eq. (6.1)

are given in Table 6.6. These values are obtained from the outputs of geometry

optimization and frequency calculations of Fc and Fc+ in gas and in DSMO

solution.

Based on the values given in Table 6.6, we calculated the redox potential, Em0/+ =

5.079 V. This result is in a very good agreement with the experimental value of

5.10 V. Note that it is calculated from the experimental value of 0.43 V for the

reduction potential of Ferrocene+1/0 couple relative to the reference saturated

calomel electrode (SCE) in DMSO reported by Connelly and Geiger [98]. A

recent value of 4.67 V for nonaqueous SCE [97] is considered in this calculation.

The agreement shows the reliability of the model used here (i.e. B3LYP/m6-

31G(d)) for the calculations of ferrocene features in agreement with our previous

calculations on ferrocene infrared spectra using the same model [28]. To the best

of our knowledge, this is the first time that this model is used to calculate the

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208

absolute redox potential of ferrocene. These findings suggest that the B3LYP/m6-

31G(d) model is suitable in the prediction of the redox potential of ferrocene-

based couples. As a result, this model can be used to develop rational design and

screening procedures aimed at designing new redox couples based on ferrocene-

derivatives with desirable redox values.

Table 6.6: Calculated values required to obtain the redox potential of Fc/Fc+ in

DSMO solution. All energy values are in hartree (Eh).

Fc Fc+

SCFE(g)a -1650.66 -1650.41

GibbsCorrb 0.14 0.137

Gc -1650.52 -1650.27

ΔGox(g)d 0.25

SCFE(solv)e -1650.67 -1650.48

∆Gsolvf -0.0037 -0.0700

∆Gox(solv)g 0.19

a. Energy of the optimized system in gas-phase. b. Thermal correction to Gibbs free energy. c. Absolute value of the Gibbs free energy. G= SCFE(g)+ GibbsCorr d. The free energy change due to oxidation reaction of Fc to Fc+ in the gas phase. ΔGox(g)=G(Fc+)-G(Fc) e. Energy of the system with solvent effects. f. The solvation free energies. g. Gibbs free energy change due to the reaction: [Fc]0 (sol) → [Fc]+ (sol).

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6.5. Conclusions

This chapter has investigated the structure and properties of ferrocene as an

important compound for alternative redox mediator preparation. The eclipsed

(D5h) and staggered (D5d) conformers of ferrocene have been investigated. No

properties of Fc have been reported to differentiate the eclipsed and staggered

conformers of Fc until recently [28].

The infrared (IR) spectra of the D5h and D5d conformers of ferrocene have been

simulated using DFT based B3LYP/m6-31G(d) model. It is found that in gas

phase, the eclipsed conformer represents the true minimum structure of ferrocene,

whereas the staggered conformer represents the saddle point structure, in

agreement with a number of other theoretical [24, 45] and recent experimental

studies [35]. The present chapter indicates that the sandwich complexes are

formed by stacking the two Cp rings with an Fe atom in the middle, rather than

being formed with the conventional ten Fe−C bonds as displayed by many of

previous studies of ferrocene. It is further discovered in this study that whenever

the centre Fe is involved, the eclipsed and staggered structures of ferrocene start

to show their unique properties and therefore the conformers can be differentiated

through the fingerprints. The 17 cm-1 IR frequency splitting in the region of 400-

500 cm-1, therefore, becomes one of such fingerprints for the eclipsed conformer

of ferrocene. In addition, the present study suggests that the earlier IR spectral

measurement of Lippincott and Nelson [39] on ferrocene was indeed a mixture of

both eclipsed and staggered ferrocene conformers.

To confirm the aforementioned results, a combined high-resolution Fourier

transform infrared (FTIR) spectra of ferrocene and density functional theory based

quantum mechanical calculations was also performed in this chapter. A number of

non-polar solvents, such as ACN, DCM, THF, and DOX, in a region of 400-1200

cm-1 were investigated. Furthermore, the solutions in high and low concentrations

are measured in the region of 400-600 cm-1, respectively. The measurements

consistently agree well with previously available IR spectra in CCl4 solution of

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210

Lippincott and Nelson [39] as well as the most recent IR spectral measurement in

dichloromethane (DCM) solution [56]. The IR spectra of ferrocene are also

simulated using density functional theory (DFT) based B3LYP/m6-31G(d) model

in dioxane solution for both eclipsed and staggered Fc conformers. All

experimental measurements in solutions unambiguously exhibit an IR spectral

splitting as predicted [99]. When combined the experimental results with theory, it

is concluded that the spectral splitting in the IR fingerprint region of ca. 500 cm-1

must have the structure of eclipsed Fc (D5h), whereas this spectral peak of the

staggered Fc (D5d) do not split. The present chapter further investigated the effects

of solvents on the IR spectra and the solvent model effects on the simulated

spectra. It is found that the IR spectra of ferrocene are not apparently solvent

dependent. Only small spectral shifts are due to different solvent models but the

solute related model, i.e., the solute molecular density (SMD) model seems to

produce the most accurate IR spectrum in the region of 400-600 cm-1 of ferrocene.

Concerning the computational design of alternative redox mediators for dye

sensitized solar cells (DSSC), the results of this chapter show that computational

methods can be employed to accurately calculate the redox potential of

ferrocene/ferrocenium (Fc/Fc+) couple. In particular, we showed that our

B3LYP/m6-31G(d) model is very accurate for such calculations on Fc/Fc+ couple.

An implication of this is the possibility that this model is efficient and accurate in

rational design of new ferrocene-based redox mediators with desirable redox

potential.

Ferrocene Chapter 6

211

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79. G.R. Knox, P.L. Pauson and D. Willison, Ferrocene Derivatives .27. Ferrocenyldimethylphosphine. Organometallics, 1992. 11(8): p. 2930-2933.

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220

Chapter 7

Summary, conclusions and outlook “I never see what has been done; I only see what remains to be done.”

Marie Curie

The full potential of the state-of-art computational methods to design new

materials for solar cells has not yet been realized. In this regard, computational

calculations have usually been performed for understanding the already existing

materials, rather than designing, predicting properties and screening new

compounds. The present thesis has addressed this issue and focused on the

computational modelling of compounds for dye sensitized solar cells (DSSC).

This thesis has focused on two components of DSSC, the dye sensitizer and the

redox couple in the liquid electrolyte.

With regard to the dye sensitizer, this thesis has given an account for the

computer-aided rational design of new dye sensitizers. The strategy employed in

the present work has been chemically modifying the structure of already well-

performing organic dyes (reference dyes) with donor, π-conjugated linker,

acceptor structure (D-π-A), to produce new dyes with reduced HOMO-LUMO

energy gap and red-shifted absorption spectra. The rationale behind such

modifications was producing new dyes with enhanced absorption spectra, as a

route to enhance the efficiency of DSSC. Density functional theory (DFT) has

been exploited to study the ground state properties, while time dependant-DFT

Summary, conclusions and outlook Chapter 7

221

(TD-DFT) has been adopted for the study of the excited states of the compounds.

Considering the size and the complexity of the compounds in this thesis, DFT and

TD-DFT provide good balance between accuracy and performance. The

theoretical models (i.e. combination of the functionals and basis sets) employed in

the DFT and TD-DFT calculations of new dyes, have been validated based on the

agreement with available experimental data for the reference dyes.

Two reference dyes with D-π-A structure have been employed in this thesis.

Modifications have been made on either the D section or on the π-conjugated

spacers (linker) of the reference dyes. With respect to the modifications of the

linkers of the reference dyes, this thesis employed two concepts, the classical

Dewar’s rules (applied on TA-St-CA reference dye), and the electronegativity

(applied on Carbz-PAHTDDT reference dye). Modifications made on the donor

moiety of the reference dye (TA-St-CA) have been based on the concept of

aromatic annulenes.

Dewar’s rules are found to serve as a useful guidance for modifying the π-

conjugated linker of reference dyes with D-π-A structure (e.g. TA-St-CA in this

thesis). Dewar’s rules can be employed to predict how molecular energy levels

change when different groups (electron donating or electron withdrawing) are

substituted on different positions of the conjugated linker. As for the substitution

of electron donating groups, it is found that substitutions on the starred positions

closest to the D moiety of the reference dye produce the lowest HOMO-LUMO

energy gap. It seems that the aforementioned substitutions are the most beneficial

ones for DSSC applications. To the best of my knowledge, this study

demonstrates for the first time that Dewar’s rule can be employed to rationally

design new dye sensitizers for the application in DSSC. The present study might

have an important practical application. It provides a systematic way (based on

Dewar’s rules) to modify an existing well-performing dye. A systematic method

of modifying dye structure provides the possibility to design a software program

for computer-aided rational design of new dye sensitizers. The input for such

software can be the structure of the reference dyes, and the outputs are the


222

structure of the new dyes. Therefore, it is recommended that further efforts be

undertaken to design and code such software program.

This thesis further suggest that modifications made on the donor moiety of the

same reference TA-St-CA dye, are able to produce new dyes with significant

appealing properties for DSSC application. Such properties include reduced

HOMO-LUMO energy gap and expanded absorption range. For example,

replacing the three [6]-annulene rings of the reference dye with three [14]-

annulene rings have produced a new dye, AN-14. Modification of the donor

moiety of the reference TA-St-CA dye has also produced another new dye in this

thesis, the AN-18 dye. This dye has been designed by replacing one of the [6]-

annulene rings of TA-Ct-CA dye with an [18]-annulene ring. The results of this

thesis indicate that both new dyes, AN-14 and AN-18, exhibit reduced HOMO-

LUMO gap and expanded absorption spectra. Furthermore, the rationally

designed AN-14 dye seems to possess a HOMO-LUMO energy gap which is very

similar to that of the N3 dye. The N3 dye is believed to be among the most

efficient ruthenium-based sensitizers for DSSC, and is usually employed as a

benchmark for the evaluation of other dyes. With regards to the absorption of the

sunlight, the TD-DFT calculations on AN-14 and AN-18 indicate that their

simulated absorption spectrum falls within the high photon flux region of the solar

spectrum. As mentioned in Chapter 1, an aim of the current study was to

rationally design new dyes with such absorption profile.

The results of the calculations on new dyes produced by the modification of the

reference TA-St-CA dye, suggest that generally the donor variation have stronger

influence on the studied properties of the new dyes than the linker modifications.

On the other hand, Dewar’s rules provide well-dictated instructions for the

modifications of the linker of the reference dye, which can be employed to

automate the process of designing new dyes. However, the current investigation

of Dewar’s rules to design new dyes was limited by only one reference dye.

Further studies to investigate more reference dyes using the same theoretical set-

up would be very interesting.


223

The present thesis has also studied the structure and properties of the reference

Carbz-PAHTDTT (S9) dye, quantum mechanically. To the best of my knowledge,

no theoretical investigations have been available on this dye until this study. The

findings of this thesis have indicated that the long-range correction to the

theoretical model in the TD-DFT simulation is important to produce accurate

absorption wavelengths for the reference S9 dye. However, calculations of the

frontier molecular energies of the S9 dye indicate that the B3LYP functional

provides the best agreement with the experiment. This finding indicates that

exchange energy is less important than correlation energy for this reference dye.

This thesis further contributes to the existing knowledge about rational computer-

aided design of new dyes, by providing a design based on the concept of

electronegativity. Two new dyes, S9-D1 and S9-D2, were rationally designed by

modifying the π-conjugated bridge of the reference S9 dye. Both new dyes

exhibited improvements over the reference dye. However, S9-D1 has shown

significant red-shifted and broadened absorption spectra, more reduced HOMO-

LUMO gap, better NLO properties as well as noticeable redistribution of the

electron density, compared to the reference dye and the S9-D1 dye. The findings

of this study also suggest that the new dye S9-D1 is a suitable candidate for the

effective sensitization of both TiO2 and SnO2 semiconductors.

With respect to the redox couple, this thesis has focused on the computational

modelling of ferrocene as an important compound for the redox couple in DSSC.

The ferrocene/ferrocenium (Fc/Fc+) redox couple can be addressed once the

structure and properties of ferrocene conformers are well understood. As a result,

this thesis has investigated two aspects of this compound by computational

modelling: (a) the structure and properties of ferrocene conformers and (b) the

ferrocene/ferrocenium redox couple. The structure of ferrocene, which have been

a disputed subject within the organometallic community, have been addressed in

the current thesis, in order to find properties that can differentiate its eclipsed

(D5h) and staggered (D5d) conformers. The present study has found that the centre

Fe atom plays an important role to differentiate the conformers. Results of this


224

research indicated that the conformers of ferrocene clearly show differences in

their simulated IR spectra. The 17 cm-1 IR frequency splitting in the region of

400-500 cm-1, has been found to be a fingerprint for the eclipsed conformer of the

ferrocene in gas phase.

The current thesis has employed the DFT-based B3LYP/m6-31G(d) model to

simulate properties of ferrocene. The agreement of the simulated IR frequencies

with experiment, without any scaling, suggests that the basis set plays an

important role in the accuracy of DFT calculations of ferrocene. The present thesis

has further investigated the effects of the solvents on the IR spectra. Furthermore,

the influence of the solvent model on the simulated spectra has been studied. It is

found that the IR spectra of ferrocene are not apparently solvent dependent. In

addition, the solute molecular density (SMD) model seems to produce the most

accurate IR spectrum in the region of 400-600 cm-1 of ferrocene.

In respect of the computational modelling of alternative redox mediators, results

of the present study suggest that the redox potential of the Fc/Fc+ couple can be

calculated with a great accuracy based on computational modelling. In particular,

the B3LYP/m6-31G(d) model has been found to be a very suitable model for such

calculations on the Fc/Fc+ redox mediator. This finding has an important

implication for future practice. It suggests that the B3LYP/m6-31G(d) model can

be employed to predict the redox potential of new rationally designed redox

mediators which are designed based on the ferrocene scaffold.

The current findings add to a growing body of literature on the computer-aided

rational design of new materials for DSSC. A future study to investigate the

particular modifications made in this thesis on other reference dyes would be very

interesting. More researches are also needed to understand the interaction of the

dye molecule with other component of the cell. For example, future studies may

address the adsorption of the new dyes designed in this thesis on the

semiconductor (e.g. TiO2) surface. Furthermore, experimental studies are also

essential to determine the efficiency of the newly designed dyes, as well as their


225

stability, in real working cells. Finally, it would be interesting to assess the

accuracy of the B3LYP/m6-31G(d) model to predict the redox potential of more

ferrocene-based redox couples. Of the more importance is designing new redox

mediators with desirable redox potential, through computer modelling and

rationally modifying ferrocene structure. New ferrocene-derivatives can be

designed by substituting different groups on the Cp rings of ferrocene.

Appendix

226

Appendix

A-I: Calculated frontier MO energy levels using cpcm-PBE0/6-31G* model in ethanol solution.

Appendix

227

A-II: Comparison of the HOMOs (left) and LUMOs (right) of the new dyes with those of the reference TA-St-CA dye.

HOMO LUMO

TA-St-CA

EDI

EDII

ED-III

EDIV

EDV

EDVI

Appendix

228

HOMO

LUMO

EWI

EWII

EWIII

Appendix

229

A-III: Simulated UV-Vis spectra of TS-St-CA, AN14 and AN-18 by long-range corrected CAM-B3LYP functional.

Although PBE0-based simulations of the UV-Vis spectra show significant shifts

for the light absorption of the new dyes towards infrared region of the spectrum,

these results should be considered with caution. To address the issue of CT

excitations, a time dependant density functional (TD-DFT) calculation using

CAM-B3LYP functional is also performed on the reference and new dyes in

Chapter 4. Fig. A-III.1 compares the UV-Vis spectra of the investigated dyes in

ethanol solution, simulated by the long-range corrected CAM-B3LYP functional.

In the figure, the absorption spectra of the reference TA-St-CA dye is shown in

black line, whereas the spectra of AN-14 and AN-18 dyes are illustrated in red

and blue lines, respectively. The positions of the main absorption bands are also

labelled by λI and λII.

This figure shows the same trend in the absorption spectra as the one in Fig. 4.7.

That is, the UV-Vis spectra of the new dyes AN-14 and AN-18 are generally red-

shifted and broadened compared to the spectrum of the reference TA-St-CA dye.

For example, the band at position I and II of the reference dye are both shifted to

longer wavelengths in the new dyes AN-14 and AN-18. The intensities of both

absorption bands (i.e. peaks at positions λI and λII) in the AN-14 dye are much

higher than the corresponding bands of the reference dye. In addition, the intensity

of the peak at λI is much higher in AN-18 than in the TA-St-CA dye. Such

findings are in agreement with our earlier findings (i.e. Fig. 4.7), which showed

that the light absorption capabilities of the dyes designed in Chapter 4 are superior

to those of the reference dye. The UV-Vis spectra simulated by CAM-B3LYP

indicate that the novel designs of the donor moieties in both AN-14 and AN-18

compounds modify the UV-Vis spectra significantly, both in peak positions and

intensities. However, such influences on the absorption spectra of the AN-14 are

more profound and promising.

Appendix

230

Fig. A-III.1: The simulated UV–Vis absorption spectra of the TA-ST-CA, AN-14 and AN-18 in ethanol solution using the (CAM-B3LYP/6-311G(d)) TD-DFT calculations.

λI

λII

Appendix

231

Fig. A-III.2 compares the UV-Vis spectra of the investigated dyes in ethanol

solution simulated by the long-range corrected CAM-B3LYP functional and

PBE0 functional. As seen in the figure, the spectra simulated by the CAM-B3LYP

functional are blue-shifted compared to those of the PBE0 functional. In addition,

the intensities of the main bands are different. For example, the simulated

absorption spectra of the reference dye using CAM-B3LYP possess a sharp

intense peak at ca. 200 nm, whereas the intensity of this peak is much lower when

simulated by PBE0 functional.

In Chapter 3, it was shown that time dependant density functional calculations of

the reference TA-St-CA dye using PBE0 functional agreed reasonably well with

the experiment, which was only measured in the region of λ< 450 nm, i.e., the

first absorption spectral peak region. As a result, for this region of the spectrum,

the PBE0 functional is more appropriate one to predict the UV-Vis absorption

spectra. On the other hand, the CAM-B3LYP functional is a long-range corrected

functional, which is able to predict the absorption wavelengths at of charge

transfer excitations (which are seen at longer wavelengths) more accurately. As a

result, it might be implied that the absorption peak positions (or wavelengths),

intensities and the absorption pattern simulated by the PBE0 functional are more

reliable in the region of λ< 450 nm. On the contrary, the absorption features

simulated by long-range corrected CAM-B3LYP functional might be more

appropriate for the spectral region of λ> 450 nm. The long-range corrected

functionals are discussed in more details in Chapter 5.

Appendix

232

Fig. A-III.2: Comparison of the simulated UV–Vis absorption spectra of TA-ST-CA, AN-14 and AN-18 dyes in ethanol solution using PBE0 and CAM-B3LYP functionals for TD-DFT calculations.

Appendix

233

A-IV: Results and discussions of the trans-S9 conformation. Since two conformers of the reference S9 dye differ by about 1 kcal/mol, it is

important to probe the conformational dependence of the properties of S9

rotamors (i.e. cis-S9 and trans-S9). Herein a comparison of the results of such

calculations is given.

For trans conformation of the reference S9 dye sensitizer, the frontier molecular

orbital energy obtained by CPCM-B3LYP/6-311G(d)//CPCM-PBE0/6-311G(d)

level of theory are calculated as -4.89 eV, -2.77 eV and 2.12 eV for HOMO,

LUMO, and HOMO-LUMO gap, respectively. These calculated values are in

excellent agreement with the cis conformer. For example, the HOMO-LUMO

energy gap of the trans form differs only by less than 0.05 eV from the calculated

values for cis-S9 conformer using the same level of theory.

Atomic charges according to the natural bond orbital (NBO) scheme of the π-

conjugated bridges of the two conformations are given in Figure S3(a)-(b). As

seen from the figure, the atomic NBO charges are almost exactly the same for

both conformers.

Fig. A-IV.1: The NBO charge of atoms in the linker of cis(a) and trans(b) conformers of

the reference S9 dye. Note that hexanyl chains are not included.

Appendix

234

The βtot are calculated as 805 esu for cis-S9, whereas 621 esu for trans-S9. It can

be seen that the hyperpolarizability of the two rotamors differ by almost 20%.

This finding is in agreement with another study on the conformational dependence

of the first hyperpolarizability of other conjugated molecules [4]. As suggested in

this reference, in such cases one can “consider only one conformation for

estimation of hyperpolarizability” [4].

Based on the mean absolute error (MAE) criterion of the BHandH functional

(employed to calculate the absorption wavelengths of the three most dominant

peaks, Refer to Table S4), the cis-S9 gives MAE of 18 nm whereas the trans- S9

form produces MAE of 29 nm. This suggests that the TDDFT calculations on the

cis-S9 are in better agreement with the experimentally measured values compared

to those of the trans conformer.

Appendix

235

A-V: Experimental absorption spectra of the Carbz-PAHTDTT (S9) and DAHTDTT-13 dyes in DCM solution. Image is reproduced from data available in the supplementary information files of Ref. (J. Org. Chem. 2011, 76, 4088–4093) and Ref. (Nature Chemistry 3, 211–215 (2011).

Appendix

236

A-VI: Estimating the experimental values for HOMO and LUMO. The Experimental energy values for HOMO, LUMO and gap are estimated from

the cyclic voltammetry measurement of the onset point of oxidation Eox of the

dye, based on the explanation and procedure given in the footnote of Table1 (P.

4090) of Ref. (J. Org. Chem. 2011, 76, 4088–4093). This reference article is

published by the same author who has synthesized and published the Carbz-

PAHTDDT dye study (i.e. Nature Chemistry 3, 211–215 (2011)) using the same

experimental settings (e.g. supporting electrolyte, reference electrode, working

electrode, solution, etc.). They cyclic voltammetry data for the Carbz-PAHTDDT

dye are given in the supplementary information file of the Ref.(Nature Chemistry

3, 211–215 (2011)).

Table A-VI.1: The experimental values from the electrochemical measurements in dichloromethane solution

HOMOexpt (eV)a

LUMOexpt (eV)a Eox (V) vs (NHE)b

E0-0 (V) vs (Abs/Em)b

Eox- E0-0 (V) vs (NHE)b

-5.08 -2.97 0.91 2.11 ‐1.20

a. Experimental HOMO and LUMO are estimated as: HOMO = -(Eonset vs Fc+/Fc -4.8 eV), LUMO = HOMO + E0-0. As described in (Table 1, P.4090) of Ref. (J. Org. Chem. 2011, 76, 4088–4093). b. Values taken from the supplementary information file: (Table S3, P.17) of Ref. (Nature Chemistry 3, 211–215 (2011).

Appendix

237

A-VII: Full tensor components for α and β.

Table A-VII.1: The polarizability and the first hyperpolarizability tensor components (in a.u) and total hyperpolarizability (in esu).

Structure αxx αxy αyy αxz αyz αzz βxxx βxxy βxyy βyyy βxxz βxyz βyyz βxzz βyzz βzzz βtot *10-30

(esu)(a)

S9(cis) 2087 -118 1157 -135 52 807 -89930 11813 -1907 1134 9127 -2829 695 -1302 506 465 804

S9-D1 2808 196 1078 -177 -126 845 252260 -8121 793 -590 -6977 178

-69 442 221 -315 2190

S9-D2 2068 93 1104 -155 -81 831 94044 17273 1781 818 -18572 -4008 -624 3242 773 -948 856

(a) βtot is converted from atomic unit (a.u) into electrostatic unit (1 a.u=8.6393 * 10-33 esu).

Appendix

238

Fig. A-VII.1: The optimized structure of S9 and the Cartesian axes.

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