Electron Localization Function Study on Intramolecular Electron

ARTICLE pubs.acs.org/JPCA

Electron Localization Function Study on Intramolecular Electron Transfer in the QTTFQ and DBTTFI Radical Anions Jaroslaw 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 ABSTRACT: The unsymmetrical distribution of the unpaired electron in the ground state of the DBTTFI•
radical anion (bi(6-n-butyl-5,7-dioxo6,7-dihydro-5H-[1,3]dithiolo[4,5-f]isoindole-2-ylidene) is theoretically predicted using the M06-2X/6-31+G(d,p) level of calculations. The results are additionally confirmed by single point calculations at B3LYP/aug-cc-pVTZ, LC-ωPBE/aug-cc-pVTZ, and M06-2X/aug-ccpVTZ 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 distribution of spin density in (QTTFQ)•
has been confirmed using M06-2X/augcc-pVTZ calculations, with subsequent study using topological analysis of electron localization function (ELF). The reorganization of the chemical bonds during intramolecular electron transfer in (QTTFQ)•
and (DBTTFI)•
has been analyzed using bonding evolution theory (BET). The reaction path has been simulated by the IRC procedure, 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 microelectronic devices, constructed on the basis of the (QTTFQ)•
and (DBTTFI)•
systems, should exploit the properties of the CdC bond.

1. INTRODUCTION Derivatives of tetrathiafulvalene (TTF, Scheme 1) have been the subject of recent research, and have been successfully applied as components in low-dimensional organic conductors.1 Intramolecular electron transfer (IET) plays a key role in the study of TTF derivatives. In the TTF-diquinone radical anion (QTTFQ , Scheme 2), TTF acts as a bridge to promote electron conduction between two groups.2 As unimolecular electronic devices push the limits of miniaturization in microelectronics,3 molecules capable of IET are at the forefront of research in nanotechnology.4
10 Thus, there is great interest in studying and understanding such processes. The in-depth understanding of IET processes can assist in the design of molecular wires. The neutral QTTFQ molecule has C2v symmetry (Scheme 3). The experimental evidence11 suggests that, in the case of (QTTFQ )•
, this symmetry is distorted by an unpaired electron localized on one quinone ring. Thermally or photochemically activated IET corresponds to electron transfer from one quinone ring to another. Recent studies have shown that few DFT functionals can be used to describe 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 of gradient systems for studies on the properties of scalar fields (electron density, electrostatic potential). BET, introduced by r 2011 American Chemical Society

Scheme 1. Lewis Structure for TTF

Krokidis et al.,15 is based on the topological analysis of electron localization function (ELF)16,17 and the elements of catastrophe theory.18 The definition of ELF is as follows: 2 !2 3
1 Dσ 5 ηðrÞ ¼ 41 þ D0σ where Dσ and D0σ represent the curvature of the electron pair density for electrons with identical spins for the system under study, and a homogeneous electron gas with the same density respectively. The ELF function gives a quantitative, orbital independent description of the electronic localization, based on strong physical grounds related to the Fermi hole. Integrating electron Received: May 17, 2011 Revised: September 8, 2011 Published: October 26, 2011 13513

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

Scheme 3. lewis structure for the QTTFQ Molecule in Neutral Form

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 density distribution in the ground state. Such a molecule, after experimental confirmation, could be used in the construction of new organic microelectronic devices. Our calculations, performed at the M06-2X/6-31+G(d,p) level, show that the DBTTFI•
radical 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 derivative of the term “DiBenzeneTTF bisImide”.

Scheme 4. Lewis Structure for the (DBTTFI)•
Radical Anion Undergoing the IET

2. COMPUTATIONAL DETAILS AND THE BET MODEL The BET model takes chemical reactive process to be a series of changes in the number and types of the critical points of the dynamic systems. Because the critical points always obey the Poincar
e
Hopf formula,27 this is very strong constraint ruling the chemical mechanisms. Changes in either the number or type of critical point of the dynamic systems considered are called catastrophes. There are seven types of elementary catastrophes according to Rene Thom’s18 catastrophe theory. BET theory, developed by Krokidis et al.,15 applies the catastrophe theory to the ELF gradient field. It classifies the elementary chemical processes according to the variation of either the number of basins or the synaptic order σ of at least one basin. Two main elementary catastrophes are of greatest importance in our case: the fold [F] and the cusp [C] catastrophe. The fold catastrophe corresponds to transformation of a wandering point, i.e., a point that is not a critical one, into two critical points of different parity. The cusp catastrophe transforms a critical point of given parity into two critical points of the same parity and one of the opposite parity. So, for example, one basin splits into two new basins and a saddle point between corresponding local maxima. To achieve a clear-cut representation for the sequence of catastrophes for a given chemical reaction, and to enable a straightforward comparison between processes, the following system of notation has been proposed.28,29 Any sequence of catastrophes is represented by a formula: ω-N1
N2-FCSHEBP...-N3, where ω represents the scalar field considered (for example the η-electron localization function (ELF) or F-electron density); N1 is the ordinal number of an analyzed sequence and can be omitted when only one reaction is considered (N1 = 1); N2 defines a number of the observed steps (domains of structural stability) larger than the number of catastrophes; “FCSHEBP...” is an abbreviation of the types of catastrophe proposed by Rene Thom,18 i.e., F = fold, C = cusp, S = swallow tail, H = hyperbolic umbilic, E = eliptic umbilic, B = butterfly, P = parabolic umbilic; and N3 denotes the

density over ELF topological basins to obtain basin Rpopulation (N), or integrating the spin density (Sz(Ωii) = (1/2) (Fα(r)
Fβ(r)) dr (where integration is over the ELF basin Ωi), to obtain the spin population (2Sz) gives insight into bond orders and properties. BET has often proved successful in explaining the nature of 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 of the IET mechanism in the QTTFQ radical anion (Scheme 2). Determining changes in the nature of the chemical bonds during IET can aid understanding of the processes occurring in organic electron conductors. To the best of our knowledge, the ELF approach has not been used to study IET processes to date, although Krokidis et al.24 used BET to study simultaneous electron transfer during the Li + Cl2 = Li+ + Cl2
reaction. It is also interesting to check whether IET based on the traditional Lewis structure (Scheme 2) displays any similarity with results obtained from the QCT method. The IET mechanism based on

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

end of the sequence (N3 = 0). When the first sequence of catastrophes (chemical reaction) is followed by a second one, N3 can be replaced by N1, whose value becomes 2 (N1 = 2). For example, for two subsequent reactions the sequence of catastrophes is represented 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 formation of the first bond, whereas the + superscript is used for those catastrophes that increase either the number of basins or the synaptic order. For example, C+ corresponds to the cusp catastrophe in which an attractor gives rise to two new attractors and a saddle point of index 1. In this way, any chemical reaction can be decomposed 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 paper30 and can serve as an example that may be represented by the following sequence of catastrophes: C4H6 + C2H4: η-1
7[C]2C[F+]2[F+]2[C]2C+-0: C6H10 using topological analysis of electron localization function (η). All DFT calculations have been performed using unrestricted Kohn
Sham orbitals for doublet electronic states. The M06-2X31 hybrid electron density functional has been used with 6-31+G(d,p)32,33 and aug-cc-pVTZ34,35 basis sets. Additionally, single point calculations have been performed with LC-ωPBE36 and B3LYP37
39 hybrid density functionals. The minima on the potential energy surface (PES) have been confirmed by nonimaginary vibrational frequencies. The zero-point vibrational energy (ΔZPVE) corrections were included in the calculation of the activation energy (ΔEa). In calculating ΔZVPE for ΔEa, one imaginary frequency has been omitted. The reaction path has been calculated using the intrinsic reaction coordinate (IRC)40,41 with a step size of 0.07 amu0.5bohr at the M06-2X/aug-cc-pVTZ computational level. Calculations with the 6-31+G(d,p)29,30 basis set have been performed using the Gaussian0942 package. Calculations with the aug-cc-pVTZ basis set and all additional single point calculations for DBTTFI molecule have been performed using GAMESS version 2009-01-12-R1.43 The stability of the DFT wave function (“Stable” keyword) was tested for both transition states and the selected points on the IRC paths, indicating neither external real nor internal instabilities. The ELF function was calculated over a rectangular grid with a step size of 0.045 bohr. Topological analysis of ELF for the QTTFQ derivatives was performed using the Topmod suite.44 In the case of the DBTTFI molecule Dgrid-4.5 was used.45

Table 1. Comparison of Selected Bond Lengths for the TS and 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 C5
C6

2.574 2.759

2.568 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 C12
C11

2.552 2.779

2.522 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 minimum structure and a transition state structure.

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

3. RESULTS AND DISCUSSION 3a. (QTTFQ)•
Molecule: Relative Energies and Geometrical Structures. The geometrical and electronic structure of

(QTTFQ )•
has been studied using 6-31+G(d,p) and aug-ccpVTZ basis sets. No essential differences were found, so only the results obtained with the larger basis set shall be presented. The meta exchange
correlation functional M06-2X proposed by Zhao et al.31 has been chosen, because it reflects the unsymmetrical distribution of the odd electron observed in the ESR spectra.2 Selected bond lengths for the optimized geometrical structure and its transition state (TS) are compared in Table 1, and an overview of the geometries is shown in Figure 1.

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Figure 2. (a)Visualization of the ELF (η(r) = 0.81) function for the (QTTFQ)•
minimum energy structure. Core basins are marked in red; valence basins corresponding to the hydrogen atoms are marked in yellow. Other valence basins are marked in various colors for clarity. (b) Organization of critical 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.

The TS has nonplanar C2v symmetry as a consequence of the sp2 hybridization of the sulfur atoms.11 The C2v symmetry is defined by the plane perpendicular to the central C7dC8 bond, with an angle breaking planarity between the planes of the quinone rings and the central C7dC8 bond. In the TS these planarity breaking angles are symmetrical, both having values of 173
, whereas in the minimum the values are 165
for the side of QTTFQ•
with an unpaired electron, and 176
for the other side. The smaller angle increases during the course of the reaction. The minimum also differs from the TS by the length of the carbon
oxygen bonds: in the TS they are both 2.336 bohr, whereas for the minimum the values are 2.305 bohr and 2.389 bohr. In the case of other bonds the observed differences are smaller 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 of 2.9 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/mol calculated at the B3LYP/6-31G(d) level and 1.85 kcal/mol in single-point calculations with the 6-311+G(d) basis set using the constrained DFT method, reported by Wu and Van Voorhis.47 The activation barrier estimated on the basis of experimental data is 8.0 kcal/mol.2

3b. Topological Analysis of the ELF Function for (QTTFQ)•
Stationary Points. The 3D plot of the ELF function and all

the attractors localized for (QTTFQ )•
in the energy minimum (Cs symmetry) are presented in Figure 2. Each atom, except for the hydrogen atom, is represented by a core basin (red area). For each 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 the TTF bridge the C7dC8 bond is represented by two disynaptic basins, Vi=1,2(C7,C8), with mean electron populations (N) of 2.02e and 2.12e, respectively. The correspondence to the Lewis formula is clear (Scheme 3), indicating that this has standard double bond character. However, each of the C4dC5 and C9d10 bonds, formally also double, is represented by a single basin, V(C4,C5) and V(C9,C10), with basin populations of 3.41e and 3.48e, respectively. These bonds exhibit a smaller number of electrons than those computed for C7dC8 (4.14e). Smaller values 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 basins Vj=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 13516

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Table 2. Ωi Basin Populations (N) [e] of the Selected Valence Basins for the TS and Energy Minimum of (QTTFQ )•
TS Ωi- basin

a

Min N(Ωi)

2Sz(Ωi) a

0.06

2.81

0.12

0.06

2.82

0.10

2.78

0.06

2.81

0.12

V2(O2)

2.72

0.06

2.82

0.10

V1(O3) V2(O3)

2.78 2.72

0.06 0.06

2.66 2.64

0.00 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) V(C5, C6)

2.43 2.43

0.04 0.04

2.31 2.31

0.00 0.00

N(Ωi)

2Sz(Ωi)

V1(O1)

2.78

V2(O1)

2.72

V1(O2)

a

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) V2(S2)

2.13 2.15

0.00 0.00

2.13 2.15

0.00 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

0.00

Sz(Ωi) = integrated spin density [e].

two or three lone pairs, depending on which side the unpaired electron resides. However, topological analysis of ELF does not support this image, and only two Vi=1,2(Oi) basins are observed for each oxygen atom (Figure 2a). The Vi=1,2(Oi) attractors (Figure 2b) are localized within the plane containing the quinone rings. The carbon
oxygen bonds, depending on formal localization of the unpaired electron in (QTTFQ)•
, are represented as single C—O or double CdO bonds (Scheme 2). In the topological analysis of ELF (Figure 2) they are reflected only by single disynaptic basins V(C,O): V(C11,O1), V(C14,O2), and V(C3,O3), V(C6,O4), respectively. The N values for the CdO bonds are smaller than the formal value of 4e, being 2.33 and 1.99e, respectively. The missing electrons (with respect to the formal values) are “contained” in the nonbonding basins corresponding to the lone pairs Vi(O), with N = 2.63e. The Lewis structure (Scheme 2) for the (QTTFQ)•
anion shows that the C—O bond on the side with the unpaired electron has a smaller bond order than that on the other side of molecule, as confirmed by the N values. Each C
S bond, formally single, is represented by a single disynaptic basin V(C,S). According to the Lewis formula, such a bond has 2e but the topological analysis shows the basis population is in the range 1.74
1.88e. Eight monosynaptic basins,

Vi=1,2(S1
4), characterize four sulfur lone pairs, and their number is consistent with the Lewis formula. Because the C
S bonds are slightly depopulated in comparison to the formal value, and the basin populations of Vi=1,2(S1
4) are much larger than the formal 2e value (Table 2), resonance hybrids with negative charge on the 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 is observed for the C1dC2 and C12—C13 bonds in the quinone fragments. For the side with the unpaired electron, the C12— C13 bond (2.568 bohr) is represented by two disynaptic basins Vi=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 unpaired electron, the analogous but shorter bond C1dC2 (2.522 bohr) is represented by a single disynaptic basin V(C1,C2), with an N value of 3.33e. This difference in bond lengths is consistent with the Lewis structure (Scheme 2), where these bonds also have different bond orders. The unpaired electron is not, as is usually the case, delocalized across the whole molecule but remains on one side of the TTF bridge. The sum of the basin populations calculated for this side of (QTTFQ )•
is greater by 0.93e than the equivalent value for the other side. More accurate analysis shows that the unpaired electron is delocalized across the whole side of the molecule. Differences in the N values between analogous basins for both sides are less than 0.06e. The largest differences are noticed for the oxygen lone pairs, Vi(O). This result is consistent with the classical 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 populations 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, and the unpaired electron is delocalized symmetrically on both sides of the TTF bridge. The unpaired electron density is spread across the whole molecule, with the largest values of the spin density being 0.03e for the oxygen lone pairs V1,2(Oi=1
4), and 0.02e for C
C bonds with the V(C3,6,11,14,C4,5,9,10) basins. The spin densities for basins corresponding to the C1
C2, C6
C1, C2
C3, C12
C13, C11
C12, and C14
C13 bonds are all smaller than 0.01e. 3c. Topological Analysis of the ELF Function for the QTTFQ•
T
•QTTFQ Reaction. The total energy curve obtained using the intrinsic reaction coordinate (IRC) method at the M06-2X/aug-cc-pVTZ level is presented in Figure 3. Its shape resembles that expected from theoretical considerations for IET, where two parabolic curves describing the reactant and product states cross at the TS. Comparison of the Lewis formulas (Scheme 2) indicates that IET is mainly associated with a change in 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”, as proposed by Krokidis et al.,15 is used. This means that only evolution of local maxima (attractors) is considered. The analysis shows three steps, with one step for each side of the reaction path, separated by the step containing the TS. The reaction can be 13517

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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.

represented, using the catastrophe sequence in place of the arrow symbol, 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. Going from the minimum to the TS, there is discernible movement of the integral spin density from the oxygen lone pairs to the C—C bonds connecting the CdO group of the quinone ring to the

TTF bridge. The unpaired electron population values for the V1(O1), V2(O1), V1(O2), V2(O2), V(C9,C11), and V(C10,C14) basins in the minimum were 0.12, 0.10, 0.12, 0.10, 0.08, and 0.08e, respectively. The equivalent values for the last point of the first step are 0.08, 0.08, 0.08, 0.08, 0.10, and 0.10e, respectively. This movement of unpaired electron density is noticeable, although very small, at about 0.04e for the whole step. The electron flow 13518

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Table 4. Comparison of Selected Bond Lengths for the TS and Minimum of Energy for (DBTTFI)•
bond

TS [bohr]

Min [bohr]

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

C9
C13

2.721

2.837

C8
C11 C11
O33

2.721 2.311

2.837 2.287

Table 3. Ωi Basin Populations (N) [e] of the Selected Valence Basins for the Transition Structure and the Energy Minimum of (DBTTFI)•


C13
O34

2.311

2.287

C13
N12

2.646

2.622

C11
N12

2.646

2.622

C23
C26

2.721

2.749

Min N(Ωi)

C24
C28

2.721

2.749

C28
O35

2.311

2.332

2.311 2.646

2.332 2.622

2.646

2.622

Ωi basin

TS N(Ωi)

V1(O33)

2.70

2.65

V2(O33)

2.75

2.70

C26
O36 C26
N27

V1(O34)

2.70

2.65

C28
N27

V2(O34)

2.75

2.70

V1(O35)

2.70

2.75

V2(O35) V1(O36)

2.75 2.70

2.80 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) V1(C24)

0.17 0.17

V2(C24) V(C23,C24)

0.17 2.44

2.30

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

causes essentially linear changes of spin densities for these basins (Figure 4). The second step begins with the catastrophe, which is observed before the first IRC point, counting from the TS. In the cusp [C], the V(C1,C2) bonding disynaptic basin and its attractor 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 molecule without the unpaired electron. Furthermore, this finding is exactly contrary to the Lewis formula, which predicts a change from double to single bond (Scheme 2). The basin population value of each Vi=1,2(C1,C2) is 1.68e. From a topological point of view, 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 TS itself, which seems to be typical for IET processes. In most cases of BET analysis20
23 there are no changes in the ELF topology associated with the TS. An explanation can be related to the shape of the total energy curve (Figure 3). The IRC path studied encompasses two overlapping potential energy curves describing the (QTTFQ)•
and
•(QTTFQ) minima. The first point after/ before the TS characterizes the molecule with a different electronic 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 whole reaction path. The electron transfer involves only the valence basins with a spin density lower than 0.01e, and unpaired electron density is redistributed from the oxygen lone pairs to the other side of the molecule through the V(C9,C11) and V(C10,C14) basins corresponding to carbon
carbon bonds connected to the C
O group in the quinone ring. Because the IRC path is symmetrical, owing to the geometry of the TS (Figure 3) the second cusp catastrophe [C] is placed between the TS and the first point, on the second shoulder of the IRC path. 3d. (DBTTFI)•
Molecule: Relative Energies and Geometrical Structures. The DBTTFI system (Figure 5 and Schemes 4 and 5) has been selected among 4047 molecules containing the TTF fragment and displayed in the Cambridge Structural Data Base.48,49 In its neutral form it has been used to construct DBTTF based organic semiconductors and transistors,.50,51 Optimization of the geometrical structure, performed at the M06-2X/6-31+G(d,p) level, converged to an energy minimum with Cs symmetry, containing unsymmetrical distribution of the electron density. This finding suggests that the radical anion of DBTTFI could be used, after experimental confirmation, as an essential fragment of organic microelectronic devices. There are many similarities between the structures of (QTTFQ )•
and (DBTTFI)•
. The most notable is the nonplanar structure of the TTF bridge and adjacent rings. The TS structure has C2v symmetry as in the case of (QTTFQ )•
. One of the two symmetry planes is perpendicular to the central C1dC2 bond, with a planarity breaking angle between the planes of the benzene rings and the central C1dC2 bond in the TTF bridge. In the TS these planarity breaking angles are symmetrical, with values of 162
. In the minimum structure this angle is 164
for one side of the TTF bridge, and 159
for the other. Similarly to (QTTFQ )•
, this angle is smaller for the side 13519

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The Journal of Physical Chemistry A

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

with an unpaired electron and increases during the course of reaction. The geometrical structure of the minimum also differs from the TS in the length of the carbon
oxygen bonds. In the TS both of these have values of 2.311 bohr, whereas for the minimum structure these values are 2.287 and 2.332 bohr for the two sides of the TTF bridge, respectively. The ΔEa value for this 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 for the DBTTFI radical anion are collected in Table 3. The ELF topology for the TTF bridge is very similar to that in (QTTFQ)•
. All the C—C, CdC, and C—N bonds are represented by single disynaptic basins V(C,C) and V(C,N). The disynaptic basins V(C,C) corresponding to the delocalized C—C bonds in the benzene rings have basin populations between 2.7 and 3.1e. The formal bond order is 1.5, and this value is well reflected by a topological bond order of 1.35
1.55. The lone pairs from the nitrogen atoms are represented by two monosynaptic nonbonding basins, Vi=1,2(N), for each atom, one with population of 0.83e and the other 1.00e. The Lewis structure (Scheme 4) shows that each nitrogen atom has one nonbonding lone pair. Due to local planarity, the lone pair is localized symmetrically above and below the plane designated by the N and C atoms. A similar situation is observed for pyrrole52 and for planar ammonia NH3 in its TS for umbrella inversion through planar D3h geometry. The total basin population N[V1(N)] + N[V2(N)] is 1.83e, and thus close to the formal value of 2e. The C—O bonds are represented by single disynaptic basins V(C13,O34) and V(C11,O33), with mean electron populations of 2.10e. The CdO bonds are represented by V(C26,O36) and V(C28,O35),

with basin populations of 2.38e, much smaller than the formal value of 4e. It is evident that the correct representation of the nature of the carbonyl groups involves ionic resonance hybrids, C+O
and C
O+. The lone pairs of the oxygen atoms are represented by the nonbonding basins Vi=1,2(O33
36), with N in the range 2.70
2.80e. The main difference between the ELF topology observed for the energy minimum and the TS is found in the region of the C23
C24 bond. This bond has mixed single and double bond character due to delocalization of the electron density and thus should be represented by a single V(C23,C24) or two Vi=1,2(C23,C24) disynaptic basins if a resonance hybrid with the double C23dC24 bond is a major contributor. However, for the minimum state, four monosynaptic nonbonding basins Vi=1,2(C23) and Vi=1,2(C24) are observed, situated near carbons C23 and C24 (Figure 6a). These basins exist only for the side of the molecule with an unpaired electron: one basin is placed under the plane designated by the carbon rings, and another above this plane. The two nonbonding basins and the corresponding core basins, C(C23) and C(24), are collinear. The basin population of Vi=1,2(C23) and Vi=1,2(C24) is 0.17e, so an additional 0.68e is localized in this bond, with a total basin population for the bond of 3.12e. This is rather an unexpected finding, so single point calculations were performed at M06-2X/aug-cc-pVQZ, LCωPBE/aug-cc-pVQZ, and B3LYP/aug-cc-pVQZ levels to confirm this topological feature. The topological analysis of ELF confirms this finding, because the ELF images obtained are quite similar to those from M06-2X/6-31+G(d,p) calculations, with differences in N values smaller than 0.06e. Analysis of the total spin value, ÆS2æ, reported by GAUSSIAN during calculations 13520

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The Journal of Physical Chemistry A yields a range of 0.751
0.752 for all levels of calculation used. The expected value is 0.75, thus confirming that no essential mixing of other electronic states occurs. However, such a topological feature might be an effect of the computational method used, 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 molecule with four Vi=1,2(C23), Vi=1,2(C24) basins, the total basin population is 1.06e greater than that on the other side. This fact clearly indicates that the unpaired electron stays on only one side of the molecule. This population asymmetry is mainly observed for the Vi=1,2(C23), Vi=1,2(C24) basins in the minimum energy structure. This shows that either an unpaired electron or electron flow, resulting from the reaction, is connected with the C23 and C24 atoms, probably by the coupled double bonds. There is also a noticeable difference observed between the two sides of the molecule for the oxygen lone pairs, V(O35), V(O36) and V(O33), V(O34). The basin populations for V(O35), V(O36), on the side with unpaired electrons are greater by 0.1e each than those on the other side. By analogy to (QTTFQ)•
, the carbon
oxygen bonds for the side with an unpaired electron are shorter by 0.045 bohr (Table 4) than those on the other side. This is reflected in the values of the basin population, where a shorter bond (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 in the DBTTFI radical anion (Scheme 4) is presented in Figure 7. The reaction follows the symmetry change Cs f C2v f Cs. There are three steps, with one step for each side of the reaction path, and a separate step containing the TS. In the first step there are changes in the basin populations mostly related to atomic rearrangement. The largest changes are obtained for the C11
O33, C13
O34, C28
O35, and C26
O36 bonds, where the respective basin populations for C11
O33 and C13
O34 decrease by 0.03e, and those for C28
O35, C26
O36 increase by 0.03e. The second step begins with the disappearance of four monosynaptic Vi=1,2(C23), Vi=1,2(C24) basins from the side of (DBTTFI)•
where the unpaired electron is localized (Figure 6). From a chemical point of view this means that the properties of the C23
C24 bond change. The N value for the C23
C24 bond is 2.44e after the catastrophe and, coming from the minimum, its basin population increases by 0.14e. The four bifurcations are folds ([F]4) and are observed simultaneously between the first IRC point, counting from the TS, and the TS itself. In the TS the unpaired electron is delocalized across the whole molecule. For the IRC path after the TS the situation is the same, but inverted by the symmetry plane perpendicular to the central C1
C2 bond. 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). The reaction mechanism can be summarized as follows: (DBTTFI)•
: η-1
3-[F]4[F+]4-0:
•(DBTTFI). This mechanism is very similar to that in (QTTFQ)•
, where the catastrophe sequence η-1
3CC+-0 is observed. The only difference is that folds are observed in place of the cusp catastrophes, which is associated with the special ELF-topology detected in (DBTTFI)•
.

4. CONCLUSIONS For the first time, BET analysis has been used to study the flow of electron density during IET in the QTTFQ and DBTTFI radical anions. Reorganization of the valence attractors and their

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basins on the η(r) field, along the IRC pathway, reveals a simple mechanism consisting of three steps separated by two cusps for (QTTFQ )•
, and 4-fold catastrophes for (DBTTFI)•
. Owing to the shape of the total energy curve, typical for IET, the catastrophes occur immediately after the TS. Analysis of ELF performed for IET in (QTTFQ )•
yields two findings that cannot be simply inferred from analysis of the Lewis formula. First, IET is not associated with change of the nonbonding basins of oxygen atoms, which are reflected in the ELF analysis by two nonbonding basins, Vi=1,2(O), regardless of the position of the unpaired electron. Second, and most importantly, IET manifests itself only in a qualitative change of the electronic structure of the C1—C2 bond in the quinone ring. From a topological point of view, the change predicted is strictly local and is constrained to a single bond: C1dC2 T C1—C2. A similar effect has been observed for the C23—C24 bond of the (DBTTFI)•
molecule, although its electronic structure seems to be more complicated. In our opinion, these two new facts should be explored further to aid the construction of future electronic devices, based on these two molecules. Topological analysis of ELF reveals the differences in unpaired electron distribution between the (QTTFQ )•
and (DBTTFI)•
molecules. In the energy minimum of (QTTFQ )•
, the unpaired electron is localized mainly on the lone pairs of O1, O2 and is redistributed to all oxygen lone pairs for the TS. In the energy minimum of (DBTTFI)•
, the unpaired electron is localized mainly in close proximity to the C23 and C24 atoms and is redistributed across the whole molecule for the TS. The analysis of the bonding presented here, together with that presented by Krokidis et al.24 for the Li + Cl2 = Li+ + Cl2
reaction, shows that the topological approach to electronic structure is a valuable tool for elucidation of electron transfer processes reaction mechanisms.

’ AUTHOR INFORMATION Corresponding Author

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

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