The 9-th Central European Symposium on Theoretical ...The 9th Central European Symposium on...

Centre for Advanced Computational Chemistry: Centre of Excellence of the SASComenius University, Faculty of Natural Sciences Slovak Academy of Sciences, Institute of Inorganic Chemistry

The 9-th Central European Symposium on Theoretical Chemistry

BOOK OF ABSTRACTS

http://www.qch.fns.uniba.sk/cestcNový Smokovec, Slovakia, September 12-15, 2010

Bratislava 2010

ISBN 978-80-223-2907-1

Editors: Jozef Noga, Miroslav Melicherčík, Ivan Černušák


Organizing Committee

Jozef Noga, chairman

Ivan Černušák

Vladimír Kellö

Miroslav Urban

Advisory committee:

Stanislav Biskupič Petr ČárskyIvan Hubač

Bogumił Jeziorski Stanislaw Kucharski

Hans LischkaPeter SurjánPeter Szalay

Miroslav Urban


The symposium was supported by

The 9th Central European Symposium on Theoretical Chemistry

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Contents

PLENARY LECTURES

Roman Čurík: A message to quantum chemists: What we learned about DFT by modelling electron-molecule collisions 10

Christoph Flamm: In silico Evolution of Early Metabolism 11

Thomas S. Hofer, Bernd M. Rode, Bernhard R. Randolf: Characterisation of anisotropic ion hydration via QM/MM models 12

Florent Louis, Romain Vandeputte, Sébastien Canneaux, Marc Ribaucour: Thermochemical data calculation by quantum chemistry methods: application to ten species involved in low-temperature oxidation mechanism of o-xylene 13

Miroslav Medveď, Šimon Budzák, Jozef Noga, Ivan Černušák, Denis Jacquemin, Eric A. Perpète: Study and design of nonlinear optical materials: from molecules, through oligomers to polymers 15

Matthew K. MacLeod, Josef Michl: Trying to Understand the Mysterious Fluorescence of σ Systems: Oligosilanes 16

Monika Musiał: Fock space coupled cluster theory for two-valence sectors 17

Ágnes Nagy: Pair density functional theory 18

Katarzyna Pernal: Treating static and dynamic correlation with range-separated density and density matrix functionals 20

Piotr Piecuch, Wei Li: Local correlation coupled-cluster methods exploiting cluster-inmolecule ansatz and their multi-level generalizations 21

András Stirling: Reaction mechanism from quantum chemistry: unbiased and biased simulations 23

SHORT LECTURES

Prokopis Andrikopoulos, Stepan Sklenak, Zdenek Sobalik: Periodic DFT study of N2O decomposition over Fe-ferrierite 25

Alexei V. Arbuznikov, Hilke Bahmann, Martin Kaupp: Local hybrids: conceptually simple hyper-GGA exchange-correlation functionals for the Kohn-Sham density functional calculation of a wide range of properties 27

Kiran Bhaskaran-Nair, Ondrej Demel, Jir Pittner: Multireference State-Specic Mukherjee’s Coupled Cluster Methods With Triexcitations 29

Petr Čársky: Prospects of using MP2 for electron scattering 31

Kalju Kahn, Bernard Kirtman, Jozef Noga, Seiichiro Ten-no: Anharmonic Vibrational Analysis with Traditional and Explicitly Correlated Coupled Cluster Methods 32


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Dariusz Kędziera, Lukasz Mentel: Wave function in the relativistic two componet methods 34

Tatiana Korona: Local treatment of electron correlation for first-order molecular properties from expectation-value CCSD theory 35

Katarzyna Kulczycka, Joanna Trylska, Joanna Sadlej: Internal flexibility of clindamycin 36

István Mayer: The promotion energy of an atom in a molecule 38

Leszek Meissner: An extension of the coupled-cluster corrected configuration interaction method 39

Mariusz P. Mitoraj, Artur Michalak, Tom Ziegler: A Combined Charge and Energy Decomposition Scheme for Analysis of Chemical Bonds and Reaction Paths 40

Dana Nachtigallová, Mario Barbatti, Jaroslaw J. Szymczak, Hans Lischka: Photodynamics of pyrimidine-based molecules: Effect of substitution and initial energy 41

László Nyulászi, Oldamur Hollóczki: Some predictions on stable molecules: failure and success 42

Ivana Paidarová, Philippe Durand: Kinetic equations and dissipation 43

Łukasz Piękoś, Artur Michalak: Molecular dynamics modeling of half-metallocene titanium(IV) ethylene polymerization catalysts 45

Konrad Piszczatowski, Grzegorz Łach, Michał Przybytek, Jacek Komasa, Krzysztof Pachucki, Robert Moszyński, Bogumił Jeziorski: Relativistic, QED and nonadiabatic effects in the interaction of hydrogen atoms 46

Michał Przybytek, Trygve Helgaker: Gaussian and Finite-Element method for the calculation of Coulomb integrals 48

Dorota Rutkowska-Zbik, Malgorzata Witko: DFT Studies on Catalytic Oxidation of Cyclohexene on Manganese Porphyrins 50

Ján Šimunek, Jozef Noga: Orbital Optimized Second-Order Many-Body Perturbation Theory Via Coupled Cluster Ansatz 52

L. Skala, V. Kapsa: Quantum mechanics and mathematical statistics 54

Ágnes Szabados: The problem of small coefficients in SS-MRPT 55

Péter Szakács, Péter R. Surján: Jahn-Teller distortion and zero-field-splitting in carbon nanotubes 56

Štefan Varga: The Brillouin zone integration problem in density fitting of extended systems 57

Libor Veis, Jiří Pittner: Quantum chemical computations on quantum computers 58


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Aleš Vítek, Lenka Ličmanová, Ivana Paidarová, René Kalus: Structural changes in the water tetramer and hexamer. A combined Monte Carlo and DFT study 60

Zoboki Tamás, Mayer István, Surján R. Péter: Electron Correlation Calculations with Strictly Localized Orbitals 62

POSTERS

Dóra Barna, Gyula Tasi: Energy decomposition of alkyl-substituted furan molecules 64

L. Bucinsky, J. Kozisek, S. Biskupic, D. Jayatilaka, M. Gall: Relativistic effects vs. X-ray constrained Hartree Fock 66

Šimon Budzák, Ivan Černušák, Miroslav Medveď: Weak interactions between air pollutants 67

Sébastien Canneaux, Catherine Hammaecher, Florent Louis, Laurent Cantrel: A Theoretical Study of the H-abstraction Reactions of H2, H2O, HI, and OH by the IO (2Π3/2) Radicals 69

Sébastien Canneaux, Eddy Thiriot, Florent Louis, Laurent Cantrel: SPyDERS: MD Modelling Software for Nuclear Safety 71

Aleksandra Chmielowska, Maria Jaworska, Piotr Lodowski: Structure and electronic properties of A-cluster in Acetyl-CoA synthase: insight from DFT 72

Ondřej Demel, Kiran Bhaskaran Nair, Jan Šmydke, Jiří Pittner: Noniterative triples correction in Mukherjee’s coupled cluster method via uncoupled approach 73

Jozef Federič, Ivan Černušák: MD modelling of tungsten carbide slab 75

R. W. Gora, R. Zalesny, W. Bartkowiak, J. M. Luis, B. Kirtman, H. Reis, M. G. Papadopoulos: Nonlinear optical properties of endohedral fullerene complexes 77

Ireneusz Grabowski, Andrew Teale, Szymon Śmiga, Karol Jankowski: Correlation potentials and electron densities obtained from correlated Optimized Effective Potential method and ab initio Wave Function Theory methods 79

Péter Jeszenszki, Ágnes Szabados, Péter R.Surján: Exact diagonalization of bosonic Hamiltonians 80

Anna Kaczmarek-Kędziera: Properties of encapsulated organic molecules 81

Stanislav Kedžuch, Ondřej Demel, Jiří Pittner, Jozef Noga: Multireference R12 Coupled Cluster Theory 82

Hyungrae Kim, Stepan Sklenak: ONIOM study of the catalytic mechanism of Dihydroneopterin Aldolase 83

Katarzyna Kowalska-Szojda, Monika Musiał, Stanisław A. Kucharski: The factorized quadruple excitations for potential energy surfaces with Λ functional 85

Anežka Křístková, Olga L. Malkina: The use of perturbation-stable localization in calculation and analysis of SO-correction to NMR chemical shifts 86


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Anežka Křístková, Olga L. Malkina, Stanislav Komorovský, Elena Malkin, Vladimir G. Malkin: NMR spin-spin couplings and overlap of densities of localized molecular orbitals 87

Piotr Kubisiak, Andrzej Eilmes: Relative Complexation Energies for Li+ Ion in Solution: Molecular Level Solvation Versus Polarizable Continuum Model Study 88

Mojmír Kývala: Secon-dorder Douglas–Kroll–Heß (DKH2) spin–orbit and parity-violating Hamiltonians 89

Piotr Lodowski, Maria Jaworska, Paweł M. Kozłowski, Tadeusz Andruniów: Quantum chemical calculations of photophysical properties of Methyl- and Adenosylcobalamin 90

Jakub Malohlava, Aleš Vítek, René Kalus: Protonated water clusters – structures and thermodynamics 91

Gergely Matisz, Walter M.F. Fabian, Sándor Kunsági-Máté: Hydrogen bonded clusters around aromatic π-systems 93

Gergely Matisz, Walter M.F. Fabian, Sándor Kunsági-Máté: Liquid structure of primary alcohols (methanol, ethanol, 1-propanol, 1-butanol) within the QCE theory 94

Katarína Mečiarová, Lukáš Demovič, Ivan Černušák: Effect of spin-orbit coupling on potential curves and spectroscopic properties of IO and I2 95

Miroslav Melicherčík, Lukáš Demovič, Michal Pitoňák, Pavel Neogrády: Applicability of Graphical Processing Units to Coupled Clusters Calculations 97

Balázs Nagy, József Csontos, Mihály Kállay, Gyula Tasi: Accurate ab initio heats of formation and standard molar entropies for several atmospherically important formyl derivatives 99

Péter Nagy, Imre Pápai: Catalytic hydrogenation of Quinolines via frustrated Lewis pairs: Mechanistic insight from theory 101

Jana Páleniková, Vladimír Kellö: Electric properties of 2-cyclopenten-1-on 103

Ewa Pastorczak, Katarzyna Pernal, Krzysztof Szalewicz: Long-range corrected dispersionless density functional 104

Lukáš F. Pašteka, Miroslav Urban: Electric properties of low-lying excited states of acetone and their interaction with water 105

Mariusz Pawlak, Mirosław Bylicki, Prasanta K. Mukherjee: Muonic systems with Debye-screened Coulomb interactions 107

Marek Pederzoli, Jiří Pittner: A non-adiabatic molecular dynamics study of azobenzene isomerization after excitation to the S1 state based on overlaps of CASSCF wave functions 108

Robert Ponec, Lukáš Bučinský, Carlo Gatti: Relativistic effects on metal-metal bonding. Comparison of the performance of ECP and scalar DKH description on the picture of metal-metal bonding in Re2Cl8(2-) 109

Mariusz Radoń, Ewa Brocławik, Kristine Pierloot: High Valent Iron-Oxo Complexes with Organic Macrocycles: DFT and Ab Initio Study 110

J. Rimarčík, M. Ilčin, L. Rottmannová, E. Klein, V. Lukeš:


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Quantum Chemical Study of the Energetics of Phenolic Compounds 112

Agnieszka Rogowska, Artur Michalak, Monika Srebro, Mariusz Mitoraj: The Influence of Substituents on the Activity of Half-Titanocene Catalysts for Ethylene Polymerization: Theoretical Study 114

Zoltán Rolik, Mihály Kállay: A local Coupled Cluster algorithm 116

Lenka Rottmannová, Ján Rimarčík, Erik Klein, Vladimír Lukeš: Thermodynamics of homolytic S–H bond dissociation in mono-substituted thiophenols 117

Eva Scholtzová, Pavel Mach: Computational study of weak interactions in the biologically active compounds 119

Jakub Šebera, Stanislav Záliš, Pavel Kubát, Kamil Lang, Tomáš Polívka: TD-DFT investigation of S1 and S2 singlet states of TMPyP(n) and complexes of TMPyP4 with sulfonated calix[m]arenes 121

Lucia Šimová, Pavel Neogrády, Miroslav Urban: Application of OVOS technique in calculations of small semiconductor clusters 123

R. Słupski, J. Komasa, K. Jankowski, J. Wasilewski: Benchmark electron density calculations on Be-like atoms 125

Szymon Śmiga, Ireneusz Grabowski: Comparison of the several correlated OEP methods in KS-DFT with correct asymptotic behavior 127

Jan Šmydke, Petra Ruth Kaprálová: Theoretical Study of Ionization and Excitation of He Gas Exposed to Intense XUV Radiation 129

Lukáš Sobek, Jiří Pittner: Femtosecond non-adiabatic molecular dynamics: a study of photochemical deactivation of indole 131

Roland Šolc, Daniel Tunega, Martin H. Gerzabek, Hans Lischka: Theoretical study of radical sites in gallic and protocatechuic acids 133

Anna Stachowicz, Jacek Korchowiec: Charge Sensitivity Analisys in Force Field Atoms Resolution 135

Miroslav Šulc, Roman Čurík: Cold electron collisions with nonpolar molecules 137

Martin Šulka, Michal Pitoňák, Miroslav Urban, Pavel Neogrády: OVOS technique with controlled accuracy in noniterative triples calculations 139

Nargis Sultana, Walter M. F. Fabian: Substituent effect on OH- addition to substituted benzocyclobutene-1, 2-diones: A DFT study 141

Robert Toboła, Fabien Dumouchel, Jacek Kłos, François Lique: Calculations of fine-structure resolved collisional rates for NH(X3Σ−)-He system 142

Daniel Tunega, Roland Šolc, Hasan Pašalić, Martin H. Gerzabek, Hans Lischka: Wetting of clay mineral surfaces – molecular dynamics simulation 143

Lucie Zárubová, Karel Oleksy: Optimalizations of the molecular clusters by the evolutional algorithms method 145


9

PLENARY LECTURES


10

A message to quantum chemists: What we learned about DFT by modelling electron-molecule collisions

Roman Čurík

J. Heyrovský Institute of Physical Chemistry ASCR Doleškova 3

18223 Prague, Czech Republic [email protected]

We explore an implementation of correlation-polarization interactions for electrons

scattering by polyatomic molecules. The short-range correlation is approximated by local

and non-local DFT models commonly used in quantum chemistry and solid state physics.

We explain a necessity of long-range corrections for needs of collision calculations and

adapt a hybrid model in which short-range correlation is connected to a long-range

polarization potential [1,2]. The long-range polarization is represented by general full

tensor components. Furthermore, we propose a robust and stable technique to calculate

momentum-space matrix elements of such a composite potential. The quality of several

selected DFT functionals is tested by scattering calculations for a class of small

hydrocarbon molecules.

[1] Padial NT and Norcross DW 1984 Phys. Rev. A 29 1742 (1984)

[2] Telega S, Bodo E and Gianturco FA Eur. Phys. J. D 29 357 (2004)

Acknowledgement

It is our pleasure to thank Prof. Baerends (Free University, Amsterdam) for encouraging

discussions and useful suggestions. This work was supported by the Czech Ministry of

Education (grants OC10046 and OC09079) and the Grant Agency of the Czech Republic

(grant 202/08/0631).


11

In silico Evolution of Early Metabolism

Christoph Flamm

Institute for Theoretical Chemistry, University of Vienna, Waehringerstrasse 17,

1090 Wien, Austria [email protected]

Metabolic networks of higher organisms share many key pathways such as

glycolysis or biosynthesis of most amino acids. In the literature several competing

hypotheses for the evolutionary mechanisms that shape these pathways and the

architecture of metabolic networks have been discussed, each of which finds support

from comparative analysis of extant genomes. Alternatively, direct simulation studies on

the the principles of metabolic evolution are rare because of the demanding pre-

requisites. A central component of such a computational model is an algebraic chemistry

model which acts as a substrate on which a metabolism can be selected. This component

must be sufficiently involved to mimic the complexity of a modern metabolic network,

without restricting the possible chemistry to the 'known' extant end results. In addition, a

genetic system that expresses catalysts and a non-trivial map from sequence/structure

features of the catalysts to their respective functions within the metabolic network must

be implemented. Finally, a fitness function that can be selected for and which evaluates

metabolic efficiency is crucial. In my presentation I will give a brief overview of the

dominating mechanisms that governing pathway evolution and the architecture of modern

metabolism, followed by an in-depyh discuss of the various components that comprise

our simulation framework. Finally first results from large-scale evolutionary simulations

will be presented.

[1] Flamm C, Ullrich A, Ekker H, Mann M, Hoegerl D, Rohrschneider M, Sauer S,

Scheuermann G, Klemm K, Hofacker IL, Stadler PF: Evolution of Metabolic

Networks: A Computational Framework. J Sys Chem 1:4 (2010).

[2] Benkoe G, Flamm C, Stadler PF: A graph-based toy model of chemistry. J Chem Inf

Comp Sci 43:1085-1093 (2003).


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Characterisation of anisotropic ion hydration via QM/MM models

Thomas S. Hofer, Bernd M. Rode, Bernhard R. Randolf

Theoretical Chemistry Division. University of Innsbruck

Innrain 52a 6020 Innsbruck, Austria

E-mail: [email protected]

While most mono-atomic ions exhibit a uniform potential in each direction of

space, some species do not follow this example leading to ansiotropic solvation

structures. This behaviour is observed in the case of main group as well as for transition

metal ions. While the presence of stereo-chemically active lone pairs is well-studied in

the case of crystals (e.g. of SnO), experimental and theoretical examinations of the

solvation of these compounds is a challenging and complex task. The construction of

classical interaction potentials enabling an accurate description of the ion-solvent

interaction has to be considered a difficult and challenging task and hence, a quantum

chemical treatment appears to be most practical approach. In particular hybrid

approaches, treating the chemical most relevant region at a quantum mechanical level

while the interactions in the remaining part are evaluated via classical potentials, appear

to be the method of choice. The recently formulated quantum mechanical charge field

molecular dynamics (QMCF MD) approach [1,2] proved to be a versatile tool for the

study of solvated species.

Applications of the QMCF MD framework to anisotropically hydrated ions are

presented. The system covered are Pd2+, Pt2+, Ge2+, Sn2+ and Pb2+.

[1] B. M. Rode, T. S. Hofer, B. R. Randolf, C. F. Schwenk, D. Xenides,

V. Vchirawongkwin, Theor. Chem. Acc. 2006, 115(2-3), 77-85

[2] T. S. Hofer, A. B. Pribil, B. R. Randolf, B. M. Rode,

Adv. Quant. Chem. 2010, 59 213-246

Acknowledgement

Financial support for this work provided by the Austrian Science Fund (FWF) is

gratefully acknowledged.


13

Thermochemical data calculation by quantum chemistry methods: application to ten species involved in low-temperature oxidation

mechanism of o-xylene

Florent LOUIS, Romain VANDEPUTTE, Sébastien CANNEAUX, Marc RIBAUCOUR

PhysicoChimie des Processus de Combustion et de l’Atmosphère (PC2A) UMR 8522 CNRS/Lille1, Université Lille 1 Sciences et Technologies, Cité scientifique, Bât C11/C5, 59655 Villeneuve d’Ascq Cedex, France

Thermokinetic modeling studies of surrogate fuel combustion are carried out to

understand the mechanisms of formation of pollutants and toxic compounds in automotive

engines. A surrogate fuel is composed of molecules representative of each family of compounds

included in a commercial fuel: alkanes, aromatic compounds, cyclanes, alkenes, oxygenated

compounds. Among aromatic compounds, xylenes are good representative of alkylbenzenes.

Their percentages in mass in an European gasoline are 3.06, 5.70, and 1.96% for o-, m-, and p-

xylene, respectively. A low-temperature oxidation thermokinetic model of o-xylene is currently

elaborated in our laboratory. Thermochemical data of species involved in the mechanism are

usually estimated using the THERM software based on Benson group additivity theory. However,

due to missing groups in THERM group database, thermochemical data of many species cannot

be estimated. The aim of this work was to determine thermochemical data of ten species (see

Table 1) using quantum chemistry methods.

Quantum chemistry calculations were performed using the GAUSSIAN03 program suite.

ΔfH°(298 K) were calculated using four composite methods (G3, G3MP2, G3B3, and CBS-QB3)

and isodesmic reaction technique to cancel the systematic error in the molecular orbital

calculations. Sets of five isodesmic reactions were used for each target species. Total energies

were corrected by ZPVE and vibration frequencies were scaled using appropriate scaling factors.

Final values of ΔfH°(298 K) were obtained by averaging the values obtained from each isodesmic

reaction and then by averaging the averaged values given by each calculation method. They are

reported in Table 1. For species 4-7 owing many conformers, ΔfH°(298 K) was calculated by a

population-weighted average of each conformer ΔfH°(298 K). The mole fraction of each

conformer was determined using a Boltzmann distribution based on the energy difference

between conformers. For species 1, 2, 5-8 ΔfH°(298 K) values are available in the literature.

Except for species 2, the differences between our determination and the literature value are less


14

than 5 kJ.mol-1. ΔfH°(298 K) of species 3, 4, 9, and 10 has been determined for the first time to

our knowledge.

Table 1: Values of ΔfH°(298 K) in kJ.mol-1 calculated in this work for the ten species.

species N° ΔfH°(298 K) species N° ΔfH°(298 K)

o-xylene 1 19,4 3-hydroxybenzaldehyde 6 -217,5

2-methylbenzyl radical 2 181,8 2,3-dimethylphenol 7 -160,2

2-methylbenzylperoxy radical 3 86,2 1-ethyl-2-methylbenzene 8 -0,9

2-methylbenzylhydroperoxyde 4 -58,6 2-(hydroperoxymethyl)benzyl radical 9 110,2

2-hydroxybenzaldehyde 5 -243,5 2-(hydroperoxymethyl)benzaldehyde 10 -144,3

S°(298 K) and Cp°(T) (300 ≤ T ≤ 1500 K) were calculated using molecular properties

determined at B3LYP/6-311++G(d,p) level of theory and statistical thermodynamics through

evaluation of translational, vibrational, electronic, and rotational partition functions. The

contribution of internal rotors such as CH3, CH2, CH2CH3, OH, CH2OOH, OOH, CHO was

determined in two different ways depending on the temperature. S°(298 K) and Cp°(300 K) were

calculated using the rigid-rotor-harmonic-oscillator model. Cp°(T) at T ≥ 400 K were calculated

by treating separately translational, vibrational, and external rotational contributions and

contribution from internal rotation. In this case, the torsion frequencies corresponding to internal

rotations were excluded in the calculation of vibrational contribution. The contribution to Cp°(T)

from an internal rotation was determined using direct integration over energy levels of the

internal rotation potential energy. The HR-public program was used for this integration. This

technique employs the expansion of the internal rotation potential in Fourier series, the

calculation of the Hamiltonian matrix on the basis of wave functions of free internal rotation, and

the subsequent calculation of energy levels by direct diagonalization o the Hamiltonian matrix.

S°(298 K) and Cp°(T) of o-xylene determined in this work are in good agreement with literature

values. This makes us trustful in S°(298 K) and Cp°(T) values determined for the other species in

this work.


15

Study and design of nonlinear optical materials:from molecules, through oligomers to polymers

Miroslav Medveď,1 Šimon Budzák,1 Jozef Noga,2 Ivan Černušák,3 Denis Jacquemin4 and Eric A. Perpète4

1 Department of Chemistry, Faculty of Science, Matej Bel University, Tajovského 40

SK-97401 Banská Bystrica, Slovakia, [email protected] 2 Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University,

Mlynská dolina, SK-842 15 Bratislava, Slovakia 3 Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences,

Comenius University, Mlynská dolina, SK-842 15 Bratislava, Slovakia 4 Unité de Chimie Physique Théorique et Structurale, Facultés Universitaires Notre-

Dame de la Paix Rue de Bruxelles, 61 5000 Namur, Belgium

Organic π-conjugated oligomers and polymers represent an excellent alternative to

traditional inorganic NLO crystals because they can be easily synthesized and chemically

modified. Extremely fast switching times, resistance to high intensity radiation,

possibility of thin-layer fabrication and low electric permitivity are important properties

in favor of organic NLO materials.

In the search for the large β, various strategies have been adopted. The most

obvious is the so-called push-pull strategy, in which a conjugated chain (e.g.

oligomethylene or phenylene) is capped at its ends by an electron-donor group on one

side and an electron-acceptor group on the other. In our recent studies we have been

interested in the so-called AB systems, where a suitable combination of delocalizability

and asymmetry can be achieved by designing π-conjugated chains from asymmetric unit

cells (containing two or more different nuclei). We successfully designed various AB

oligomers containing B, N, and C skeleton atoms with interesting NLO properties.

We will discuss various aspects of theoretical investigation of NLO properties

including (i) electron correlation effects, (ii) suitability of hybrid as well as recently

proposed LC-DFT methods, (iii) numerical differentiation problems, (iv) extrapolation

(from oligomeric values to polymeric limit) techniques and others. Possibilities of

investigation of NLO properties of infinite periodic systems will also be outlined.

This work has been supported by the Grant Agency of the Slovak Republic VEGA

(projects No. 1/0356/09 and No. 1/0428/09).


16

Trying to Understand the Mysterious Fluorescence of ó Systems: Oligosilanes

Matthew K. MacLeod and Josef Michl

University of Colorado, Boulder, CO, USA, and Academy of Sciences of the Czech Republic,Prague, Czech Republic

Saturated hydrocarbons absorb in the vacuum UV part of the spectrum but produce verybroad and weak fluoresce bands at much longer wavelengths. The huge Stokes shifts suggestprofound differences between the equilibrium geometries of the ground and the singlet excited state.That should not be surprising, since electronic excitation in saturated systems involves electrons ofthe bonds that hold the molecule together. The nature of the geometry changes that take place uponexcitation is not known.

We have been examining the silicon analogs of saturated hydrocarbons, the peralkylated

n 2n+2oligosilanes Si R . Like hydrocarbons, they contain saturated and tetravalent tetrahedral atomsin the main chain or cycle (Si instead of C), only single bonds, and no lone pairs. Oligosilaneshowever are easier to study since they absorb throughout the near UV region, and their spectra aremuch simpler, although they, too, contain fairly numerous closely spaced transitions. The differenceoriginates in the lower electronegativity of the backbone Si atoms relative to the lateral alkylsubstituent atoms, and in some ways the oligosilanes resemble fluorocarbons more thanhydrocarbons.

Like hydrocarbons, short-chain peralkylated oligosilanes (n < 8) generally fluoresce atstrikingly long wavelengths, with huge Stokes shifts. A compound with no observable absorptionabove 250 nm can emit in the blue or even in the green part of the visible spectrum. Remarkably,some oligosilanes fluoresce in two different spectral regions. In contrast, longer-chain peralkylatedoligosilanes (n > 6) generally exhibit Franck-Condon allowed fluorescence with a minimal Stokesshift and apparently very little difference between ground state and excited state equilibriumgeometries. The behavior of these more normal emitters can be understood in terms of extensiveó-electron delocalization, and has been dealt with elsewhere (some conformers of the chain with n= 7 show Stokes-shifted fluorescence and others fluoresce with no Stokes shift).

We shall report the results of calculations at several levels of theory (CC2, CASPT2, TD-DFT) that we have performed to answer the following questions: (i) What are the equilibriumgeometries of the highly distorted first excited states of peralkylated oligosilanes? (ii) Can oneunderstand the nature of the geometrical distortion from the ground state in simple intuitive terms?


17

Fock space coupled cluster theory for two-valence

sectors

Monika Musia�l

University of Silesia, Institute of Chemistry

Szkolna 9

40-006 Katowice, Poland

[email protected]

The Fock space (FS) coupled cluster (CC) theory offers a very convenient tool

for the description of excited, ionized and electron attached states. At the level

of one-valence sectors the FSCC provides ionization potentials (IP) and electron

affinities (EA) for the (0,1) and (1,0) sectors, respectively. For the two-valence

sectors we obtain double ionization potentials (DIP), double electron affinity (DEA)

and excitation energies (EE) which correspond to (0,2), (2,0) and (1,1) sectors,

respectively. The same quantities are obtained with the equation-of-motion (EOM)

CC approach and the IP-EOM as well as EA-EOM are identical to FS values unlike

the two-valence situation. In this talk an efficient computational scheme for the

treatment of the two-valence sectors within the Fock space CC theory is described

as well as a comparative analysis of the DIP, DEA and EE values obtained via EOM

formalism.


18

Pair density functional theory

Á. Nagy

Department of Theoretical Physics University of Debrecen,

H–4010 Debrecen, HungaryInstitution...

[email protected]

The pair density is a fundamental quantity. It is similar in role to the electron

density of the density functional theory. According to the Hohenberg-Kohn theorems in

the nondegenerate ground state the density determines the external potential and the

ground-state energy takes its minimum at the true electron density. It was shown [1, 2]

that the Hohenberg-Kohn theorems can be extented: in the nondegenerate ground state

the pair density determines the external potential and the groundstate energy takes its

minimum at the true pair density

In the density functional theory the electron density is generally calculated by

solving the Kohn-Sham equations. It was shown [3] that Kohn-Sham-like equations can

be constructed in the pair density functional theory. It turned out that the problem of an

arbitrary ground-state system with even electrons can be reduced to a two-particle

problem. The effective potential in this auxiliary equation contains an unknown term, the

Pauli potential.

In order to perform calculations one has to approximate the Pauli term. Exact

relations for functionals are proved to be important in constructing approximate

functionals in the density functional theory. Therefore virial theorem and hierarchy of

equations were obtained for the potential vp [4]. The electron-electron cusp condition and

asymptotic behaviour of the effective potential of the two-particle equation were also

derived [5]. Recently, exact differential and integral constraints for the pair density have

been presented [6].

A novel method for determining the Pauli potential has recently been proposed [7].

Starting from a reliable description of the pair density an analytical expression has been

obtained for atomic systems. In the derivation a recent method [8] of constructing the

exact Hamiltonian corresponding to the correlated three-parameter variational wave


19

function was utilized and test calculations were done for the Be and isoelectronic C2+ and

O4+ ions [7].

[1] A. Gonis, T. C. Schulthess, J. van Ek and P. E. A. Turchi, Phys. Rev. Lett. 77 (1996),

2981.

[2] P. Ziesche, Phys. Lett. A 195 (1994), 213; Int. J. Quantum. Chem. 60 (1996), 149.

[3] Á. Nagy, Phys. Rev. A, 66, 022505 (2002).

[4] Á. Nagy and C. Amovilli, J. Chem. Phys. 121, 6640 (2004).

[5] Á. Nagy and C. Amovilli, J. Chem. Phys. 128, 11411 (2008); J. Chem. Phys. 132,

109902 (2010).

[6] Á. Nagy and C. Amovilli, Chem. Phys. Lett. 469, 353 (2009).

[7] C. Amovilli and Á. Nagy, J. Chem. Phys. 129 204108(2008).

[8] C. Amovilli, N. H. March, I.A. Howard and Á. Nagy, Phys. Lett. A372 4053 (2008).

Grant OTKA No. K67923 is gratefully acknowledged.


20

Treating static and dynamic correlation with range-separated density and density matrix functionals

Katarzyna Pernal

Institute of Physics, Technical University of Lodzul. Wólczańska 219

93-005 Lodz, [email protected]

It is well known that static and long-range correlation effects are not well treated by local or semilocal density functionals. They are accurate, however, for systems where dynamic correlation dominates. On the other hand, recently proposed functionals of one-electron reduced density matrix (density matrix) proved capable of treating static correlation effects correctly.

We propose a new method, based on range-separation of Coulomb electron-electron interaction. It employs density and density matrix functionals in the short- and long-range regimes, respectively.

The method has been successfully applied to the homogeneous electron gas. The long-range correlation energy of the electron gas is excellently reproduced by a modified Buijse-Baerends density matrix functional [1].

The same functional combined with a short-range PBE (Perdew-Burke-Ernzerhof) density functional reproduces accurately dissociation curves of simple molecules. Therefore, the new approach corrects the deficiency of the density functional in the dissociation limit, where static correlation effects are present.

The new method scales with the 4th power of the number of basis set functions. An efficient projected gradient algorithm is employed in the optimization process [2]. The total computational cost is comparable to that of DFT methods.

[1] K. Pernal, Phys. Rev. A 81, 052511 (2010).[2] E. Canc?s and K. Pernal, J. Chem. Phys. 128, 134108 (2008).

Acknowledgement This work was supported by Polish Ministry of Science and Higher Education grant No. N N204 159036


21

Local correlation coupled-cluster methods exploiting cluster-in-molecule ansatz and their multi-level generalizations

Piotr Piecuch and Wei Li

Department of Chemistry, Michigan State University

East Lansing, Michigan 48824 USA

[email protected]

Coupled-cluster (CC) methods have greatly impacted modern quantum chemistry,

but, as all electronic structure approaches that aim at the accurate description of many-

electron correlation effects, they face significant challenges when dealing with the in-

creasingly complex molecular problems chemists are interested in. This includes prohibi-

tive costs of CC calculations for larger molecular systems. To help to address this chal-

lenge, we have extended [1,2] a number of CC methods, including CCSD, CCSD(T), and

the completely renormalized extension of CCSD(T), abbreviated CR-CC(2,3) [3], to lar-

ger systems with hundreds of atoms through the use of the local correlation, cluster-in-

molecule (CIM) ansatz [1,2,4]. The resulting CIM-CCSD, CIM-CCSD(T), and CIM-CR-

CC(2,3) methods are characterized by (i) the linear scaling of the CPU time with the

system size when the same level of theory is applied to all CIM subsystems, (ii) the use

of orthonormal orbitals in subsystem calculations, (iii) the natural coarse-grain par-

allelism, which can be further enhanced by the additional fine-grain parallelism of each

subsystem calculation, (iv) the high computational efficiency, enabling calculations for

large molecular systems at high levels of CC theory, (v) the purely non-iterative character

of local triples corrections to CCSD energies, and (vi) the applicability to the covalently

and weakly bound molecular systems. In addition, one can use the flexibility of the CIM

local correlation ansatz to mix different CC or CC and non-CC methods within a single

calculation, enabling the rigorous formulation of multi-level local correlation theories [2]

that combine the high-level CC methods, such as CR-CC(2,3), to treat, for example, the

reactive part of a large molecular system with the lower-order ab initio (e.g., MP2)

scheme(s) to handle the chemically inactive regions without splitting it into ad hoc

fragments and saturating dangling bonds. By comparing the results of the canonical CC

calculations with the single- and multi-level CIM-CC calculations for normal alkanes


22

[1,2], water clusters [1], the diffusion of atomic oxygen on the silicon surface [5], and the

proton transfer in the aggregates of dithiophosphinic acids with water [2], we de-

monstrate that the CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) approaches, and

their multi-level extensions accurately reproduce the corresponding canonical CC corre-

lation and relative energies, including chemical reaction pathways, while offering savings

in the computer effort by orders of magnitude.

[1] (a) W. Li, P. Piecuch, J. R. Gour, and S. Li, J. Chem. Phys. 131, 114109 (2009). (b) W. Li, P. Piecuch, and J. R. Gour, in: Theory and Applications of Computational Chemistry - 2008, AIP Conference Proceedings, Vol. 1102, edited by D.-Q. Wei and X.-J. Wang (AIP, Melville, NY, 2009), p. 68. (c) W. Li, P. Piecuch, and J. R. Gour, in: Progress in Theoretical Chemistry and Physics, Vol. 19, Advances in the Theory of Atomic and Molecular Systems: Conceptual and Computational Advances in Quantum Chemistry, edited by P. Piecuch, J. Maruani, G. Delgado-Barrio, and S. Wilson (Springer, Dordrecht, 2009), p. 131. (d) W. Li and P. Piecuch, J. Phys. Chem. A, in press; Articles ASAP; Publication Date (Web): April 7, 2010. [2] W. Li and P. Piecuch, J. Phys. Chem. A 114, 6721 (2010). [3] (a) P. Piecuch and M. Włoch, J. Chem. Phys. 123, 224105 (2005). (b) P. Piecuch, M. Włoch, J. R. Gour, and A. Kinal, Chem. Phys. Lett. 418, 467 (2006). [4] (a) S. Li, J. Ma, and Y. Jiang, J. Comput. Chem. 23, 237 (2002). (b) S. Li, J. Shen, W. Li, and Y. Jiang, J. Chem. Phys. 125, 074109 (2006). [5] P. Arora, W. Li, P. Piecuch, J. W. Evans, M. Albao, and M. S. Gordon, J. Phys. Chem. C, in press; Articles ASAP; Publication Date (Web): July 6, 2010.

Supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of

Basic Energy Sciences, Office of Science, U.S. Department of Energy (Grant No. DE-

FG02-01ER15228; P.P).


23

Reaction mechanism from quantum chemistry:

unbiased and biased simulations

Andras Stirling

Chemical Research Center of the Hungarian Academy of Sciences

Budapest, Hungary

[email protected]

The continuously increasing processor capacity allows the use of more realistic

models and more demanding computational technics to study chemical reactions.

Larger models can provide access to really collective atomic motions and in the same

time ensure a chemically more reliable environment for the reactions in silico. The

size and complexity of these models put the free energy surface into focus instead of

the potential energy surface. Indeed, much deeper insight can be obtained into the

reaction mechanisms by exploring free energy surfaces spanned by suitable reaction

coordinates.

Chemical reactions are usually activated events, thus their observations in molec-

ular dynamics simulations is highly unlikely. Therefore the simulations have to be

biased in some way to render these rare events observable and to measure their free

energy barriers. In this talk I will give an overview of the most important meth-

ods and illustrate some of these with actual calculations on different reactions. An

important methodological issue is the selection of appropriate reaction coordinates

(order parameters) and I will also address this problem.


24

SHORT LECTURES


25

Periodic DFT study of N2O decomposition over Fe-ferrierite

Prokopis Andrikopoulos, Stepan Sklenak and Zdenek Sobalik J. Heyrovsky Institute of Physical Chemistry of the ASCR, v. v. i.

Dolejškova 2155/3, 182 23 Prague 8, Czech Republic [email protected]

INTRODUCTION

To borrow the title from a recent science paper [1], nitrous oxide is no laughing matter.

Its twofold impact on the environment as ozone depleting agent and a potent greenhouse

gas, places an increased importance on the research of N2O elimination from industrial

streams [2-4]. Iron-exchanged zeolites provide a promising catalytic system for this

process and in particular iron-exchanged Ferrierite (Fe-FER) with a higher catalytic

activity than the more prevalent ZSM-5 and Beta zeolite frameworks [5]. To ascertain

where this superiority lies, we embarked on an in-depth computational analysis of the Fe-

FER system.

Figure 1.Transition State structure of adjacent cooperating active sites of the β1xβ1 type on

Fe-FER. The Fe···NNO-Fe moiety is formed facilitating an easier N-O bond scission.

COMPUTATIONAL DETAILS

Spin polarized periodic DFT calculations were carried out employing the VASP code [6-

9]. The Kohn–Sham equations were solved variationally in a plane-wave basis set using

the projector-augmented wave (PAW) method of Blöchl [10], as adapted by Kresse and

Joubert [11]. The exchange-correlation energy was described by the PW91 generalized


26

gradient approximation (GGA) functional [12-13]. Brillouin zone sampling was restricted

to the Γ-point. The plane-wave cutoff of 400 eV was utilized for geometry optimizations

while a smaller cutoff of 300 eV was used for the molecular dynamics simulations (MD).

The MD simulations were run for 5 ps at 300 K and the structures of ten distinct

"snapshots" collected from the last 500 fs of each MD simulation were optimised. The

most stable conformer was then used for subsequent calculations.

RESULTS AND DISCUSSION

Initially, the iron-centered active sites for the reaction, incorporated in the unit cell of

FER, were optimized with Molecular Dynamics. Three distinctive active sites were

investigated namely Alpha, Beta-1 and Beta-2 accommodating Fe(II). Concerning the

latter two types, the possibility of cooperation between sites is illustrated (Figure 1),

contrary to the isolated Alpha sites. The study of the Alpha type site can be used as an

approximate system for other zeolite frameworks where cooperation among sites is less

likely to occur. Having the active site for the reaction optimized as thoroughly as

possible, we commence on studying the mechanism of the decomposition of N2O.

Another uncertainty, the nature of nitric oxide role on the reaction can also be addressed

through this computational effort.

REFERENCES [1] D.J. Wuebbles, Science 326 (2009) 56. [2] 2009 U.S. Greenhouse Gas Inventory Report, Environmental Protection Agency, (http://tinyurl.com/emissionsreport). [3] M. Prather, Science 279 (1998) 1339. [4] A.R. Ravishankara, J.S. Daniel, R.W. Portmann, Science 326 (2009) 123; M. Dameris, Angew. Chem. 122 (2010) 499; Angew. Chem. Int. Ed. 49 (2010) 489. [5] K. Jisa, J. Novakova, M. Schwarze, A. Vondrova, S. Sklenak, Z. Sobalik, J. Catal. 262 (2009) 27; I. Melian-Cabrera, C. Mentruit, J.A.Z. Pieterse, R.W. van den Brink, G. Mul, F. Kapteijn, J.A. Moulijn, Catal. Comm. 6 (2005) 301. [6] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [7] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15. [8] G. Kresse, J. Hafner, Phys. Rev. B 48 (1993) 13115. [9] G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251. [10] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [11] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [12] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Phys. Rev. B 46 (1992) 6671. [13] J.P. Perdew, Y. Wang, Phys. Rev. B, 45, (1992), 13244.


27

Local hybrids: conceptually simple hyper-GGA exchange-correlation functionals for the Kohn-Sham density functional calculation of a wide

range of properties

Alexei V. Arbuznikov, Hilke Bahmann, Martin Kaupp

Institute of Physical and Theoretical Chemistry, University of Würzburg Am Hubland

D-97074 Würzburg, Germany E-mail: [email protected]

Among the most popular exchange-correlation functionals, a particular place is

occupied by the well-known “global hybrid functionals” (like B3LYP, PBE0 or TPSSh)

that provide high accuracy in the description of many molecular properties. Due to their

inclusion of a certain percentage of the “exact” (Hartree-Fock-like) exchange energy,

global hybrids are able to balance the elimination of Coulomb self-interaction and

inclusion of nondynamical correlation. However, their performance is restricted by

insufficient flexibility, since the description of different properties may require very

different amounts of exact exchange. The flexibility is fundamentally enhanced by

passing to a position-dependent exact-exchange admixture governed by a so-called local

mixing function (LMF) that leads to the notion of local hybrid functionals. The latter

constitute a new promising generation of hyper-GGA functionals for the simultaneous

accurate description of various properties within Kohn-Sham DFT.

The overall performance of local hybrids is a matter of a very subtle balance

between their basic ingredients: (i) ansatz and parameterization of the LMF; (ii) density-

functional approximation of the exchange mixed with the exact exchange; (iii) nature of

the (dynamic) correlation functional. Up to now, the best performance has been attained

partially in a semi-empirical way with a scaled ratio of von Weizsäcker kinetic energy

density to local kinetic energy density as LMF [1] (the latter may also include spin

polarization [2] and electron density itself), LSDA exchange, and LSDA correlation.

Further progress can be aided by insights from the adiabatic connection (AC) formalism

[3] and careful analysis of exact constraints (Lieb-Oxford bound, density-scaling

properties, etc.) a density functional should obey.


28

Our best local hybrids include a minimal number of adjustable parameters (one or

two) and turn out to be superior in the description of atomization energies, reaction

barrier heights [1,2,4], NMR chemical shifts, EPR g tensors [5], and electric response

properties (polarizabilities and hyperpolarizabilities) [6] compared to traditional hybrids

that often suffer from being overparameterized. A brief comparison will be also made for

the analytical structure and performance of our local hybrids to those designed in other

research groups [7], as well as to more complicated hyper-GGA functionals [8].

Currently, local hybrids are more computationally expensive than global hybrids.

However, we show that the situation can be significantly improved by avoiding an

explicit evaluation of the exact-exchange energy density on a grid, and by applying a

more efficient way for the evaluation of the LMF-including two-electron integrals.

Finally, an outlook on the extension of local hybrids to the computation of other

properties (including higher-order response ones) will be given.

[1] H. Bahmann, A. Rodenberg, A. V. Arbuznikov, M. Kaupp J. Chem. Phys. 126 (2007)

011103.

[2] A. V. Arbuznikov, H. Bahmann, M. Kaupp, J. Phys. Chem. A 113 (2009) 11898.

[3] A. V. Arbuznikov, M. Kaupp, J. Chem. Phys. 128 (2008) 214107.

[4] M. Kaupp, H. Bahmann, A. V. Arbuznikov, J. Chem. Phys. 127 (2007) 194102.

[5] A. V. Arbuznikov, M. Kaupp, J. Chem. Theory Comput. 5 (2009) 2985.

[6] A. V. Arbuznikov, M. Kaupp, Int. J. Quantum Chem., in press.

[7] J. P. Perdew, V. N. Staroverov, J. Tao, G. E. Scuseria, Phys. Rev. A 78 (2008)

052513.

[8] M. M. Odashima, K. Capelle, Phys. Rev. A 79 (2009) 062515.

This work has been funded by Deutsche Forschungsgemeinschaft (project KA1187/10-1)

within Priority Program 1145, “Modern and universal first-principles methods for many-

electron systems in chemistry and physics”.


29

Multireference State-Specific Mukherjee’s

Coupled Cluster Methods With Triexcitations

Kiran Bhaskaran-Nair, Ondrej Demel, and Jirı Pittner

J. Heyrovsky Institute of Physical Chemistry, v.v.i.18223 Prague 8, Czech Republic

[email protected]

The standard coupled cluster (CC) method, like other single reference methods,

exhibits a poor performance when quasidegeneracies are encountered, unless high-

level excitations are included. Such situations are, however, often of great chemical

interest, for example during bond breaking, double bond twisting, for diradicals, and

reaction intermediates; therefore a multireference (MR) generalization of CC theory

is highly desirable. Such a generalization is not unique; one possibility is based on

the Jeziorski-Monkhorst ansatz, where every reference determiant has is own set

of cluster amplitudes. The state-universal method (SUCC) gives energies of several

states in one calculation, but often suffers from severe convergence difficulties due to

the intruder state problem. The state-specific methods, where only one eigenvalue

of the effective Hamiltonian has a physical meaning, are free from the intruder state

problem, and have thus attracted a great attention in the last decade.

The first proposed state-specific MRCC method, Brillouin-Wigner coupled cluster

(BWCC), is insensitive to intruder states, has only linear scaling with the number

of references, and exhibits a very simple structure of amplitude equations coupled

only through the exact energy. However, it lacks the important property of the

standard CC theory, size-extensivity. The state-specific MRCC method formulated

by Mukherjee et. al. (MkCC) [1], and later developed by Evangelista et. al. [2],

Kallay et. al. [3], and Pittner et. al. [4] seems presently to be the most promising.


30

We have developed a linked formulation of the MkCC method and implemented

it at the truncation level with non iterative triples (MR MkCCSD(T)) and with

iterative triexcitations (MR MkCCSDT) in the ACES II package. Recently the

uncoupled MkCC formalism [5] has also been investigated, in order to determine

how its performance changes with the size of the basis set, size of the model space,

various multireference character of different molecules, and inclusion of connected

triple excitations. The assessment of these methods has been performed on the

spectroscopic constants of the first three electronic states of the oxygen molecule,

on the singlet-triplet gap in methylene and twisted ethylene, and on several other

systems, where a comparison with other multireference coupled cluster treatments

and with experimental data is possible.

Considering the computational cost, the MR MkCCSDT method aim to provide

a benchmark treatment of small systems, while the MR MkCCSD(T) variants can

be used for application calculations of medium-sized molecules.

References

[1] U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. 110, 6171 (1999).

[2] F. A. Evangelista, A. C. Simmonett, W. D. Allen, H. F. Schaefer III, and J.

Gauss, J. Chem. Phys. 128, 124104 (2008).

[3] S. Das, D. Mukherjee, and M. Kallay, J. Chem. Phys. 132, 074103 (2010).

[4] K. Bhaskaran-Nair, O. Demel, and J. Pittner, J. Chem. Phys. 129, 184105

(2008).

[5] O. Demel, K. Bhaskaran-Nair, and J. Pittner, J. Chem. Phys. in Press .


31

Prospects of using MP2 for electron scattering

Petr Čársky ...

J. Heyrovský Institute of Physical Chemistry. Academy of Sciences of the Czech RepublicDolejškova 3

18223, Prague 8, Czech Republic [email protected]

The idea of using diagrammatic approach similar to the Brueckner-Goldstone

linked cluster perturbation expansion goes already to the dark age of the theory of

electron scattering. Its first application to atomic targets at the second-order theory was

reported already in 1960’s [1]. The first application of the full second-order optical

potential to molecular targets was reported by a decade later [2]. It was the calculation on

the hydrogen molecule. Since then no application was attempted because of technical

difficulties of such calculations. The purpose of this contribution is to show that the

calculations of this type are now feasible even on commonly used computers of the

Opteron type. Merits and limitations of second-order calculations will be mentioned.

[1] H. P. Kelly, Phys. Rev. 131, 684 (1963), 136, 896 (1964), 160, 44 (1967)

[2] A. Klonover and U. Kaldor, Chem. Phys. Lett. 51, 321 (1977)


32

Anharmonic Vibrational Analysis with Traditional and Explicitly Correlated Coupled Cluster Methods

Kalju Kahn, Bernard Kirtman, Jozef Noga, Seiichiro Ten-no

Department of Chemistry and Biochemistry, University of California, Santa Barbar

CA 93106,[email protected]

Achieving the spectroscopic accuracy in ab initio calculation of vibrational spectra

is challenging due to two well-understood limitations. First, accurate energy derivatives

require a good description of electron correlation. Second, meaningful correlated

calculations require large one-electron basis sets. Furthermore, dipole moment and

hyperpolariability derivatives, which determine the infared and Raman intensities,

respectively, also strongy depend on the level of theory. We have now explored the

convergence of quadratic, cubic and quartic force constants with traditional and explicitly

correlated coupled cluster methods [1]. The convergence of harmonic frequencies with

Dunning’s cc-pVXZ family of basis sets in traditional CCSD(T) calculations is slow

(Figures 1 and 2).

Figure 1. Convergence of the harmonic

frequency of HF in traditional and

explicitly correlated CCSD(T)

calculations.

Figure 2. Convergence of the harmonic

stretching frequency of H2O in

traditional and explicitly correlated

CCSD(T) calculations.


33

We find a similar frustratingly slow convergence for many cubic and quartic

constants in traditional calculations (Figures 3 and 4). The addition of diffuse functions

often markedly improves convergence. An excellent convergence of harmonic

frequencies and cubic force constants is provided by explicitly correlated R12/B, R12/C

and F12/C methods with R12-suited basis sets. The Slater type geminal, however,

outperforms the linear r12 for quartic force constants and vibrational anharmonicity

constants in water.

Figure 3. Convergence of the cubic

force constant in HF in traditional and

explicitly correlated calculations.

Figure 4. Convergence of the mixed

cubic force constant in H2O in traditional

and explicitly correlated calculations.

We have carried out a systematic analysis of core correlation and quadruple

excitation contributions to quadratic, cubic and quartic force constants. Core correlation

and quadruple contributions significantly affect harmonic frequencies but their effect to

vibrational anharmonicity constants is small. The converged force constants from

explicitly correlated CCSD(T) calculations succeed in reproducing the fundamental

frequencies of water molecule with spectroscopic accuracy after corrections for post-

CCSD(T) effects are made.

[1] K. Kahn, B. Kirtman, J. Noga, and S. Ten-no, Anharmonic Vibrational Analysis of

Water with Traditional and Explicitly Correlated Coupled Cluster Methods, J. Chem.

Phys. 133 (2010).


34

Wave function in the relativistic two componet

methods

Dariusz Kedziera, �Lukasz Mentel

Department of Chemistry and Photochemistry of PolymersGagarina

87-100 Torun, Poland

[email protected]

Rapid growth of interest in the field of the chemistry of heavy elements was

followed by the development of the two–component methods of relativistic quantum

chemistry. The ongoing progress in this kind of methods was monitored only by the

accuracy of the obtained energies for one–electron systems. Finally, the solutions

for energy became available and soon a wide variety of two–component methods

have earned to be called accurate or even exact [1–5]. Nowadays, the scientific

effort can be directed to generalizations and seeking similarities between methods

different on first sight. Moreover, the present understanding allows to look at the

problems that were hidden behind the energy issue, for instance the properties of

the two–component wave functions.

References

[1] B.A.Hess, Phys. Rev. A 33, 3742 (1986).

[2] M. Barysz, A.J. Sadlej, J. Chem. Phys. 116, 2696 (2002)

[3] W. Kutzelnigg, W. Liu, J. Chem. Phys. 123, 241102 (2005)

[4] M. Ilias, T. Saue, J. Chem. Phys. 126, 064102 (2007).

[5] D. Kedziera, M. Barysz, Chem. Phys. Lett. 446, 176-181 (2007)


35

Local treatment of electron correlation for

first-order molecular properties from

expectation-value CCSD theory

Tatiana Korona

University of Warsaw, Faculty of Chemistry

ul. Pasteura 1

02-093 Warsaw, Poland

[email protected]

Expectation-value coupled cluster (CC) theory of first-order molecular properties

[1, 2] is an attractive alternative to response CC theory, as it allows to calculate

these properties without a need to solve an additional expensive set of equations for

the zeroth-order Lagrangian multipliers. On the other hand, the sizes of molecules

treatable by CC theory can be significantly extended if local methods are applied for

electron correlation. In this contribution the accuracy of local approximations has

been studied for expectation-value coupled cluster theory restricted to single and

double excitations (XCCSD), applied to first-order one-electron molecular proper-

ties, such as dipole and quadrupole moments. It has been found that the standard

local settings suitable for the local CCSD energy often lead to significant errors for

the multipole moments. However, the analysis of the Møller-Plesset expansion of the

XCCSD formula allows to formulate a modified set of local approximations, which

is better adapted for a description of first-order properties. The existence of local

options appropriate for the local XCCSD method opens a possibility to perform

low-cost calculations of first-order properties on the local CCSD level [3].

References

[1] Jeziorski, B., Moszynski, R., Int. J. Quantum Chem. 48, 161 (1993).

[2] Korona, T., Jeziorski, B., J. Chem. Phys. 125, 184109 (2006)

[3] Korona, T., submitted to Theor. Chem. Acc.


36

Internal flexibility of clindamycin

Katarzyna Kulczycka 1,2,* , Joanna Trylska2, Joanna Sadlej3

1Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw

Żwirki i Wigury 9302-089 Warsaw, Poland

2College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw

Żwirki i Wigury 9302-089 Warsaw, Poland

3Faculty of Chemistry, University of WarsawPasteura 1

02-093 Warsaw, Poland*[email protected]

Clindamycin is one of the antibiotics (lincosamides) which are used to treat many

diseases caused mostly by Gram-positive bacteria but also to boost immunity.

Lincosamides interact with the large subunit (50S) of the bacterial ribosome and inhibit

the process of bacterial protein synthesis. The increase of resistance in many strains of

bacteria against known antibiotics is caused by their expanded usage in medical practice.

This is a very important reason for continuous work to find new, better, more effective

drugs.

Currently, there are two available structures of clindamycin in the complex with the

50S1,2 ribosomal subunit (Protein Data Bank). The conformations of both antibiotics in

these complexes are significantly different. In this work we investigate internal dynamics

of clindamycin using the Car-Parrinello molecular dynamics. We performed molecular

dynamics simulations starting from both crystal conformers. The CP2K package was

used in our calculations.

[1] Schluenzen, F.; Zarivach, R.; Harms, J.; Bashan, A.; Tocilj, A.; Albrecht, R.; Yonath, A.; Franceschi, F. Nature, 2001, 413, 814-821.[2] Tu D.; Blaha G.; Moore P.B. Steitz TA, Cell, 2005,121, 257-270.

Acknowledgement


37

The authors acknowledge support from ICM University of Warsaw (BST1450/2009,

G31-4 and G18-4), Polish Ministry of Science and Higher Education (N N301 245236)

and Foundation for Polish Science (Focus program). The research for this talk was

partially supported by the EU through the European Social Fund, contract number UDA-

POKL.04.01.01-00-072/09-00.


38

The promotion energy of an atom in a molecule

Istvan Mayer

Chemical Research Center, Hungarian Academy of Sciences

H-1525 Budapest, P.O. Box 17

Hungary

[email protected]

Using the concept of the effective minimal basis set introduced some time ago,

a proper definition is proposed for the atomic promotion energy in the molecule,

which the atom can be assigned after the orbital deformations are introduced but

before any bonding, delocalization and charge transfer effects are taken into account.

The first pivoting calculations indicate that these promotion energies can be quite

substantial and are characteristic for the chemical nature of the atom.

Acknowledgement: Support of the Hungarian Scientific Research Fund—grant OTKA

No. 71816—is acknowledged.


39

An extension of the coupled-cluster corrected

configuration interaction method

Leszek Meissner

Institute of Physics, Nicolaus Copernicus University


e-mail: [email protected]

The standard coupled-cluster (CC) approach for correlation energy calculations provides a

set of nonlinear equations for cluster amplitudes and the energy expression. The set of CC

equations is usually solved using Jacobi-type iterative schemes combined with additional pro-

cedures for speeding up the convergence. An alternative route leading to the coupled-cluster

method can be obtained by introducing a modification of the configuration interaction (CI)

matrix. While the first approaches of this type have been called Coupled-Cluster Corrected

CI methods or, more frequently, Coupled Electron Pair Approximations (CEPAs), their

quite recent reformulation using intermediate Hamiltonian formalism is known as the size-

consistent self-consistent CI method ((SC)2 CI). Within the scheme the CC wave function

is partitioned into the linear and nonlinear components and contributions from the latter

one are incorporated through modification of the CI matrix. The solution is obtained by

diagonalization of the dressed CI matrix that must be done in a self-consistent manner since

the dressing depends on the matrix eigenvector. A possible generalization of this approach

can be obtained by treating the problem in a more formal way. The standard set of CC

amplitude equations does not depend on the CC energy that is calculated after determin-

ing the cluster amplitudes, however, simple manipulations can make the equations energy

dependent. A further rearrangement of the equations shows that diagonalization techniques

can be used to solve them. The scheme is quite flexible so even Newton-Raphson algorithm

can be used within this framework. Some numerical examples showing the convergence of

different iterative methods are presented.


40

A Combined Charge and Energy Decomposition Scheme for Analysis of Chemical Bonds and Reaction Paths

Mariusz P. Mitoraja,b, Artur Michalaka, Tom Zieglerb

a Jagiellonian University, R.Ingardena 3, 30-060 Cracow, Poland. b Department of Chemistry, University of Calgary, 2500 University Dr NW, Calgary, Alberta Canada.

In the present work we have introduced a new scheme for the electronic structure analysis

by combining the Extended Transition State (ETS) method1 with the Natural Orbitals for

Chemical Valence (NOCV)2. The ETS-NOCV3 charge and energy decomposition scheme makes

it not only possible to decompose the deformation density, Δρ, into the different components

(such as σ, π, δ, etc.) of the chemical bond, but it also provides the corresponding energy

contributions to the total bond energy. Thus, the ETS-NOCV scheme offers a compact,

qualitative and quantitative, picture of the chemical bond formation within one common

theoretical framework. The applicability of the ETS-NOCV scheme is demonstrated for various

types of covalent and donor-acceptor bonds. We also included the applications involving inter-

and intra-molecular (agostic) hydrogen bonding (see Figure below). Finally, we will show that

ETS-NOCV can be used not only to analyze the stationary points on PES, but its is also able to

describe the changes in electronic structure along the reaction paths. Decomposition of energetic

reaction barrier into the stabilizing (electronic and electrostatic) and destabilizing (Pauli repulsion

and geometry reorganization) components will be discussed in a detailed way for the examples

of reactions of industrial importance (activation of B-H bond of ammonia borane, β-hydride

eliminations, Diels-Alder cycloadditions).

Figure. The contours of relevant deformation density contributions describing the bonding between the cationic nickel based fragment and the n-propyl group together with the corresponding energies obtained from ETS-NOCV scheme3.

agosticorborb ρρσ ΔΔ ,1

[1] Ziegler, T., Rauk, A. Theor. Chim. Acta 46, 1, (1977). [2] Nalewajski, R.F.; Mrozek, J.; Michalak, A. International Journal of Quantum Chemistry 61,589,(1997); Michalak, A.; Mitoraj, M.; Ziegler, T. J. Phys. Chem. A. 112(9), 1933, (2008). [3] Mariusz P. Mitoraj, Artur Michalak and Tom Ziegler J. Chem. Theory Comput. 5 (4), 962.


41

Photodynamics of pyrimidine-based molecules: Effect of substitution and initial energy

Dana Nachtigallová1, Mario Barbatti2, Jaroslaw J. Szymczak2 and Hans Lischka1,2

1Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech

Republic, Flemingovo nam. 2, CZ-16610 Prague 6, Czech Republic 2Institute for Theoretical Chemistry – University of Vienna,

Waehrinegrstrasse 17, A 1090 Vienna, Austria

Substitution on the hetero-aromatic ring of the nucleic acid bases and their analogues can

significantly influence their excited state lifetime by changing the location of conical

intersections and/or due to the increasing of barriers on the trajectory towards them.

Consequently a relaxation mechanism responsible for a very rapid internal conversion to the

electronic ground state becomes inefficient.

In this study we present the results of an ab initio on-the-fly surface-hopping dynamics

simulation study of 2,4-diamino-pyrimidine for which the lifetime of the order of picoseconds

was measured.[1] Effect of substitution is discussed by comparison with the excited state

behavior of 4-amino-pyrimidine. Dynamics simulations are performed with different initial

energies to discuss the effect of pump energy used in the experiment.

The substitution on the pyrimidine ring of uracil changes its excited state lifetime

dramatically. Exploring the PES helps to explain this effect caused by changes of reaction

paths towards conical intersections.[2]

[1] Z. Gengeliczki, M. P. Callahan, C. I. Pongor, B. Sztára, D. Nachtigallová, P. Hobza, M.Barbatti, H. Lischka, M. S. de Vries; Phys. Chem. Chem. Phys. 12 (2010), 5375.

[2] D. Nachtigallová, H. Lischka, J.J. Szymczak, M. Barbatti, P. Hobza, Z. Gengeliczki, G. Pino, M. P. Callahan, M. S. de Vries; Phys. Chem. Chem. Phys. 12 (2010), 4924.


42

Some predictions on stable molecules: failure and success.

László Nyulászi, Oldamur Hollóczki, ...

Budapest University of Technology and Economics Department of Inorganic and Analytical Chemistry

Szt Gellért tér 4 H-1111 Budapest, Hungary

[email protected]

The stability of N-heterocyclic carbenes (NHC) together with their successful

catalytic applications [1] induced a search for other stable compounds with divalent

carbon (CR2 type compounds). We have suggested a simple computational tool for these

predictions: stable carbenes exhibit more than 90 kcal/mol stabilization energy in the

isodesmic reaction below [2].

CR2 + CH4 => CH2 (singlet) + CH2R2

In the meantime all the synthesized new stable carbenes fulfilled this criterium,

while we were not always successful in the use of this simple predicting tool. Further

predictions using more detailed stability checks [3] will also be presented.

The stability of carbene complexes is also an important issue, and the complexes

with main group elements are of particular importance in this respect. Our recent results

on the stability of carbene complexes resulting in hexacoordinate silicon compounds will

be presented showing the “interplay” between computational prediction and experiments.

[1] Arduengo III, A. J.; Bertrand, G. L. Chem. Rev. 2009, 109, 3209-3210.

[2] Forró, A.; Veszprémi, T.; Nyulászi, L. Phys. Chem. Chem. Phys. 2000, 3127.

[3] Hoffmann, R.; Schleyer, P. v. R.; Schaefer, H. F. Angew. Chem. Int. Ed. Engl. 2008,

47, 7164.


43

Kinetic equations and dissipation.

Ivana Paidarova 1, Philippe Durand 2

1 J. Heyrovsky Institute of Physical Chemistry, ASCR, v.v.i., Dolejskova 3,

CZ-182 23 Praha 8, Czech Republic2 LCPQ, IRSAMC, Universite de Toulouse et CNRS,

31062 Toulouse cedex 4, France

[email protected], [email protected]

The communication stems from our recent work ”Unstable states: from quantum

mechanics to statistical physics” [1], which represents a synthesis of our contribu-

tions towards a unified formulation of dynamics and thermodynamics of irreversible

processes in the spirit of the ideas of Jaynes [2] and Prigogine [3]. It is achieved

by a formalism borrowed from the quantum theory of resonances. The irreversible

dynamics is described by means of projected resolvents, effective Hamiltonians and

effective Liouvillians. The long macroscopic lifetimes are derived from short micro-

scopic lifetimes by perturbation in the complex plane.

In this talk, we focus on kinetic equations of irreversible processes. We present

an approach which extends the linear response theory to non-linear responses far

from equilibrium. It is shown how the empirical kinetic equations can be justified

by first principles. The approach has a general validity and can be applied to many

domains of physics. The origins and manifestations of the energy dissipation and a

brief discussion of entropy production are revealed by means of three simple dissipa-

tive models in distinct fields of physics and chemistry: chemical kinetics, magnetism

and ferroelasticity.

1. Chemical kinetics. The rate constants of the reaction A ⇀↽ B are determined

from first principles. The model implies an unstable transition state assimi-

lated to a short-lived resonance [4, 5].

2. A non-linear dissipative model of magnetism [6]. The model assumes an ”adia-

batic hypothesis” and links the non-linear response with a kinetic equation that

is analogous to the phenomenological laws of transport appearing in the ex-

tended thermodynamics. The approach is illustrated on an elementary model


44

of molecular magnet. We discuss the shapes of the hysteresis loops and give

an energetic and entropic analysis along the lines initiated by Jaynes and Pri-

gogine.

3. Dissipative processes in ferroelastics [7]. A simple model of dissipative pro-

cesses is extended to shape memory alloys displaying a pseudoelastic be-

haviour. The characteristic feature of this model is a three-level response to

the acting stress field describing the transition between two opposite states of

saturation through the intermediate parent structural state. The dissipation

is fully associated with the symmetric part of the response function.

References

[1] I. Paidarova and Ph. Durand in: E. J. Brandas and C. Nicolaides (Eds.) Unsta-

ble States in the Continuous Spectra. Analysis, Concepts, Methods and Results,

Advances in Quantum Chemistry, 60, (2010) (in press)

[2] E. Jaynes, Phys. Rev., 106, 620 (1957)

[3] I. Prigogine, Nature, 246, 67 (1973)

[4] Ph. Durand and I. Paidarova, Int. J. Quantum Chem. (2010), (DOI:

10.1002/qua.22584)

[5] I. Paidarova and Ph. Durand, Int. J. Quantum Chem. (2010), (DOI:

10.1002/qua.22630)

[6] Ph. Durand and I. Paidarova, Europhysics Letters, 89, 67004 (2010)

[7] I. Paidarova, V. Paidar, and Ph. Durand, Solid State Phenomena, Proceedings

of PMT 2010: Solid-Solid Phase Transformation in Inorganic Materials, Avignon

(submitted)

This work was supported by the Grant Agency of the Academy of Sciences of the

CR grant no. IAA401870702.


45

Molecular dynamics modeling of half-metallocene titanium(IV) ethylene polymerization catalysts

Łukasz Piękoś, Artur Michalak

K. Gumiński Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University,

R. Ingardena 3, 30-060 Kraków, Poland [email protected]

In the present work results of molecular dynamics simulations of half-metallocene titanium(IV) catalysts are presented. Molecular systems under consideration include non-bridged half-metallocene titanium(IV) complexes with aryloxo ligand acting as catalysts in ethylene polymerization process. Catalysts with various ligands and at various catalytic process stages are considered.

Methodology includes Car-Parinello molecular dynamics on the ab initio DFT level (CPMD software package) and Born-Oppenheimer molecular dynamics on the semiempirical level (MSINDO software package). Despite lower accuracy semiempirical approach is still useful due to ca. 3.5 orders of magnitude difference in performance comparing to DFT approach. Such performance allows for simulations on the timescale far beyond ab initio methods. Free molecular dynamics is used to study spontaneous transitions (including conformational changes and ethylene insertion reactions). Constrained molecular dynamics in slow-growth approach is used to obtain free energy profiles of ethylene insertion reaction.

Presented results include spontaneous conformational transitions affecting catalyst reactivity. Example where six stable conformations (including several transitions between them) can be observed on one simulation is also presented. Spontaneous insertion of ethylene is observed, followed by conformational changes which make catalytic cycle in one simulation.

Projections of presented trajectories (i.e. plots of selected coordinates) as well as animated visualizations are presented.


46

Relativistic, QED and nonadiabatic effects in the

interaction of hydrogen atoms

Konrad Piszczatowski†, Grzegorz �Lach†, Micha�l Przybytek†, Jacek Komasa§,

Krzysztof Pachucki‡, Robert Moszynski†, Bogumi�l Jeziorski†

†Faculty of Chemistry, University of Warsaw

Pasteura 1

02-093 Warszawa, Poland

§ Faculty of Chemistry, A. Mickiewicz University

Grunwaldzka 6

60-780 Poznan, Poland

‡ Institute of Theoretical Physics, University of Warsaw

Hoza 69

00-681 Warszawa, Poland

[email protected]

The dissociation energy of molecular hydrogen was determined theoretically with

a careful estimation of error bars by including nonadiabatic, relativistic, and quan-

tum electrodynamics (QED) corrections. The relativistic and QED corrections were

obtained at the adiabatic level of theory by including all contributions of the order

α2 and α

3 as well as the major (one-loop) α4 term, where α is the fine structure

constant. The computed α0, α

2, α3, and α

4 components of the dissociation energy

of the H2 isotopomer are 36118.7978(2), −0.5319(3), −0.1948(2), and −0.0016(8)

cm−1, respectively, while their sum amounts to 36118.0695(10) cm−1 [1], where

the total uncertainty includes the estimated size (±0.0003 cm−1) of the neglected

relativistic nonadiabatic/recoil corrections. The obtained theoretical value of the

dissociation energy is in excellent agreement with the most recent experimental de-

termination 36118.0696(4) cm−1 [2]. This agreement would have been impossible

without inclusion of several subtle QED contributions which have not been consid-

ered thus far for molecules. A similarly good agreement is observed for the leading

vibrational and rotational energy differences.

For the D2 molecule our theoretical value of the dissociation energy 36748.3633(9)

cm−1 [1] was significantly different from the experimental value 36748.343(10) cm−1


47

[3]. However, the most recent measurements [4] gave the value 36748.3629(7) cm−1,

which is in complete agreement with our result.

Using perturbative theory of nonadiabatic effects proposed by Pachucki and Ko-

masa [5] as well as our relativistic and QED corrections to the interaction potential

we have also calculated the s-wave scattering length for H – H collisions in the elec-

tronic singlet state [6]. The nonadiabatic value (0.2732 bohr) differs by about 40%

from the adiabatic one (0.4316 bohr). However, we have found that using atomic

reduced mass instead of nuclear one in the adiabatic calcualtions, we are able to

reproduce the nonadiabatic result with an error of less than 3%.

References

[1] K. Piszczatowski, G. �Lach, M. Przybytek, J. Komasa, K. Pachucki, and B.

Jeziorski, J. Chem. Theory Comput. 5, 3039 (2009).

[2] J. Liu, E. J. Salumbides, U. Hollenstein, J. C. J. Koelemeji, K. S. E. Eikema,

W. Ubachs, and F. Merkt, J. Chem. Phys. 130, 174306 (2009).

[3] Y. P. Zhang, C. H. Cheng, J. T. Kim, J. Stanojevic, E. E. Eyler, Phys. Rev.

Lett 92, 203003 (2004).

[4] J. Liu, D. Sprecher, C. Jungen, W. Ubachs, and F. Merkt, J. Chem. Phys 132,

154301 (2010).

[5] K. Pachucki and J. Komasa, J. Chem. Phys. 129, 034102 (2008).

[6] K. Piszczatowski, J. Komasa, K. Pachucki, A. van der Avoird,

G. C. Groenemboom, R. Moszynski, B. Jeziorski – to be published.


48

Gaussian and Finite-Element method

for the calculation of Coulomb integrals

Micha�l Przybytek, Trygve Helgaker

Center for Theoretical and Computational Chemistry

University of Oslo

Postbox 1033, Blindern

0315 Oslo, Norway

[email protected]

One of the most important challenges in the present time computational chemistry

is an efficient treatment of large biomolecular systems and nanomaterials comprising

as many as several thousands atoms. Both the most popular quantum chemical

methods which can be used for such systems, Hartree-Fock and Density Functional

Theory, need calculation of the Coulomb integrals. In the orbital approach, when

the Gaussian basis set is employed, the number of the Coulomb integrals (and thus

the computational cost) scales as O(N4), where N is the number of atoms. For that

reason, the calculations for truly large systems become prohibitively expensive, and

therefore much effort has been made to reduce the scaling of the computational cost,

possibly down to the most desirable linear O(N) regime.

One of the techniques aimed to achieve the linear scaling in the problem of comput-

ing the matrix elements of the Coulomb operator is the Gaussian and Final-Element

Coulomb method proposed originally in 2007 in the group of Kimihiko Hirao [1]. The

method consists of two main stages. First, the Poisson equation ∇2V (r) = −4πρ(r)

is solved to obtain the potential V (r) related to the electronic density given by ρ(r).

The potential is expanded in a mixed basis set consisting of two types of functions.

The Finite-Element shape functions describe the smooth part of the potential, while

the Gaussian functions with preoptimized exponents and centered on atoms are re-

sponsible for expressing the large variations of the potential close to the nuclei. The

expansion coefficients are obtained by means of solving large and sparse system of

linear equations. In the second stage, the matrix elements of the Coulomb operator


49

are actually calculated as an overlap integral Jab = �φaφb|V � =∫

φa(r)φb(r)V (r) dr.

As a result, in the Gaussian and Finite-Element method the problem of calculat-

ing four-center two-electron integrals with the integral kernel 1/r12 is reduced to

the problem of evaluating two- and three-center one-electron overlap integrals (with

functions of different kind) and solving the system of linear equations. Therefore

the computational cost and scaling property for large systems can be significantly

reduced.

References

[1] Y. Kurashige, T. Nakajima, and K. Hirao, J. Chem. Phys. 126, 144106 (2007).


50

DFT Studies on Catalytic Oxidation of Cyclohexene on Manganese Porphyrins

Dorota Rutkowska-Zbik, Malgorzata Witko

Institute of Catalysis and Surface Chemistry, PAS ul. Niezapominajek 8

30-239 Krakow, Poland [email protected]

Among popular homogeneous catalysts for hydrocarbon oxidation,

metalloporphyrins play a crucial role. This is due to their biological function as cofactors

in P450 class of enzymes responsible for bio-oxidation of both endogenous and

exogenous compounds. On the one hand, metalloporphyrins are able to insert oxygen

atom into C-H bonds, on the other, they may deliver oxygen atom to the double C=C

bonds, yielding epoxide. This dual reactivity is clearly manifested in the case of alkenes,

whose C=C bond and potentially reactive single C-H bonds in α (allylic) position with

respect to the double bond, are both prone to oxygenation. In particular, experiments with

cyclohexene oxidation catalyzed by metalloporphyrins showed that, beside the

cyclohexane oxide, unsaturated products of allylic oxidation (cyclohexen-3-ol and

cyclohexen-3-on) are formed, and the final selectivity pattern is determined by a

competition between the allylic C-H bond and the C=C double bond for the catalyst.

Therefore, the aim of the present work is the theoretical investigation of manganese

porphyrin reactivity towards cyclohexene by using DFT to study the epoxidation and

hydroxylation pathways. For geometric structure evaluation the LDA-VWN and GGA-

BP86 functionals are used. Electronic parameters of the systems are obtained at the

GGA-BP86 and GGA-RPBE levels. Extended all-electron basis sets of contracted

Gaussians are applied. For singlet state systems calculations are performed in a spin-

polarized manner. The charge transfers accompanying complex formations are accounted

for by changes of Mulliken charges for selected atoms or fragments of investigated

systems. The covalent strength of the bonds is measured by Mayer bond indices.

Additionally, spin densities are computed.

The calculations show that a physisorbed prereaction complex is formed in the first

stage of interaction between cyclohexene and manganese porphyrin. Although allylic


51

hydroxylation and epoxidation are initiated by different physisorbed prereaction

complexes, they may transform into each other. Once beyond the stage of physisorption,

the substrate is not able to switch easily between the reactivity funnels.

Formation of cyclohexen-2-ol proceeds via oxygen rebound mechanism. The

hydrogen atom is abstracted by the catalyst oxo group. The analysis of the energy profile

for the reaction indicates that the alcohol is formed after the hydrogen migration step

without prior dissociation of the hydrocarbon radical from the catalyst active site. The

reaction involves spin crossing since the catalyst is initially in its singlet state, while

during catalytic process it is promoted to its triplet state.

The key intermediate on the reaction pathway leading to epoxide lies lower on the

potential energy surface than the intermediate leading to alcohol, which explains high

reactivity of manganese porphyrins toward olefin epoxidation.

The intermediate structures, found for both pathways, clearly indicate that each may

lead to only one reaction product.


52

Orbital Optimized Second-Order Many-Body Perturbation Theory Via Coupled Cluster Ansatz

Ján Šimuneka, Jozef Nogaa,b

a Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University Mlynská dolina CH2

SK-84215 Bratislava, Slovakia [email protected]

b Institute of Inorganic Chemistry, Slovak Academy of Sciences SK-84215 Bratislava, Slovakia

[email protected]

Recently, we have published a study on the one-particle basis set relaxation effect in the

explicitly correlated coupled cluster theory.[1] Our primary goal was to show the error

introduced by the assumption of the generalized Brillouin theorem when one uses the

explicitly correlated R12 based methods with relatively small main computational

(atomic orbital) basis sets. Among others, we have investigated the performance of the

traditional coupled cluster singles (CCS) model if one starts from the reference

determinant corresponding to a Hartree-Fock (HF) solution with very small (or minimal)

basis set, while in the subsequent CCS calculation the virtual space is created using a

much larger basis set. Due to the Thouless theorem [2] the result should be close to the

HF solution with this large basis, nevertheless, it deviates from the correct solution due to

the non-variational nature of the traditional CCS solution. Our observation was that the

energies were generally overestimated. Obviously, variational treatment of coupled

cluster singles (VCCS) leads to the Hartree-Fock solution but such an approach gives rise

to an infinite expansion of connected terms of the effective Hamiltonian. We have

proposed an alternative new approach to obtain the Slater determinant ground state

solution within an independent-particle approximation using the exponential ansatz for

the wave function (Thouless theorem) and exact treatment in terms of variational coupled

cluster singles [3,4].


53

Based on our previous work, we propose orbital optimized second-order many-

body perturbation theory via coupled cluster Ansatz. Comparison with conventional CC2

approach will be presented for small set of reactions.

[1] Noga, J.; Šimunek, J. Chem. Phys. 2009, 356, 1-6.

[2] Thouless, D. J. Nucl. Phys. 1960, 21, 225-232.

[3] Šimunek, J.; Noga, J. AIP Conf. Proc. 2010, in press.

[4] Noga, J.; Šimunek, J. Chem. Theory Comput. 2010, in press.

Acknowledgement

This work has been supported by the Alexander von Humboldt Foundation.

Support from the Grant Agency of the Ministry of Education of the Slovak Republic and

Slovak Academy of Sciences VEGA project No. 2/0079/09 as well as by the Slovak

Research and Development Agency (LPP-0031-07) are also acknowledged. This work

has benefitted from the Centers of Excellence program of the Slovak Academy of

Sciences (COMCHEM, Contract no. II/1/2007).


54

Quantum mechanics and mathematical statistics

L. Skala, V. Kapsa,

Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2, Czech Republic

University of Waterloo, Department of Applied Mathematics, Waterloo, Ontario N2L 3G1, Canada

[email protected]

Basic mathematical apparatus of quantum mechanics like the wave function, coordinate

and momentum operator, corresponding commutation relation, kinetic energy, uncertainty

relations, continuity equation and equations of motion is discussed from the point of view of

probability theory and mathematical statistics. It is shown that the mathematical structure of

quantum mechanics can be understood as generalization of classical mechanics in which the

statistical charakter of results of measurement is taken into account and general properties of

statistical theories are correctly respected.


55

The problem of small coefficients in SS-MRPT

Agnes Szabados

Laboratory of Theoretical Chemistry, Lorand Eotvos University

Pazmany Peter setany 1/A

1117 Budapest, Hungary

[email protected]

Among various multireference perturbation approaches (MRPT) the state-specific

(SS) MRPT developed by Mukherjee et al.[1] is one that possesses many desirable

features. Derived from the parent coupled-cluster (CC) theory, SS-MRPT operates

with the Jeziorski-Monkhorst parametrization of the wavefunction. When com-

puting the PT approximation, amplitude equations are linearized, and the energy

correction is computed as the eigenvalue of the second order effective Hamiltonian.

In spite of the manifest intruder free character of the theory, we have found

unexpected divergences in our recent SS-MRPT studies[2]. The effect can be con-

sidered as a PT counterpart of convergence difficulties experienced in related CC

methods[3, 4]. The source of the problem has been attributed to small coefficients

figuring in the expansion of the reference function.

In the present study we give a perturbative analysis of the eigenvalue equation

of the effective Hamiltonian and look for appropriate workarounds of the divergence

problem.

References

[1] P. Ghosh, S. Chattopadhyay, D. Jana, D. Mukherjee, Int. J. Mol. Sci. 3, 733

(2002).

[2] M. R. Hoffmann, D. Datta, S. Das, D. Mukherjee, A. Szabados, Z. Rolik, P. R.

Surjn, J. Chem. Phys. 131 204104 (2009).

[3] A. Engels-Putzka, M. Hanrath, Mol. Phys. 107, 143 (2009).

[4] M. Kallay, S. Das, J. Chem. Phys. 132, 074103 (2010).


56

Jahn-Teller distortion and zero-field-splitting in

carbon nanotubes

Peter Szakacs and Peter R. Surjan

Eotvos Lorand University, Laboratory of Theoretical ChemistryPazmany Peter setany 1/A

H-1117 Budapest

[email protected]

The splitting of the spatial and the spin degeneracy in triplett carbon nanotubes

was studied.

Ionized or excited carbon nanotubes corresponding to Cnv pointgroup undergo

Jahn-Teller distortion, if at least one open shell degenerate molecular orbital exsists

in the system [1]. The Jahn-Teller distortion energy was calculated to describe the

degree of the distortion. The magnitude of the phenomenon was found to decrease

with increasing tube length or tube diameter. Calculations were carried out using

the semiempirical modell of Longuett-Higgins and Salem. This method is able to

optimize bond lengths.

Relativistic effects like spin-spin coupling may resolve the degeneracy of MS = 0

states, e.g. triplets (zero-field-splitting, ZFS). The amount of energy splitting is

usually very small. Dependence of ZFS on tube length, Jahn-Teller distortion, tube

diameter and chirality of the tube was investigated using the XHUGE (extended

Hubbard method with geometry optimization) semiempirical method [2].

References

[1] P. Szakacs, D. Kocsis, P. R. Surjan, J. Chem. Phys 132, 034309, 2010.

[2] P. Szakacs, A. Szabados, P. R. Surjan submitted.


57

The Brillouin zone integration problem in density

fitting of extended systems

Stefan Varga

Institute of Inorganic Chemistry, Slovak Academy of SciencesDubravska cesta 9

SK-845 36 Bratislava, Slovak Republic

[email protected]

Except for the special case of the Coulomb repulsion contribution [1–3], reciprocal

space integration cannot be avoided when applying the density fitting formalism to

infinite systems with translational periodicity [4, 5]. Careless application of usual

quadrature schemes can be an insidious source of additional numerical error in this

case. The situation is especially unpleasant when working with slow decay Coulomb

fitting metric. We analyse this case and show that it indeed leads to difficult-to-

integrate functions. A simple way how to reformulate the problem in the form

of smooth, easily integrable terms is suggested. Implementation and illustrative

calculations on one-dimensional infinite chain systems are presented as well.

References

[1] S. Varga, M. Milko, J. Noga, J. Chem. Phys. 124, 034106 (2006)

[2] S. Varga, Int. J. Quantum Chem. 108, 1518 (2008)

[3] A. M. Burow, M. Sierka, F. Mohamed, J. Chem. Phys. 131, 214101 (2009)

[4] S. Varga, Phys. Rev. B 71, 073103 (2005)

[5] L. Maschio, D. Usvyat, F. R. Manby, S. Casassa, C. Pisani, M. Schutz,

Phys. Rev. B 76, 075101 (2007)

Acknowledgement. Financial support from COMCHEM, a virtual Center for

Advanced Computational Chemistry sponsored by the Slovak Academy of Sciences

and from Slovak grant agency VEGA (Grant No. 2/0079/09) is acknowledged.


58

Quantum chemical computations on quantum

computers

Libor Veis and Jirı Pittner

J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech

Republic, v.v.i.

Dolejskova 3

18223 Prague 8, Czech Republic


Quantum computers are appealing for their ability to solve some tasks much

faster than their classical counterparts, e.g. efficiently factore integers. Also quan-

tum physics (chemistry) could in principle benefit from them. One possibility is an

efficient solution of many-body Hamiltonian eigenvalue problem [1]. As was shown

in the seminal work by Aspuru-Guzik et. al. [2], quantum computers, if available,

would be able to perform the full configuration interaction (FCI) energy calcula-

tions with only a polynomial scaling. This is of course in contrast to conventional

computers where FCI scales exponentially.

We have developed a code for simulation of quantum computers and implemented

our version of the quantum full configuration interaction (QFCI) method which

uses the iterative phase estimation algorithm [3]. This approach reduces demands

on the total number of quantum bits (qubits) as only one is needed in the read-

out part of the quantum register and the whole algorithm proceeds in an iterative

manner. We have tested its performance on the four lowest lying electronic states of

methylene molecule (CH2). This molecule was chosen as a benchmark, because both

of the lowest lying 1A1 states exhibit a multireference character at the equilibrium

geometry.

It has been shown that with a suitably chosen initial state of the quantum register,

one is able to achieve the probability amplification regime of the iterative phase

estimation even in this case.


59

References

[1] D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 83, 5162 (1999).

[2] A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, Science 309,

1704 (2005).

[3] M. Dobsıcek, G. Johansson, V. Shumeiko, and G. Wendin, Phys. Rev. A 76,

030306 (2007).

The authors gratefully acknowledge the financial support of the Grant Agency of

the Czech Republic (grant no. 203/08/0626) and the Grant Agency of the Charles

University in Prague (grant no. 114310).


60

Structural changes in the water tetramer and hexamer. A combined Monte Carlo and DFT study.

Aleš Víteka), Lenka Ličmanováa), Ivana Paidarováb), René Kalusa)

a)University of Ostrava, Department of Physics,

30. dubna 22, 701 03 Ostrava, Czech Republic.

[email protected]

b)J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic,

Dolejškova 3,182 23 Praha 8, Czech Republic

From the point of view of theoreticians, molecular clusters are generally considered

the most challenging objects of molecular physics, mainly due to many degrees of

freedom and the configuration space extremely complicated. The primary importance of

water clusters among molecular clusters is presently beyond any doubt. Their relevance

for atmospheric chemistry as well as for biological applications has been mentioned

many times in the literature.

In the past, many thermodynamical simulations have been performed for water

clusters, using simple empirical (e. g. TIPnP, n = 3, 4, 5, 6) [1 – 3] or semiempirical (e. g.

TTM3F) [4] interaction models. It has been shown, that theoretically calculated

thermodynamical properties (e. g. heat capacity curve) depends very sensitively on used

interaction model and small change of description of potential energy surface leads to

completely different theoretical results.

On the other hand, a time demandingness of accurate high level quantum chemistry

methods is the reason, why haven’t been used for thermodynamic simulations that require

large amounts of repeated calculations of energy in different configurations (of the order

of thousands to millions).

Our work is focused on simulation of water tetramer and hexamer using parallel

tempering Monte Carlo. Heat capacity curves have been calculated for temperature

interval 25 – 225 K. Simulated annealing method has been used to obtain frequency of

occurrence of isomers for different temperatures. Our empirical interaction models used


61

in Monte Carlo simulations are based on modified TIP6P potential improved by inclusion

of polarizable energy via induced dipoles. Parameters are adjusted on DFT energies of

representative sets of configurations directly of water tetramer or hexamer.

The B97-1 exchange-correlation functional has been used in the present work

together with augmented correlation-consistent basis sets of atomic orbitals up to triple-

zeta quality. The DFT data have been corrected using an empirical correction scheme.

Such a correction doesn’t raise the computational costs, however, with the combination of

the DFT enable to achieve energies close to those obtained by high-level quantum

chemistry methods.

We have also developed a new combination of Boltzmann-reweighting [5] and

multiple histograms [6] methods together with parallel tempering Monte Carlo in order to

obtain the thermodynamic data of clusters in the quantum chemical accuracy. This

approach reduce significantly the number of required repeated quantum chemistry

calculations to acceptable amount, thus only thousands of quantum chemistry energies

are sufficient for well converged thermodynamical data.

[1] W. L. Jorgensen and J. J. Tirado-Rivers, J. Am. Chem. Soc. 110, 1657 (1988).

[2] M. W. Mahoney and W. L. Jorgensen, J. Chem. Phys. 112, 8910 (2000).

[3] H. Nada and J. P. J. M. Eerden, J. Chem. Phys. 118, 7401 (2003).

[4] G. S. Fanourgakis and S. S. Xanteas, J. Chem. Phys. 128, Art. No. 074506 (2008).

[5] J. P. Hansen and I. R. MacDonald, Theory of simple liquids (Academic Press, London, 1986).

[6] A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 63, 1195 (1989).

Acknowledgement The work has been financially supported by the Grant Agency of the Academy of Sciences of the Czech Republic (grant no. IAA401870702).


62

Electron Correlation Calculations with Strictly LocalizedOrbitals

Zoboki Tamás(a), Mayer István (b) , Surján R. Péter(a)

(a) Eötvös Loránd University, Institute of Chemistry, Laboratory of TheoreticalChemistry

Pázmány Péter sétány 1/A1117 Budapest, Hungary

(b) Chemical Research Center, Hungarian Academy of SciencesH-1525 Budapest, P.O. Box 17, Hungary

In this work, different types of computational methods are presented in order to app-

roximate the correlation energy for a given molecular fragment chosen on the basis of our

chemical intuition. For this purpose we use strictly localized molecular orbitals (SLMOs)

which have the maximal projection in the occupied subspace. It can be shown that if

we project these SLMOs in the occupied space we get their counterparts which are exact

occupied orbitals and also extremely localized[1]. The SLMOs and their projections are

paired in the sense of Löwdin’s pairing theorem.

For approximating the correlation energy, we introduce three different types of appro-

aches all based on the usage of the active block of the Fockian[2].

[1] T. Zoboki, I. Mayer, J. Comp. Chem. (2010) accepted

[2] P. R. Surján, I. Mayer, T. Zoboki in preparation


63

POSTERS


64

Energy decomposition of alkyl-substituted furan molecules

Dóra Barna, Gyula Tasi

Department of Applied and Environmental Chemistry, University of Szeged

Rerrich B. tér 1. H-6720, Szeged, Hungary

[email protected]

The total energy is perhaps the most significant outcome of a quantum chemical

computation. But despite all of its importance the total energy is only a single number saying

nothing about the interactions present in the system from a chemical point of view. In order to

obtain a detailed and more useful description of the occurring interactions, one should

decompose the total energy into atomic and diatomic contributions which are chemically

meaningful. To do this, one can choose from several, more or less arbitrary decomposition

techniques. One of them [1] is based on the extended virial theorem [2], which, within the

Born-Oppenheimer framework, applies for general (not necessarily variational) wave

functions built up by using finite local one-electron basis sets. In addition to the energy

decomposition, the extended virial theorem makes the evaluation of the quantum chemical

basis sets possible. The extended formula contains three virials because of the fixed nuclei as

well as the fixed centers and exponents of the basis functions, and after its rearrangement, one

can express the total energy with the help of the kinetic energy and the virials.

2 2 0q jq j jqHF

E E ET V R P T V R P ZR Pα

α α

ςς

∂ ∂ ∂+ + + − = + + ∆ + ∆ + ∆ =∂∂ ∂∑ ∑ ∑

eq. (1)

( )E T V T R P Z= + = − − ∆ + ∆ + ∆ eq. (2)

In the stationary points of the potential energy surface together with the basis functions

centered on the nuclei, i.e., using atomic orbitals and assuming “orbital following”, eqs. (1)

and (2) reduce to eqs. (3) and (4).

2 0T V Z+ + ∆ = eq. (3)

E T Z= − − ∆ eq. (4)

This last equation obtained for the total energy can be applied to its exact decomposition into

atomic ( ( )E A ) and diatomic ( ( )E AB ) components.

( ) ( ) ( ) ( )12A A B A A B

E E A E AB E A E AB> ≠

= + = +∑ ∑ ∑ ∑ eq. (5)


65

But on formation of a molecule, the states of the atoms involved undergo changes. It is also

obvious that, for a particular element, the atomic energy component depends on the chemical

environment. To get diatomic energies, which are characteristic of the interatomic interactions

present in the system, one might set the atomic energies ( ( )E A ) to the value of the free atoms

( ( )0E A ), via partial redistribution of the original diatomic energy components [3].

( ) ( ) ( ) ( )~

0 AB A

E A E A E A E ABλ≠

= = + ∑ eq. (6)

( ) ( )( ) ( )~

1 A BE AB E ABλ λ= − + eq. (7)

The new diatomic energy components ( ( )~E AB ) now contain all the energy changes due to

the formation of the molecule.

This decomposition method, when performed on an adequate theoretical level, results

in diatomic energy contributions which, after the partial redistribution, are “on the chemical

scale”. The second order Møller–Plesset perturbation (MP2) level is accurate enough to

characterize the strength of the chemical bonds present in the system. The results of these

calculations reflect the experimental bond dissociation energies quite accurately, especially in

the case of the diatomic molecules. The best example is the new diatomic energy component

obtained at the MP2 level for the carbon monoxide, which is equal to the bond dissociation

energy within the experimental error reported. The order of the experimental bond

dissociation energies of various carbon-oxygen and carbon-carbon bonds can also be

reproduced with the transformed diatomic energy contributions.

The energy decomposition based on the extended virial theorem was used on some

alkyl-substituted furan molecules. With the help of the resulted transformed diatomic

contributions the strength of the various carbon-carbon and carbon-hydrogen bonds as well as

the order of the bonding energies were evaluated. This order might be interpreted on the basis

of the number and position of the alkyl groups in the molecule. But in absence of

experimental bond dissociation energies to support the outcome of the energy decomposition

one would need results of high-level theoretical model chemistries, which computations

would be very time-consuming.

[1] G. Tasi, D. Barna, Int. J. Quant. Chem. 109. (2009) 2599.

[2] G. Tasi, I. Mayer, Chem. Phys. Lett. 449 (2007) 221.

[3] S. F. Vyboishchikov, Int. J. Quant. Chem. 108. (2008) 708.


66

Relativistic effects vs. X-ray constrained Hartree Fock

L. Bucinsky, J. Kozisek, S. Biskupic, D. Jayatilaka and M. Gall

Institute of Physical Chemistry and Chemical Physics, STU-Bratislava

Radlinského 9

SK-812 37 Bratislava, Slovaka

[email protected]

This study is presenting the relativistic effects and the effects of the X-ray constrained

Hartree-Fock/DFT (XC-HF) approach [1] for the mer,trans-[Ru(Cl)3(Hind)2(NO)]

complex. The quasirelativistic infinite order two component (IOTC) [2,3] and Douglas-

Kroll-Hess 2nd order (DKH2) [4,5] calculations were carried out at both 1-component

(scalar relativistic effects) and 2-component (scalar relativistic effects + SO coupling)

level of theory. The experimentally determined (X-ray refinement) charge density is

compared with XC-HF and XC-BLYP electron density. The X-ray constraint and

relativistic effects in electron densities as well as the difference of the DKH2 and IOTC

electron densities are presented. Picture change effects [6,7] in the DKH2 and IOTC

electron density and structure factors of the studied compound are investigated by

analytical means. The relativistic effects and PCE is considered also for radial

distribution of (NR, DKH2, IOTC, DCH)electron densities of the radon atom. The PCE

correction of DKH2 and IOTC electron densities and structure factors was performed

using the Tonto software package [8].

[1] Jayatilaka, D. & Grimwood, D. J. (2001). Acta Cryst. A57, 76-86.

[2] Barysz, M. & Sadlej, A. J. (2002) J. Chem. Phys. 116, 2696.

[3] Kędziera, D., Barysz, M. (2007) Chem. Phys. Lett. 446, 176.

[4] Wolf, A., Reiher, M. & Hess, B. A. (2002). J. Chem. Phys. 117, 9215-9226.

[5] Reiher, M. & Wolf, A. (2004a). J. Chem. Phys. 121, 2037-2047.

[6] Wolf, A. & Reiher, M. (2006a). J. Chem. Phys. 124, 064102.

[7] Mastarlez, R., Lindth, R. & Reiher, M. (2008). Chem. Phys. Lett. 465, 157-164.

[8] Jayatilaka, D. & Grimwood, D. J. (2000). TONTO. A Research Tool for Quantum

Chemistry. The University of Western Australia, Nedlands, Western Australia, Australia.

see at: http://www.theochem.uwa.edu.au/tonto

Acknowledgement

The support from the grants: APVV (contract No. APVV-0093-07) and VEGA (contracts

No. 1/0817/08 and 1/0127/09) is gratefully acknowledged.


67

Weak interactions between air pollutants

Šimon Budzák1, Ivan Černušák2, Miroslav Medveď1

1 Department of Chemistry, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-97400 Banská Bystrica, Slovakia, [email protected],

2 Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina, SK-842 15 Bratislava, Slovakia,

Carbon monoxide belongs to important air pollutants. It constitutes substantial part of the fuel emissions, represents non-negligible part of the cigarette-smoke and is also present in volcanic gases [1]. In this contribution we investigate the intermolecular interactions of neutral H2O, SO2 species and important atmospheric ion NO+ with CO.

Weak interactions in this dimers were studied with standard ab initio methods including MP2 and CCSD(T) method, using augmented correlation corrected polarized series of basis sets. Due to large computational demands the OVOS (Optimized virtual orbital space) approach was used. Interaction energy and its components, vibrational spectra and dipole moments for local minima are reported. In order to find in which layer of atmosphere is formation of such complexes possible, the dependence of Gibbs energy of their formation on temperature was studied.

In the most stable conformations the carbon atom of CO is oriented towards the partner molecule (see Figure 1). The interaction energies are: -32.3 kJ/mol for NO+...CO, -8.2 kJ/mol for CO...H2O and -7.0 kJ/mol for CO...SO2, while the Gibbs energies are -10.5 kJ/mol for NO+...CO, 14.3 kJ/mol for CO...H2O and 6.4 kJ/mol for CO...SO2 at 200 K during the night in the troposphere.

Figure 1 Most stable conformations of studied dimmers


68

[1] Barbara J, Pitts F, Pitts JN. Chemistry of the Upper and Lower Atmosphere, Amsterdam: Elsevier, 2000.

AcknowledgementWe appreciate the financial support from Slovak Grant Agency VEGA (grant 1/0428/09) and Matej Bel University Grant Agency (grant 02/02/2010)


69

A Theoretical Study of the H-abstraction Reactions of H2, H2O, HI,and OH by the IO (2Π3/2) Radicals

Sébastien CANNEAUX,a,d Catherine HAMMAECHER,bFlorent LOUIS, a,d Laurent CANTRELc,d

a PhysicoChimie des Processus de Combustion et de l’Atmosphère (PC2A) UMR 8522 CNRS/Lille1, Université Lille 1 Sciences et Technologies, Cité scientifique, Bât C11/C5, 59655 Villeneuve d’Ascq Cedex, France b Université Catholique de Louvain, Bâtiment Lavoisier, Place L. Pasteur 1, B-1348 Louvain-la-Neuve, Belgiumc Institut de Radioprotection et de Sûreté Nucléaire, DPAM, Centre de Cadarache, BP3, 13115 Saint Paul Lez Durance, Cedex, Franced Laboratoire de Recherche Commun IRSN-CNRS-Lille1 "Cinétique Chimique, Combustion, Réactivité" (C3R), Centre de Cadarache, BP3, 13115 Saint Paul Lez Durance, Cedex, France

During a loss-of-coolant accident due to a break in the Reactor Coolant System

(RCS) of a nuclear Pressurized Water Reactors (PWR), part of the nuclear fuel could

melt and release fission products which will be transported through the RCS and its break

to the reactor containment building, and then possibly to the environment. Radioiodine is

one of the most radiotoxic fission products released from the damaged fuel due to its

ability to form volatile species, and the potential accidental release of volatile iodine to

the environment is a key safety issue for emergency response planning. The gaseous part

of iodine at the RCS break has a great impact on the potential iodine outside releases, and

kinetic limitations occuring in gaseous phase are suspected to promote gaseous iodine

species. To better predict the iodine speciation reaching the containment building,

depending on accident scenarios, the thermokinetic parameters of the main gaseous

reactions which govern the overall iodine behavior in the RCS have to be determined.

Such kinetic reactions could be later implemented in the ASTEC severe accident

simulation software.

In a first step, the reactions of iodine atoms I (2P3/2) with H2, H2O, HI, and OH have

been studied theoretically [1]. The aim of this methodological work was to demonstrate

that standard theoretical methods are adequate to obtain quantitative rate constants for the

reactions involving iodine-containing species.


70

In a second step, the computational procedure has been extended to some relevant

reactions involving the iodine oxide radical IO in its ground state (2Π3/2) and the same

species (H2, H2O, HI, and OH). Quantum chemistry calculations and TST kinetic models

are used in this work to compute the temperature dependence of the rate constants for the

abstraction reactions by iodine oxide radicals. Results will be presented and discussed in

this poster.

[1] Canneaux, S.; Xerri, B.; Louis, F. ; Cantrel, L. J. Phys. Chem. A, 2010, in press.


71

SPyDERS: MD Modelling Software for Nuclear Safety

Sébastien CANNEAUX,a,c Eddy THIRIOT,b,c Florent LOUIS, a,c Laurent CANTRELb,c

a PhysicoChimie des Processus de Combustion et de l’Atmosphère (PC2A) UMR 8522 CNRS/Lille1 , Université Lille 1 Sciences et Technologies, Cité scientifique, Bât C11/C5, 59655 Villeneuve d’Ascq Cedex, France b Institut de Radioprotection et de Sûreté Nucléaire, DPAM, Centre de Cadarache, BP3, 13115 Saint Paul Lez Durance, Cedex, Francec Laboratoire de Recherche Commun IRSN-CNRS-Lille1 "Cinétique Chimique, Combustion, Réactivité" (C3R), Centre de Cadarache, BP3, 13115 Saint Paul Lez Durance, Cedex, France

The French Institut de Radioprotection et de Sûreté Nucléaire (IRSN) and the

German Gesellschaft für Anlagen und Reaktorsicherheit mbH (GRS) are jointly

developing the ASTEC (Accident Source Term Evaluation Code) software to simulate

severe accidents, which can arise in a pressured-water nuclear reactor (PWR), from

initiating event up to the possible radiological release of fission products (FP) outside.

IODE module of ASTEC is devoted to model the FP behavior inside the nuclear

containment building and more especially the iodine radiochemistry. The FP modeling, in

terms of physical chemistry processing, need the knowledge of numerous properties

which some cannot be experimentally determined. Thus, cooperation began with the

laboratory PC2A from University of Lille 1 to determine some data with a theoretical

chemistry approach.

At the instigation of IRSN, a new molecular dynamics program, named SPyDERS,

is in the making. The initial objective of this code is to calculate energetic values related

to the solvation, such as Henry's law constants (HLC), for compounds of nuclear interest

such as iodine oxides and iodine nitroxides whose volatilities are still questionable.

In this poster, the approach will be detailed and the first operating tests of

SPyDERS will be discussed.


72

Structure and electronic properties of A-cluster in Acetyl-CoA synthase: insight from DFT

Aleksandra Chmielowska, Maria Jaworska, Piotr Lodowski

Institute of Chemistry, University of Silesia Szkolna 9


Acetyl-CoA synthase (ACS) is a bacterial enzyme which catalyses the synthesis of

Acetyl-CoA from coenzyme-A (CoASH), CO and methyl group coming from corrinoid-

iron-sulfur protein (CoFeSP):

CH3-Co(III)FeSP + CO + CoASH ↔ CH3CO-SCoA + Co(I)FeSP + H+ The active centre of ACS consists of A-cluster, dinuclear nickel complex bounded

to the sulfur-iron cubane: Fe4S4 – NipNid. Nip and Nid denote nickel atoms proximal and

distal to the cubane, respectively.

The geometry of A-cluster was optimized with use of DFT/OLYP method and two

main structural conformations were found, closed (I) and open (II) ones. Similar

calculations were performed for A-cluster with ligands (CH3, H, CO, H2O) linked to Nip.

The influence of polar solvent on the structures was taken into account by PCM model.

Atomic charges and spin densities for all structures of A-cluster were analyzed.

Acknowledgement: Calculations were performed at the Wrocław Centre for Networking

and Supercomputing, WCSS, Wrocław, Poland, under calculational Grant No. 51/96.


73

Noniterative triples correction in Mukherjee’s

coupled cluster method via uncoupled approach

Ondrej Demel, Kiran Bhaskaran Nair, Jan Smydke, Jirı Pittner

J. Heyrovsky Institute of Physical Chemistry, v.v.i., Academy of Sciences of the

Czech Republic

Dolejskova 3, 18223 Prague 8, Czech Republic

[email protected]

Multireference coupled cluster methods are accurate quantum chemical ab ini-

tio methods designed for treatment of quasidegenerate systems(e.g. biradicals) and

larger sections of potential energy surfaces (e.g. torsion of double bond, dissocia-

tion). However, the multireference generalization of coupled cluster approach is not

unique.

Proposed by Mukherjee et al. [1, 2], the MR MkCC is a Hilbert space state-specific

method which is rigorously size-extensive and resistant to intruder states.

Recently, an uncoupled variant of MR MkCC has been developed by Mukherjee

et. al. [3]. Unlike the original method, the couplings between the cluster equa-

tions corresponding to different references include cluster amplitudes of only one

reference configuration, as well as matrix elements of effective Hamiltonian and its

eigenvector. The reported results showed an excellent agreement between the un-

coupled and standard versions of MkCC method at the singles and doubles level.

This performance was later found to be preserved even when connected triples are

included[4].

In this poster, we report an aplication of the uncoupled MkCC method for nonit-

erative triples correction. The advantage of this scheme lies in the fact that approx-

imate treatment of the coupling terms in the triples equation is sufficient to avoid

the intruders; and, since the coupling terms include only amplitudes of one reference

configuration, iterating of triples equations is no longer required.


74

References

[1] U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys 110, 6171 (1999).

[2] U. S. Mahapatra, B. Datta, and D. Mukherjee, Chem. Phys. Lett. 299, 42 (1999).

[3] S. Das, D. Datta, R. Maitra, and D. Mukherjee, Chem. Phys. 349, 115 (2008).

[4] O. Demel, K. Bhaskaran Nair, J. Pittner, submitted.


75

MD modelling of tungsten carbide slab

Jozef Federič, Ivan Černušák

Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University Mlynská dolina CH1

84215 Bratislava, Slovakia [email protected]

We present structural data for tungsten carbide slab from ab initio molecular

dynamics simulations. The motivation is our participation in the EURATOM materials

research, covering simulations of various composites that contain tungsten, carbon or

beryllium atoms. The inner wall of the fusion reactor is made from tungsten, some parts

contains carbon. Tungsten carbide can be formed in the divertor which exhausts impurity

particles and removes heat load from the plasma in the fusion reactor. This is

accompanied by the erosion and deposition of the material, among others tungsten

carbide is formed. We simulated various models of WC slab with the goal to study the

effects of impinging particles on the WC surface in the future. The simulations are

performed using CP2K program, which uses mixed Gaussian and plane waves approach

[1,2].

Three model systems were simulated using NVT ensemble at 300 K temperature,

with 0.5fs step. Model I consists of three layers of atoms: two layers of tungsten and one

layer of carbon in between. Model II contains one extra layer of carbon atoms and model

III contains another layer of tungsten atoms. All systems were in hexagonal closed pack

structure as can be seen in Figure. The periodic boundary conditions were applied along

X and Y axis.

I II III

Figure 1: Three models of tungsten carbide slabs.


76

There are two lattice constants in hexagonal closed pack structure. The lattice

constant a is a horizontal distance between two neighbouring atoms of same type and c is

a vertical distance between two neighbour atoms of same type.

Figure 2: Tungsten carbide hexagonal closed pack structure

The experimental values for lattice constants are a=2.906 Å and c=2.837 Å. We

obtained the following values for a: 2.9084 Å ± 0.005 (model I), 2.9052 Å ± 0.004

(model II) and 2.9074 Å ± 0.005 (model III) and for c 2.8046 ± 0.005 (model I), 2.9356

Å ± 0.005 (model II) and 2.8459Å ± 0.054 (model III). The results for models I and III

are in good agreement with the experimental data.

[1] Quickstep: fast and accurate density functional calculations using a mixed Gaussian

and plane waves approach, J. VandeVondele, M. Krack, F. Mohamed, M. Parrinello, T.

Chassaing and J. Hutter, Comp. Phys. Comm. 167, 103 (2005).

[2] Quickstep: Make the atoms dance, M. Krack and M. Parrinello, Forschungszentrum

Jülich, NIC Series, Vol. 25, 29 (2004).

Support from grants APVV-LPP-0150-09, EURATOM-CU contract No. N° FU07-

CT-2006-00441, VEGA 1/0428/09 is acknowledged. We appreciate the computational

support under the HPC-FF project in Jülich Supercomputing Centre.


77

Nonlinear optical properties of endohedral

fullerene complexes

R. W. Gora,1 R. Zalesny,1 W. Bartkowiak,1 J. M. Luis,2 B. Kirtman,3 H. Reis4 and

M. G. Papadopoulos4

1 Theoretical Chemistry Group, Institute of Physical and Theoretical Chemistry,Wroclaw University of Technology

Wybrzeze Wyspianskiego 27, 50-370 Wroc�law, [email protected]

2 Institute of Computational Chemistry and Department of Chemistry,University of Girona

Campus de Montilivi 17071 Girona, Catalonia, Spain

3 Department of Chemistry and Biochemistry, University of CaliforniaSanta Barbara, California 93106, USA

4 Institute of Organic and Pharmaceutical Chemistry,The National Hellenic Research Foundation

48 Vas. Constantinou Avenue, 11635 Athens, Greece

Growing demand for new photonic materials is a strong impulse for synthesis and

physico–chemical characterization of new molecular systems that show a large non–

linear response to an external electric field. Among this broad group of compounds

are also the endohedrally doped fullerenes. Although such complexes captured inter-

est of scientists, still there is a lack of fundamental studies that would complement

collected experimental data. Previous theoretical studies focused on the structure,

stability and interactions in the host–guest systems. Due to the size of these systems,

as well as the formal and numerical complexity of the problem, relatively little is

known about the role of vibrations of “trapped” atoms or molecules in the nonlinear

optical response of endohedral complexes. Whitehouse and Buckingham proposed

a model, which predicts that in such systems vibrational contributions (in electric

dipole approximation) to the polarizability should be significantly larger than the

corresponding electronic counterparts [1]. Unfortunately, in the literature there are

no reliable calculations to confirm such predictions.


78

One of the main objectives of this project is verification of the Whitehouse and

Buckingham model. The following two complexes were selected as the model sys-

tems: Li@C60 and Ti@C28. The existence and stability of these complexes has been

confirmed experimentally. The studies, whose results will be presented, were based

on ab initio methods taking into account the electron correlation as well as the

density functional theory.

References

[1] D. B. Whitehouse, A. D. Buckingham, Chem. Phys. Lett. 207, 332 (1993).

This work was partially supported by Wroclaw University of Technology and

computational grant from Wroclaw Center for Networking and Supercomputing

(WCSS).


79

Correlation potentials and electron densities obtained from correlated Optimized Effective Potential method and ab initio Wave Function

Theory methods

Ireneusz Grabowski, Andrew Teale, Szymon Śmiga, Karol Jankowski

Institute of Physics, Nicolaus Copernicus University,87-100 Toruń, Poland

[email protected] www.fizyka.umk.pl/~ig

Direct comparison of the correlation potentials, electron densities and correlation energies, generated from few variants of correlated Optimized Effective Potential Method (OEP), standard Density Functional Theory (DFT) and from ab intio Wave Function Theory Methods (WFT), has been employed for analyzing the impact of the correlation effects on those quantities. These methods have been applied to a few atomic and molecular systems. The correlation potentials, energies and densities generated from orbital-dependent OEP (OEP2-sc [1], OEP-ccpt2 [2]) and from WFT methods - Coupled Cluster (CCSD, CCSD(T) ) and second-order Many Body Perturbation Theory (MP2) show very similar and systematic behaviour, reconfirming the correctness of the ab initio DFT (OEP2) methods [3]. In a contrast it has been demonstrated that the VWN5 and LYP correlation functionals do not represent any substantial dynamical correlation effects on the KS-correlation potentials [3] and electron density [4].

[1] R. J. Bartlett, I. Grabowski, S. Hirata, S. Ivanov J. Chem. Phys. 122, 034104 (2005) [2] I. Grabowski, V. Lotrich, R.J. Bartlett J. Chem. Phys. 127, 154111 (2007) [3] I. Grabowski, A. Teale, Sz. Śmiga, K. Jankowski, R.J. Bartlett, In preparation 2010 [4] K. Jankowski, K. Nowakowski, I. Grabowski, J. Wasilewski J. Chem. Phys. 130, 164102 (2009)


80

Exact diagonalization of bosonic Hamiltonians

Peter Jeszenszki, Agnes Szabados, Peter R.Surjan

Eotvos Lorand University, Institute of Chemistry, Laboratory of Theoretical

Chemistry

Pazmany Peter setany 1/A.

1117 Budapest, Hungary

[email protected]

Bosonic systems have been extensively studied over the last decade [1-3] due to

the interest generated by quantum gas experiments. A sample of quantum gas can

be produced by trapping atoms at low temperature in an optical lattice generated

by the application of lasers and static magnetic fields. The size of the traps is large

on the quantum chemical scale (1000 nm), for this reason the atoms interact only via

scattering processes. The total spin of an atom results by coupling the nuclear and

electron spins. If this value is an integer, the atoms are to be treated as quasi-bosons

and follow the Bose-Einstein statistics.

In the present work the wave functions of bosonic quantum systems are obtained

by exact diagonalization of the Hamiltonian. In this area exact solutions have been

mainly obtained by iterative methods combined with sparse matrix techniques. We

present a direct-CI code supplemented with the Davidson algorithm applying the

Bose-Hubbard model Hamiltonian.

References

[1] F.Dalfovo, S.Giorgini, L.P.Pitaevskii, S.Stringari, Rev. Mod. Phys., 71, No. 3

(1999).

[2] R.M.Noack, S.R.Manmana, AIP Conf. Proc., 789, 93-163 (2005).

[3] M.Lewenstein, A.Sanpera, V.Ahufinger, B.Damski, A.Sen(De), U.Sen, Advances

in Physics, 56, 243-379 (2007).


81

Properties of encapsulated organic molecules

Anna Kaczmarek-Kedziera

Faculty of Chemistry, Nicolaus Copernicus University

Gagarina 7, 87-100 Torun, Poland

E-mail: [email protected]

Encapsulation of organic molecules in nanomaterials can be applied for tuning the

properties of carbon nanotubes, fullerenes or zeolites. It is particularly interesting

in the case of the nanotubes, since unlike the modification of the outer surface of

the tubule, does not cause the loss of the one–dimensionality and may not involve

the surface defects [1–3].

The introductory investigation was performed for the small organic molecules

enclosed in the various type of cages: single-walled carbon nanotube, boron-nitride

tube and C92 fullerene buckyball. The analysis involved the host–guest interaction

and the electric and optical properties of the complexes.

References

[1] K. Yanagi, K. Iakoubovskii, H. Matsui, H. Matsuzaki, H. Okamoto, Y. Miyata,

Y. Maniwa, S. Kazaoui, N. Minami and H. Kataura, J. Am. Chem. Soc. 129,

4992 (2007).

[2] K. Yanagi, Y. Miyata, Z. Liu, K. Suenaga, S. Okada and H. Kataura, J. Phys.

Chem. C 114, 2524 (2010).

[3] W. He, Z. Li, J. Yang and J. G. Hou, J. Chem. Phys. 128, 164701 (2008).


82

Multireference R12 Coupled Cluster Theory

Stanislav Kedžuch1, Ondřej Demel2, Jiří Pittner2 and Jozef Noga1,3

1Institute of Inorganic Chemistry, Slovak Academy of Sciences, SK-84536 Bratislava, Slovak Republic

2J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, CZ-18223 Prague 8, Czech Republic

3Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, SK-84215, Bratislava, Slovak Republic

In order to account for static correlation, the explicitly correlated coupled cluster

theory based on the R12 Ansatz is formulated with respect to a multideterminantal

reference using the Brillouin-Wigner approach. Though the latter avoids appearance of

the intruder states, one pays for this desired feature by the loss of size extensivity.

However, to some extent this can be remedied by an a posteriori correction. Since the

BWCC method offers simplest form of amplitude equations among Hilbert space MRCC

ones, we have chosen it as the first step when developing MRCC-R12 approaches. It is

shown that introducing of the basis set incompleteness correction via an explicit inclusion

of the correlation factor into the wave function, separately for each reference, is easily

realizable. Test calculations for the H4 model using an R12 optimized 9s6p4d3 f basis

and its subsets with increasing highest angular momentum show the potential of the MR-

CC-R12 approach. R12 results with mere s functions are very close to values obtained by

using a conventional approach and the full 9s6p4d3 f basis set.

Acknowledgement: This work has been supported by the Grant Agency of the Ministry

of Education of the Slovak Republic and Slovak Academy of Sciences (VEGA project

No. 2/0079/09) and by the Slovak Research and Development Agency (APVV, LPP-

0343-09), as well as by the Grant Agency of the Czech Republic (GACR Project No.

203/07/0070). Also, this work has benefitted from the Centers of Excellence program of

the Slovak Academy of Sciences

(COMCHEM, Contract no. II/1/2007).


83

ONIOM study of the catalytic mechanism of Dihydroneopterin Aldolase

Hyungrae Kim, Stepan Sklenak

J. Heyrovsky Institute of Physical ChemistryAcademy of Sciences of the Czech Republic

Dolejskova 3 Prague 8 CZ-18223, Czech Republic

[email protected]

Dihydroneopterin Aldolase (DHNA) catalyzes the conversion of 7,8-

dihydroneopterin (DHNP) to 6-hydromethyl-7,8-dihydropterin (HP) in the folate

biosynthetic pathway, one of principal targets for developing antimicrobial agents [1].

The complete path for the catalytic reaction by E. coli DHNA (EcDHNA) was

investigated using ONIOM method [2]. The aldol reaction proceeds via a sequential

mechanism involving the consecutive proton transfer from C2’ of DHNP via ε-amino

group of Lysine 98, catalytic water to N5 of DHNP and the cleavage of the C1’-C2’

bond. The last step triggers the liberation of Glycoaldehyde (GA) from the active site.

GA release set off the transformation of intermediate structure to final product

(HP), that involves the reorganization of DHNA+intermediate structure complex, reverse

proton transfer from N5 via catalytic water, ε-amino group of Lysine 98 to Tyrosine 53’

hydroxyl group and protonation of C1’ and resulting chirality change of C1’.

We used the 1.07 Å resolution X-ray structure of EcDHNA [3] for our calculations

because of its higher reliability. To incorporate the possible long-range effect of real

enzyme, 81 residues were selected as model system based on the distance (16.2 Å) from

the active site center (C2’). A two-layered ONIOM method as implemented in the

Gaussian 09 program was used in this work. We chose the density functional method

B3LYP employing the 6-31G** basis set as the high level. The semi-empirical PM3

method was selected as low level.

[1] Structural basis for the aldolase and epimerase activities of Staphylococcus aureus

Dihydroneopterin Aldolase. J. Blaszczyk, Y. Li, J. Gan, H. Yan and X. Ji. J. Mol. Biol.

368, 161–169 (2007)

[2] S. Humbel, S. Sieber, K. Morokuma, J. Chem. Phys. 105, 1959 (1996)


84

[3] H. Yan. Unpublished results.

Acknowledgement

We thank Prof. Dr. Honggao Yan (Michigan State University) for providing us the

unpublished ecDHNA structure and significantly valuable discussions.


85

The factorized quadruple excitations for potential

energy surfaces with Λ functional

Katarzyna Kowalska-Szojda, Monika Musia�l, Stanis�law A. Kucharski

University of Silesia, Institute of Chemistry

Szkolna 9


[email protected], [email protected], [email protected]

In this work we discuss a possibility of incorporating the fifth-order factorized

connected quadruples [1] into the Λ based coupled cluster functional. The scheme,

scaling as n7, is denoted as ΛCCSD(TQf ), i.e. coupled cluster singles and doubles

with noniterative triples and noniterative factorized quadruples. The factorized

quadruples work well for the near equilibrium geometry but when combined with Λ

based functional provide also reliable description for the distorted geometries. We

discuss the performance of the method by studying the potential energy curves for

F2 and H2O molecules and relating them to the standard CC approaches such as

CCSD, CCSDT, CCSDTQ, CCSD(T) and also ΛCCSD(T) and CCSD(TQf ). The

Λ based corrections improve noticeably the curves bringing them closer to the FCI

or CCSDTQ reference.

References

[1] S. A. Kucharski, R. J. Bartlett, J. Chem. Phys., 108, 9221 (1998).

[2] M. Musia�l, R. J. Bartlett, J. Chem. Phys., 133, xxx (2010).


86

The use of perturbation-stable localization in

calculation and analysis of SO-correction to NMR

chemical shifts

Anezka Krıstkova, Olga L. Malkina

Institute of Inorganic Chemistry, Slovak Academy of Sciences

Dubravska cesta 9

845 36 Bratislava, Slovakia

[email protected]

The perturbation-stable (PS) localization procedure, initially developed for analy-

sis of NMR indirect nuclear spin-spin coupling constants [1], has been implemented

for the calculation of the spin-orbit (SO) correction to the NMR chemical shift.

In this poster we present the first benchmark calculations testing the numerical

stability of the results obtained with the new localization scheme. Also, the new

localization procedure has been applied for the analysis of the solvent effect of the

Lewis bases on the 13C SO-shift in iodoalkynes in order to check its usefulness for

interpretation purposes.

References

[1] Anezka Krıstkova, diploma thesis, 2009

We gratefully acknowledge the financial support from COMCHEM, a virtual Cen-

ter for Advanced Computational Chemistry sponsored by the Slovak Academy of

Sciences, and Slovak grant agencies VEGA (grant no. 2/0079/09) and APVV (grant

LPP-0326-09).


87

NMR spin-spin couplings and overlap of densities

of localized molecular orbitals

Anezka Krıstkova, Olga L. Malkina, Stanislav Komorovsky, Elena Malkin,

Vladimir G. Malkin

Institute of Inorganic Chemistry, Slovak Academy of Sciences

Dubravska cesta 9

845 36 Bratislava, Slovakia

[email protected]

One of the most important magnetic resonance parameters are indirect nuclear

spin-spin couplings, which are used in various fields of (bio)chemistry for establishing

the molecular structure from NMR spectroscopy data. Their detailed understanding

in terms of molecular and electronic structure, which has been pursued since the

beginning of NMR spectroscopy, is still of central importance in many fields of

research.

In this poster we present a new method of interpretation of spin-spin coupling,

based on its decomposition into contributions from individual localized molecular

orbitals (LMOs) [1], and on the visualization of spin-spin coupling pathways by

real-space functions [2]. In particular, the correlation between the overlap of LMO

densities and the Fermi-contact contribution to spin-spin coupling constants will be

demonstrated.

References

[1] R. Marek, A. Krıstkova, K. Malinakova, J. Tousek, J. Marek, M. Hocek, O. L.

Malkina, V. G. Malkin, J. Phys. chem., 114, 6689 – 6700 (2010)

[2] O. L. Malkina, V. G. Malkin, Angew. Chem. Int. Edition, 42, 4335-4338 (2003)

We gratefully acknowledge financial support from the Slovak grant agency APVV

(grants No. LPP-0326-09 and VVCE-0004-07).


88

Relative Complexation Energies for Li+ Ion in Solution: Molecular Level Solvation Versus Polarizable Continuum Model Study

Piotr Kubisiak, Andrzej Eilmes

K. Gumiński Department of Theoretical Chemistry, Jagiellonian University Ingardena 3

30-060, Kraków, Poland

Solvation of inorganic ions in organic solvents plays a great role in chemistry and

biochemistry since many chemical reactions occur in solution. Modeling of the ion–

solvent interactions is therefore of great importance. Typical quantum-chemical

calculations providing information about the structure of complexes and their binding

energies represent the situation in the vacuum and neglect the effect of the environment.

In solution the properties of the complex are affected by the solvent molecules and this

should be reflected in the relative complex stabilities. Effects of this kind are also highly

relevant for ion–polymer interactions in polymer-based solid electrolytes where the

polymer matrix surrounding the ion acts as the solvent, influencing the interactions in the

complex.

In the present work[1] we have studied relative complexation energies of Li+ ion in

two commonly used solvents, acetonitrile and diethyl ether. We have used molecular-

level representation of solvation, embodied in explicit solvent molecules surrounding the

complex to determine the trends in relative binding energies. Our results indicate that

with increasing number of included explicit solvent molecules the differences in

complexation energy between the complexes of different coordination numbers decrease.

Simultaneously we have conducted PCM calculations using various combinations of

atomic radii and molecular surface modeling the molecular cavity in the solvent. We have

shown that the best reproduction of energies for different coordination numbers has been

found for van der Waals molecular surface and Pauling or UFF atomic radii and that

PCM calculations can provide a low-cost alternative for the time-consuming explicit

solvation approach with comparable level of accuracy.

[1] Eilmes, A.; Kubisiak, P. J. Phys. Chem. A 2010, 114, 973


89

Second-order Douglas–Kroll–Heß (DKH2)spin–orbit and parity-violating Hamiltonians

Mojmır Kyvala

Institute of Organic Chemistry and BiochemistryAcademy of Sciences of the Czech Republic

Flemingovo namestı 2, 166 10 Praha 6, Czech [email protected]

Analytical expressions have been derived for the one-electron DKH2 spin–orbitHamiltonian and for the one-electron DKH2 parity-violating Hamiltonian through the free-particle Foldy–Wouthuysen (fpFW) transformation followed by the Douglas–Kroll–Heßtransformation of the one-electron Dirac Hamiltonian and of the nuclear spin-independentpart of the one-electron 4-component parity-violating Hamiltonian respectively.

Matrix elements of the one-electron Breit–Pauli (approximate Foldy–Wouthuysen,aFW), fpFW (DKH1) and DKH2 spin–orbit Hamiltonians have been evaluated betweenthe components of the ground scalar pseudo-relativistic (DKH2 CASSCF) state 3Pg ofatoms C, Si, Ge, Sn and Pb to estimate the error introduced by using lower-order spin–orbit Hamiltonians in ab initio all-electron quasi-relativistic calculations of, e.g., zero-field splittings or spin-forbidden transition probabilities in molecules containing heavyelements.

Similarly, matrix elements of the one-electron aFW, fpFW and DKH2 parity-violatingHamiltonians have been evaluated between the components of the two lowest scalarpseudo-relativistic (DKH2 CASSCF) states 2Pu and 4Pg of atoms B, Al, Ga, In andTl to estimate the error introduced by using lower-order parity-violating Hamiltoniansin ab initio all-electron quasi-relativistic calculations of, e.g., electronic energy shifts orelectronic excitation frequency shifts due to parity violation in molecules containing heavyelements.

The active spaces contained 4 (3) electrons in the 4 valence atomic orbitals sp3 or14 (13) electrons in the 14 atomic orbitals (n − 1)d5sp3d5. Different orbitals wereoptimized for different states. Instead of the true atomic (spherical) symmetry, a bit lowersymmetry of the largest binary subgroup of SO(3), the point group D2h, was exploited forconvenience.


90

Quantum chemical calculations of photophysical propertiesof Methyl- and Adenosylcobalamin

Piotr Lodowski1

, Maria Jaworska1, Paweł M. Kozłowski2, Tadeusz Andruniów3

1University of Silesia, Institute of Chemistry, Szkolna 9, 40-006 Katowice, Poland, 2Department of Chemistry, University of Louisville, Louisville, Kentucky 40292, USA, 3Department of Molecular Modelling and Quantum Chemistry, Institute of Physical and Theoretical Chemistry, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Two B12 dependent human enzymes, methylmalonyl-CoA mutase and methionine synthase, incorporate active alkylcobalamins derived from cyanocobalamin (vitamin B12, CNCbl). Methylcobalamin (MeCbl) functions as methyl donor in methionine synthase, with heterolytic cleavage of the cobalt – carbon bond to form cob(I)alamin. Adenosylcobalamin (AdoCbl or coenzyme B12) is the cofactor of enzymes, which catalyze the rearrangement reactions that proceed via mechanisms involving organic radicals generated by homolysis of the coenzyme cobalt – carbon bond to produce an adenosyl radical and cob(II)alamin.

Over the past few years transient absorption spectroscopy has been applied by Sension and co-workers [1] to investigate nature of electronically excited states and photochemistry of alkylcobalamins. While these recent spectroscopic studies provided a new insight into the electronic structure of cob(III)alamins, the nature of their excited states remains largely unexplained.

The analysis of the electronic structure of methyl- and adenosylcobalamin has been performed by means of time-dependent density functional theory (TDDFT). Calculations were carried out using the gradient corrected Becke–Perdew (BP86) functional together with the TZVPP basis set and COSMO solvent model. In the calculations a simplified cobalamin model was used, in which all the corrin side chains were replaced by hydrogen atoms and the 5,6-dimethylbenzimidazole trans axial base was replaced by an imidazole. The calculations were carried out with the use of TURBOMOLE program.

Full geometry optimization was performed for the ground state (S0) and the first singlet excited state (S1). The S1 excited state for both investigated cobalamins is characterized as a MLCT(SBLCT) type and is derived from the d/π → π* excitation, where π and π* orbitals are localized on the corrin ring. For the ground and excited S1 state, potential energy curves were determined as a function of Co-CMe and Co-CAdo bond lengths. The bond length was repeatedly stretched with the step size of 0.05 Ǻ, and the geometries of S0 and S1 states were reoptimized at every point. At each optimized point the manifold of singlet and triplet states were calculated at the TDDFT/BP86/TZVPP level of theory.

[1] D.A. Harris, A.B. Stickrath, E.C. Carroll and R.J. Sension, J. Am. Chem. Soc, 129, 24 (2007) 7583 Acknowledgement: This work was supported by Ministry of Science and Higher Education (Poland) under grant No. N204 028336. The TURBOMOLE calculations were carried out in the Wrocław Centre for Networking and Supercomputing, WCSS, Wrocław, Poland, under calculational Grant No. 51/96. and in the Academic Computer Centre CYFRONET of the University of Science and Technology in Cracow, ACC CYFRONET AGH, Kraków, Poland,under grant No. MNiSW/SGI3700/UŚląski/111/2007.


91

Protonated water clusters – structures and thermodynamics

Jakub Malohlava, Aleš Vítek, René Kalus

Department of Physics, Faculty of Science, University of Ostrava 30. dubna 22

70103 Ostrava, Czech Republic [email protected]

This work focuses on protonated water cluster because of their importance in

charge transport and related biological and physical processes. Thermodynamical

parameters of H+(H2O)n clusters with n = 2 – 8 were obtained by Monte Carlo

simulations using the parallel tempering approach [1] combined with the multiple

histogram algorithm [2]. Structures of H+(H2O)n were obtained at T = 0 K by Monte

Carlo simulations using the simulated annealing algorithm [3]. Two empirical models

proposed by Kozack and Jordan [4] were used – the hydronium model where the

hydronium ion, H3O+, interacts with n – 1 water molecules, and the proton model where

the proton, H+, interacts with n water molecules.

Figure: Equilibrium structure at T = 0 K and temperature dependence of the heat

capacity of H+(H2O)5 calculated for the hydronium model.

[1] Swendsen R.H.and Wang J.-S.: Phys. Rev. Lett. 57, 2607 (1986).

[2] Ferrenberg A.M. and Swendsen R.H.: Phys. Rev. Lett. 61, 2635 (1988).

[3] Kirkpatrick S., Gelatt C. D., and Vecchi M. P.: Science 220, 671 (1983).

[4] Kozack R. E., Jordan P. C.: J. Chem. Phys. 96 , 3131 (1992).


92

Acknowledgement

Grant Agency of the Academy of Sciences of the Czech Republic, grant No.

IAA401870702; University of Ostrava, Students Grant Competition, grant No.

SGS7/PřF/2010.


93

Hydrogen bonded clusters around aromatic π-systems

Gergely Matisza,b, Walter M.F. Fabianb, Sándor Kunsági-Mátéa,*

aUniversity of Pécs, Department of General and Physical Chemistry Ifjúság 6., 7624 Pécs, Hungary

bKarl-Franzens University of Graz, Institute of Chemistry Heinrichstr. 28, 8010 Graz, Austria *email: [email protected]

The hydrogen bonded liquids were investigated widely nowadays, both with

Molecular Dynamics (Monte Carlo) simulations beyond the pairwise additive

approximations [1] and the static approach quantum cluster equilibrium QCE model [2]

of F. Weinhold. However, it is obvious to assume that the structure of hydrogen bonded

liquids is modified by the presence of the solute molecules. This effect can be

pronounced in the case of aromatic molecules where the C-H…π and O-H…π bonds are

in competition with the hydrogen bonds which stabilize the clusters in the liquid phase

[3]. Although few experimental results are available in the literature for the benzene –

methanol clusters [e.g. 3,4] the influence of the aromatic ring (i.e. benzene, anthracene)

on the hydrogen bonded clusters is not discussed yet at higher theoretical levels [5]. Here

we present a study of methanol – benzene (anthracene) at the MP2(fc) level of theory to

show the possible structural patterns in the liquid relative to pure methanol calculated at

the same level of theory [6]. The structures determined will be applied in the QCE model

to investigate the structure of the corresponding binary liquid mixtures.

[1] Valdéz-González et al., J. Chem. Phys. 127 (2007) 224507.

[2] F. Weinhold, J. Chem. Phys. 109 (1998) 367.; J. Chem. Phys. 109 (1998) 373.

[3] S. Kunsági-Máté et al., Chem. Phys. Lett. 473 (2009) 284.

[4] R.N. Pribble et al., J. Chem. Phys. 106 (1997) 2145.

[5] B. Brutschy, Chem. Rev. 100 (2000) 3891.

[6] G. Matisz et al., THEOCHEM, in press, doi: 10.1016/j.theochem.2010.07.003

Acknowledgement: This project was supported by the Intergovernmental projects NKTH

(HU 4/2009, RO-14/07). Computations with the Gaussian 09 Rev.A.02. were done on

IBM HPC supercomputer located at the Babes-Bolyai University in Cluj Napoca.


94

Liquid structure of primary alcohols (methanol, ethanol, 1-propanol, 1-butanol) within the QCE theory

Gergely Matisza,b, Walter M.F. Fabianb, Sándor Kunsági-Mátéa,*

aUniversity of Pécs, Department of General and Physical Chemistry Ifjúság 6., 7624 Pécs, Hungary

bKarl-Franzens University of Graz, Institute of Chemistry Heinrichstr. 28, 8010 Graz, Austria *email: [email protected]

The hydrogen bonded liquids, like water [1] and various alcohols [2,3] was

investigated previously in several publications via the Quantum Cluster Equilibrium

(QCE) model of F. Weinhold [4]. The advantage of this model (QCE) that we can obtain

the cluster distribution in the liquid phase relatively easily based on ab initio cluster

geometries and cluster properties. For the homolog series of unbranched aliphatic primer

alcohols none a complete investigation was presented until now regarding their structure

within the QCE model. Although force field based MD calculations are possible, they are

not reliable enough to predict the liquid structure adequately.

In our recent publication [5] we have investigated the pure liquid methanol at the

MP2(fc) level of theory in the framework of the QCE model. Here were extend those

studies to the higher homologes of the unbranched aliphatic primary alcohols using the

B3LYP density functional which proved to be adequate in the case of pure methanol.

[1] S.B.C. Lehmann, B. Kirchner et al., J. Chem. Theory Comput. 5 (2009) 1640.; 1650.

[2] P. Borowski et al., Mol. Phys. 101 (2003) 1413.

[3] R. Ludwig, Chemphyschem 6 (2005) 1369.; 1376.

[4] F. Weinhold, J. Chem. Phys. 109 (1998) 367.; J. Chem. Phys. 109 (1998) 373.

[5] G. Matisz et al., THEOCHEM, in press, doi: 10.1016/j.theochem.2010.07.003

Acknowledgement: This project was supported by the Intergovernmental projects NKTH

(HU 4/2009, RO-14/07). Computations with the Gaussian 09 Rev.A.02. were done on

IBM HPC supercomputer located at the Babes-Bolyai University in Cluj Napoca.


95

Effect of spin-orbit coupling on potential curves and spectroscopic properties of IO and I2

Katarína Mečiarová, Lukáš Demovič and ivan černušák

Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina 84215 Bratislava, Slovakia

[email protected]

Potential energy curves (PEC‘s), spectroscopic constants, equilibrium geometries and dissociation energies were calculated for the ground and excited states of iodine oxide and iodine molecule using the complete active space second-order perturbation theory (CASSCF/CASPT2) and coupled cluster theory through quasiperturbative triple excitations (CCSD(T)), implemented in the moLcas 7.3 program package [2]. The ground state of IO(X2Π) and I2 (X 1Σ+) were computed at the CCSD(T) level. Potential energy curves for excited states of IO (a4Σ-, A2Π) and I2 (A

3Π), which have multi-configuration nature, were computed at the CASSCF/CASPT2 level. The second order spin-free Douglas-Kroll-Hess Hamiltonian was applied to calculate relativistic effects within the spin-adapted CCSD(T) and the CASPT2 method. To include spin-orbit effects, which are important for both ground and excited state of IO and I2 due to the presence of the heavy I, we employed the Restricted Active Space State Interaction method (CASPT2/RASSI-SO), introduced by Roos and Malmqvist [1].

For energy predictions, relativistic basis set ANO-RCC with large contraction (for iodine (22s19p13d5f3g)/[10s9p8d5f3g] and for oxygen (14s9p4d3f2g)/[8s7p4d3f2g]) has been used in all the calculations. C2 symmetry with averaging the degenerate pairs of electronic states was used. Two active spaces were used in the CASPT2 spin-free calculations for IO: the first consisted of 9 valence electron in 6 orbitals (16a/10b inactive and 2a/4b active), followed by CASPT2 calculations with 17 correlated electrons; the second included 9 valence electron in 12 orbitals (16a/10b inactive and 6a/6b active). Two active space were used for I2 molecule: 10 valence electron in 6 orbitals (28a/20b inactive and 2a/4b active) and 10 valence electron in 16 orbitals (28a/20b inactive and 8a/8b active).

Spectroscopic constants (equilibrium bond lengths Re, harmonic frequencies ωe, anharmonicity constants ωexe and ro-vibrational constants αe) and equilibrium geometries were determined by fourth-fifth-order polynomial fit and VIBROT program. Calculated spectroscopic constants, geometries and dissociation energies were compared with existing experimental and theoretical data from the literature.


96

[1] B. Roos and P.-A. Malmqvist, Phys. Chem. Chem. Phys., 6, 2919 (2004) [2] Aquilante, F; De Vico, L; Ferre, N, et al., Journal of computational chemistry, 31, 224-247 (2010)

Acknowledgment This work was supported by Slovak Research and Development Agency under the contract No. LPP-0110-07, grant APVV-20-018405, VEGA (1/0428/09) and EUROATOM, contract No. N° FU07-CT-2007-00051. Computational support from the Centre of Excellence program of the Slovak Academy of Sciences (COMCHEM, Contract no. II/1/2007) is gratefully acknowledged.


97

Applicability of Graphical Processing Units to Coupled Clusters Calculations

Miroslav Melicherčík, Lukáš Demovič, Michal Pitoňák, Pavel Neogrády

Comenius University, Faculty of Natural Sciences Department of Physical and Theoretical Chemistry

Mlynská dolina CH-1 842 15 Bratislava, Slovakia

[email protected]

Graphical processing unit (GPU) appears to be an excellent tool for the acceleration

of quantum chemistry calculations. We propose some levels of the GPU based software

integration into the coupled clusters singles, doubles [1, 2] and perturbative triples [3, 4]

method CCSD(T).

The GPU is especially efficient for massively parallelized problems, such as

matrix-matrix multiplication [5], as shown on figure 1. Implementation of such routines

in BLAS (basic linear algebra subroutines) library for GPU, named CUBLAS, is included

in the CUDA software development toolkit [6].

Figure 1 Time dependence of matrix-matrix multiplication on size of square matrices N

(blas – single-threaded blas, thrblas – two-threaded blas, cublas – blas on GPU)

First, we simply accelerated CCSD(T) method by replacing the BLAS routines with

corresponding CUBLAS routines and got average speedup 1.24 for CCSD part and 1.80


98

for (T) part of calculation. Second, we wrote program that simulates the most time

consuming part of CCSD(T) procedure – part for calculation of noniterative triples.

Within this program, all calculations were performed on GPU and data transfer was done

only at the beginning and at the end of procedure. We achieved average overall speedup

of 3.96 times. Results are summarized in Table 1.

Table 1 Results for (T) simulation

Number of occupied orbitals 20 30 Number of virtual orbitals 200 350

8 cores on CPU 10m 28.147 s 231m 15.709s NVIDIA Tesla S1070 (960 cores) 2m 18.662 s 68m 10.819 s

Speedup 4.53 3.39

[1] J. Čížek, J. Chem. Phys. 45, 4256 (1966)

[2] G. D. Purvis, R. J. Bartlett, J. Chem. Phys. 76, 1910(1982)

[3] M. Urban, J. Noga, S. J. Cole, R. J. Bartlett, J. Chem. Phys. 83, 4041 (1985)

[4] K. Raghavachari, G. W. Trucks, J. A. Pople, M. Head-Gordon, Chem. Phys. Lett.

157, 479 (1989)

[5] NVIDIA CUDA Programming Guide 2.3

<http://developer.download.nvidia.com/compute/cuda/2_3/toolkit/docs/NVIDIA_

CUDA_Programming_Guide_2.3.pdf>

[6] CUBLAS Library documentation 2.3

<http://developer.download.nvidia.com/compute/cuda/2_3/toolkit/docs/CUBLAS

_Library_2.3.pdf>

This work was supported by the Slovak Grant Agency VEGA (contract No. 1/0428/09),

Grant Agency of Comenius Univeristy (No. UK/501/2010)


99

Accurate ab initio heats of formation and

standard molar entropies for several

atmospherically important formyl derivatives

Balazs Nagy†, Jozsef Csontos‡, Mihaly Kallay‡, and Gyula Tasi†

† University of Szeged, Department of Applied and Environmental Chemistry

Rerrich B. ter 1.

H-6720 Szeged, Hungary

and‡ Budapest University of Technology and Economics, Department of Physical

Chemistry and Materials Science

P.O. Box 91

H-1521 Budapest, Hungary

[email protected]

Several, so-called chemistry-climate models [1] have been developed to incorporate

the effects of chemical processes in climate modeling. To provide reliable information

these models require accurate kinetic and thermochemical data for the reactions

which play significant role in atmospheric chemistry. Nevertheless, the chemistry of

the troposphere and stratosphere is dominated by free radicals, and experimental

work with radicals is challenging and usually the accuracy of the measurements is

not satisfactory. Therefore, high-accuracy model chemistries can play a crucial role

in providing reliable data for climate modeling.

In the present study, a slightly modified HEAT-345(Q) model chemistry [2] was

applied in order to calculate accurate thermodynamic functions for several open- and

closed-shell formyl derivatives relevant to atmospheric chemistry. Heats of formation

along with standard molar entropies of the radicals FCO, cis- and trans-HOCO, and

NH2CO, as well as the molecules CF2O, HFCO, HClCO, and FClCO were calculated.

The molecular structures of the species, the zero-point vibrational energies as well

as the harmonic frequencies along with the anharmonicity constants were studied

at the CCSD(T)/cc-pVQZ level of theory with all electrons correlated. Single-point

energy calculations were performed invoking coupled-cluster theory up to the pertur-

bative quadruple excitation level [CCSDT(Q)] with the correlation consistent basis


100

sets up to aug-cc-pCV5Z. Extrapolation techniques were used to obtain the com-

plete basis set limit in the HF-SCF, CCSD(T), and CCSDT calculations. Additional

contributions including the diagonal Born-Oppenheimer, and relativistic, scalar and

spin-orbit, corrections were also taken into consideration. The total molecular en-

ergies were obtained assuming the additivity of the various contributions.

Heats of formation were calculated using the formation reaction of the species

from the elemental reference compounds. For carbon atom the gaseous state was

used as reference and its 0 K heat of formation was set to the ab initio value,

∆fH◦0 (Cgas) = 711.65±0.32 kJ/mol [3]. To calculate the heat of formation at 298.15

K the thermal correction (∆fH◦298 − ∆fH

◦0 ) was obtained from the NIST-JANAF

tables resulting in ∆fH◦298(Cgas) = 717.13 ± 0.32 kJ/mol.

Standard molar entropies were calculated at 298.15 K at pressure of 1 bar via

the standard formulae of statistical mechanics, i.e., within the rigid-rotor harmonic-

oscillator approximation using the calculated harmonic frequencies and rotational

constants.

The estimated uncertainties of the calculated properties were taken from a re-

cent study [4], where the errors introduced by the present protocol were analyzed

thoroughly.

The accuracy of all the calculated heats of formation and most of the molar

entropies surpasses that of previous experimental and theoretical investigations, and

in these cases our values are recommended as new references.

References

[1] J. Austin, D. Shindell, et al., Atmos. Chem. Phys. 3, 1 (2003).

[2] Y. J. Bomble, J. Vazquez, et al., J. Chem. Phys. 125, 064108 (2006).

[3] G. Tasi, R. Izsak, et al., ChemPhysChem, 7, 1664 (2006).

[4] J. Csontos, Z. Rolik, et al., J. Phys. Chem. A, submitted for publication (2010).


101

Catalytic hydrogenation of Quinolines via frustrated Lewis pairs: Mechanistic insight from theory

Péter Nagy, Imre Pápai

Chemical Research Center of HAS P.O. Box 17

H-1525 Budapest, Hungary [email protected]

In the past few years, there has been considerable interest in exploring the reactivity of bulky Lewis acid/base pairs towards small molecule activation. Following the concept of frustrated Lewis pairs (FLPs) introduced by Stephan and coworkers, a number of intermolecular and intramolecularly linked donor/acceptor pairs have been identified that cleave molecular H2 heterolytically under mild conditions.1

Based on a theoretical investigation, a mechanistic model have been proposed that provides a rationale for the unique reactivity of FLPs.2 The model has been built upon density functional theory based identification of the stationary points and single point vibrational analysis or polarisable continuum model calculations. From the calculated gas-phase and solution-phase Gibbs free energies one may conclude that the reactivity is associated with transient intermediates formed between the FLP components, which offer cooperative acid-base interactions with a hydrogen molecule.

However, the scope of synthetic applications of FLPs as hydrogenation catalyst is fairly limited, because these pairs add readily to olefins and acetylenes hampering the hydrogenation process. To bypass that undesirable reactivity, a novel intermolecular FLP has been designed that involves a sterically more demanding mesityl borane combined with small-size bases.3 These pairs show enhanced selectivity in catalytic hydrogenation of a variety of organic compounds.

Quinoline and mesityl borane can also act as an FLP towards hydrogen cleavage, however, the reaction yields tetrahydro products. Consequently, the recently developed borane can be used as an efficient catalyst in the hydrogenation of heteroaromatic rings. Our DFT calculations focusing on the mechanism of these reactions reveal the details of possible reaction pathways. The species depicted in the figure was identified as a key intermediate.


102

B(C6F5)2Mes / Quinoline / H2 system

[1] D. W. Stephan and G. Erker, Angew. Chem. Int. Ed. 2010, 49, 46.

[2] T. A. Rokob, A. Hamza, A. Stirling, T. Soós and I. Pápai, Angew. Chem., Int. Ed., 2008, 47, 2435.

[3] G. Erős, H. Mehdi, I. Pápai, T. A. Rokob, P. Király, G. Tárkányi and T. Soós, Angew. Chem. Int. Ed 2010, 49, 1.


103

Electric properties of 2-cyclopenten-1-on

Jana Páleniková, Vladimír Kellö

Department of Physical and Theoretical Chemistry, Faculty of Natural SciencesComenius UniversityMlynska Dolina CH-1

842 15 Bratislava, Slovakia [email protected]

The aim of this study is to compare behavior of dipole moments and dipole polarisabilities of organic molecule 2-cyclopenten-1-one (2CP) in the ground state S0 and three electronic excited states S1 (n→π*), T1 (n→π*) and T2 (π→π*). The geometry of 2-cyclopenten-1-one in its ground state S0 was optimized using the CASPT2 method, including ALASKA for analytical gradients, with the 6-311+G(d,p) basis set. Calculations of the electric properties were carried out using coupled cluster methods CCSD and CCSD(T), in conjunction with the Pol [1] basis set and the Z2Pol [2] basis set. The two-determinant CCSD method [3] was used for open-shell singlet. All calculations were performed using the system of quantum chemical programs MOLCAS.

The order of vertical excitation energies 2CP computed using CCSD method with Pol basis set is T1 (3,62 eV), S1 (3,96 eV) and T2 (3,98 eV). There is a large change in dipole moment of the 2CP molecule due to excitation to the T1 and S1 states. Total dipole moment decreased by about 60%. This change is due to excitation in n (nonbonding) orbital located on oxygen atom to π* (π-antibonding) orbital located mainly along the C-C bond. Polarisabilities of the T1 and S1 excited states are much less affected by the excitation from the ground state. The largest change occurs by excitation in the z axis.

[1] A.J. Sadlej, Coll. Czech. Chem. Commun. 53, 1995 (1988).[2] Z. Benková, A.J. Sadlej, R.E. Oakes, S.E. Bell: J. Comput. Chem. 26, 145 (2005).[3] P. Neogrady, P. G. Szalay, W. P. Kraemer, et al.: Collect. Czech. Chem. Commun.

70, 951 (2005).

This work was supported by the Slovak Grant Agency VEGA under the contract No. 1/0520/10. The support is gratefully acknowledged.


104

Long-range corrected dispersionless density

functional

Ewa Pastorczak1, Katarzyna Pernal2, Krzysztof Szalewicz3

1 Technical University of Lodz, Institute of Applied Radiation Chemistry

Wrblewskiego 15

93-590 Lodz, Poland

[email protected] Technical University of Lodz, Institute of Physics

Wolczanska 219

90-924 Lodz, Poland3 Department of Physics and Astronomy, University of Delaware

Newark, Delaware 19716, USA

A new density functional, based on dispersionless density functional (DL09) [1]

and Hirao’s long-range correction scheme [2], is proposed.

The DL09 functional is known to predict very accurately the dispersionless parts

of intermolecular interactions, whereas the dispersion part can be computed ab initio

or by a function fitted to computed ab initio values. However, its long-range sepa-

ration performance for a number of systems (e.g. C6H6) dimer could be improved.

Also, DL09 is not suitable for the problems involving forming or breaking chemical

bonds.

The new, long-range corrected DL09, where the exchange part consists of short-

range density functional part and long- and short-range parts of Hartree-Fock ex-

change (given with different coefficients), with reoptimized parameters is expected

to perform as well as, or better, than DL09 for all the systems with intermolecular

interactions and additionally calculate accurately the reaction barrier energies.

References

[1] Pernal K., Podeszwa R.,Patkowski K., Szalewicz K., Phys. Rev. Lett. 103,

263201 (2009).

[2] Iikura H., Tsuneda T., Yanai T., Hirao K., J. Chem. Phys. 115, 3540 (2001).


105

Electric properties of low-lying excited states of acetone and their interaction with water

L. F. Pašteka1, M. Urban1,2

1Department of physical and theoretical chemistry, Faculty of natural Sciences,Comenius University, Mlynská dolina, 842 15 Bratislava, Slovakia

[email protected]

2Slovak University of Technology in Bratislava, Faculty of Materials Science and Technology, Institute of Materials Science, J. Bottu 25, 917 24 Trnava, Slovakia

Dipole moments, polarizabilities and hyperpolarizabilities are important molecular properties, for example in connection with optical shifts resulting from the rearrangement of the solvent upon the excitation of the solute molecule. Acetone, investigated in this paper, serves as a prototype of a variety of carbonyl compounds. Their electric properties affect the intermolecular interactions of molecules with the environment in organic and biochemical systems, in which chemiexcitation can occur easily.

The present work focuses on computing the electric properties of low lying singlet and triplet valence states as well as the ground state of acetone. Structures of these states were optimized at the aug-cc-pVTZ/CASPT2 level of the theory. Geometry of the ground state is in the C2v symmetry and geometry of the excited states is in Cs symmetry, since the oxygen leans out of the carbon plane during the excitation, except for 1,3σ-π* state, which is in C2v symmetry with the methyl groups twisted by 180°.

Subsequently, the same method was used in numerical derivatives of energy with respect to the strength of an external electric field (the FFPT approach). In this scheme the 3, 5, 7, 9, 11 and 13-point central differentiation formulae with equidistant step of size of 0.001 a.u., 0.002 a.u., 0.004 a.u., and 0.008 a.u. were used. We also differenciated the polynomial fit through all of the points with various degrees of the polynomes. This approach gave us enough results to be able to enumerate the accuracy of the resulting value in terms of an interval to which all the results belong. For each state the first four energy derivatives are calculated, which allows obtaining the dipole moment, dipole polarizability and first two hyperpolarizabilities.

Dipole moment expectation values obtained from CASSCF computations were also used to calculate higher derivatives and some of the off-diagonal terms of the tensor of polarizability and hyperpolarizability.

Vertical and adiabatic excitation energies are also presented. They primarily serve as a toll for justification of methods used in our computations, since these are the only available experimental data for excited states of acetone.

Significant changes of the geometry and electronic structure upon excitation substantially affect all these molecular properties of acetone.


106

We were also interested how interaction with water may affect properties and geometries of the studied states. Monosolvated geometries of each of the studied states were optimized at CASPT2/aug-cc-pVDZ level of theory. Water binds through the H-bond to the oxygen atom in the acetone molecule. There are four such CS configurations for the excited states (see figure below), of which one is by ~2 kcal/mol lower in energy than the other three. This is due to the antiparallel orientation of the acetone and water dipole moments (d), thus total dipole is almost zero and there is small charge separation.

Monosolvatation energies were also computed. BBSE for water-acetone interaction energies is quite large (1-3 kcal/mol) so all energies were counterpoise corrected with inclusion of geometry relaxation effect.

c)

a) b) d)

Acknowledgements: This research was supported by the Slovak Grant Agency, grant VEGA-1/0520/10 and by the Slovak Research and Development Agency APVV, contract No. LPP-0155-09. and by Comenius University, grant UK/294/2010.


107

Muonic systems with Debye-screened Coulomb

interactions

Mariusz Pawlakab, Miros�law Bylickia and Prasanta K. Mukherjeec

aInstitute of Physics, Nicolaus Copernicus University

Grudziadzka 5, 87-100 Torun, Poland

[email protected] of Chemistry, Nicolaus Copernicus University

Gagarina 7, 87-100 Torun, PolandcIndian Association for the Cultivation of Science

Jadavpur, Kolkata-700 032, India

We investigate ground states of exotic systems (ppµ, ddµ and ttµ) with Coulomb

interactions weakened by the Debye screening. We noticed that for strong screen-

ing the binding energy per particle becomes in three-particle systems larger than

in bound two-particle subsystems. Despite the repelling interaction of the nuclei,

this leads to so-called Borromean states: bound three-body states for the screen-

ing beyond the critical value for the two-body binding of nucleus-muon pair. The

method of computation involves a basis set of functions dependent explicitly on all

interparticle distances.


108

A non-adiabatic molecular dynamics study of

azobenzene isomerization after excitation to the

S1 state based on overlaps of CASSCF wave

functions

Marek Pederzoli and Jirı Pittner

J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the CzechRepublic, v.v.i., Dolejskova 3 , 18223 Prague 8, Czech Republic


Mario BarbattiMax-Planck-Institut fur Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470

Mulheim an der Ruhr, Germany.

[email protected]

Hans LischkaInstitute for Theoretical Chemistry, University of Vienna, Waehrinegrstrasse 17, A

1090 Vienna, Austria.

[email protected]

The mechanism of azobenzene photoisomerization has been debated for decades

and various mechanisms have been proposed for photoisomerization after excitation

to S1 and S2 excited states. We carried out ab initio non-adiabatic dynamical

simulations of cis-to-trans isomerization upon S1 excitation employing the Tully’s

surface hopping method with potential-energy surfaces and couplings determined

”on the fly”. The non-adiabatic couplings have been computed based on overlap of

CASCSF wavefunction.

We confirmed that the azobenzene photoisomerization after n-π excitation occurs

purely as an torsional motion via a S0/S1 conical intersection located near the

midpoint of this rotational pathway.


109

Relativistic effects on metal-metal bonding. Comparison of the performance of ECP and scalar DKH description on the picture of

metal-metal bonding in Re2Cl8(2-)

Robert Ponec,a Lukáš Bučinský,b Carlo Gattic aInstitute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic v.v.i., Prague 6, Suchdol 2, 165 02 Czech Republic bInstitute of Physical Chemistry and Chemical Physics, Slovak University of Technology in Bratislava, Bratislava, Slovakia cIstituto di Scienze e Tecnologie Molecolari del CNR (CNR-ISTM) e Dipartimento di Chimica Fisica ed Elettrochimica, Università di Milano, Via Golgi 19, I-20133, Milano, Italy

The picture of the metal-metal bonding in the Re2Cl8(2-) anion is analyzed using the

so-called domain averaged Fermi holes (DAFH) []. Besides the comparison of scalar

DKH2/B3LYP and ECP/B3LYP DAFH bonding analysis, the systematic comparison of

the “exact” atoms in molecules (AIM) [] generalized form of DAFH analysis with the

approximate Mulliken-like approach is presented. Furthermore the geometry of the

Re2Cl8(2-) anion has been reoptimized at the all-electron (AE) non-relativistic and 1-

component (scalar) and 2-component DKH2 level of theory.

The DAFH bonding analysis based on the AE-DKH2/B3LYP calculations yields

quantitatively the same conclusions as the ECP/B3LYP calculation using the AIM

population analysis. The DAFH analysis at the AE-DKH2/B3LYP level but using the

Mulliken population analysis on the other hand fails. The scalar and spin-orbit relativistic

effects at the AE-DKH2/B3LYP are not significant for the Re-Re, Re-Cl bond distances

and the angle ReReCl.

[1] Ponec R., Yuzhakov G.: Theor. Chem. Acc. 2007, 118, 791-797.

[2] Bader R.F.W.: Atoms in Molecules. A Quantum Theory, Clarendon Press, 1994.

Acknowledgement

The author (R.P.) thanks for the support of this study by the grant of the Grant Agency of

the Czech Republic, grant No: 203/118/09. The support from the grants: APVV (contract

No. APVV-0093-07) and VEGA (contracts No. 1/0817/08 and 1/0127/09) is also

gratefully acknowledged by L.B.


110

High Valent Iron-Oxo Complexes with Organic

Macrocycles: DFT and Ab Initio Study

Mariusz Radona, Ewa Broc�lawikb, Kristine Pierlootc

aDepartment of Theoretical Chemistry, Jagiellonian University Ingardena 3, 30-060

Krakow, Poland. bInstitute of Catalysis and Surface Chemistry Niezapominajek 8,

30-239 Krakow, Poland. cDepartment of Chemistry, Catholic University of Leuven

Celestijnenlaan 200F, B-3001 Heverlee (Leuven), Belgium

High valent iron-oxo complexes with organic macrocycles (porphyrin, corrole, etc.)

are usually described as Fe(IV)-oxo coupled to organic radical, so called Cpd I-type

species [1]. Nonetheless, some experiments suggest that these complexes might

have a metastable and highly reactive form, tentatively assigned as an Fe(V)-oxo

electromer [2]. The putative Fe(V)-oxo electromer might be important for catalytic

activity of cytrochrome P450 and syntethic iron-porphyrins [2]. In contrast, the

theory was sceptical as to existence of true Fe(V)-oxo species in heme environment

until very recently [1, 3, 4].

In this study [4] we investigate the relative energies of various electromeric states

for model complexes with porphyrin [FeO(P)+, FeO(P)(Cl)] and with a smaller

mimick of porphyrin [FeO(η2-N2C3H5)+

2 ] using ab initio CASPT2, RASPT2, and

CCSD(T) calculations, as well as standard DFT methods (B3LYP, B3LYP*, OLYP,

BP86). Our results suggest that all the studied complexes have a low lying Fe(V)-

oxo electromer, sometimes appearing even as the ground state. We note, however,

that the DFT results are strongly functional dependent. In particular, the hybrid

functionals strongly favor the Fe(IV)-oxo-radical form, incorrectly predicting the

Fe(V)-oxo form too high in energy. This observation might be relevant for model-

ing oxidative activity of cytochromes P450 and related enzymes, where the hybrid

functionals are used routinely.


111

References

[1] A. Ghosh: Acc. Chem Res 38, 943 (2005).

[2] (a) R. Zhang and M. Newcomb: Acc. Chem. Res. 41, 468 (2008); (b) X. Sheng,

J.H. Horner, M. Newcomb: J. Am. Chem. Soc. 130 13310 (2008).

[3] (a) F. Ogliaro, S.P. de Visser, J.T. Groves, S. Shaik: Angew. Chem. Int. Ed. 40

2874 (2001); (b) H. Chen, J. Song, W. Lai, W. Wu, S. Shaik: J. Chem. Theory

Comput. 6, 940 (2010).

[4] M. Radon, E. Broclawik, K. Pierloot: in preparation (2010).

This work was supported by the Polish State Ministry of Science and Higher

Education, by the Flemish Science Foundation and from the Concerted Research

Actions of the Flemish Government.


112

Quantum Chemical Study of the Energetics of Phenolic Compounds

Rimarčík J., Ilčin M., Rottmannová L., Klein E., Lukeš V.

Faculty of Chemical and Food Techology, SUT Bratislava Radlinského 9

SK-81237 Bratislava, Slovakia [email protected]

Hydrogen atom transfer (HAT) represents the generally accepted mechanism of

phenolic compounds (ArOH) antioxidant action. The first step of the mechanism is

phenolic O–H bond cleavage [1]. The main aim of this work is to compute reaction

enthalpies related to this process, i.e. O–H bond dissociation enthalpies (BDE) for

selected phenolic compounds. We have studied polysubstituted phenol with OH, CN or

CH3 groups (Fig 1).

Gaussian 03 program package was employed in this work [2]. Geometries of each

compound and radical were optimized using DFT method with UB3LYP functional

without any constraints using 6-311++G** basis set. Real minima were confirmed using

vibrational analysis (no imaginary frequency). All conformers were calculated and for

next processing were chosen only most stable structures.

We have calculated BDEs of phenol and substituted phenols with two, three, four

and five CN, CH3, or OH groups. We have investigated the effect of various substitutions

on O–H bond dissociation enthalpy. Cyano group was chosen as an electron-withdrawing

substituent. Results for cyano substituted phenols are compiled in table 1. Methyl group

has very low electron-donating character. OH represents an electron-donating group and

there is usual more than one hydroxy group in natural phenolic antioxidants.

Figure 1. Schematic structure of studied molecules. Various mono, di,.tri, tetra and

penta substituted phenols with a) OH, b) CN and c) CH3 groups.


113

Table 1. Bond dissociation enthalpies of cyano substituted phenols, in kJ mol-1. Data in parentheses stand for available experimental BDEs.

molecule BDE molecule BDE molecule BDE

F1CNa 353 (368) F2CNe 372 F3CNf 371

F1CNb 358 (374, 393) F2CNf 364 F4CNa 381

F1CNc 356 (377–398) F3CNa 373 F4CNb 376

F2CNa 361 F3CNb 370 F4CNc 372

F2CNb 367 F3CNc 367 F5CNa 382

F2CNc 369 F3CNd 372

F2CNd 368 F3CNe 378 Phenol 347

[1] GUGUMUS, F. Oxidation inhibition in organic materials. Vol. 1. Boca Raton: CRC Press, 1990. Chapter 4, Stabilization of plastics thermal oxidation, p. 156-157. [2] Pople J. A. et al.: GAUSSIAN 03, Revision A.1, Gaussian, Inc., Pittsburgh, PA, 2003.

Acknowledgement

The work has been supported by Scientific Grant Agency (VEGA Project 1/0137/09).


114

The Influence of Substituents on the Activity of Half-Titanocene Catalysts for Ethylene Polymerization: Theoretical Study

Agnieszka Rogowska, Artur Michalak, Monika Srebro, Mariusz Mitoraj

the Jagiellonian University, Ingardena 3,

30-060 Krakow, Poland

Polyethenes belong to the most widely used polymers, with annual production of

approximately 80 million metric tons. Due to the growing demand for such materials

there is still a need for development of new organometallic systems revealing the better

catalytic performance in the ethylene polymerization processes. Here, the combined

theoretical and experimental studies are of great importance as they enable to fully

characterize the structure-activity relationship. In this study we would like to present our

latest results on theoretical investigations of a series of the Ti-based organometallic

catalysts, at the density functional theory (DFT) level.

This theoretical study is focused on half-titanocene pentamethylcyclopentadienide

complexes (Figure) with aryloxo-based ligands (R=H, F, OCH3). It was demonstrated in

the recent experimental studies[1] that these type of catalysts could have much better

performance in the high-temperature ethylene polymerization processes even in

comparison with the commonly used in the industry Constrained Geometry Catalyst.

The main goal of the present research was to explore the influence of substituents

on the activity of the half-titanocene catalysts, concerning both, the energy barriers as

well as character of metal-ligand bonding. The Ziegler–Rauk energy-partitioning scheme

(ETS, Extended Transition State)[2] has been used to analyze the electrostatic, Pauli

repulsion, and orbital interaction contribution to the bond energy. The combined ETS-

NOCV (Natural Orbitals for Chemical Valence)[3] analysis was further applied in order

to describe bonding in terms of the contributions to the deformation density originating

from the electron donation (ligand to metal) and back-bonding (metal to ligand).


115

[1] Kim, T.-J.; Kim, S. K.; Kim, B.-J.; Hahn, J. S.; Ok, M.-A.; Song, J. H.; Shin, D.-H.;

Ko, J.; Cheong, M.; Kim, J.; Won, H.; Mitoraj, M.; Srebro, M.; Michalak, A.; Kang,

S. O. Macromolecules 2009, 42, 6932.

[2] Ziegler, T., Rauk, A. Theor. Chim. Acta 1977, 46, 1; Ziegler, T.; Rauk, A. Inorg.

Chem. 1979, 18, 1755;

[3] Mitoraj, M.; Michalak,A; Ziegler, T. J. Chem. Theory Comput., 2009, 5(4), 962;

Mitoraj, M.; Michalak,A; Ziegler, T. Organometallics, 2009, 28 (13), 3727

Acknowledgement to the Foundation for Polish Science MPD Programme co-financed by

the EU European Regional Development Fund.


116

A local Coupled Cluster algorithm

Zoltan Rolik, Mihaly Kallay

Budapest University of Technology and Economics (BME)

P.O.Box 91

H-1521 Budapest, Hungary


Many methods use localized orbitals to reduce the calculation cost of electron cor-

relation for large molecules utilizing the weak interaction between orbitals localized

far away from each other. In addition, our Coupled Cluster (CC) approach applies

the idea behind the optimized virtual orbitals [1, 2]. Unlike many methods which

divide the molecules into molecular fragments, we divide the CC energy among the

localized occupied orbitals [3]. The partial CC energy contributions belonging to

the occupied orbitals are the quantities that we estimate. For each occupied orbital

a small optimized basis set is determined [4]. Each partial CC energy contribution

is approximated using the optimized basis sets.

The presentation also shows some promising preliminary numerical results.

References

[1] Ludwik Adamowicz, Rodney J. Bartlett, and Andrej J. Sadlej J. Chem. Phys.

88, 5749 (1988).

[2] Pavel Neogrady, Michal Pitonak and Miroslav Urban, Mol. Phys. 103, 2141

(2005).

[3] Wei Li, Piotr Piecuch, Jeffrey R. Gour, and Shuhua Li J. Chem. Phys. 131,

114109 (2009).

[4] Frank Neese, Frank Wennmohs, and Andreas Hansen J. Chem. Phys. 130,

114108 (2009).


117

Thermodynamics of homolytic S–H bond dissociation in mono-substituted thiophenols

Lenka Rottmannová, Ján Rimarčík, Erik Klein, Vladimír Lukeš

Institute of Physical Chemistry and Chemical Physics, Slovak University of Technology in Bratislava, Radlinského 9, SK-812 37 Bratislava, Slovak republic

[email protected], [email protected], [email protected], [email protected]

Sulfur-centered radicals represent an important field in chemistry due to their role

in organic synthesis, biochemistry or atmospheric chemistry. Therefore, this study is

devoted to S–H bond cleavage in thiophenols, ArSH → ArS● + H●. This work presents

the study of 14 mono-substituted thiophenols (Fig. 1).

SHX SH

Y Fig. 1 Studied thiophenols, X = OMe, Me, F, Cl, Br, COOMe, CF3, NO2, Y = OMe, Me, Cl, Br, CF3, NO2

Selected compounds and their radicals were studied using DFT/UB3LYP/6-

311++G** approach using Gaussian 03 program package [3]. BDEs were approximated

from total electronic energies.

Calculated BDEs were compared with available experimental values. Bordwell et

al. [1] studied mono-substituted thiophenols employing electrochemical (EC) method that

uses the equilibrium acidity (pKa) and oxidation potential (Eox) values of the conjugated

anion for BDE calculation. Zhu et al. [2] obtained BDEs using thermodynamic cycle

(TDC) method. The method is close to EC method. All experimental values represent

solution-phase values in dimethylsulfoxide (DMSO). Semi-empirical methods do not

provide correct BDE values for thiophenols. However, they reliably reproduce the

substituent effect on BDE. MP2 method overestimates individual BDEs, however

provides the range of substituent induced BDE changes in good agreement with

experiments. Used DFT approach describes BDEs and substituent induced changes in

best accordance to experimental works.


118

Tab. 1 BDE values in kJ.mol–1 of substituted thiophenols and Hammett constants.

Substituent ECa TDCb PM3c AM1c DFT MP2c σp,md

— 331 331 377 363 334 352 p-OMe 322 322 372 358 321 345 –0.27 p-Me 328 328 375 361 329 349 –0.17 m-Me 330 330 376 362 333 352 –0.07 p-F 376 359 349 0.06 m-OMe 378 363 356 0.12 p-Cl 331 331 376 362 332 353 0.23 p-Br 332 332 379 363 333 354 0.23 m-Cl 335 335 378 363 337 0.37 m-Br 378 363 0.39 m-CF3 338 338 380 365 340 0.43 p-COOMe 381 368 0.45 p-CF3 383 368 0.54 m-NO2 384 368 0.71 p-NO2 341 341 388 370 347 361 0.78 a Data taken from Ref. [1]. b Data taken from Ref. [2]. c Data taken from Ref. [4]. d Data taken from Ref. [5]. References

[1] Bordwell F.G., Zhang X.-M., Satish A.V., Cheng J.-P.: J. Am. Chem. Soc. 119 (1997)

9125.

[2] Zhu Q., Zhang X.M., Fry A.J.: Polym. Degrad. Stab. 57 (1997) 43.

[3] Pople J. A. et al.: GAUSSIAN 03, Revision A.1, Gaussian, Inc., Pittsburgh, PA, 2003.

[4] Klein E., Lukeš V., Cibulková Z., Polovková J.: J. Mol. Struct. (Theochem) 758, 149

(2006).

[5] Hansh C., Leo A., Taft R. W.: Chem. Rev. 91 (1991) 165.

Acknowledgement

This work was supported by the Scientific Grant Agency of the Slovak Republic

(Projects VEGA 1/0127/09 and 1/0137/09).


119

Computational study of weak interactions in the biologically active compounds

Scholtzová Eva and Mach Pavel

Institute of Inorganic Chemistry, Slovak Academy of Sciences,Dúbravská cesta 9

SK-845 36 Bratislava, Slovak [email protected]

Imidazo [2,1-b] thiazoles are intensively studied in the connection with search for

biologically active compounds. The fused rings system of imidazo [2,1-b] thiazoles

exhibits biological activities like antitumor, antitubercular, cardiovascular, herbicidal,

antibacterial, and antihelmintic activity. Presented imidazo [2,1-b] thiazoles are

interesting also due to weak interactions acting in these structures which are on the border

of the weak hydrogen bonds and electrostatic interactions. Because of their non/local

(long-range) character, these dispersion interactions are accurately accounted for only by

correlated wavefunction based methods like MP2, CCSD(T) or DFT-D method, which

adds to the energy special empirical dispersion term. The aim of this study is a detailed

analysis of weak interactions in the presented biologically active structures. The RI-MP2

and DFT-D methods implemented in the TURBOMOLE package were used for

calculation of the interaction energies of the individual weak interactions.

In the case of two imidazo [2,1-b] thiazoles (A and B) the dispersion interaction is

dominant. In the cluster of (A) structure (Fig. 1) the most tightly bound is 1-3 dimer (-

18.2 kcal/mol) against 2-3 dimer (-8.2kcal/mol) and 1-2 one (-7.1 kcal/mol). For smaller

model of C5-N5C N1 interaction the calculated DFT-D interaction energy at B97-

D/TZVPP (-9.6 kcal/mol) level of theory showed good agreement with more rigorous RI-

MP2 energy extrapolated to the CBS limit (-12.08 kcal/mol). One should keep in mind

that generally MP2 method at CBS limit overestimates dispersion energy, roughly by

20%, so both methods are in harmony.

In the case of (B) structure, there are stacks of parallel molecules, from which we

can singlet out two dimers (Fig. 2): one with C–H O short contacts and another with C–

H N1 contacts. The interaction energy is in the first case -22.5 kcal/mol (B97-D/TZVPP

level) and in the second -21.3 kcal/mol. As standard DFT method (B3LYP) supply for


120

these interactions only small bonding energies (-3.9 kcal/mol for the first case) and

slightly repulsive (2.4 kcal/mol in the second case), it is clear that bonding is in high

extend due to the dispersion. In the next step the RI-MP2 method and extrapolation of the

interaction energy to the CBS limit was used for the calculation of the interaction

energies of the individual weak interactions in the both (A) and (B) structures. The

analysis of calculated data showed that both (A) and (B) structures are stabilized mainly

by dispersion energy and also by weak hydrogen bonds of C–H···N> C–H···O> C–H···S

type and C–H···π and π···π stacking type of weak interactions (Table 1).

Tab. 1 Interaction energies for (A) and (B) structures.

ig. 1 Cluster model for examination of dispersion energy

tion of dispersion energy in (B).

cknowledgement: Finantial support for this research by the Slovak Grant Agency (grant no. VEGA /0150/09) is gratefully acknowledged.

D–H···A (A) D–H···A (B)C1–H1B···S1 -1.11 C8–H18···S1 -1.37C5–H5B···N1 -5.38 C20–H20···N1 -3.29C5–H5C···N1 -12.08 C16–H16···O1 -2.52C1–H1C···O1 -2.56 C5–H5C···O1 -3.054x CH···π -6.03 intra CH···π -0.9

F

in (A).

Fig. 2 Cluster models for examina

A2


121

TD-DFT investigation of S1 and S2 singlet states of TMPyP(n) and complexes of

TMPyP4 with sulfonated calix[m]arenes

Jakub Šebera1, Stanislav Záliš1, Pavel Kubát1, Kamil Lang2, Tomáš Polívka3

[email protected] J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech Republic,

Dolejškova 3, CZ 18223, Prague, Czech Republic 2 Institute of Inorganic Chemistry, v.v.i., Academy of Sciences of the Czech Republic, 250 68

Řež, Czech Republic3 Institute of Physical Biology, University of South Bohemia, Zámek 136, Nové Hrady 37333,

Czech Republic

Photophysical and binding properties predetermine tetrakis (4-N-methylpyridyl)

porphyrin (TMPyP4) as efficient photosensitizer in many artificial light-harvesting systems as

well as in medicine for photodynamic therapy of tumors or bacteria/virus inactivation.

Organizing TMPyP4 molecules through noncovalent host−guest interaction with a range of

guests like nucleic acids/proteins, calixarenes, cyclodextrins, carbon nanotubes, PAMAM

dendrimers, graphene, cucurbituril or their incorporation into micelles, methyl viologen-

hybrid and nafion films, semiconductors, layered silicates, laponite, hydrogels and other solid

materials finds immense importance in creating ordered structures of specific functionality.

Isoelectronic TMPyP2 and TMPyP3 can modulate properties of resulting supramolecular

complexes due to rotational barrier of N-methylpyridyl groups.

Water-soluble p-sulfonatocalixarenes clxm possess the three-dimensional, flexible,

π-electron rich cavities that can adopt different conformations, form complexes with many

compounds and have diverse biomedical applications e.g they can serve as transportation

vehicles for porphyrin drugs. The number of conformations increases with the number of

4-hydroxy-benzenesulfonate units in the system, although this also depends on the solvent

and the nature of the guest.

We have used TD-DFT and DFT calculations to study (photoinduced) charge transfer

in tetrakis(n-N-methylpyridyl)porphyrins TMPyPn (n=2,3,4) and TMPyP4/p-

sulfonatocalix[m]arenes clxm (m=4,6) complexes and to interpret transient absorption

spectroscopy, cyclic voltametry experiments and UV-Vis absorption spectra. Density

functionals MPW1B95 and B3LYP were used. The effect of solvent (water) was described by

Conductor-like Screening Model (COSMO). Excitation of TMPyPn into S1 state is


122

accompanied by increasing of electron density at methylpyridyl groups in the following order:

TMPyP2 < TMPyP3 < TMPyP4. Further results on characterization of S1 and S2 singlet states

will be presented. The examples of the investigated complexes are depicted in Figure 1.

Figure 1. DFT optimized geometries of TMPyP4-clx4 (left) and TMPyP4-clx6 (right). Both

systems have partly ionized OH groups.

Acknowledgement: The access to the METACentrum supercomputing facilities is highly

acknowledged. This research was supported by the Czech Science Foundation (No.

P208/10/1678).


123

Application of OVOS technique in calculations of small semiconductor clusters.

L. Šimováa, P. Neográdya and M. Urbana,b

aDepartment of Physical and Theoretical chemistry, Faculty of Natural

Sciences,Comenius University, Mlynská dolina, 842 15 Bratislava, Slovakia bSlovak University of Technology in Bratislava, Faculty of Materials Science and Technology, Institute of Materials Science, J. Bottu 25, 917 24 Trnava, Slovakia

[email protected]

Following our previous work on small semiconductor clusters Ga2N2, In2N2,

[1,2] we now present CCSD(T) calculations of germanium nitrides and phosphides.

Gallium, Indium and Germanium species are of interest in the semiconductor

materials science and are technologically interesting due to their applications in

optoelectronics and nanotechnologies. Information on the structure, energetics and

molecular properties of small clusters of these species in different spectroscopic

states, can be useful for understanding basic processes in the above mentioned areas.

We hope that accurate CCSD(T) data for small clusters containing Ga, In, Ge,

N, P and C or Si can be eventually exploited as benchmark results for various DFT

techniques, which can be applied for larger clusters related to technological

applications.

Fig.1: Lowest energy structures of 4- and 6- atomic gallium phosphide and

aluminium phosphide clusters.

Clearly, in CCSD(T) calculations of molecules containing Ga, In, or Ge their

subvalence d-shell must be correlated. This requires [2] using large (aug)-cc-pCVXZ

or similar basis sets constructed having in mind correlation of deeper shells of these

elements, which is computationally demanding. We will show that the OVOS

(Optimized Virtual Orbital Space) technique [3] with the virtual space of (aug)-cc-

pCVXZ basis sets reduced to the size corresponding to less extended valence-only


124

(aug)-cc-pVXZ bases allows investigations of complexes containing group 13 and 14

elements with no reduction of the accuracy.

References:

[1] M. Kraus, L. Šimová, P. Neogrády, M. Urban, Mol. Phys. 108, 467 (2010);

[2] L. Šimová, D. Tzeli, M. Urban, I. Černušák, G. Theodorakopoulos, I.D. Petsalakis,

Chem. Phys. 349, 98 (2008).

[3] P. Neogrády, M. Pitoňák, J. Granatier, M. Urban, Coupled Cluster Calculations: Ovos As

An Alternative Avenue Towards Treating Still Larger Molecules, in Recent Progress in

Coupled Cluster Methods, Eds. P. Čársky, J. Paldus, J. Pittner, Springer, 2010.

Acknowledgements: The support by the the Slovak Grant Agency VEGA--1/0520/10

and by EURATOM CU assoc., Task 4.2 - P1c is acknowledged.


125

Benchmark electron density calculations on

Be-like atoms

R. S�lupskia), J. Komasab), K. Jankowskic), and J. Wasilewskic)

a)Computing Centre, Nicholas Copernicus University,PL-87-100 Torun, Poland

b)Department of Chemistry, Adam Mickiewicz University,PL-60-780 Poznan,Poland

c)Faculty of Physics, Astronomy, and Informatics, Nicholas Copernicus University

PL-87-100 Torun, Poland

Electron densities obtained in the most accurate variational calculations on the

ground state of several members of the beryllium-isoelectronic series are applied in

comparative studies of the performance of several broadly used ab initio methods in

representing electron densities in the presence of varying non-dynamical correlation

effects. The present calculations involved from 4800- to 9000-term exponentially cor-

related Gaussians (ECG) basis functions defined by carefully optimized nonlinear

parameters [1]. The densities for the remaining methods are calculated by means of

GAUSSIAN03 for basis sets partially optimized for the individual ions. To concen-

trate our attention on the correlation effects, we employ a density-based graphical

approach directly hinged on difference radial density (DRD) distributions defined

with respect the Hartree-Fock (HF) radial density in the following way:

dA(r) = DA(r) − DHF (r), (1)

with

DA(r) = 4πr2ρA(r), (2)

where A indicates the method of accounting for correlation effects.

The benchmark DRDs are obtained when using DHF (r) generated for the Froese-

Fischer numerical Hartree-Fock wave function.

It has been demonstrated [2] that, although the impact of correlation effects

on the electron density is relatively weak, the DRD distribution curves provide a


126

reliable description of the impact of electron correlation effects both at the WFT

and DFT levels.

To provide the possibility of precise comparison of different results we report also

values of total radial densities for several r-values.

References

[1] J. Komasa, J. Chem. Phys. 110, 790 (1999)

[2] K. Jankowski, I. Grabowski, K. Nowakowski, and J. Wasilewski, J. Chem. Phys.

130, 164102 (2009).


127

Comparison of the several correlated OEP

methods in KS-DFT with correct asymptotic

behavior.

Szymon Smiga, Ireneusz Grabowski

Institute of Physics, Nicolaus Copernicus UniversityGrudziadzka 5/7


[email protected]

In recent years, a large emphasis is placed on the development of methods for the

proper inclusion of the electron correlation effects [1, 2] in the Optimized Effective

Potential (OEP) methods and the correct asymptotic behavior of the exchange-

correlation potentials [4, 5]. To show that the inclusion of the additional linear

correction term to OEP exchange potential improves asymptotic behavior of the

OEP potentials, to different types of the ab initio KS–OEP calculations has been

performed for a few atoms (He, Be, Ne). Conventional correlated OEP results,

has been compared with the results obtained with the correlated OEP calculations

where the optimized local potential have the Slater type of asymptotic behavior

In addition to compere KS-OEP result with ab initio wave function theory results,

MP2 and CC calculations has been performed.

The results were compared in the terms of total ground state energies, correlation

energies, exchange–correlation potentials and the electron radial density [3]. Ana-

lysis of the energies, potentials and the electron radial density clearly showed, that

the results obtained in the correlated OEP calculations with linear correction signi-

ficantly improves shape of exchange-correlation potentials while the total energies

remain essentially the same. The highest occupied orbital energies from the asymp-

totically corrected exchange-correlation potentials are found to provide significantly

more accurate approximations to the ionization potential than those without the

asymptotically corrected exchange-correlation potentials.


128

Figure.1. Comparison of the exchange-correlation potential of the helium atom

obtained for few KS-OEP methods and MP2, CC calculations.

Literatura

[1] I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett. J. Chem. Phys., 116:4415,

2002.

[2] I. Grabowski and V. Lotrich. Mol. Phys., 103:2087, 2005.

[3] I. Grabowski K. Jankowski, K. Nowakowski and J. Wasilewski. J. Chem. Phys.,

130, 2009.

[4] R. Nesbet R. Colle. Optimized effective potential in finite-basis-set treatment.

J. Phys. B, 34(12):2475, 2001.

[5] R. Bartlett S.Ivanov, S. Hirata. Finite-basis-set optimized effective potential

exchange-only method. J. Chem. Phys., 116, 2002.


129

Theoretical Study of Ionization and Excitation of

He Gas Exposed to Intense XUV Radiation

Jan Smydke, Petra Ruth Kapralova

J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of theCzech Republic, v.v.i., Dolejskova 3, 182 23 Praha 8, Czech Republic

andInstitute of Physics, Academy of Sciences of the Czech Republic, v.v.i.,

Na Slovance 2, 182 21 Praha 8, Czech Republic


A recent advent of extreme ultraviolet (XUV) and soft X-ray (SXR) lasers enables

investigation of interactions of high-frequency, high-amplitude electromagnetic field

with atomic and molecular gases. A theoretical description of an isolated He atom

in strong femtosecond and nanosecond pulses of 50 nm laser radiation is presented.

The interaction of the field and the atom can be described in a semiclassical

dipole approximation due to the large strength of the field (109−1016 W cm−2) and

relatively small size of the investigated atoms compared to the wavelength of the

radiation, such that the Hamiltonian is given by

H = H0 + Az0 f(t)ε0ω

c(z1 + z2) sinωt

where H0 denotes the field-free Hamiltonian; Az0, the pulse strength at the maxi-

mum; f(t), the pulse modulation (0 < f(t) < 1); ε0, the permitivity of vacuum; c,

the speed of light; ω, the field oscillation; and z1, z2 the electronic coordinates.


130

In analogy to the Born–Oppenheimer approximation, the slow pulse modulation

can be adiabatically separated from the fast field oscillation and electronic motion.

In this spirit, the adiabatic states are represented by the quasistationary states |Φk〉

of the Floquet Hamiltonian, which is defined as

HF = H0 + Azε0ω

c(z1 + z2) sinωt− ih

∂

∂t

where Az represents a constant vector potential of a continuous electromagnetic

wave.

Finally, the nonadiabatic time-dependent wavefunction |Ψ(t)〉 is obtained by ex-

panding it in the basis of the quasistationary states

|Ψ(t)〉 =∑

k

|Φk;Az〉χk(t)

and solving the expansion coefficients. (Note the field strength Az = Az0f(t) is a

time-dependent parameter of the basis.)

Due to the ionization effect, which causes the quasistationary states to include an

outgoing part of the ionized electron, we apply the complex scaling transformation of

the Floquet Hamiltonian, which enables to calculate the quasistationary resonances

(i.e. “meta-stable states”). Thus the obtained quasienergies are complex, where

their imaginary parts represent ionization rate constants.

In this contribution, we present the first results, namely the calculated ionization

rate constant as a function of laser strength. These data will be readily useful for an

interpetation of an experiment using long laser pulses, which will be performed at

Institute of Physics. In a subsequent calculation, we are going to provide ionization

yields for short laser pulses.

The calculations are performed with our own codes using a complex scaling Full-CI

method and a (t, t′)-method for the quasistationary states.


131

Femtosecond non-adiabatic molecular dynamics: a study of photochemical deactivation of indole

Lukáš Sobek, Jiří Pittner

J. Heyrovsky Institute of Physical Chemistry of the ASCR Dolejškova 2155/3, 182 23 Prague 8, Czech Republic

[email protected] [email protected]

Photochemical behavior of indole can be explained by the presence of polarity

dependent channel of radiationless deactivation attributable to hydrogen predissociation

from NH bond in non-polar non-hydrogen bonding solvents and photoinization in water

as presented in [1]. Our goal is performing the simulation of the deexcitation process with

the quasi-classical molecular dynamics (MD) in which non-adiabatic transitions are

computed by the Tully's fewest switches surface hopping algorithm [2].

We employed the state-averaged complete active space self-consistent field

method (SA-CASSCF) using standard split-valence double zeta Gaussian basis set 6-31

G with polarization functions on carbon atoms and on the hydrogen atom of the NH

group. Correct description of σ* orbital located near NH bond needed s- and p-diffuse

functions (exponent 0.0639) located on the nitrogen atom and s-diffuse function

(exponent 0.036) centered on the adjacent hydrogen atom. The active space involved 10

electrons in 8 orbitals. Four lowest quantum states of indole, i.e. S0, S1 (La), S2 (Lb) (both

of ππ* character) and S3 (σπ*) were treated with weight 0.25 in the state-averaging

procedure.

Potential energy profiles along the NH-bond stretch were computed by means of

coordinate-driven minimum-energy-path approach: for a given value of bond distance all

remaining intramolecular coordinates were optimized with CASSCF analytical gradient.

Initial conditions for the MD simulation were sampled using the Wigner distribution for

temperature 300 K, starting from S2 state (excitation UVc computed wavelength 250 nm).

Total 69 trajectories were run for 500 fs each. We performed exponential fitting of the S2-

state-depopulation curve and obtained the half-time of depopulation of 11.9 fs.


132

[1] A.L.Sobolewski, W.Domcke: Ab initio investigations on the photophysics of indole,

Chem.Phys.Letters 329 (2000) 130 - 137

[2] J.C.Tully: Mixed quantum-classical dynamics, Faraday Discuss 110 (1998) 407-419


133

Theoretical study of radical sites in gallic and protocatechuic acids

Roland Šolc,1 Daniel Tunega,1,2 Martin H. Gerzabek,1 and Hans Lischka2

1 Institute of Soil Research, University of Natural Resources and Applied Life Sciences, Peter-Jordan-Strasse 82b, A-1190 Vienna, Austria,

2 Institute for Theoretical Chemistry, University of Vienna, Währinger Strasse 17, A-1090 Vienna,Austria


Humic acids (HA) represent a group of organic macromolecules with high

structural complexity and multiple properties. HAs contain stable organic radical

moieties and are involved in important biochemical and chemical environmental

processes. The high structural heterogeneity and complexity of humic acids leads to

problematic their characterization and interpretation of experimental data. Despite, it is

known that the major part of HAs functional groups include carboxylic (R-COOH),

phenolic (R-OH), and/or carbonyl (C=O) group. Thus, a viable approach is to examine

appropriate small organic molecules as models of humic macromolecules or their

components [1,2]. While simple organic acids do not approach the structural and

functional complexity of real humic acids, detailed studies demonstrated that certain

important features can be remarkably similar [3,4].

Hydroxybenzoic acid derivatives such as gallic acid (GA) or protocatechuic acid

(PA) represent very suitable models for a study of radical sites in HAs [5]. In this work,

a theoretical investigation of the radical stability of GA and PA is presented. All

calculations were performed by means of a density functional theory approach (DFT).

In the first step, all possible radical, anion, and radical-anion structures were generated

and the full geometry optimization was performed on them at the B3LYP/TZVP level of

theory. The solvent effect on the radical stability and geometry was investigated as well.

The EPR and NMR parameters were calculated using the B3LYP/EPRII approach, both

for gas phase and solvent optimized geometries. Calculated EPR and NMR values were

compared with available experimental data.

[1] Kummert, R., Stumm, W., J. Colloid Interface Sci. 75, 373 (1980).

[2] Banaya, L., Garnier, J.-M., Environ. Sci. Technol. 33, 1398 (1999).


134

[3] McBride, M. B.,Wesselink, L. G., Environ. Sci. Technol. 22, 703 (1988).

[4] Boily, J.-F., Fein, J. B., Chem. Geol. 148, 157 (1998).

[5] Giannakopoulos, E., Stathi, P., Dimos, K., Gournis, D., Sanakis, Y., Deligiannakis,

Y., Langmuir, 22, 6863, (2006).

Acknowledgment - We are grateful for the financial support from the Austrian Sciences Fund (project P20893-N19), and the German Research Foundation, the priority program SPP 1315 (project GE1676/1-1). The authors also acknowledge the technical support and computer time at the Vienna Scientific Cluster.


135

Charge Sensitivity Analisys in Force Field Atoms Resolution

Anna Stachowicz and Jacek Korchowiec

Jagiellonian University, Department of Theoretical Chemistry ul. R. Ingardena 3, 30-060, Kraków, Poland


Charge Sensitivity Analysis (CSA) was formulated in the nineties [1]. The formalism

is rooted in Density Functional Theory (DFT) and can be applied at different resolutions: local,

molecular orbital, atoms-in-molecule (AIM), fragment and global. It refers to such concepts

as electronegativity and hardness/softness data; all of them are rigorously defined within DFT.

CSA provides a thermodynamic-like description of the system’s equilibrium charge distribution

and allows to describe its response to external potential and/or electron population perturbations.

It has normally been used as a method complementary to ab initio calculations but it can likewise

be treated as an independent semi-empirical method. One of the realizations of CSA

is Electronegativity Equalization Method (EEM) for evaluating the charge distribution

in a molecule at global equilibrium [2].

EEM is a very fast method and is usually adopted in AIM resolution in Molecular

Mechanics/Dynamics (MM/MD) software for computing initial charge distribution. It should

be expected that by extending CSA to force field atom resolution the area of its application will

be enlarged, e.g., to polarizable force fields. To enable this the atomic hardnesses and

electronegativities have to be parameterized. This is the goal of our work. The AMBER force

field has been employed here and the set of parameters for all standart atom types of the force

field has been determined by fitting to the ab initio charge distribution of a set of test molecules.

Ab initio charges were obtained via two methods, namely Mulliken Population Analysis (MPA)

and charges derived from electrostatic potential fitting procedure. The optimization was

performed with an evolutionary algorithm on a population of 50 entities.

The results obtained were satisfactory. The agreement between ab initio and EEM charges was

good, especially for MPA charges. The correlation coefficient R2=0.9699 was obtained,

which is accurate enough to start applying EEM in the MM/MD calculations.


136

[1] R. F. Nalewajski, J. Korchwiec, Charge Sensitivity Approach to Electronic Structure and

Chemical Reactivity, Word Scientific Co. Pte. Ltd., Singapore, 1997

[2] W. J. Mortier, S. K. Gosh, S. Shankar, J. Am. Chem. Soc., 108 (1986) 4315


137

Cold electron collisions with nonpolar molecules

M. Sulc, R. Curık

J. Heyrovsky Institute of Physical Chemistry

Dolejskova 3

182 23 Prague 8, Czech Republic

[email protected]

We investigate collisions of cold electrons (incident energy below 1 eV) with di-

atomic nonpolar molecules by combination of the body frame rigid rotor approxima-

tion with the adiabatic frame transformation [1, 2]. Electron-molecule interaction is

in case of e−–N2 process described for benchmarking purposes in an ab-initio man-

ner by the static-exchange plus polarisation (SEP) model similar to [3]. Even this

approximation leads to an acceptable agreement with experimental data measured

at the ASTRID laboratory [4]. The reactance matrix is further parametrised with

a few quantities. Their energy dependence is then determined from the experimental

data by fitting of the total and backward scattering cross-sections. This information

makes consequently the physical description within our approach complete and we

can in principle predict individual rotational state-to-state cross-sections and thus

separate the (rotationally) elastic and inelastic processes, which is experimentally

unachievable. Obtained theoretical results therefore find application especially in

plasma related fields such as astrophysics, physics of interstellar media as well as

semiconductors (micro-devices) production [5]. Results are compared to data avail-

able in literature [6] and also to predictions based on the Modified Effective Range

Theory (MERT) models [7].

Acknowledgements

We gratefully appreciate the substantial financial support of the Grant Agency of the

Czech Republic (grant no. 202/08/0631), the Grant Agency of the Czech Academy of

Sciences (grant no. KJB400400803) and the Grant Agency of the Charles University

in Prague (grant no. 113210).


138

References

[1] W.M. Huo and F.A. Gianturco. Computational methods for Electron-Molecule

Collisions. Plenum Press, New York, 1995.

[2] U. Fano and S. Chang. Theory of electron-molecule collisions by frame transfor-

mations. Phys. Rev. A, 6:173–185, 1972.

[3] S. Telega and F.A. Gianturco. Electron–molecule scattering in gases at very

low energies: a comparison of theory and experiment for the nitrogen target.

Mol. Phys., 104(November):3147–3154, 2006.

[4] S.V. Hoffmann, S.L. Lunt, N.C. Jones, D. Field, and J.-P. Ziesel. An undulator-

based spherical grating monochromator beamline for low energy electron-

molecule scattering experiments. Rev. Sci. Instrum., 73:4157–4163, 2002.

[5] M.A. Morrison. The physics of low-energy electron-molecule collisions (a guide

for the perplexed and the uninitiated). Aust. J. Phys., 36:239–286, 1983.

[6] M.J. Brunger and S.J. Buckman. Electron-molecule scattering cross-sections I –

experimental techniques and data for diatomic molecules. Phys. Rep., 357:215–

458, 2002.

[7] W.A. Isaacs and M.A. Morrison. Modified effective range theory as an alternative

to low-energy close-coupling calculations. J.Phys. B, 25:703–725, 1992.


139

OVOS technique with controlled accuracy in noniterative triples calculations

Martin Šulka, Michal Pitoák, Miroslav Urban, Pavel Neogrády

Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University Mlynská dolina CH1

84215 Bratislava, Slovakia [email protected]

Performance of optimized virtual orbital space (OVOS) technique with controlled

accuracy approach, introduced by Kraus et al. [1], was studied. They have shown that

there is roughly linear dependence between the Y2,MP2 correction and post-MP2

corrections (Y2,CCSD, Y2,T3) in coupled cluster CCSD(T) method in logarithmic scale. This

fact opens up the possibility to control the accuracy of the whole calculation via the

Y2,MP2 correction.

Eight molecules from S22 series [2] were chosen in our calculations. For four of

them, dependence between post-MP2 corrections and Y2,MP2 correction is shown in

Figure 1.

Figure 1 Dependence between log(Y2,MP2) and log(Q), where Q is Y2,CCSD and Y2,T3


140

We can see that both post-MP2 corrections are nearly linearly dependent on Y2,MP2

and at the same time the triples correction is much smaller than CCSD correction. From

the controlled accuracy point of view, it is optimal to perform calculation of all

contributions with the same level of accuracy. Since the error introduced by triples step in

CCSD(T) is smaller than that introduced at CCSD level, we can make some profit from

additional reducing of virtual space just before the triples step, up to such extension at

which we reach the same level of accuracy (expressed in terms of Y2,CCSD and Y2,T3

corrections) in both CCSD and T3 steps. In our calculations we wanted to evaluate the

measure of possible reduction before the triples step in CCSD(T). Table 1 summarizes

our results, where the final dPOVOS results in eventual additional reduction before the

triples step.

Table 1 Reductions of virtual space at CCSD and T3 levels at the same level of accuracy

(POVOS) and their difference (dPOVOS)

Average possible reduction in our case was about 32 percent. Since the triples step is the

most demanding step in CCSD(T) calculation (scales with N7), this would mean

considerable saving of computational time.

[1] Kraus, M. Pitoák, P. Hobza, M. Urban, P. Neogrády – To be published

[2] P. Jureka, J. Šponer, J. erný, P. Hobza; Phys Chem Chem Phys 8, 1985-1993, 2006

Acknowledgement

This work was supported by the Slovak Research and Development Agency, contracts

No. APVV-20-018405, APVV-LPP-0155-09, and the Slovak Grant Agency VEGA under

contract No. 1/0428/09.


141

Substituent effect on OH- addition to substituted benzocyclobutene-1, 2-diones: A DFT study

Nargis Sultana and Walter M. F. Fabian

Institut für Chemie, Karl-Franzens-Universität Graz Heinrichstrasse 28/I 8010 Graz, Austria

[email protected]

A DFT study on the reaction route and chemical reactivity for the addition of OH- (a

nucleophile) to substituted (poly) carbonyl compounds is carried out by using [B3LYP/6-31+G (d, p)].

1,2-dicarbonyls undergo three types of reaction following addition of OH–, (1) benzyl–benzilic acid

rearrangement (path A); (2) fission of the α-carbon – carbonyl carbon bond (path B); and (3) fission of

the carbonyl carbon – carbonyl carbon bond (path C).1

In all cases, the primary element of such reactions is the formation of tetrahedral adduct (2) as an

intermediate. In this study, the extremes of substituent effect on the formation of (2)resulting from the

attack of OH- as a nucleophile on the substituted benzocyclobutene-1,2-dione (I) leading toadduct (2)

has been explored. The model systems used in the calculations contains [OH (H2O)4]– + [I.(H2O)2],

Y=-OCH3 and -NO2 groups. The investigation of chemical reactivity has been accomplished by

conventional density functionaltheory2; electrophilicity indexes.

O

O O

OH

OH

OCOOH

OHCOO

COO

O

OHR1 R2

R2R1

_

1 2

R1

R2

R1

R2

_path A

path BR1

_+

4

path C

3

+ R2H

5 6

R1CHO + R2COO_

7 8

O

O

Y

Benzocyclobutene-1,2-dione (I)

Y= -OCH3, -NO2

[1] Bwden, K.; Fabian, W.M.F. J. Phys. Org. Chem. 2001, 14, 794.

[2] Fuentealba, P., Contreras, R.R., Reviews of Modern Quantum Chemistry, World

Scientific, 2002, Volume II.


142

Calculations of fine-structure resolved collisional

rates for NH(X3Σ−)-He system

Robert Tobo�la1, Fabien Dumouchel2, Jacek K�los3, Francois Lique2

1Faculty of Chemistry, University of Warsaw,

Pasteura 1,

02-093 Warsaw, Poland

[email protected]

2LOMC - Universite du Havre,

25 Rue Philippe Lebon,

BP 540 - 76 058 Le Havre Cedex, France

3Department of Chemistry and Biochemistry - University of Maryland,

College Park,

20742-2021 Maryland, USA

We present the first to date fine-structure-resolved collisional rate coefficients for

NH(X3Σ−)-He van der Waals complex. The calculations are based on the state-of-

the-art potential energy surface of Cybulski at al. [H. Cybulski, R. V. Krems, H.

R. Sadeghpour, A. Dalgarno, J. K�los, G. C. Groenenboom, A. van der Avoird, D.

Zgid, and G. Cha�lasinski, J. Chem. Phys. 122, 094307 (2005)]. Close-coupling cal-

culations of the collisional excitation cross sections of the fine-structure levels of NH

by He are calculated for total energies up to 3500 cm−1, which yield, after thermal

average, rate coefficients up to 350 K. The fine-structure splitting of rotational levels

is taken into account rigorously. The propensity rules between fine-structure levels

are reported, and it is obvious that F -conserving cross sections are much larger

than F -changing cross sections, as expected from theoretical considerations. The

calculated rate coefficients are compared with available experimental measurements

at room temperature and a fairly good agreement is found between experimental

and theoretical data. The agreement confirms the relatively good quality of the

scattering calculations in this work.


143

Wetting of clay mineral surfaces – molecular dynamics simulation

Daniel Tunega,1,2 Roland Šolc,1 Hasan Pašalić,2 Martin H. Gerzabek,1 and Hans Lischka2

1 Institute for Soil Science, University of Natural Resources and Applied Life Sciences, Peter-Jordan Strasse 82b, A-1190 Vienna, Austria

2 Institute for Theoratical Chemistry, University of Vienna, Währingerstrasse 17, A-1090 Vienna, Austria


Wettability of minerals is primarily related to an energetic characteristic of surfaces

affecting processes as adhesion, friction, detergency, biofilm growth, etc. The wetting

ability of a solid surface is mainly determined by its chemical composition, structure and

topography [1]. The solid-liquid contact angle method is often used to characterize

wettability of surfaces and to determine its surface free energy.

Clay minerals represent a group of geochemically and industrially important

materials. They also belong to a substantial part of inorganic soil matter and significantly

affect overall properties of soils. Owing to compositional variability ad structural

complexity various clay minerals behave considerably differently with respect to wetting.

In order to elucidate structural and compositional factors affecting

hydrophilic/hydrophobic character of clay minerals, interactions of water nanodroplets

with basal surfaces of selected clay minerals (particularly kaolinite and phlogopite) were

investigated by means of classical molecular dynamics simulations at room temperature.

From the evolution and shape of the nanodroplet on the surfaces it was possible to

characterize hydrophobic/hydrophilic character of studied surfaces. In case of the

kaolinite octahedral surface formed from surface hydroxyl groups, the water droplet was

completely spread and a monomolecular network of hydrogen-bonded water molecules

was formed. In opposite, the tetrahedral surface, which is formed from basal oxygen

atoms, is less interacting with the water nanodroplet and the shape of the droplet is

partially preserving. The molecular simulations clearly showed a difference between both

basal surfaces of kaolinite. While the octahedral surface is clearly hydrophilic, the

tetrahedral surface has partially hydrophobic character. Structural and energetic aspects

of both surfaces are obtained as well.


144

Fig. 1 Water density profile (in g/cm3) of water

nanodroplet on tetrehadral kaolinite surface.

(500 water molecules, 2 ns MD, 300K).

[1] Bachmann, J. et al., (2000) Soil Sci. Soc. Am. J., 64, 564-567.

Acknowledgement - We are grateful for the financial support from the Austrian Sciences

Fund (project P20893-N19), and the German Research Foundation, the priority program

SPP 1315 (project GE1676/1-1). The authors also acknowledge the technical support and

computer time at the Vienna Scientific Cluster.


145

Optimalizations of the molecular clusters by the evolutional algorithms method

Lucie Zárubová, Karel Oleksy

Department of Physics, Faculty of Science, University of Ostrava 30. dubna 22

70103 Ostrava, Czech Republic [email protected]

This work focuses on searching for suitable parametrs in our computer programme

based on genetic algorithms. We tested various parameters – for Lennard-Jones clusters with

10 and 30 molecules we tested dependence of number of optimizations on the number of

processors used; for water clusters (H2O)n of n = 2-13 molecules we tested dependence of

energy evolution during the program progress, which was confronted with [1]; and for water

cluster with 11 molecules we tested suitability of various evolution operators (probability of

genotype mutation, phenotype mutation, cut by plane, crossover coordination, crossover

cluster) used.

0 10 20 30 40

4,30

4,32

4,34

4,36

4,38

4,40

4,42

4,44

4,46

Optimalization number

Ene

rgy

[eV]

0.2 1.0 0.8 0.6 0.4

Figure: Dependence of energy for water cluster (H2O)11 on probability of cut by plane (0.2-1.0) used


146

[1] Wales, D.J. a Hodges, M.P. Chem. Phys. Lett., 286, 65. 1998. [2] Hartke, B. Global Geometry Optimalization of Molecular Clusters: TIP4P Water Zeitschrift für Phys. Chemie, 214, 9 1251-1264. 2000. [3] Cartwright, H. M. An introduction to Evolutionary Computation and Evolutionary Algorithms Springer-Verlag Berlin Heidelberg. 2004. Acknowledgement

Grant Agency of the Academy of Sciences of the Czech Republic, grant No. IAA401870702;

University of Ostrava, Students Grant Competition, grant No. SGS7/PřF/2010.

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