Electron Localization Function Study on Intramolecular Electron Transfer in the QTTFQ and DBTTFI...

Published: October 26, 2011

r 2011 American Chemical Society 13513 dx.doi.org/10.1021/jp204585s | J. Phys. Chem. A 2011, 115, 13513–13522

ARTICLE

pubs.acs.org/JPCA

Electron Localization Function Study on Intramolecular ElectronTransfer in the QTTFQ and DBTTFI Radical AnionsJaroslaw Kalinowski,† Slawomir Berski,*,‡ and Agnieszka J. Gordon‡

†Laboratory of Physical Chemistry, Department of Chemistry, A. I. Virtasen aukio1, P.O. Box 55, FI-00014 University of Helsinki,Finland‡Faculty of Chemistry, University of Wroclaw, 14 F. Joliot-Curie, 50-383 Wroclaw, Poland

1. INTRODUCTION

Derivatives of tetrathiafulvalene (TTF, Scheme 1) have beenthe subject of recent research, and have been successfully appliedas components in low-dimensional organic conductors.1 Intra-molecular electron transfer (IET) plays a key role in the study ofTTF derivatives. In the TTF-diquinone radical anion (QTTFQ ,Scheme 2), TTF acts as a bridge to promote electron conductionbetween two groups.2 As unimolecular electronic devices pushthe limits of miniaturization in microelectronics,3 molecules capableof IET are at the forefront of research in nanotechnology.4�10

Thus, there is great interest in studying and understanding suchprocesses. The in-depth understanding of IET processes canassist in the design of molecular wires.

The neutral QTTFQmolecule has C2v symmetry (Scheme 3).The experimental evidence11 suggests that, in the case of(QTTFQ)•�, this symmetry is distorted by an unpaired electronlocalized on one quinone ring. Thermally or photochemicallyactivated IET corresponds to electron transfer from one quinonering to another. Recent studies have shown that few DFT func-tionals can beused todescribe the (QTTFQ )•� anion correctly.11,12

One of the quantum chemical topology (QCT)13,14 methods,the bonding evolution theory (BET),15 was used in this study.QCT adopts the methods of differential topology and theory ofgradient systems for studies on the properties of scalar fields(electron density, electrostatic potential). BET, introduced by

Krokidis et al.,15 is based on the topological analysis of electronlocalization function (ELF)16,17 and the elements of catastrophetheory.18 The definition of ELF is as follows:

ηðrÞ ¼ 1 þ Dσ

D0σ

!224

35�1

where Dσ and Dσ0 represent the curvature of the electron pair

density for electrons with identical spins for the system understudy, and a homogeneous electron gas with the same densityrespectively. The ELF function gives a quantitative, orbital indep-endent description of the electronic localization, based on strongphysical grounds related to the Fermi hole. Integrating electron

Scheme 1. Lewis Structure for TTF

Received: May 17, 2011Revised: September 8, 2011

ABSTRACT: The unsymmetrical distribution of the unpaired electron inthe ground state of the DBTTFI•� radical anion (bi(6-n-butyl-5,7-dioxo-6,7-dihydro-5H-[1,3]dithiolo[4,5-f]isoindole-2-ylidene) is theoreticallypredicted using the M06-2X/6-31+G(d,p) level of calculations. Theresults are additionally confirmed by single point calculations atB3LYP/aug-cc-pVTZ, LC-ωPBE/aug-cc-pVTZ, and M06-2X/aug-cc-pVTZ levels. DBTTFI, containing the TTF (tetrathiafulvalene) fragment,may be used in the construction of organic microelectronic devices,similarly to the radical anion of QTTFQ. The unsymmetrical distributionof spin density in (QTTFQ)•� has been confirmed using M06-2X/aug-cc-pVTZ calculations, with subsequent study using topological analysis ofelectron localization function (ELF). The reorganization of the chemicalbonds during intramolecular electron transfer in (QTTFQ)•� and(DBTTFI)•� has been analyzed using bonding evolution theory (BET). The reaction path has been simulated by the IRCprocedure, and the evolution of valence basins has been described using catastrophe theory. The simple mechanisms: (QTTFQ)•�:η-1�3-CC+-0: �•(QTTFQ) and (DBTTFI)•�: η-1�3-[F]4[F

+]4-0:�•(DBTTFI), each consisting of three steps, have been

observed. Two cusp or 4-fold catastrophes occur immediately after the TS. Our study shows that potential future microelectronicdevices, constructed on the basis of the (QTTFQ)•� and (DBTTFI)•� systems, should exploit the properties of the CdC bond.

13514 dx.doi.org/10.1021/jp204585s |J. Phys. Chem. A 2011, 115, 13513–13522

The Journal of Physical Chemistry A ARTICLE

density over ELF topological basins to obtain basin population(N), or integrating the spin density (Sz(Ωii) = (1/2)

R(Fα(r) �

Fβ(r)) dr (where integration is over the ELF basinΩi), to obtainthe spin population (2Sz) gives insight into bond orders and pro-perties. BET has often proved successful in explaining the natureof chemical reactions and processes such as proton transfer,19,20

isomerization,21 and pericyclic reactions.22,23

The main purpose of this paper is a detailed examination ofthe IET mechanism in the QTTFQ radical anion (Scheme 2).Determining changes in the nature of the chemical bonds duringIET can aid understanding of the processes occurring in organicelectron conductors. To the best of our knowledge, the ELFapproach has not been used to study IET processes to date,although Krokidis et al.24 used BET to study simultaneouselectron transfer during the Li + Cl2 = Li+ + Cl2

� reaction. Itis also interesting to check whether IET based on the traditionalLewis structure (Scheme 2) displays any similarity with resultsobtained from the QCT method. The IET mechanism based on

the former, introduced before the advent of quantum chemistry,25

is likely to be less reliable than modern bonding analysis.Another objective of the current study was to find a molecule

with both the TTF fragment and unsymmetrical spin densitydistribution in the ground state. Such a molecule, after experi-mental confirmation, could be used in the construction of neworganic microelectronic devices. Our calculations, performed atthe M06-2X/6-31+G(d,p) level, show that the DBTTFI•� radi-cal anion26 should display such properties (Scheme 4).DBTTFI(Scheme 5) is bi(6-n-butyl-5,7-dioxo-6,7-dihydro-5H-[1,3]dithiolo-[4,5-f]isoindole-2-ylidene, and the adopted acronym is a deriva-tive of the term “DiBenzeneTTF bisImide”.

2. COMPUTATIONAL DETAILS AND THE BET MODEL

The BET model takes chemical reactive process to be a seriesof changes in the number and types of the critical points of thedynamic systems. Because the critical points always obey thePoincar�e�Hopf formula,27 this is very strong constraint rulingthe chemical mechanisms. Changes in either the number or typeof critical point of the dynamic systems considered are calledcatastrophes. There are seven types of elementary catastrophesaccording to Rene Thom’s18 catastrophe theory. BET theory,developed by Krokidis et al.,15 applies the catastrophe theory tothe ELF gradient field. It classifies the elementary chemical pro-cesses according to the variation of either the number of basins orthe synaptic order σ of at least one basin. Two main elementarycatastrophes are of greatest importance in our case: the fold [F]and the cusp [C] catastrophe.

The fold catastrophe corresponds to transformation of awandering point, i.e., a point that is not a critical one, into twocritical points of different parity. The cusp catastrophe trans-forms a critical point of given parity into two critical points ofthe same parity and one of the opposite parity. So, for example,one basin splits into two new basins and a saddle point betweencorresponding local maxima.

To achieve a clear-cut representation for the sequence of cata-strophes for a given chemical reaction, and to enable a straight-forward comparison between processes, the following system ofnotation has been proposed.28,29 Any sequence of catastrophes isrepresented by a formula: ω-N1�N2-FCSHEBP...-N3, where ωrepresents the scalar field considered (for example the η-electronlocalization function (ELF) or F-electron density); N1 is theordinal number of an analyzed sequence and can be omitted whenonly one reaction is considered (N1 = 1);N2 defines a number ofthe observed steps (domains of structural stability) larger thanthe number of catastrophes; “FCSHEBP...” is an abbreviation ofthe types of catastrophe proposed by Rene Thom,18 i.e., F = fold,C = cusp, S = swallow tail, H = hyperbolic umbilic, E = elipticumbilic, B = butterfly, P = parabolic umbilic; and N3 denotes the

Scheme 2. lewis structure for the (QTTFQ)•� Radical Anion Undergoing the IET

Scheme 3. lewis structure for the QTTFQ Molecule inNeutral Form

Scheme 4. Lewis Structure for the (DBTTFI)•� RadicalAnion Undergoing the IET



end of the sequence (N3 = 0). When the first sequence of cata-strophes (chemical reaction) is followed by a second one,N3 canbe replaced byN1, whose value becomes 2 (N1 = 2). For example,for two subsequent reactions the sequence of catastrophes is repre-sented by η-1�N2-F[C]2CF

+CC...-2-N20-[F]2C

+C+FF...-0.For processes where some bifurcations occur simultaneously,

catastrophes are denoted by [AA] or [A]N4, where N4 stands for

the number of catastrophes (N4 = 2 in this case). For instance,[F]3 describes 3-fold catastrophes occurring simultaneously.

Symbols in bold (e.g., C, F) are used to emphasize formationof the first bond, whereas the + superscript is used for those cata-strophes that increase either the number of basins or the synapticorder. For example, C+ corresponds to the cusp catastrophe inwhich an attractor gives rise to two new attractors and a saddlepoint of index 1. In this way, any chemical reaction can be decom-posed into a well-defined sequence of electron pair topologies,identified with commonly used chemical concepts.

The reaction between 1,3-butadiene (C4H6) and ethylene(C2H4) was studied previously by one the authors of this paper

30

and can serve as an example that may be represented by thefollowing sequence of catastrophes: C4H6 + C2H4: η-1�7-[C]2C[F

+]2[F+]2[C]2C

+-0: C6H10 using topological analysis ofelectron localization function (η).

All DFT calculations have been performed using unrestrictedKohn�Shamorbitals for doublet electronic states. TheM06-2X31

hybrid electron density functional has been used with 6-31+G-(d,p)32,33 and aug-cc-pVTZ34,35 basis sets. Additionally, singlepoint calculations have been performed with LC-ωPBE36 andB3LYP37�39 hybrid density functionals. The minima on thepotential energy surface (PES) have been confirmed by non-imaginary vibrational frequencies. The zero-point vibrationalenergy (ΔZPVE) corrections were included in the calculationof the activation energy (ΔEa). In calculating ΔZVPE for ΔEa,one imaginary frequency has been omitted. The reaction path hasbeen calculated using the intrinsic reaction coordinate (IRC)40,41

with a step size of 0.07 amu0.5bohr at the M06-2X/aug-cc-pVTZcomputational level.

Calculations with the 6-31+G(d,p)29,30 basis set have beenperformed using the Gaussian0942 package. Calculations withthe aug-cc-pVTZ basis set and all additional single point calcula-tions for DBTTFI molecule have been performed using GA-MESS version 2009-01-12-R1.43 The stability of the DFT wavefunction (“Stable” keyword) was tested for both transition statesand the selected points on the IRC paths, indicating neitherexternal real nor internal instabilities.

The ELF function was calculated over a rectangular grid with astep size of 0.045 bohr. Topological analysis of ELF for theQTTFQ derivatives was performed using the Topmod suite.44

In the case of the DBTTFI molecule Dgrid-4.5 was used.45

Graphical representation of the ELF function was carried outusing the UCSF Chimera program.46

3. RESULTS AND DISCUSSION

3a. (QTTFQ)•� Molecule: Relative Energies and Geome-trical Structures. The geometrical and electronic structure of(QTTFQ)•� has been studied using 6-31+G(d,p) and aug-cc-pVTZ basis sets. No essential differences were found, so onlythe results obtained with the larger basis set shall be presented.The meta exchange�correlation functional M06-2X proposedby Zhao et al.31 has been chosen, because it reflects the un-symmetrical distribution of the odd electron observed in the ESRspectra.2 Selected bond lengths for the optimized geometricalstructure and its transition state (TS) are compared in Table 1,and an overview of the geometries is shown in Figure 1.

Scheme 5. Lewis Structure of the DBTTFI Molecule in Neutral form

Table 1. Comparison of Selected Bond Lengths for the TSand Minimum of Energy for (QTTFQ)•�

bond TS [bohr] Min [bohr]

C1�C2 2.552 2.568

C2�C3 2.779 2.735

C3�C4 2.759 2.758

C4�C5 2.574 2.568

C5�C6 2.759 2.758

C1�C6 2.779 2.735

C3�O3 2.336 2.389

C6�O4 2.336 2.389

C9�C10 2.574 2.568

C10�C14 2.759 2.764

C14�C13 2.779 2.833

C12�C13 2.552 2.522

C12�C11 2.779 2.833

C9�C11 2.759 2.764

C11�O1 2.336 2.305

C14�O2 2.336 2.305

C7�C8 2.539 2.546

Figure 1. Geometry overview for QTTFQ radical anion as a minimumstructure and a transition state structure.



The TS has nonplanar C2v symmetry as a consequence of thesp2 hybridization of the sulfur atoms.11 The C2v symmetry isdefined by the plane perpendicular to the central C7dC8 bond,with an angle breaking planarity between the planes of the quinonerings and the central C7dC8 bond. In the TS these planaritybreaking angles are symmetrical, both having values of 173�,whereas in the minimum the values are 165� for the side ofQTTFQ•� with an unpaired electron, and 176� for the otherside. The smaller angle increases during the course of the reac-tion. The minimum also differs from the TS by the length of thecarbon�oxygen bonds: in the TS they are both 2.336 bohr,whereas for the minimum the values are 2.305 bohr and 2.389bohr. In the case of other bonds the observed differences aresmaller than 0.04 bohr between the minimum and the TS.The activation energy (ΔEa) for this reaction is 2.8 kcal/mol

at the M06-2X/aug-cc-pVTZ level, very similar to the value of2.9 kcal/mol reported by Vydrov et al.12 from M05-2X/6-31+G-(d,p) calculations. It is slightly larger than values of 1.70 kcal/molcalculated at the B3LYP/6-31G(d) level and 1.85 kcal/mol insingle-point calculations with the 6-311+G(d) basis set using theconstrained DFT method, reported by Wu and Van Voorhis.47

The activation barrier estimated on the basis of experimental datais 8.0 kcal/mol.2

3b. Topological Analysis of the ELF Function for (QTTFQ)•�

Stationary Points. The 3D plot of the ELF function and allthe attractors localized for (QTTFQ)•� in the energy minimum(Cs symmetry) are presented in Figure 2. Each atom, except forthe hydrogen atom, is represented by a core basin (red area). Foreach two-center bond, the bonding disynaptic basin (green area)is localized. According to the interpretation of Silvi and Savin,17

these bonds have a covalent (shared-electron) character. In theTTF bridge the C7dC8 bond is represented by two disynapticbasins, Vi=1,2(C7,C8), with mean electron populations (N) of2.02e and 2.12e, respectively. The correspondence to the Lewisformula is clear (Scheme 3), indicating that this has standarddouble bond character. However, each of the C4dC5 and C9d10bonds, formally also double, is represented by a single basin,V(C4,C5) and V(C9,C10), with basin populations of 3.41e and3.48e, respectively. These bonds exhibit a smaller number ofelectrons than those computed for C7dC8 (4.14e). Smallervalues of N correspond to longer C4dC5 and C9dC10 bonds,and larger N values correspond to a shorter C7dC8 bond(Tables 1 and 2).The nonbonding electron density of the oxygen atoms Oi

(i = 1, 4) is described by the nonbonding monosynaptic basinsVj=1,2(Oi). Their basin populations range from 2.64e to 2.82e.According to the Lewis formula (Schemes 2 and 3), one can expect

Figure 2. (a)Visualization of the ELF (η(r) = 0.81) function for the (QTTFQ)•� minimum energy structure. Core basins are marked in red; valencebasins corresponding to the hydrogen atoms are marked in yellow. Other valence basins are marked in various colors for clarity. (b) Organization ofcritical points (3,�3) in the ELF field for the transition structure. All basins are labeled. Lines corresponding to the bond path are marked for clarity.



two or three lone pairs, depending on which side the unpairedelectron resides. However, topological analysis of ELF does notsupport this image, and only two Vi=1,2(Oi) basins are observedfor each oxygen atom (Figure 2a). The Vi=1,2(Oi) attractors(Figure 2b) are localized within the plane containing thequinone rings.The carbon�oxygen bonds, depending on formal localization

of the unpaired electron in (QTTFQ)•�, are represented as singleC—O or double CdO bonds (Scheme 2). In the topologicalanalysis of ELF (Figure 2) they are reflected only by single dis-ynaptic basinsV(C,O):V(C11,O1), V(C14,O2), andV(C3,O3),V(C6,O4), respectively. The N values for the CdO bonds aresmaller than the formal value of 4e, being 2.33 and 1.99e,respectively. The missing electrons (with respect to the formalvalues) are “contained” in the nonbonding basins correspondingto the lone pairs Vi(O), with N = 2.63e. The Lewis structure(Scheme 2) for the (QTTFQ)•� anion shows that the C—Obond on the side with the unpaired electron has a smaller bondorder than that on the other side of molecule, as confirmed bythe N values.Each C�S bond, formally single, is represented by a single

disynaptic basin V(C,S). According to the Lewis formula, such abond has 2e but the topological analysis shows the basis popula-tion is in the range 1.74�1.88e. Eight monosynaptic basins,

Vi=1,2(S1�4), characterize four sulfur lone pairs, and their numberis consistent with the Lewis formula. Because the C�S bonds areslightly depopulated in comparison to the formal value, and thebasin populations ofVi=1,2(S1�4) are much larger than the formal2e value (Table 2), resonance hybrids with negative charge onthe S atoms must be taken into account.The most important difference in the ELF topology between

parts of (QTTFQ )•� separated by the central C7dC8 bond isobserved for the C1dC2 and C12—C13 bonds in the quinonefragments. For the side with the unpaired electron, the C12—C13 bond (2.568 bohr) is represented by two disynaptic basinsVi=1,2(C12,C13), with basin populations of 1.69e and 1.71e (i.e.,3.4e in total). For the side of the molecule without an unpairedelectron, the analogous but shorter bond C1dC2 (2.522 bohr) isrepresented by a single disynaptic basin V(C1,C2), with an Nvalue of 3.33e. This difference in bond lengths is consistent withthe Lewis structure (Scheme 2), where these bonds also havedifferent bond orders.The unpaired electron is not, as is usually the case, delocalized

across the whole molecule but remains on one side of the TTFbridge. The sum of the basin populations calculated for this sideof (QTTFQ )•� is greater by 0.93e than the equivalent value forthe other side. More accurate analysis shows that the unpairedelectron is delocalized across the whole side of the molecule.Differences in the N values between analogous basins for bothsides are less than 0.06e. The largest differences are noticed forthe oxygen lone pairs, Vi(O). This result is consistent with theclassical Lewis structures.The highest values of the spin density, in the range 0.04�

0.06e, are obtained for oxygen lone pairs, Vi=1,2(O1), Vi=1,2(O2),and the C9—C11, C10—C14 bonds connecting the quinone C—O group to the TTF bridge, represented by the V(C9,C11)and V(C10,C14) basins (Table 2). The unpaired electron popu-lations for the basins, corresponding to the C1dC2 and C12—C13 bonds, are less than 0.02e.The geometrical structure of the transition state for the

(QTTFQ )•� T �•(QTTFQ ) reaction has C2v symmetry, andthe unpaired electron is delocalized symmetrically on both sidesof the TTF bridge. The unpaired electron density is spread acrossthe whole molecule, with the largest values of the spin densitybeing 0.03e for the oxygen lone pairs V1,2(Oi=1�4), and 0.02e forC�C bonds with the V(C3,6,11,14,C4,5,9,10) basins. The spin den-sities for basins corresponding to the C1�C2, C6�C1, C2�C3,C12�C13, C11�C12, and C14�C13 bonds are all smallerthan 0.01e.3c. Topological Analysis of the ELF Function for the

QTTFQ•� T �•QTTFQ Reaction. The total energy curve ob-tained using the intrinsic reaction coordinate (IRC) method atthe M06-2X/aug-cc-pVTZ level is presented in Figure 3. Itsshape resembles that expected from theoretical considerationsfor IET, where two parabolic curves describing the reactant andproduct states cross at the TS. Comparison of the Lewis formulas(Scheme 2) indicates that IET is mainly associated with a changein the CdO bonds and associated lone pairs Vi=1,2(O1�4).Bonding evolution theory (BET) has been applied to analyze the

mechanism of electron redistribution during IET for (QTTFQ)•�.From three possible levels of BET analysis the “current level”, asproposed by Krokidis et al.,15 is used. This means that onlyevolution of local maxima (attractors) is considered. The analysisshows three steps, with one step for each side of the reaction path,separated by the step containing the TS. The reaction can be

Table 2. Ωi Basin Populations (N) [e] of the SelectedValence Basins for the TS and Energy Minimum of(QTTFQ)•�

TS Min

Ωi- basin N(Ωi) 2Sz(Ωi)a N(Ωi) 2Sz(Ωi)

a

V1(O1) 2.78 0.06 2.81 0.12

V2(O1) 2.72 0.06 2.82 0.10

V1(O2) 2.78 0.06 2.81 0.12

V2(O2) 2.72 0.06 2.82 0.10

V1(O3) 2.78 0.06 2.66 0.00

V2(O3) 2.72 0.06 2.64 0.00

V1(O4) 2.78 0.06 2.66 0.00

V2(O4) 2.72 0.06 2.64 0.00

V(C11, O1) 2.21 0.01 2.00 0.01

V(C14, O2) 2.21 0.01 2.00 0.01

V(C3, O3) 2.21 0.01 2.33 0.00

V(C6, O4) 2.21 0.01 2.33 0.00

V(C3, C4) 2.43 0.04 2.31 0.00

V(C5, C6) 2.43 0.04 2.31 0.00

V(C9, C11) 2.43 0.04 2.54 0.08

V(C10, C14) 2.43 0.04 2.54 0.08

V1(C7,C8) 2.03 0.00 2.02 0.00

V2(C7,C8) 2.13 0.00 2.12 0.00

V1(S1) 2.13 0.00 2.13 0.00

V2(S1) 2.15 0.00 2.15 0.00

V1(S2) 2.13 0.00 2.13 0.00

V2(S2) 2.15 0.00 2.15 0.00

V1(S3) 2.13 0.00 2.13 0.00

V2(S3) 2.15 0.00 2.15 0.00

V1(S4) 2.13 0.00 2.13 0.00

V2(S4) 2.15 0.00 2.15 0.00a Sz(Ωi) = integrated spin density [e].



represented, using the catastrophe sequence in place of the arrowsymbol, as (QTTFQ)•�: η-1�3-CC+-0: �•(QTTFQ).The topology of the ELF function in the first step corresponds

to that observed for (QTTFQ)•� in the energy minimum. Goingfrom the minimum to the TS, there is discernible movement ofthe integral spin density from the oxygen lone pairs to the C—Cbonds connecting the CdO group of the quinone ring to the

TTF bridge. The unpaired electron population values for theV1(O1),V2(O1),V1(O2),V2(O2),V(C9,C11), andV(C10,C14)basins in the minimum were 0.12, 0.10, 0.12, 0.10, 0.08, and0.08e, respectively. The equivalent values for the last point of thefirst step are 0.08, 0.08, 0.08, 0.08, 0.10, and 0.10e, respectively.Thismovement of unpaired electron density is noticeable, althoughvery small, at about 0.04e for the whole step. The electron flow

Figure 3. QTTFQ stationary points together with the energy curve for the occurring IET.

Figure 4. Population graph for the unpaired electron for selected basins along the first step of IET.



causes essentially linear changes of spin densities for thesebasins (Figure 4).The second step begins with the catastrophe, which is

observed before the first IRC point, counting from the TS. Inthe cusp [C], the V(C1,C2) bonding disynaptic basin and itsattractor disappear, and two new bonding disynaptic basins,Vi=1,2(C1,C2), two attractors (3,�3), and a saddle point (3,�1)are created. This catastrophe is found on the side of the moleculewithout the unpaired electron. Furthermore, this finding isexactly contrary to the Lewis formula, which predicts a changefrom double to single bond (Scheme 2). The basin populationvalue of each Vi=1,2(C1,C2) is 1.68e. From a topological point ofview, the C1�C2 bond has features typical of a double bond,although the total basin population of 3.36e is smaller than the

formal value of 4e. The catastrophe is associated with the TSitself, which seems to be typical for IET processes. In most casesof BET analysis20�23 there are no changes in the ELF topologyassociated with the TS. An explanation can be related to theshape of the total energy curve (Figure 3). The IRC path studiedencompasses two overlapping potential energy curves describingthe (QTTFQ)•� and�•(QTTFQ)minima. The first point after/before the TS characterizes the molecule with a differentelectronic structure described by the other energy curve.The distribution of the integral spin density does not change

rapidly near the TS but rather changes slowly along the wholereaction path. The electron transfer involves only the valencebasins with a spin density lower than 0.01e, and unpaired electrondensity is redistributed from the oxygen lone pairs to the otherside of the molecule through the V(C9,C11) and V(C10,C14)basins corresponding to carbon�carbon bonds connected to theC�O group in the quinone ring. Because the IRC path is sym-metrical, owing to the geometry of the TS (Figure 3) the secondcusp catastrophe [C] is placed between the TS and the first point,on the second shoulder of the IRC path.3d. (DBTTFI)•�Molecule: Relative Energies andGeometrical

Structures.TheDBTTFI system (Figure 5 and Schemes 4 and 5)has been selected among 4047molecules containing the TTF frag-ment and displayed in the Cambridge Structural Data Base.48,49

In its neutral form it has been used to construct DBTTF basedorganic semiconductors and transistors,.50,51 Optimization of thegeometrical structure, performed at the M06-2X/6-31+G(d,p)level, converged to an energy minimum with Cs symmetry, con-taining unsymmetrical distribution of the electron density. Thisfinding suggests that the radical anion of DBTTFI could be used,after experimental confirmation, as an essential fragment of org-anic microelectronic devices.There are many similarities between the structures of

(QTTFQ )•� and (DBTTFI)•�. The most notable is the non-planar structure of the TTF bridge and adjacent rings. The TSstructure has C2v symmetry as in the case of (QTTFQ )•�. Oneof the two symmetry planes is perpendicular to the centralC1dC2 bond, with a planarity breaking angle between theplanes of the benzene rings and the central C1dC2 bond inthe TTF bridge. In the TS these planarity breaking angles aresymmetrical, with values of 162�. In the minimum structure thisangle is 164� for one side of the TTF bridge, and 159� for theother. Similarly to (QTTFQ )•�, this angle is smaller for the side

Figure 6. Visualization of the ELF function for a fragment containingthe most important basins for the transition structure and minimum in(DBTTFI)•�.

Table 4. Comparison of Selected Bond Lengths for the TSand Minimum of Energy for (DBTTFI)•�

bond TS [bohr] Min [bohr]

C9�C13 2.721 2.837

C8�C11 2.721 2.837

C11�O33 2.311 2.287

C13�O34 2.311 2.287

C13�N12 2.646 2.622

C11�N12 2.646 2.622

C23�C26 2.721 2.749

C24�C28 2.721 2.749

C28�O35 2.311 2.332

C26�O36 2.311 2.332

C26�N27 2.646 2.622

C28�N27 2.646 2.622

Table 3. Ωi Basin Populations (N) [e] of the SelectedValence Basins for the Transition Structure and the EnergyMinimum of (DBTTFI)•�

Ωi basin

TS

N(Ωi)

Min

N(Ωi)

V1(O33) 2.70 2.65

V2(O33) 2.75 2.70

V1(O34) 2.70 2.65

V2(O34) 2.75 2.70

V1(O35) 2.70 2.75

V2(O35) 2.75 2.80

V1(O36) 2.70 2.75

V2(O36) 2.75 2.80

V(C11,O33) 2.27 2.38

V(C13,O34) 2.27 2.38

V(C28,O35) 2.27 2.10

V(C26,O36) 2.27 2.10

V1(C23) 0.17

V2(C23) 0.17

V1(C24) 0.17

V2(C24) 0.17

V(C23,C24) 2.44 2.30

Figure 5. Optimized geometrical parameters for the DBTTFI radicalanion and its transition structure.



with an unpaired electron and increases during the course ofreaction. The geometrical structure of the minimum also differsfrom the TS in the length of the carbon�oxygen bonds. In the TSboth of these have values of 2.311 bohr, whereas for theminimum structure these values are 2.287 and 2.332 bohr forthe two sides of the TTF bridge, respectively. The ΔEa value forthis reaction is 1.35 kcal/mol at the M06-2X/6-31+G(d,p) level.3e. Topological Analysis of the ELF Function for (DBTTFI)•�

Stationary Points. Selected basin populations calculated forthe DBTTFI radical anion are collected in Table 3. The ELFtopology for the TTF bridge is very similar to that in(QTTFQ)•�. All the C—C, CdC, and C—N bonds arerepresented by single disynaptic basins V(C,C) and V(C,N).The disynaptic basins V(C,C) corresponding to the delocalizedC—C bonds in the benzene rings have basin populationsbetween 2.7 and 3.1e. The formal bond order is 1.5, and thisvalue is well reflected by a topological bond order of 1.35�1.55.The lone pairs from the nitrogen atoms are represented by twomonosynaptic nonbonding basins, Vi=1,2(N), for each atom, onewith population of 0.83e and the other 1.00e. The Lewis structure(Scheme 4) shows that each nitrogen atom has one nonbondinglone pair. Due to local planarity, the lone pair is localized sym-metrically above and below the plane designated by the N and Catoms. A similar situation is observed for pyrrole52 and for planarammonia NH3 in its TS for umbrella inversion through planarD3h

geometry. The total basin population N[V1(N)] + N[V2(N)] is1.83e, and thus close to the formal value of 2e. The C—O bondsare represented by single disynaptic basins V(C13,O34) andV(C11,O33), with mean electron populations of 2.10e. TheCdO bonds are represented by V(C26,O36) and V(C28,O35),

with basin populations of 2.38e, much smaller than the formal valueof 4e. It is evident that the correct representation of the nature ofthe carbonyl groups involves ionic resonance hybrids, C+O� andC�O+. The lone pairs of the oxygen atoms are represented bythe nonbonding basins Vi=1,2(O33�36), with N in the range2.70�2.80e.The main difference between the ELF topology observed

for the energy minimum and the TS is found in the region of theC23�C24 bond. This bond has mixed single and double bondcharacter due to delocalization of the electron density andthus should be represented by a single V(C23,C24) or twoVi=1,2(C23,C24) disynaptic basins if a resonance hybrid with thedouble C23dC24 bond is a major contributor. However, forthe minimum state, four monosynaptic nonbonding basinsVi=1,2(C23) and Vi=1,2(C24) are observed, situated near carbonsC23 and C24 (Figure 6a). These basins exist only for the side ofthemolecule with an unpaired electron: one basin is placed underthe plane designated by the carbon rings, and another above thisplane. The two nonbonding basins and the corresponding corebasins, C(C23) and C(24), are collinear. The basin population ofVi=1,2(C23) and Vi=1,2(C24) is 0.17e, so an additional 0.68e islocalized in this bond, with a total basin population for the bondof 3.12e. This is rather an unexpected finding, so single pointcalculations were performed at M06-2X/aug-cc-pVQZ, LC-ωPBE/aug-cc-pVQZ, and B3LYP/aug-cc-pVQZ levels to con-firm this topological feature. The topological analysis of ELF con-firms this finding, because the ELF images obtained are quitesimilar to those from M06-2X/6-31+G(d,p) calculations, withdifferences in N values smaller than 0.06e. Analysis of the totalspin value, ÆS2æ, reported by GAUSSIAN during calculations

Figure 7. DBTTFI stationary points and the energy curve for occurring IET.



yields a range of 0.751�0.752 for all levels of calculation used.The expected value is 0.75, thus confirming that no essentialmixing of other electronic states occurs. However, such a topo-logical feature might be an effect of the computational methodused, so the result should be treated with caution.Comparison of the basin populations between different sides

of the molecule reveals asymmetry. For the side of the moleculewith four Vi=1,2(C23), Vi=1,2(C24) basins, the total basin popula-tion is 1.06e greater than that on the other side. This fact clearlyindicates that the unpaired electron stays on only one side of themolecule. This population asymmetry is mainly observed for theVi=1,2(C23), Vi=1,2(C24) basins in the minimum energy struc-ture. This shows that either an unpaired electron or electron flow,resulting from the reaction, is connected with the C23 and C24atoms, probably by the coupled double bonds. There is also anoticeable difference observed between the two sides of themolecule for the oxygen lone pairs, V(O35), V(O36) andV(O33), V(O34). The basin populations for V(O35), V(O36),on the side with unpaired electrons are greater by 0.1e each thanthose on the other side. By analogy to (QTTFQ)•�, the carbon�oxygen bonds for the side with an unpaired electron are shorterby 0.045 bohr (Table 4) than those on the other side. This isreflected in the values of the basin population, where a shorterbond (2.287 bohr) exhibits larger values of N (Table 4 and 3).3f. Topological Analysis of the ELF Function for the

(DBTTFI)•� T �•(DBTTFI) Reaction. The IRC path for IET inthe DBTTFI radical anion (Scheme 4) is presented in Figure 7.The reaction follows the symmetry changeCsfC2vfCs. Thereare three steps, with one step for each side of the reaction path,and a separate step containing the TS. In the first step there arechanges in the basin populationsmostly related to atomic rearrange-ment. The largest changes are obtained for the C11�O33, C13�O34, C28�O35, and C26�O36 bonds, where the respectivebasin populations for C11�O33 and C13�O34 decrease by0.03e, and those for C28�O35, C26�O36 increase by 0.03e.The second step begins with the disappearance of four monosyn-apticVi=1,2(C23),Vi=1,2(C24) basins from the side of (DBTTFI)•�

where the unpaired electron is localized (Figure 6). From achemical point of view this means that the properties of theC23�C24 bond change. The N value for the C23�C24 bond is2.44e after the catastrophe and, coming from the minimum, itsbasin population increases by 0.14e. The four bifurcations arefolds ([F]4) and are observed simultaneously between the firstIRC point, counting from the TS, and the TS itself. In the TS theunpaired electron is delocalized across the whole molecule. Forthe IRC path after the TS the situation is the same, but invertedby the symmetry plane perpendicular to the central C1�C2bond. Thus, four nonbonding monosynaptic basins, Vi=1,2(C9)and Vi=1,2(C8), appear in the valence space of the C8�C9 bond,in four simultaneously occurring fold catastrophes ([F+]4). Thereactionmechanism can be summarized as follows: (DBTTFI)•�:η-1�3-[F]4[F

+]4-0:�•(DBTTFI). Thismechanism is very similar

to that in (QTTFQ)•�, where the catastrophe sequence η-1�3-CC+-0 is observed. The only difference is that folds are observedin place of the cusp catastrophes, which is associated with thespecial ELF-topology detected in (DBTTFI)•�.

4. CONCLUSIONS

For the first time, BET analysis has been used to study the flowof electron density during IET in the QTTFQ and DBTTFIradical anions. Reorganization of the valence attractors and their

basins on the η(r) field, along the IRC pathway, reveals a simplemechanism consisting of three steps separated by two cusps for(QTTFQ )•�, and 4-fold catastrophes for (DBTTFI)•�. Owingto the shape of the total energy curve, typical for IET, the cata-strophes occur immediately after the TS.

Analysis of ELF performed for IET in (QTTFQ )•� yields twofindings that cannot be simply inferred from analysis of the Lewisformula. First, IET is not associated with change of the non-bonding basins of oxygen atoms, which are reflected in the ELFanalysis by two nonbonding basins, Vi=1,2(O), regardless of theposition of the unpaired electron. Second, and most importantly,IET manifests itself only in a qualitative change of the electronicstructure of the C1—C2 bond in the quinone ring. From a topo-logical point of view, the change predicted is strictly local and isconstrained to a single bond: C1dC2 T C1—C2. A similareffect has been observed for the C23—C24 bond of the(DBTTFI)•�molecule, although its electronic structure seems tobe more complicated. In our opinion, these two new facts shouldbe explored further to aid the construction of future electronicdevices, based on these two molecules.

Topological analysis of ELF reveals the differences in unpairedelectron distribution between the (QTTFQ)•� and (DBTTFI)•�

molecules. In the energy minimum of (QTTFQ )•�, the un-paired electron is localized mainly on the lone pairs of O1, O2and is redistributed to all oxygen lone pairs for the TS. In theenergy minimum of (DBTTFI)•�, the unpaired electron islocalized mainly in close proximity to the C23 and C24 atomsand is redistributed across the whole molecule for the TS.

The analysis of the bonding presented here, together with thatpresented by Krokidis et al.24 for the Li + Cl2 = Li+ + Cl2

� reac-tion, shows that the topological approach to electronic structureis a valuable tool for elucidation of electron transfer processesreaction mechanisms.

’AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected]. Tel: +48 (0)71 3757246. Fax: +48(0)71 3282348.

’ACKNOWLEDGMENT

We are grateful to the Wroclaw Centre for Networking andSupercomputing for generous allocation of the computer time.Dr Charles M. Gordon is gratefully thanked for the final proof-reading of the manuscript.

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Electron Localization Function Study on Intramolecular Electron Transfer in the QTTFQ and DBTTFI...

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