6923
J. Phys. Chem. 1995, 99, 6923-6925
Torsional Low-Frequency Reorganization Energy of Biphenyl Anion in Electron Transfer Reactions John R. Miller,* Basil Pavlatos Paulson, Radhika Bal, and Gerhard L. Closst Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 Received: February 17, 1995@
Experiments have been performed to examine the effect of the inter-ring torsional motion of biphenyl, which is concluded to have a substantial effect on electron transfer (ET) rates. Intramolecular ET rate constants were measured in 2-methyltetrahydrofuran solution of molecules having the form donor-spacer-acceptor (DSA) in which the donor is either 4-biphenyl (B) or 2-(9,9'-dimethy1)fluorene (2F), which has similar energetics and electronic structure to biphenyl but lacks biphenyl's inter-ring torsional flexibility. When 2F replaces B, the rate of the weakly exoergic ET to naphthalene increases by a factor of 8.0, whereas the highly exoergic ET to benzoquinone decreases by a factor of 2.5. These changes in ET rates are attributed to a reorganization energy of 0.13 eV for the internal, torsional vibration of biphenyl. The size of this reorganization energy is compared to results of other types of experiments and of calculations on biphenyl.
The Marcus identified reorganization free energy as a principle factor controlling the rates of electron transfer (ET) reactions in solution. Reorganization energy results from the configuration changes of the surrounding solvent as well as intemal changes of the reacting molecules. In the development of electron tranfer theory, many investigators emphasized the fact that the solvent contributions come from modes of such low frequencies that they can be treated cla~sically,'-~but the intemal reorganization energies usually come from skeletal vibrations having high frequencies which require a quantum mechanical treatment.6-12 These internal reorganization energies have been deduced by several methods, including EXAFS measurements and their comparison with rates of electron exchange reactions,13molecular orbital calculation^,^^^^^ Raman ~ p e c t r o s c o p y , l ~and - ~ ~measurements of ET rates as a function of free energy.15,24-33 Electron transfer experiments in this laboratory have made extensive use of the molecule bipheny1.24*25.34-37 In biphenyl's SO ground state the two phenyl rings are twisted by %45" in the gas phase38-40but are thought to be coplanar in the anion, cation, or excited ~ t a t e . The ~ ~ .internal ~ ~ twisting motion has a very low vibrational frequency of about 70 cm-' in neutral biphenyl.41 Because this frequency is low compared to kT % 200 cm-' at room temperature, the biphenyl group might be expected to contribute a reorganization energy due to a torsional mode having such a low frequency that its effect would be indistinguishable from those of classical solvent reorganization. This paper describes experiments performed to test the notion that such low frequency internal reorganizations are important in ET reactions and to determine the magnitude of such an effect. We have measured the intramolecular electron transfer rate D-SA == DSA-, (D = donor, A = acceptor, and S = 3,16-substituted Sa-androstane spacer) for the compounds 2FSN and 2FSQ, where 2F = 2-(9,9'-dimethyl)fluorene, N = 2-naphthalene, and Q = 2-benzoquinone. The experiment compares the ET rates of the fluorene donor molecules with the corresponding 4-biphenyl (B) derivatives: BSN and BSQ. The 2F group is rigidly planar and therefore cannot have any low frequency torsional motions. Although 2F differs from B in this way, it is otherwise expected to be essentially identical
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Deceased May 24, 1992. @Abstractpublished in Advance ACS Abstracts, April 1, 1995.
0022-365419512099-6923$09.0010
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to biphenyl as a donor. Specifically, the ET energetics (see results) are almost identical, as are the JG molecular orbitals. The coefficients of fluorene's LUMO at and near the point of attachment to the steroid spacer are almost identical to those of biphenyl. Therefore, it is expected that the electronic couplings in the fluorene-containing molecules will be identical to the biphenyl-containing molecules.
Experimental Section Methods for preparation of the compounds have been d e ~ c r i b e d . ~Anions ~ , ~ were generated by irradiating solutions of the DSA compounds in 2-methyltetrahydrofan (MTHF) with 30-ps, 20-MeV electron pulses from the Argonne Linac. Irradiation generates solvated electrons ( e 2 x M) which attach to the donor and acceptor groups to form an equal distribution of D-SA and DSA-. The intramolecular ET reaction is then observed by measuring absorbance at 650 nm of biphenyl or dimethylfluorenyl anions as the reaction proceeds to equilibrium. Experimental methods for sample preparation, acquisition of transient absorption data, and fitting of the data have been described elsewhere.36
Results and Discussion The electron transfer rates and free energy changes measured in MTHF are presented in Table 1. The rates for BSN and BSQ were reported earlier as a part of a study of rate as a function of free energy change These rates are well described by eq 1, which considers that the electron transfer process is coupled to two types of structural changes having 0 1995 American Chemical Society
6924 J. Phys. Chem., Vol. 99, No. 18, I995
Miller et al.
TABLE 1: Energetics and Rates for Intramolecular assumption that A,(BSA) = A,(2FSA) we conclude that the low Electron Transfer (s-l) from Anions of Biphenyl or Fluorene frequency torsional reorganization for biphenyl is 0.75 - 0.60 Groups to 2-Naphthalene (N) or 1,4-Benzoquinone (Q)" = 0.15 eV. D = biphenyl D = 2-fluorene kF/kB Al(2FSA) Replacement of the B group with the 2F group (B 2F) DSN -AGO (eV) 0.050 f 0.007 0.062 f 0.012 increased the observed ET rate to naphthalene by a factor of 8. k(D-SN)c 1.5 x lo6 1.2 x lo7 8.0 0.573 Of this a factor of 1.25 is due to the increased free energy change 1.42 x lo7 (8.0) !C,~~(D-SN)~ 1.78 x lo6 to AGO = -0.062 eV, according to eq 1. The remainder of the DSQ -AGoe(eV) 2.10 2.112 increase, a factor of 6.4, is attributed to the decrease in AI.In k(D-SQ)' 2.5 x lo8 1.0 x lo8 0.40 0.619 the highly exoergic ET to the benzoquinonyl acceptor, the ~,A,(D-SQ)~ 3.43 x lo8 1.38 x 10' (0.40) replacement B 2F causes the rate to decrease by a factor of a The steroid spacer S = (5~)-3,16-androstane. The observed rate 2.5, of which only a factor of 1.07 is due to the difference in constants are compared to calculations from eq 1. Values of 11(2FSA) 2F were deduced by adjusting its value to make the calculated ratio k ~ l k ~ free energy change. The fact that the replacement B causes the rate to increase for the weakly exoergic reaction but match the observed ratio. Free energy changes were obtained from electron transfer equilibria, D-SN * DSN-, D = B and 2F. ET rate to decrease for the highly exoergic reaction confirms that the constants measured in 2-methyltetrahydrofuran. Uncertainties are changes in rate are due to changes in reorganization energy. A f25%. Rate constants calculated by eq 1 with V = 6.2 cm-'. 1, = change in electronic coupling would have been expected to 0.45 eV, hv = 1500 cm-', 11 = 0.75 eV for BSN and BSQ, 11= 0.573 increase or decrease both rates by the same amount, not to eV for ZFSN, and 1,= 0.619 eV for 2FSQ. The values of 11for the change them in opposite directions, so the results are consistent 2F compounds were chosen to make the calculated ratios k ~ l match k~ with the expectation that the replacement B 2F will have the experimental ratios of 8.0 and 0.40. e Free energy changes were almost no effect on electronic couplings. estimatedz5from electrochemical measurements reported in the literature. -AGO = 2.112 for 2FSQ was taken as 12 mV more negative The magnitude of the change in rate with the replacement B than -AGO for BSQ, based on the measured electron transfer equilibria, 2F was larger for the weakly exoergic reaction. The opposite for the D-SN's. would have been expected for a change in reorganization energy of high frequency modes. If the 0.15-eV decrease in reorganization energy were in a high frequency mode, then the increase and decrease would be by factors of 2.0 and 5.0, in much poorer agreement with experimental factors of 8 and 2.5. The wellknown sensitivity of highly exoergic ET rates to high frequency modes is diagnostic: the data are most consistent with the conclusion that 0.15 f 0.02 eV of low frequency internal reorganization energy accompanies conversion of biphenyl to biphenyl anion. The conclusion that the observed differences in ET rates are due principally to the torsional mode of biphenyl is further reorganization energies A1 and 1".1,is the reorganization energy supported by semiempirical molecular orbital calculations using for high frequency molecular vibrations-represented by a single the AM145 Hamiltonian. Liang and calculated a mode with an average frequency of 1500 cm-'. 1 1 is the torsional reorganization energy of ~ 0 . 1 0eV for the torsional reorganization energy due to low frequency modes and can be motion in biphenyl. While this is smaller than the 1 b = 0.15 described classically because these quanta are smaller than kT eV found in these experiments, a similar discrepancy is found at room temperature (200 cm-I). Most of A1 is solvent for other types of internal reorganization energies calculated reorganization energy (A,) from the reorientation of polar solvent by the AM1 method. Further, Liang and Miller found that the molecules, but 1 1 may also include the reorganization energy intemal reorganization energy for fluorene was almost identical from low frequency intemal motions (LE),such as the torsional to that for biphenyl, when the torsional motion was excluded.46 vibration of biphenyl: A1 = As 11i. Some of the observed difference of 0.15 eV could be due to a Free energy changes, AGo(BSN) = -0.05 eV and AGo(FSN) smaller solvent reorganization energy for the 2F group due to = -0.062 eV, were determined from the equilibrium constants steric hindrance of solvation by the methylene and 9,9 methyl of the electron transfer reactions. The 2F group is therefore groups. A very crude estimate that this decrease is about 5% more difficult to reduce than the B group by 0.012 eV. This of 0.3 eV = 0.02 eV could be made by noting that these groups difference is attributed to the fact that the 2F group has two prevent access of solvent to about 10% of the surface area of more alkyl substituents than the B group. Without the alkyl the n-system, keeping the solvent about twice as far away over substituents fluorene might be expected to be more easily that region. If this estimate were correct, then the torsional reduced because the enforced planarity is the conformation reorganization energy for B/B- is 0.13 f 0.03 eV. preferred by the anion. While the solvent reorganization energy depends on the ET rates in BSN, BSQ, and six other molecules having B as donor-acceptor distance, this internal, low frequency reorgathe donor were well-described by eq 1, with A1 = 0.75 eV, 1" nization energy is expected to be independent of distance. It = 0.45 eV, hv = 1500 cm-', and the electronic coupling V = would also be expected to contribute ~ 0 . 1 eV 3 to the total low 6.2 cm-'. The summation is over w ,the quantum number for frequency reorganization energy in bimolecular reactions of the high frequency mode in the final state. Equation 1 can also biphenyl anions where ET occurs between species in or nearly give a good description of the rates 2FSN and 2FSQ if AI is decreased. Rates calculated in this way by eq 1 with 1 1 = 0.75 in contact. Such a torsional reorganization energy would be eV for BSN and BSQ and lower values for 2FSN and 2FSQ expected in ET involving conversion of biphenyl to its cation such as the photoinduced ET of Gould et al.I5 A similar low are also shown in Table 1. The lower values, A1 = 0.573 eV for 2FSN and AI = 0.619 eV for 2FSQ were determined by frequency torsional reorganization might be important in many studies involving transition metal complexes with bipyridyl adjusting them to make the calculated ratios k 2 ~ l kfrom ~ eq 1 match the experimental ratios of 8.0 and 0.40. We shall average ligands, especially in reactions in which an electron is transferred these results to Al(2FSA) = 0.60 f 0.03 eV. Under the to a ligand as in MLCT transitions.
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J. Phys. Chem., Vol. 99, No. 18, 1995 6925
Torsional Reorganization Energy of Biphenyl Anion From the dependence of ET rates on AGO for a series of biphenyl-substituted steroids including BSN and BSQ we concluded that As = 0.75 eV in MTI-F.25 This should now be revised to 1, = 0.62 eV and 1 l i = 0.13 eV. The value 1, = 0.75 eV was already substantially smaller than predicted by the model of two spheres in a dielectric continuum, so the new value will increase this discrepancy. It is possible to make some comparison of the reorganization free energy change for torsional vibration in biphenyl, obtained here from kinetic measurements, with other types of information on biphenyl available in the literature. If 80 and 8- are the preferred angles for biphenyl and biphenyl anion, then Ali x G(B,8-) - G(B,B0) x G(B-,80) - G(B-,&), where G(B,8-) is the free energy of neutral biphenyl B at the torsional angle 8- preferred by B-. These two forms of the expression for 1fi are approximate because they take free energies at definite angles instead of the more appropriate statistical-mechanical averages over the free energy surfaces for B and B-. If entropy terms are not large, then an approximation to the free energy surface for neutral biphenyl is given by the energy surface calculated at the 6-31G*, MP4 level,4O which finds a minimum 8O x 45". Because 8- x 0, the barrier at 8 = 0 provides an estimate to 1s G(B,8-) - G(B,80) = 0.151 eV which compares favorably with the measurement of reported in this work. The results from a variety of ab initio methods gave similar values for the barrier height, although fits of solution NMR data to empirical torsional potentials estimated barriers ~ 3 - 4times ~ m a l l e r . ~Torsional ~ ~ ~ * changes also affect the cation and triplet state of biphenyl.42 The change to planarity in the triplet state is associated with an entropy change of -6.1 GibbsIm01.~~For the conversion B --L B- the entropy change is small, based on measurements of the equilibrum B- N B N-,34,50where N = naphthalene, which is not torsionally flexible. In summary, substitution of rigidly planar 2-fluorene for torsionally flexible biphenyl results in substantial effects on intramolecular ET rates. The value of the torsional reorganization free energy of biphenyl, l l i = 0.13 f 0.03 eV, obtained here is reasonable in view of previous information from spectroscopy and theory.
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Acknowledgment. This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, US-DOE under Contract No. W-31-109ENG-38. References and Notes (1) Marcus, R. A. J . Chem. Phys. 1956, 24, 966-78. (2) Marcus, R. A. Discuss. Faraday SOC. 1960, 29, 21-31. (3) Levich, V. G. In Advances in Electrochemistry Electrochemical Engineering; Delahay, Tobias, Eds.; Wiley: New York, 1966; Vol. 4, p 249. (4) Levich, V. G. In Physical Chemistry; Eyring, Henderson, Jost, Eds.; Academic Press: New York, 1970; Vol. Mb. (5) Dogonadze, R. R. Ber. Bunsen-Ges. Phys. Chem. 1971, 75, 62834. (6) Kestner, N. R.; Logan, J.; Jortner, J. J. Phys. Chem. 1974, 78, 2148-66. (7) Van Duyne, R. P.; Fischer, S. F. Chem. Phys. 1974, 5, 183.
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