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J. Phys. Chem. C 2008, 112, 1672-1678
Buckycatcher. A New Opportunity for Charge-Transfer Mediation? Alexander A. Voityuk*,†,‡ and Miquel Duran*,‡ Institucio´ Catalana de Recerca i Estudis AVanc¸ ats, Barcelona 08010, Spain, and Institut de Quı´mica Computational, Departament de Quı´mica, UniVersitat de Girona, 17071 Girona, Spain ReceiVed: July 4, 2007; In Final Form: October 8, 2007
This contribution deals with a computational study of hole transfer (HT) and excess electron transfer (EET) in complexes of a buckyball and a molecular catcher having two concave buckybowls as described by Sygula et al. (J. Am. Chem. Soc. 2007, 129, 3842). Three systems are considered: (1) the inclusion complex consisting of the fullerene and catcher subunits, (2) a system formed by two catchers, and (3) a supermolecular system consisting of two fullerene and two catcher molecules. Such a type of organic system is of potential interest in the design of nanoelectronic devices. HT and EET electronic couplings of the subunits in the systems are calculated using the HF/6-31G* method and the semiempirical INDO/S scheme; the calculation of the reorganization energy is carried out within the B3LYP/6-31G* method. On the basis of the computed values of electronic couplings and reorganization energies, we predict that excess charge (hole or electron) should be strongly confined to a single subunit in the complexes. Then, we suggest that excess charge propagation within the fullerene-catcher system in the solid state occurs as superexchange mediated hopping; in this process, fullerene molecules function as stepping stones, while the catcher effectively mediates the charge transport between buckyballs. The properties of the buckycatcher, acting as a charge-transfer mediator from and to fullerenes, are found to be quite different for electron- and hole-transfer processes. We estimate the absolute rate of the hole and the excess electron hopping between fullerenes, kHT ) 1.28 1012 s-1, while kEET ) 1.07 109 s-1 and find that the HT is much faster than the EET because of (1) the stronger HT coupling between neighboring buckybowls of the catchers and (2) the smaller HT reorganization energy relative to that for EET.
Introduction Recently, a rather stable inclusion complex (Figure 1) has been reported between C60 and a catcher, namely, a bowl-shaped polycyclic hydrocarbon. This complex is formed because of the π-π interaction between the convex surface of the fullerene and the concave faces of the corannulene subunits of the buckycatcher.1 Among various interesting applications of such systems, one may imagine their use as building elements in molecular electronics. Actually, fullerenes and their derivatives are already widely employed in solar cells (photovoltaic devices)2 and may also be key elements for different molecular electronic devices.3-5 For organic systems, photochemical or electrochemical doping is used to introduce charge carriers; depending on the injected charge, two types of charge transfer (CT) can be activated: (i) a positive charge or hole transfer (HT), when a radical-cation state migrates within a system and (ii) an excess electron transfer (EET), which is associated with migration of a radical-anion state. The last 20 years have been very important for understanding CT mechanisms underlying in molecular electronics.6,7 The performance of a molecular device depends critically on the efficiency of charge transfer between its subunits, which in turn is determined by the electronic interactions present in the system.8 In particular, delocalization of an excess charge over the system is directly associated with CT properties and electron transport mechanisms.9 Recently, it has been shown that the * E-mail:
[email protected];
[email protected]. † Institucio ´ Catalana de Recerca i Estudis Avanc¸ ats. ‡ Universitat de Girona.
mobility of charge carriers within a device is closely related to the CT rate.10,11 A detailed discussion of how these CT processes can be described at the molecular level is given in excellent reviews.12,13 Three key parameters, (a) the donor-acceptor energy gap, (b) the electronic coupling, and (c) the reorganization energy associated with charge migration, determine the probability of electron transfer in the nonadiabatic regime.12,13 Because the CT efficiency is related to the electronic coupling, Vda, of donor and acceptor states (it is proportional to V2da), the quantum chemical calculation of Vda provides valuable information about the electronic effects in the charge-transfer process.8,13,14 The computational aspects of estimating electronic coupling have already been considered in detail in several reviews.13,15 The effects of structural and dynamical disorder on charge transfer in π-stacked arrays of conjugated organic molecules have also been considered in detail.14,16 In the present paper, we calculate CT parameters for three key systems: the buckyball-catcher inclusion complex, catchercatcher dyad, and the supermolecular system consisting of two fullerene and two catcher units. Both the hole transfer and excess electron transfer are considered. Comparison of the EET and HT parameters provides useful insight into the electronic interactions in the systems. Computational Details Application of quantum chemical calculations to study conductivity in a π-stacked system (polyacetylene) was considered by Rodriguez-Monge and Larsson.17 In particular, they
10.1021/jp075209e CCC: $40.75 © 2008 American Chemical Society Published on Web 01/12/2008
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J. Phys. Chem. C, Vol. 112, No. 5, 2008 1673 DNA π stacks,22 we also used this scheme for calculations of the charge-transfer parameters for complexes 1-3. Estimation of Electronic Couplings. Two methods were employed to calculate electronic couplings (1) the generalized Mulliken-Hush (GMH) method,23,24 and the fragment-charge model (FCM).25 We used two- and multistate variants of these methods. When applying the two-state approach, particular attention has been given to properly select one-electron states corresponding to the “+” and “-” combinations of the donor and acceptor states. Within the two-state GMH approach, the electronic coupling Vda is expressed via the energy and dipole moment differences for adiabatic states ∆E ) E2 - E1, ∆µ ) µ2 - µ1 and the transition dipole moment µ12.23,24
Vda )
∆E|µ12|
x∆µ2 + 4µ122
(1)
A very useful characteristic of determining the donor and acceptor states is the effective donor-acceptor distance, which can be derived from the difference of the diabatic dipole
Figure 1. Chemical structure of complexes 1-3; r is the distance between the catcher bottom and the closest C-C bond of the fullerene. Angle R stands for the opening of the catcher jaws. In the X-ray structure (reference system) of the complex, r ≈ 5 Å and R ≈ 85.4°.
showed that the electronic coupling calculated using Koopmans’ theorem in the Hartree-Fock, CASPT2, and CASSI methods are quantitatively very similar for various intermolecular distances. Also, comparison of the CASPT2 energetics and electronic couplings for HT and EET in small π-stacked complexes of nucleobases with the corresponding data derived within Koopmans’ approximation suggests that charge-transfer parameters for the radical-cation and radical-anion systems can be estimated using the highest occupied and lowest unoccupied molecular orbitals (HOMOs and LUMOs) of a neutral system.18,19 Thus, in the present work we carried out HartreeFock calculations (HF/6-31G*) of electronic couplings for systems 1 and 2 (Figure 1). The DFT method (B3LYP/6-31G*) was used to compute the internal reorganization energy for the HT and EET processes. The Gaussian03 program20 was used to carry out these computations. Because the INDO/S method21 provides very reasonable estimates for electronic couplings in
moments, Rda (in Å) ) ∆µda(in D)/4.803, ∆µda ) x∆µ2+4µ122.23 Comparison of Rda with a distance between the donor and acceptor sites estimated from the structural parameters of the system provides a simple way to discriminate the diabatic states of interest. Because of symmetry (we assume that complex 1 has C2V geometry, while complexes 2 and 3 have C2h symmetry), the electronic coupling is nonzero only when states of the same symmetry are considered. The computational procedure to derive electronic couplings has already been described in detail elsewhere.26 Internal Reorganization Energy. The internal reorganization energy λi was calculated at the B3LYP/6-31G* level; for the radical-anion and radical-cation states, the unrestricted KohnSham method was applied. By definition, λi for the EET reaction in complex 1, C60 + Catcher f C60 + Catcher , turns out to be a sum of the reorganization energies of the subunits, λi ) λi(C60) + λi(Catcher). If we consider the charge transfer between identical donor and acceptor, for example, between C60 subunits in complex 3, then λi ) 2λi(C60). To estimate λi for a molecule X (X ) C60, Catcher), we computed the following terms: (1) the energy E0(X) of neutral X at the optimized geometry, (2) the energy E- (X-) of the corresponding anion radical at the optimized geometry, (3) the energy E-(X) of neutral X calculated at the geometry of the anion radical X-, and (4) the energy E0(X-) of the radical-anion state at the geometry of corresponding neutral molecule X. Thus, the reorganization energy λi(X) becomes
1 λi(X) ) [E-(X) - E-(X-) + E0(X-) - E0(X)] 2
(2)
A similar approach was used to calculate the reorganization energy for the HT process. Geometries. As starting point for geometry optimization of 1, we used the atomic coordinates of the complex arising from X-ray data. Optimizations were carried out within the modified tight-binding model (MTB),27 which provides very accurate energetic and structural parameters for hydrocarbons. The mutual position of the catcher subunits in 2 and 3 are taken from structural data.1 Note that the π-π interaction between the fullerene and the catcher depends on the contact distances between the subunits, which in turn are determined mainly by the two parameters r and R shown in Figure 1.
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TABLE 1: Electronic Couplings of Excess Electron Transfer for Various Geometries of Complex 1a |V|, HF/6-31G* geometryb 1a: r ) 5 Å, R ) 85.4° 1b: r ) 5 Å, R ) 80° 1c: r ) 5 Å, R ) 90° 1d: r ) 6 Å, R ) 85.4˚ 1e: r ) 7 Å, R ) 85.4°
RC...C Rmin
transitionc
∆E
∆µda
GMH
FCM
3.48
3.26 L+1 f L+5 1.64 17.7 L+2 f L+8 1.805 20.0 2.85 L f L+5 1.57 16.5
0.096 0.140 0.196
0.090 0.132 0.152
3.62
3.42 L+1 f L+5 1.69
18.3
0.134
0.104
3.64
3.49 L+2 f L+8 2.00
24.3
0.111
0.072
3.83 L f L+6 1.83 L+2 f L+9 2.13
26.7 29.0
0.032 0.025
0.021 0.040
3.56
a RC‚‚‚C, average contact distance in Å; Rmin, C‚‚‚C separation for shortest contacts in Å; ∆E, excitation energy in eV; ∆µda, difference of the diabatic dipole moment in D; V, electronic coupling in eV. b Geometric parameters r and R are shown in Figure 1. c L+K labels the one-electron states of the radical-anion with an excess electron on LUMO+K of the neutral system.
Results and Discussion First, we consider the electronic interaction between fullerene and its catcher in complex 1; then, we focus on the electronic goupling between buckybowls of neighboring catchers (complex 2), and finally, we consider the charge transfer in supermolecular system 3. Fullerene-Catcher electronic Interaction. Intersurface Contacts. Usually, one assumes that two carbon atoms belonging to different subunits are in contact when their distance is shorter than 3.80 Å.28 This distance was also taken here as the criterion to suggest contacts between the buckyball and the catcher. In the reference structure, r ) 5 Å and R ) 85.4° (complex 1a in Table 1) there are 112 contacts between the two subunits; the average distance between contacting carbon atoms is of 3.55 Å; in the shortest contacts, the C‚‚‚C separation is found to be ca. 3.20 Å. According to MTB calculations, a small decrease of angle R (Figure 1), from 85.4° to 80.0°, is accompanied by remarkable shortening (by ∼0.4 Å) of closest contacts 1b (Table 1), which leads to repulsion between subunits: the energy of the system increases by ca. 6 kcal/mol. However, no meaningful change in the total energy is found when increasing the angle by going from the reference geometry to structure 1c (Table 1); the structural changes bring about a small increase of contact distances. As expected, the separation between the subunits increases rapidly with the value of r (geometries 1a, 1d, and 1e in Table 1). In particular, when r ) 7 Å and R ) 85.4° the shortest distance between subunits, 3.83 Å, falls out of the range of the C‚‚‚C contact (3.80 Å). Excess Electron Transfer. Injection of an excess electron into the complex yields a radical-anion system. Three lowest-energy states of the system correspond to the threefold degenerate T1u level of C60; due to the π-π interaction with the buckycatcher, these states are slightly split, within 0.07 eV. According to our calculations, the excess charge in the anion radical is almost completely localized (99%) on the fullerene (Figure 2A, Table 2). The lowest excited state, where the excess electron is confined mainly to the catcher, lies ca.1.6 eV higher than the ground state of the radical anion (Table 2) and thus cannot be thermally populated. Table 1 lists adiabatic parameters. Coupling values derived using the fragment-charge model25 are also given in Table 1. In all cases, the GMH and FCM values agree quite well. For geometries 1a and 1c, the coupling is calculated to be 0.1 eV. When the catcher clasps its jaws (structure 1b in Table 1) the coupling increases significantly. However, as noted above, this structure lies 6 kcal/mol higher
Figure 2. One-electron states of the complex (structure 1) accounting most for the effective electronic coupling of C60 and buckycatcher: (A) hole transfer; (B) excess electron transfer (HF/6-31G* calculation).
TABLE 2: Excess Charge Distribution in the Ground and Excited States of Complex 1a radical anion statea E, eV q(catcher) 0 1 2 3 4 5 6
0.000 0.127 0.132 1.530 1.536 1.661 1.787
-0.005 -0.012 -0.012 -0.988 -0.947 -0.094 -0.023
radical cation q(C60)
stateb E, eV q(catcher) q(C60)
-0.995 -0.988 -0.988 -0.012 -0.053 -0.906 -0.977
0 1 2 3 4 5 6
0.000 0.092 0.128 0.163 0.190 0.336 0.359
0.132 0.020 0.011 0.316 0.008 0.876 0.693
0.868 0.980 0.989 0.684 0.992 0.124 0.307
a State K of the radical anion is generated by placing an excess electron in LUMO+K of the neutral complex. b State K of the radical cation is generated by placing an electron hole in HOMO-K of the neutral comopex.
in energy than the reference system 1a, and therefore it cannot contribute to the CT probability substantially. In the complex with r ) 7 Å (structure 1e), the coupling decreases by a factor of ∼2.5 as compared to the reference system. Overall, the coupling of the fullerene and the catcher is quite effective and not very sensitive to the parameters r and R. However, because the energy gap between the relevant diabatic states is quite large (1.5 eV), the catcher does not provide intermediate states where an excess electron can reside during charge transfer from/to fullerene. Thus, the catcher may mediate EET only via superexchange. As can be seen from Figure 2A, the wave function LUMO+5 is not uniformly delocalized over of the catcher. Hence, to obtain an efficient charge transfer between C60 and an electron donor/acceptor X in the C60catcher-X system X should be bound to the corannulene fragments that contribute most to the adiabatic state. Our calculations show that the INDO/S method is of limited use for calculations of EET electronic couplings. The INDO/S coupling matrix elements calculated for structures 1a-1e are by a factor of 2-4 smaller than the corresponding HF values, and therefore this method cannot be employed to derive the
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J. Phys. Chem. C, Vol. 112, No. 5, 2008 1675
TABLE 3: Hole Transfer Electronic Couplings Calculated for Several Geometries of Complex 1a |V|, HF/6-31G*
|V|, INDO/S
geometryb
transitionc
∆E
∆µda
GMH
FCM
GMH
1a 1b 1c 1d 1e
H f H-5 H-1 f H-5 H f H-5 H f H-5 H f H-4
0.254 0.432 0.149 0.107 0.139
22.3 22.2 22.4 26.3 28.9
0.096 0.148 0.063 0.053 0.0403
0.104 0.166 0.065 0.054 0.038
0.080 0.123 0.050 0.036 0.024
a ∆E, excitation energy in eV; ∆µ, dipole moment difference in D; V, electronic coupling in eV. b Geometric parameters are given in Table 1. c H-K labels one-electron states of the cation radical with a hole on HOMO-K of the neutral system.
TABLE 4: HT and EET Electronic Couplings V (eV), Diabatic Dipole Moment Difference ∆µda (D), and Effective Donor-Acceptor Separation Rda (Å) Calculated for the Catcher Dimer model
transitionc
∆E
∆µda
Rda
|V|, GMH
HT HF/6-31G* INDO/S EET HF/6-31G*
H f H-3 H f H-3 L f L+3
0.39 0.35 0.13
16.48 19.69 23.62
3.4 4.1 4.9
0.195 0.176 0.064
EET parameters for the systems under study. On the contrary, as shown below, INDO/S provides very good estimates for HT couplings. Hole Transfer. The calculated HT parameters for different geometries of complex 1 are gathered in Table 3. Loss of an electron by the complex leads to the formation of a radical cation. C60 has fivefold degenerate highest occupied MOs of Hu symmetry. In the complex, five low-energy electronic states originate from the Hu state of C60 and found to be of similar energy; the total splitting calculated with HF/6-31G* is ca. 0.19 eV (Table 3). Although in these states the hole is localized mostly on the fullerene, an admixture of catcher orbitals can be seen clearly (Figure 2B, Table 2). According to our calculations, in the ground state of the radical cation (a hole in the HOMO of the neutral complex) 78% and 22% of the hole is localized on the fullerene and the catcher, respectively. The second relevant adiabatic state (the hole in the HOMO-5) exhibits inverse hole distribution, namely, 21% and 79%, and lies only 0.25 eV higher in energy than the ground state (Table 2). The HT electronic coupling of 0.10 eV is very similar to that calculated for EET. These results reflect the similar nature of the EET and HT diabatic states (qualitatively, the coupling is proportional to the overlap of diabatic states of donor and acceptor). Similar to EET, the HT coupling depends moderately on the structural parameters r and R of the complex. The electronic couplings calculated using the INDO/S method are in good agreement with the HF data, being consistently smaller than HF values by ca. 20-30%. Note that the same relation between HF and INDO/S couplings was found for π stacks of nucleobases, where INDO/S values are in better agreement with CASPT2 results than the HF data.22 Thus, the INDO/S scheme seems to provide reliable estimates for HT electronic couplings for π-stacked systems. Calculated excess charge distributions in the ground and excited states of the radical cation and the radical anion (Table 2) show that delocalization of the hole is essentially larger than that of the excess electron. Catcher-Catcher Electronic Interaction. As can be seen from Figure 1, the adjacent buckybowls of neighboring catchers are quite close to each other, and therefore, a significant electronic coupling between the corresponding diabatic states is expected. To estimate the matrix element for HT, we carried
out HF/6-31G* and INDO/S computations of a system consisting of two catchers arranged as in the crystal structure.1 Because the donor and acceptor sites in the dimer are identical, the electronic coupling is determined by half of the adiabatic energy splitting. In such cases, the GMH and FCM schemes are reduced to the half splitting method. The HOMO and HOMO-3 of the catcher dimer correspond to “-” and “+” combinations of the diabatic states of interest (see Figure 3A). The short distance between adjacent buckybowls leads to the strong coupling of the diabatic states, V ) 0.196 eV (Table 4). The hole transfer results in ∆µda ) 16.5 D, which corresponds to the donoracceptor distance of 3.4 Å similar to a typical distance between π-stacked subunits. As seen from Table 4, the INDO/S data are found to be in good agreement with the HF results. For HT (HOMO f HOMO-3), INDO/S predicts V ) 0.175 eV. For EET, the situation is somewhat different as compared to the HT. As seen from Figure 3, the effective distance between donor and acceptor for EET is larger than that for HT (our calculation predicts Rda ) 4.9 Å); the difference of the diabatic dipole moments is larger, ∆µda ) 23.6 D. Accordingly, the electronic coupling is substantially smaller, V ) 0.062 eV. Thus, one can expect that HT should be more effectively mediated by the catchers than the EET. Charge Hopping between Fullerenes. Let us consider here INDO/S computational results for supermolecule 3. Because the calculations are performed for the entire system, the model explicitly accounts for the contributions from all possible superexchange pathways for the charge transfer. In system 3, the 10 highest occupied MO, arising from the Hu electronic level of the fullerene subunits, lie within a narrow interval of 0.11 eV. One-electron states localized on the catchers are ca. 1 eV higher in energy than the ground state of the radical cation. HOMO-10 and HOMO-13 localized on adjacent buckybowls are very similar to the states shown in Figure 3A. The energies of these states (relative to the ground state of the radical cation) are 0.52 and 1.04 eV, respectively. The shortest distance between carbon atoms, which belong to different fullerene subunits, is 9.8 Å. (geometrical centers of the fullerenes are separated by 16.6 Å). The electronic coupling derived from one-electron states HOMO and HOMO-3 (Figure 4A) is 6.85 × 10-3 eV. The difference of the diabatic dipole moments, ∆µda, is calculated to be 54.0 D, which corresponds to the effective donor-acceptor distance of 11.3 Å. This indicates that the centers of the diabatic states are shifted toward each other. Another pair of diabatic states derived from HOMO-1 and HOMO-2 (Figure 4B) is coupled much weaker, 1.25 × 10-3 eV. The difference of the diabatic dipole moments in this case is 79.4 D, corresponding to Rda ) 16.5 Å, which agrees very closely with the C60-C60 distance of 16.6 Å. Overall, the HT coupling of fullerene subunits in 3 can be estimated as 7 × 10-3 eV. This coupling value corresponds to the nonadiabatic regime for the hole transfer, which occurs as superexchange mediated hopping between fullerene subunits functioning as stepping stones. It is interesting to compare the calculated coupling value with an estimate derived from the superexchange model. In a system d-b1-b2-a, where the donor and acceptor are separated by two consecutive bridges, the coupling is13 2 VSE da ) Vd-b1Vb1-b2Vb2-a/∆
(3)
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Figure 3. HOMOs and LUMOs of the catcher responsible for mediation of (A) hole transfer and (B) excess electron transfer (HF/6-31G* calculation).
Figure 4. HOMOs of system 3 responsible for hole transfer between the fullerene subunits (INDO/S calculation). The diabatic states constructed from HOMO and HOMO-4 (panel A) are coupled stronger, V ) 6.85 × 10-3 eV, than the states built as ( combinations of HOMO-1 and HOMO-2 (panel B), V ) 1.25 × 10-3 eV.
where ∆ is the energy gap between donor and bridge levels. In eq 3, the effect of the direct coupling (through-space interaction of the fullerene units is negligibly weak). Taking into account that INDO/S value of Vd-b1 ) Vb1-a is 0.08 eV (Table 3) and Vb1-b2 is of 0.18 eV (Table 4) and ∆ ∼0.8 eV, we obtain VSE da ∼
1.8 10-3eV. This value is by a factor of 4 smaller than the V ) 6.85 × 10-3 eV calculated for the supermolecular system. Using the HF data for systems 1 and 2, one can estimate the coupling for hole and excess electron transfer within superexchange model. For HT, insertion of Vd-b1 ) Vb1-a ) 0.1 eV,
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J. Phys. Chem. C, Vol. 112, No. 5, 2008 1677
Vb1-b2 ) 0.2 eV, ∆ ∼0.4 eV into eq 3 gives VSE da (HT) ) 12.5 × 10-3 eV. For EET, with Vd-b1 ) Vb1-a ) 0.14 eV, Vb1-b2 ) 0.06 eV, ∆ ≈ 1.2 eV (difference of vertical electron affinities calculated using B3LYP/6-31G*), we get VSE da (EET) ) 0.82 × 10-3 eV. Because the rate for the nonadiabatic charge transfer is proportional to the coupling squared, we may conclude that the hole hopping between fullerene subunits should be faster by at least 2 orders of magnitude than the excess electron transfer. Reorganization Energy. The internal reorganization energy was calculated at the B3LYP/6-31G* level for the catcher and C60 molecules using eq 2. For the fullerene, we found that electron attachment is associated with a reorganization energy of ca. 0.15 eV, whereas when an electron is removed, the reorganization energy is significantly smaller, namely 0.04 eV. Thus, the reorganization energy for EET and HT between the fullerene subunits amounts to 0.30 and 0.08 eV, respectively. Note that the smaller reorganization energy for HT should lead to more efficient hole hopping relative to EET. Excess Charge Delocalization. Excess charge delocalization depends strongly on the relative magnitudes of the electronic coupling, the energy gap and the reorganization energy. Within a two-state model, the difference of the excess charges q1 and q2 on subunits 1 and 2, ∆q ) q2 - q1, is determined by29
∆q )
∆0 + λ∆q
(4)
x(∆0 + λ∆q)2 + 4V122
2π p
|V|2
x4πλkBT
[
exp -
Acknowledgment. This work has been supported by Project No. CTQ2005-04563 of the Spanish Ministerio de Educacio´n y Ciencia (MEC). References and Notes
where V12 is the electronic coupling, ∆0 is the difference between diabatic energies, and λ stands for the reorganization energy. If the donor and acceptor are identical, then ∆0 ) 0 and the ratio of the reorganization energy and the coupling determines the charge distribution. From eq 4, we can derive that when |λ/V12| > 5 95% of excess charge will be confined to one of the subunits. Obviously, the charge localization will increase with |∆0|. When |λ/V12| e 2, the charge is delocalized over both sites. Because in the supermolecular system the ratio |λ/V12| is estimated to be greater than 6, the excess charge should be confined to a single fullerene for both HT and EET. Absolute Hopping Rates. We estimate the absolute rate for hole and excess electron hopping using Marcus’ formula for the nonadiabatic reaction12
k)
systems. The reorganization energies for both excess electron transfer and hole transfer were calculated using the B3LYP/631G* level of theory. On the basis of the computed values of electronic couplings and reorganization energies, we predict that excess charge (hole or electron) should be strongly confined to single subunit in the complexes. Then, we suggest that excess charge propagation within the fullerene-catcher system in the solid state occurs as superexchange mediated hopping; in the process, fullerene molecules function as stepping stones, while the catcher effectively mediates the charge transport between buckyballs. The hole transfer is found to be much faster than the excess electron transfer, kHT ) 1.28 × 1012 s-1 while kEET ) 1.07 × 109 s-1, despite the fact that the EET and HT electronic couplings between the fullerene and the catcher are very similar, ca. 0.1 eV. The fast hole transport is due mainly to the stronger HT coupling between neighboring buckybowls of the catchers and the smaller donor-bridge energy gap as compared to the corresponding parameters for EET. Also, the smaller HT reorganization energy (relative to that for EET) favors the hole transport.
]
(∆G + λ)2 4λkBT
(5)
Because the charge transfer occurs between an identical donor and acceptor, the free energy for the HT and EET reactions is zero. Inserting the calculated parameters (V(HT) ) 6.85 × 10-3 eV, λ(HT) ) 0.08 eV; V(EET) ) 0.8 × 10-3 eV, λ(EET) ) 0.30 eV) into eq 5, we obtain kHT ) 1.28 × 1012 s-1 while kEET ) 1.07 × 109 s-1. Thus, we predict HT to be much more feasible in comparison to EET, kHT/kEET ) 1200. Concluding Remarks In the present paper, we consider the charge-transfer properties of the molecular complex between the buckyball and the catcher described recently by Sygula et al.1 We estimated the electronic couplings for hole and excess electron transfer in a supermolecular system consisting of two fullerene and two catcher subunits. It has been found that the INDO/S method gives reliable coupling matrix elements for HT, whereas it seems to be of limited use to study EET in π-stacked hydrocarbon
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