J. Phys. Chem. 1993,97, 8929-8936
8929
Electronic Factor for Electron Transfer through Cyclohexane-Type Spacers Manuel Braga’ and Sven Larsson Department of Physical Chemistry, Chalmers University of Technology and University of Gbteborg, S-412 96 Cbteborg, Sweden Received: February 23, 1993; In Final Form: June 2, 1993
-
-
The electronic factor A for electron transfer is calculated for a number of donor-acceptor systems of the general type D- B A D B A- and D B A+ D+ B A using ab initio methods. B is cyclohexane-type spacer which is bonded to the donor D and the acceptor A. All geometries have been optimized for the neutral system. We obtain a good agreement with the experimental results of Closs, Miller, and co-workers with an exponential decrease of A as a function of distance R between D and A. In some other systems, where experimental results are not available, we obtain a nonexponential A(R) with a change of sign between three and four spacer units.
1. Introduction
Electron transfer (ET) has become an important phenomenon in chemistry and biology and may find technical applications in molecular electronic devices. A typical ET system consists of a donor ( D ) where the electron is initially localized in an orbital $od and an acceptor ( A ) which receives the electron in an orbital (pa. In terms of electronic states the process is described as a radiationless transition from a state of the type DA to a state of the type D+A-. The bridge ( B )between thementionedsubsystems may consist of various types of spacer molecules. There is no accessible orbital on the bridge, or more correctly: the states D + B A and DBtA- have a high energy compared to keT. The well-known textbook model for electron tunneling is deceptive in two important respects: It does not explicitly take into account reorganization at the donor and acceptor sites at ET, nor does it consider explicitly the electrons of the “tunneling barrier” B on an equal footing with the electrons of D and A. An interesting question is whether the rate of the reaction DBA D+BA-, for increasing length of B but with the same D and A, decreases exponentially with distanceas in the case of a rectangular 1D tunneling barrier. Closs and Miller and their co-workers succeeded in synthesizing systems with rigid bridges consisting of trans-cyclohexanerepeat units and the steroid molecule S-a!-andr~stane.~-$ Using a pulsed radiolysis technique they determined the ET rate for different spacer molecules. The electronic factor, V, could be calculated using reasonable assumptionsin the rate equation. Vdecreases exponentially with the distance between the aromatic molecules, quite consistent with the rectangular potential barrier model for tunneling. Here, we disregard the weak nonexponential decrease introduced via the solvent reorganization energy &. By varying the donor and acceptor molecules as well as solvent, they found a rate versus exoergonicity relationship which followed the one predicted for the inverted region.6 The experimental results of refs 1-5 show among other things a dependence on rotamer conformation. The bridge apparently cannot be treated just as a rectangular tunneling barrier. This means that the electrons of the bridge must be included in the quantum mechanical treatment. Models which do just that have been s~ggested.~-l2In an early model of McConnell the communicating orbitals of B were considered to be small components of d orbitals on -CH* repeat units.7 In such a case, when the interactions between the communicatingorbitals along the chain are small, an exponential decrease is 0btained.~J3 Another method especially designed for conjugated bridges was suggested by Halpern and Orgel.8 The most general treatment, however, is to includeall the electronsof the bridge.”1°J4 In that case one finds that not only A systems facilitate ET but also
-
proteins, saturated organicbridges, and solvents. An exponential decrease occurs in the latter case but not necessarily for proteins or organic bridges. Other simplified models have been developed which lead to an exponential decrease, for example, along a peptide chain.” Path integral methods, in a sense generalizationsof the tunneling model, have also been used.l2 With the advent of modern computing technology and computer programs for thecalculation of electronicstructure, it has become possible to carry out accurate quantum chemical calculations on rather extensive systems.1”3 In a symmetric system one may simply calculate an energy difference A between an odd and an even state for the ionized system and identify this energy difference with twice the matrix element V, i.e., V = A/2. To simplify, one may use the Hartree-Fock (HF) method together with Koopman’s theorem (KT) to obtain A approximately as an orbital energy difference. A number of such systems have been studied recently, and it was generally found that KT works well in the case of saturated bridges.l7-Z4 Closs and Miller found an exponential decrease of A with distance for a set of systems with the same type of connection to the bridge, in their extensive studies. (A1 = 1 eV) with a!values in the range 0.4-0.5A-l. These results agree with the theoretical results to be presented here. However, in the present paper we also confirm earlier results22that a system where phenyl groups are used for both A and D, instead of naphthyl and biphenylyl, does not give an exponential decrease, but one of the type
A = A2(R- R , ) exp[-a(R - R,)] (A2 = fl eV A-1). We found in the present case R1 = 11.54 A and a! = 0.12. Unfortunately these systems (if they can be synthesized) are not amenable to experimental observations of the same type as those studied in refs 1-5. Closs et al. first studied ET in the case when D is a negative ion and A is neutraL3 When the KT approximation is used, the relevant energy difference is between LUMO and LUMO + 1. Later they studied hole transfer, i.e., with D neutral and A a positive ion.4 In that case the energy differencebetween HOMO and HOMO - 1 provides an approximate value for A. Experimentally similar rates were found for a given distance in the two very different cases. 2. Calculations
Calculations a r e carried out for t h e series CHIC4n++2H6n+r-CH2*-(?I = 1-5) and C6H&4n+&n+4 1 show a fast decrease of A2 for n up to 3. For n = 4 and n = 5 there is again an increase compared to n = 3 for the splittings calculated with the STO-3G basis set. For the larger basis sets, (AI is smaller for n = 4 than for n = 3, but the shape of the curves is similar for all basis sets (Figure 4). Somewhat surprisingly the shape is also the same for the semiempirical CNDO/S method.22 A is the result of interaction between the P MOs of the phenyl groups and a number of bridge M O S . ~In Figure 5 we show the calculated orbital energies for the highest occupied orbitals for the C~HS-C~,+&,+~-C~HS series using the Dunning double-{ basis. Between n = 3 and 4 HOMO and HOMO - 1 interchange u and g character (A changes sign). This may be due to the increased interaction between P, and the highest bridge as orbital, which is increasing its energy rapidly with n. This a, orbital, however, is not very well defined and changes character as the bridge becomes longer. For the smallest bridge the symmetry of the whole molecule is higher (C2h). There are occupied b, and a, orbitals of high energy, but only b, interacts with the P, MO. As the length of the bridge is increased there are two a, MOs which both interact with P,. As a consequence of this interaction the P, moves up in energy until the initial ordering ( r S< ru)is reversed for n L 4. For n = 5 there is a further increase of A. On a continuous scale A appears to change sign close to d Y 11.5 A. It is not surprising from these considerations that a nonexponential behavior may result from the particular electronic structure of the oligo(cyc1ohexane) chain when the number of units is increased and the proximity in energy of the phenyl r levels and the bridge MOs. Although eq 1 works for simple bridges even in cases when A changes sign,7J3J1it does not work in the present case. We tried instead a function of the type seen in eq 2. The fitting was
+
where
V = A / 2 and S = AJhv
(5)
A simplified model is assumed including a single important mode with Y = 1500 cm-1. A, is taken from ref 34. A, was calculated from the Marcus expression:6 A,=
[z;d+--q[----] 1
1
1
1
2r.a R cop We notice that the rate depends on R via A, in addition to the dependence of R in A. By fitting the reaction rate versus free energy curve to the experimental numbers, Closs et al. found an experimental value for (7) in the case of a steroid (androstane) bridge. This value may also be used for other bridges to be able to calculate A from the experimental numbers. This has been done in Table I, where the Vvalues are updated from ref 3 using the new rav= 5.07 A of ref 4 and the value AG = -0.05 e V . 3 ~We ~ assumed for the compound with the androstane bridge the same values of A, and A, as used in ref 3.
4. Results
CHA4,,+2Hw&H22-. A plot of log A2 as a function of the distance between the methylene groups for different basis sets is given in Figure 3. We obtain an almost exponential decrease of A2 with the edge-edge distance for the three basis sets used. As in the case of norbomadiene20 the double-{values are considerably larger than those obtained with the STO-3G single-f basis set. There is close agreement between the values obtained with the two double-{ bases. The deviations from a perfect exponential behavior are small. As pointed out by Ohta et aLL6there is a strong dependence of the calculated electronic coupling on the conformation of the end groups relative to the cyclohexanespacer, Le., on the dihedral angle between the -CH2- group and the cyclohexane. In the present study we have considered only systemsin which the -CHI groups are located at the equatorial position and close to perpendicular to the poly(cyc1ohexane) chain. In the case of 1,4-trans-(e,e)-dimethylene-cyclohexanethis conformation cor-
+
+
8932 The Journal of Physical Chemistry, Vol. 97, No. 35, 1993
I
I
I
6
8
10
Braga and Larsson
I 12
R
I
I
14
16
(4
Figure 3. log A2 (A in eV) as a function of edge-edge distance R for the trans-(e,e)-CHrC4n+~Hsn+t+r-CH~~system. Open circles, ab initio, Dunning double-{ basis set; open triangles, ab initio, 4-31G basis set; open squares, ab initio, STO-3G basis set. -1
-2
-3
-4
-v -4
-5,
-6,
I 6
I 8
I 10
I 12
I 14
R
1 16
I 18
I 20
(4
Figure 4. log A2 (A in ev) as a function of edge-edge distance R for the rrUns-(e,e)-CsHs-C~2Hs~+*-CsHs system for hole transfer. Open circlcs,
Dunning double-l' basis set; open triangles, 4-31G basis set; open squares, STO-3Gbasis set. determined by first requiring the function to take the calculated to the systems measured by Closs et al.3.5 corresponds to value for n = 1. Then RIand cy were varied to obtain the best c(LUM0+3) - c(LUM0+2) in theKTapproximation. For these fit. The result is shown in Figure 6. The best values for R I and MOs we find a decrease factor 6 = 0.98 A-1. u are 11.54 A and 0.125 eV A-1, respectively. The fitting is good N a p h t h y l - C ~ + ~ r B i p b e a y l y The l . members of this series for n = 2-5 but less good for n > 5 . In fact there appears to be have been studied experimentally by Closs, Miller, and co-workers additional nonexponential behaviors for n > 5 . both for electron3and hole4 transfer. Here we have obtained the In the anion case, as mentioned above, the LUMO and LUMO electronic factor from a6 initio calculations with an STO-3G 1 have a small component on the connecting atom. Consistent basis set. Our results for the electron transfer (anions) and hole with the results of ref 14,1111 is small. It also decreases rapidly transfer (cations) together with the updated experimental data with distance (Figure 7). The 1A1 that correspond most closely are presented in Table I.
+
The Journal of Physical Chemistry, Vol. 97, No. 35, 1993 8933
Electronic Factor for Electron Transfer
ag a g a g ag
a, a ,
a,
n=5
n=1
n-2 n=3 Figure 5. Orbital energies in the rrons-(e,e)-C6H~-C4~2H~4-CsHs ( n = 1-7) series.
n=6
n=7
0 0
-5
0
-
-6-
R
(4
Figure 6. Fitting to the bcst calculated results (open circles, ab initio, Dunning double-{ basis set) of the type A = A2(R - R1) exp[-a(R -&)I A2 = 1 eV A-1, R1 = 11.54 A, and & = 5.76 A.
The system with a single cyclohexane in the bridge [ClOHT ( C S H ~ O ) - C ~ H ~ -may C ~ bechosen H~] torepresent the whole series. The HOMO is localized on the naphthalene molecule with a large component on the C atom connecting to the cyclohexane spacer. HOMO - 1 is localized on the biphenylyl group and also has a large component on the connecting atom. LUMO and LUMO - 1 also have large components on the connecting atoms and are lower than the next pair of MOs by about 1 eV. The MO pairs which are involved in the experimental ET reactions, (LUMO and LUMO 1) for electron transfer and (HOMO and HOMO - 1) for hole transfer, are thus with a large component
+
where
on the connecting atoms. This is consistent with the experimental result4 that the rates for hole and electron transfer are quite similar. LUMO + 2 is localized on naphthalene and LUMO + 3 on biphenyl. However, the latter MO is almost entirely localized on the distant benzene ring with no component on the connecting atom to the cyclohexane molecule. HOMO - 2 and HOMO 3 are localized on naphthalene and biphenyl, respectively. However, the latter has no component on the connecting atom in spite of being localized on the benzene ring closer to the cyclohexane. The results for the 2,bDecalin and 2.6-perhy-
8934 The Journal of Physical Chemistry, Vol. 97, No. 35, 1993
-74 6
Braga and Larsson
I
I
I
I
I
8
10
12
14
16
R
I 18
(4
Figure 7. Log A* (A in eV) as a function of the edge-edge distance (R)for the t r u n r - ( e , e ) - C s H 5 - C 4 ~ ~ H 6 ~ ~system ~ 6 H 5for electron transfer. Full circles, LUMO, LUMO 1; open circles, LUMO + 2, LUMO + 3. Results obtained with the Dunning basis set.
+
droanthracene spacers are qualitatively similar to those described for the single cyclohexane spacer. The calculated electronic coupling for the C-1,3 and D-2,7 isomers is considerably larger than the values deduced experimentally by Closs et al.3-5. In the C-1,3 and D-2,7 isomers the interaction between the naphthyl and biphenylyl groups can be enhanced by the existence of one (C-1,3) or two (D-2,7) cyclohexane-CHr groups strategically placed between the donor and acceptor. The Hs of these cyclohexane-CH2- groups may provide an alternative pathway for the direct interaction between donor and acceptor. To test this possibility we have calculated the D-2,5 isomer in which there is no such pathway. We obtained much smaller values for the electronic coupling: 52.8 cm-I and 129 cm-1 for electron and hole transfer, respectively, which indicates a considerable reduction in the donor-acceptor interaction. It is worth noting that in the case of the D-2,5 isomer the edge-edge distance between the naphthalene and the biphenyl is shorter than in the D-2,7 molecule: 6.58A in the former and 7.48 A in the latter. It seems then that neither the distance nor the number of intervening u-bonds between the donor and the acceptor (in D-2,5 and D-2,7 we have the same number of a-bonds consideringthe shortest path along the spacer chain) are the only important factors determining the electronic coupling and that stereoelectronic factors might play a fundamental role as was pointed out by Closs et a1.3J6and discussed in the comprehensive review of Newton.” Naphthyl-AndrostaneBiphenylyl. The calculated Vvalue for electron transfer is considerablysmaller than the value calculated from the Closs-Miller experiments (1.3 cm-1 compared to 5.7 cm-1). We have no answer for the moment as to the sources of this error. The benzene ring of the biphenylyl group connected to the steroid spacer makes an angle of about 13’ (this angle corresponds to the dihedral angle between the plane of the benzene ring closest to the androstane spacer and the C-H bond at the same position). This torsion is mainly due to the interaction with one of the Hs of the methyl group at the C13 on the androstane bridge. Since theandrostane spacer has two methyl groups which eventually can influence the coupling between donor and acceptor we have also performed a calculation in which these groups were
removed keeping the same geometry as for the original steroid. The value for A does not change to any significant degree. In a separate calculation we have optimized the geometry of the naphthyl-androstane-biphenylyl molecule without the methyl groups on the steroid spacer. The main difference between both systemsis a smallerdihedral angle between theconnecting benzene from the biphenylyl group and the steroid spacer (about 5O). However, the calculated Vis significantly lowered (V = 0.75 cm-1). This result indicates that the calculated coupling is very sensitive to the molecular geometry and that this is possibly the source of the difference between our calculated value and the experimental determined by Closs et al. Finally, the structure of the HOMOS and LUMOs is qualitatively similar to that corresponding to the oligo(cyc1ohexane)spacer described before. In Figure 8 we have plotted the log Az versus the edge-edge distance for all the molecules with the naphthyl-biphenylyl donoracceptor pairs. For comparison the updated experimental values (Table I) were also included. The decrease of the electronic factor with the distance shows an almost perfect exponential behavior except for the C-1,3 and D-2,7 compounds. The calculated ps are 1.52 and 1.37A-I for electron and hole transfer, respectively (Table 11). 5. Discussion
The decreaseof the theoretical A with the distanceis satisfactory except for the C-1,3 and D-2,7 isomers where we obtain a larger IAJthan the experimental one, and this value is also off the line corresponding to exponential decrease. There is no immediate explanation for this deviation other than the possible error sources involved in the derivation of V from the experimental rates. For the remaining moleculesthe decrease of IAI is roughly exponential with distance. Although the decrease factors are different for electron and hole transfer our calculated values are close to those obtained in the experiments. There are many possible sources of error to explain the disagreement for the largest bridge, androstane. The solvent may affect the geometry of the molecule. There is a large sensitivity in A to rotamer angles.I6J8J In the calculation of A we have not explored the full surface of avoided
The Journal of Physical Chemistry, Vol. 97, No. 35, 1993 8935
Electronic Factor for Electron Transfer
-2.
4
D27
-3.
-4 N
Q
-F
A26
-5
Steroid
\
D26
-6
-7
I
I
I
I
I
I
I
I
5
6
7
0
9
10
11
12
R
(4
Figure 8. log A2 (A in eV) as a function of edge-edge distance R for the naphthyl-bridge-biphenylyl systems. Open squares, electron transfer; open triangles, hole transfer; open circles, updated experimental values for electron transfer.
TABLE Ik Summary of Calculated Exponential Decrease Factors B (A-l) system C ~ r % ~ t 2 H s * + , - C H 2'~ CsHsx4*2Hsrr~4*sh~ C 1oHrbridge-C 12H9C
electron transfer 0.98 1.52
hole transfer 1.05 0.25 1.37
I, 6 = 2a, eq 1. /3 = 2a, eq 2 for hole transfer; anion value is c(LUM0+3) - c(LUM0+2). 6 = 2a, eq 1; bridge: C4n+2&+4and androstane. crossings. The STO-3G basis may also be inadequate for a correct description of the through-bond interaction in a system of this size. Many import conclusions may be drawn from the work of Miller et al. Their work provides unambiguosproof of the inverted region in Marcus theory.' It shows that ET can take place through saturated sytems. This is consistent with other experimental result^^^-^^ as well as theoretical r e s ~ l t s . ~ , ' ~ , ' ~Of, ' ~great -~~ importance is the demonstration of the influence of the stereoelectronic effects in the electronic factor which is consistent with the theoretical r e s ~ l t s . ' ~ J ~ J * ~ ~ ' The results of the present paper support the conclusions of Closs et ~ 1 . However, 3 ~ we have found that the electronic factor need not decrease exponentiallywith distance between donor and acceptor. As has been shown earlier'g this behavior appears also for a -(CH2-)" chain. The largest A for such a chain is obtained for the all-trans case. If a dihedral angle is turned from 180' to,'O the electronic factor decreases to zero and changes sign in most cases. At the same time the length of the chain decreases which clearly leads to a nonexpontial behavior. However, in the mentioned work we did not perform any geometry optimizations. Although the results proved the importance of conformation, one might argue that a A, sampled over a number of conformations of the bridge, decreases exponentially with distance. In the present case we have geometry optimized a rigid system and found a clear example of nonexponential behavior. The theoretical methods are still missing symmetry-breakingand other correlation effects. However, in an extensive work19-23 we have not found that this type of correction is very important for similar
systems. Besides it would be quite far fetched to believe that the correlation correctionswould account precisely for the corrections needed for an exponential A. The model suggested by McConnell leads to exponential decrease with distance.' Other models suggest that the decrease is exponential along a peptide chain, for example, while the sum of many contributions may be nonexponential.ll Theoretically there is no reason to expect an exponential decrease of A, as has been found by a number of authors.18JO-42 In many cases, experimental as well as theoretical results support an exponential decrease even if is not obvious that an exponential theory isvalid. Such is the case with the polynorbornyl bridge^'^.^^ and an all-trans-CH2- chain.Ig Also one may expect that if the system under study has well-separated repeat units, or approaches that type of system, IAI decreases exponentially.13 However,in the strong coupling case when all thevalence electrons of the bridge have to be included in the treatment, the behavior is exponential only on some average (see for example ref 41 for a peptide chain). The present results suggest very strongly that this is not due to crude methods but is an inherent property of some systems. Unfortunately this also means that it is hardly possible to predict the general behavior of A if the number of interacting MOs of the bridge is too large. It is close to impossible to "understand" the magnitudes of positive and negative contributions to A. The quantum mechanical nature of barrier penetration is such that A may have positive as well negative values. A change of sign when the bridge is extended by repeat units should therefore be considered less surprising. Still it would be good to have an experimental confirmation of this, not least for a deeper understanding of ET in biological systems.
Acknowledgment. We are grateful for support from the Brazilian agency CNPq (ConselhoNacional de Desenvolvimento Cientifico e Tecnologico) and the Swedish Natural Science Research Council (NFR). References and Notes (1) Calcaterra,L. T.;Closs, G. L.; Miller, J. R.J . Am. Chem. Soc. 1983, 105, 670.
8936 The Journal of Physical Chemistry, Vol. 97, No. 35,1993 (2) Miller, R. L.; Calcaterra, L. T.; Closs, G. L. J. Am. Chem.Soc. 1984, 106,3047. (3) Closs, G. L.; Calcaterra, L. T.; Green, N. J.; Penfield, K. W.; Miller, J. R. J. Phys. Chem. 1986, 90, 3673. (4) Johnson, M. D.; Miller, J. R.; Green, N. S.;Closs, G. L. J. Phys. Chem. 1989,93, 1173. ( 5 ) Closs, G. L.; Miller, J. R. Science 1988, 240, 440. (6) Marcus, R. A. J. Chem.Phys. 1956,24,966; Annu.Rev.Phys. Chem. 1964, 15, 155. Sutin, N. Prog. Inorg. Chem. 1983, 30,441. (7) McConnell, H. J. Chem. Phys. 1961, 35, 508. (8) Halpcm, J.; Orgel, L. E. Discuss. Faraday Soc. 1960, 29, 32. (9) Larsson, S.J . Am. Chem.Soc. 1981,103,4034. L a w n , S . 1.Chem. Soc., Faraday Trans. 2 1983, 79, 1375. (10) Hopfield, J. J. Proc.Natl. Acad.Sci. U.S.A. 1974,71,4135. Beratan, D. N.; Hopfield, J. J. J. Am. Chem. Soc. 1984,106, 1584; J. Chem. Phys. 1984,81,5753. Beratan, D. N.; Onuchic, J. N.; Hopfield, J. J. J. Chem.Phys. 1985,83, 5325; 1987, 86, 4488. (11) Beratan, D. N.; Betts, J. N.;Onuchic, J. N. Science 1991,252,1285.
Onuchic, J. N.; Beratan, D. N.; Winkler, J. R.; Gray, H. B. Annu. Reu. Biophys. Biomolec. Struct. 1992, 21, 349. (12) Kuki, A.; Wolynes, P. G. Science 1987,236,1647. Kuki, A. Srruct. Bonding (Berlin) 1991, 75, 49. Marchi, M.; Chandler, D. J. Chem. Phys. 1991, 95, 889. (13) Larsson, S. J. Phys. Chem. 1984,88, 1321. (14) Larsaon, S.; Matos, J. M. 0. J. Mol. Struct. 1985, 120, 35. (15) Newton, M. D. Int. J. Quantum Chem. 1980, S14,363. Logan, J.; Newton, M. D. J. Chem. Phys. 1983, 78, 4086. Newton, M. D. J. Phys. Chem. 1988,92,3049. (16) Ohta, K.; Closs, G. L.; Morokuma, K.; Green, N. J. J. Am. Chem. Soc. 1986,108, 1319. (17) Balaji, V.;Ng, L.; Jordan, K. D.; Paddon-Row, M. N.; Patney, H. K. J. Am. Chem. Soc. 1987,109,6957. Paddon-Row, M. N.; Jordan, K. D. In Modern Modelsof Bondingand Delocalization;Liebman, J. F.,Greenberg, J. F., Eds.; VCH Publishers: New York, 1989; p 115. Paddon-Row, M. N.; Wong, S . S . Chem. Phys. Lett. 1990,167,432. Paddon-Row, M. N.; Jordan, K. D. J. Phys. Chem. 1992, 96, 1188. (18) Liang, C.; Newton, M. D. J. Phys. Chem. 1992,96,2855; 1993,97, 3199. (19) Broo, A.; Larsson, S.Chem. Phys. 1990,148, 103. (20) Braga, M.; Broo, A.; Larsson, S . Chem. Phys. 1991, 156, 1. (21) Braga, M.; Larsson, S.Chem. Phys. 1992,162, 369. (22) Braga, M.; Larsson, S . Int. J. Quantum Chem. 1992, 44, 491. (23) Bfaga, M.; Larsson, S.J. Phys. Chem. 1992, 96, 9218. (24) Siddharth, P.; Marcus, R. A. J. Phys. Chem. 1990,94,2985; 1992, 96, 3213.
Braga and Larsson (25) Dewar, M. J. S.;Zocbisch, E. G.; Hcaly, E. F. J. Am. Chem. Soc. 1985,107, 3902. (26) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J. B.;
schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, J. S.;Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whitaide, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.; Pople, J. A. GAUSSIAN 90; Gaussian Inc.: Pittsburgh, PA, 1990. (27) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J. Chem. Phys. 1%9,51, 2657. (28) 2252. (29) (30) (31) (32) (33)
Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56,
Dunning, T. H. J. Chem. Phys. 1970,53, 2823. Braga, M.; Larsson, S.Chem. Phys. Lett. 1992, 200, 573. Newton, M. D. Chem. Rev. 1991, 91, 767. Levich, V. 0. Ado. Electrochem. Electrochem. Eng. 1966, 4, 249. Dogonadze, R. R. In Reactions ofMolecules at Electrodes; Hush, N. S.,Ed.; Wiley-Interscience: New York, 1971. (34) Katner, N. R.; Logan, J.; Jortner, J. J. J. Phys. Chem. 1974, 78, 2148. (35) van Duyne, R. P.; Fischer, S.F. Chem. Phys. 1974,5,183. Fischer, S. F.; van Duyne, R. P. Chem. Phys. 1977, 26,9. (36) Ulstrup, J.; Jortner, J. J. Chem. Phys. 1975, 63, 4358. (37) Joran, A. D.; Leland, B. A.; Geller, G. G.; Hopfield, J. J.; Dervan, P. B. J. Am. Chem. Soc. 1984, 106,6090. Wasielewski, M. R.; Niemczyk, M. P. J . Am. Chem. Soc. 1985,107,1080. Wasielewski, M. R.; Niemczyk, M. P.; Svec, W. A.; Peritt, E. D. J. Am. Chem. Soc. 1985, 107, 5562.
Wasielewski, M. R.; Niemczyk, M. P.; Johnson, D.G.; Svec,W. A.; Minsek, D. W. Tetrahedron 1989,45, 4785; J. Am. Chon. Soc. 1985, 107, 1080. (38) Bolton, J. R.; Ho, T. F.; Liauw, S.;Simicarczuk, A,; Wan, C. S.K.; Weedon, A. C. J. Chem. Soc., Chem. Commun. 1985,559. Connolly, J. S.; Bolton, J. R. In Photoinduced Electron Transfeer, Fox, M. A., Chanon, M., Eds.; Elsevier: Amsterdam, 1988; Part D, p 303. Schmidt, J. A,; McIntosh, A. R.; Weedon,A. C.; Bolton, J. R.;Co~olly,J. S.;Hurley, J. K.; Wasielewski, M. R. J. Am. Chem. Soc. 1988, 110, 1733. (39) Penfield, K. W.; Miller, J. R.; Paddon-Row, M. N.; Cotsaris, E.; Oliver, A. M.; Hush,N. S.J. Am. Chem. Soc. 1987,109,5061. Liang, N.; Miller, J. R.; Closs, G. L. J. Am. Chem. Soc. 1989, 1 1 1 , 8740. (40) Naleway, C. A.; Curtiss, L. A.; Miller, J. R.J. Phys. Chem. 1991, 95,8434. Curtiss, L. A.; Naleway. C. A.; Miller, J. R. J. Phys. Chem. 1993, 97, 4050. (41) Larsson, S. Chem. Scr. 1988,28A, 15. (42) Paddon-Row, M. N.; Shephard, M. J.; Jordan, K. D. J. Phys. Chem. 1993, 97, 1743.
