J. Phys. Chem. 1994,98, 8959-8961
8959
Calculation of Electron-Transfer Rate Constants in the Inverted Region from Absorption Spectra Nhtor E. Katz,? Sandra L. Mecklenburg, Darla K. Graff, Pinyung Chen, and Thomas J. Meyer' Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill,North Carolina 27599-3290 Received: April 14, 1994"
Nanosecond transient absorption spectroscopy was used to measure back-electron-transfer rate constants kb in the series [(4,4'-(X)2bpy'-)Re1(CO)3(py-PTZ'+)]+ with X = C02Et, C(O)NEt2, H, Me, MeO, NH2 and also the 2,2'-bipyrazine (bpz) and 3,4,7,&tetramethyl- 1,lO-phenanthroline (Medphen) complexes in propylene carbonate (PC). These states are formed following Re' (4,4'-(X)zbpy) excitation and -PTZ Re" electron transfer. The reactions occur in the Marcus inverted region and In kb varies linearly with AGO as predicted by the energy gap law. In the complexes with X = Me, MeO, and Me4phen, weak, ground-state absorption bands corresponding to ligand-to-ligand charge transfer (LLCT) transitions between py-PTZ and 4,4'-(X)2bpy or Me4phen were detected. These bands are not present in the spectra of the corresponding 4-ethylpyridine model complexes. From the Hush analysis of the ground state absorption bands, the electron-transfer matrix elements Hat,are 44 cm-l (X = Me), 51 cm-l (X = MeO), and 61 cm-l (Me4phen) with A,-,' = 0.4 eV in PC. XO' is the sum of the solvent reorganizational energy and the coupled low frequency vibrations treated classically. By combining Hab, A,-,', and kinetic parameters obtained in the kinetic study, it is possible to calculate kb from a form of the energy gap law. The calculated values for kb are within a factor of 10 of the experimental values, e.g., kb = 3.1 X lo's-l, kb(ca1c) = 3.0 X lo8 s-l for x = Me. These results point to the feasibility of using absorption band measurements routinely to calculate electron-transfer rate constants in the inverted region.
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Hush has shown1 that in mixed-valence complexes and, more generally, for donor-acceptor pairs, quantitative relationships exist between optical and thermal electron transfer. In the classical limit with weak electronic coupling, the free energy of activation (AG*) is related to the absorption band energy ea^), thereorganizational energy (A), and the freeenergychange (AGO) bylJ
The delocalizationenergy (Hab)from electroniccoupling between donor and acceptor is related to the integrated absorption band intensity. For a Gaussian band, this relationship is given by'
where e,, is the molar absorptivity coefficient, ; ,,, is the absorption maximum in cm-1, A i 1 p is the full width at halfheight in cm-I, and r is the distance separating the redox sites in angstroms. In principle, these relationships allow simple absorption band measurements to be used to calculate rate constants for electron transfer. This has been tested experimentally3in a few cases in the normal region by comparing absorption band measurements with direct observation of electron transfer rate constants. Gould et al.3e have used emission spectra and quantitative measurement of radiative decay to calculate back electron transfer rate constants following photoexcitation of donor-acceptor pairs. We report here an application of the Hush approach to electron transfer in the inverted region in a molecular assembly. In earlier papers4 the role of driving force, solvent, temperature, and ionic strength have been explored for back electron transfer in [(4,4'-(X)2bpy*-)Re1(C0)3(py-PTZ*+)]+ [X = COzEt, C(0)NEt2, H, Me, MeO, NH2, 2,2'-bipyrazine (bpz), and 3,4,7,8tetramethyl-1 ,lo-phenanthroline (Me4phen)l. These reactions t Current address: Facuitad de Bioqufmica, Quimica y Farmacia, Universidad Nacional de TucumBn, Argentina. 0 Abstract published in Advance ACS Abstracts, August 1 , 1994.
0022-3654/94/2098-8959%04.50/0
occur deeply in the inverted region, and as shown in Figure 1 in propylene carbonate (PC) and reported earlier in 1,Zdichloroethane (DCE),"ln kbvaries linearly withdriving forceas predicted by the energy gap law:5 In kb = In Po
+ In F(ca1c)
(3a)
where
h (1000 cm-')
In these relations, Eo = (IAG'l- A',) where Eo is the energy gap and A'o is the sum of the solvent reorganizational energy and the contribution to the intramolecular reorganizational energy by low frequency modes treated classically. SMand ~ U are M the electron-vibrational coupling constant and the vibrational spacing 0 1994 American Chemical Society
8960
Katz et al.
The Journal of Physical Chemistry, Vol. 98, No. 36, 1994
6.0
19
h
I
“g
4.0
I
x
v
w
2.0 I
1.5
2.0
2.5
AG’(~v) Figure 1. In kb vs AGO for [(4,4’-(X)2bpy)Re1(CO)3(py-PTZ)]+ in
propylene carbonate. The AGO values were measured by cyclic voltammetry where AGO = A E I=~E1/2(PTZ+/O)-E1/2(4,4‘-(X)zbpYo/-) in propylene carbonate with 5 mM TBAH as the added electrolyte.The deviation from the linear relationship for the Me4phen derivative is expected given the differencesbetween bpy and phen as acceptor ligands in nonradiative decay.s*
SCHEME 1
0.0
P Figure 2. Visible absorptionspectra of [(4,4’-(CH3)2bpy)ReI(CO)p(pyPTZ)] (solid line) and [(4,4’- (CHp)2- bpy)Re1(CO)3(4-Etpy)] (dashed +
+
line) in propylene carbonate. Inset: UV-visible spectrum of [(4,4’(CH3)2bpy)Re1(CO)3(py-PTZ)]+ in propylene carbonate.
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energy quantity in eq 2, Hab 44 cm-1.8 Habvalues have also been calculated for [Me4phen)Re1(C0)3(py-PTZ)]+ (61 cm-1) and [ (4,4’-(MeO)2bpy)Re1(C0)3(py-PTZ)]+ (5 1 cm-I). A E l / 2 and the energiesof the LLCT band in 1,2-dichloroethane [(4,4’-(X)2bpy*-)Re1(CO)3(py-PTZ*+)]+ (DCE, 2.10 eV, 2.02 X lo4cm-I), propylene carbonate (PC, 2.05 eV, 1.99 X 104 cm-I), and CH3CN (2.07 eV, 1.96 X 104 cm-I) have been measured. From these values and the relationship, Ea&-A E l p w,w = 0.33 eV (DCE), 0.42 eV (PC), and 0.43 eV (CH3CN). In this limited data set, the variation of Ao‘ with for the average acceptor mode. The AGO values in Figure 1 were the solvent dielectric function (l/Dop - l/Ds) is linear, although measured by cyclic voltammetry with AGO = A E l p = E1/2the slope (0.73) is smaller than the calculated one.Il The values (PTZ+/O) - E1/2(4,4’-(X)2bpy0/-) in propylene carbonate with 5 of X’O for CH3CN and PC are consistent with X’O 0.4 eV mM TBAH (tetra-n-butylammonium hexafluorophosphate) as estimated from self-exchange measurements“ and X’O 0.4 eV the added electrolyte. The work term correction is negligible from the temperature-dependence of back electron transfer in since Os= 65.1 for propylene carbonate.4a (PTZ*+-bpy*-)Re1(C0)3C1in PCe48 The ligand-to-ligand charge-transfer (LLCT) absorption band Back electron transfer occurs deeply in the inverted region that is the optical equivalent of thermal electron transfer in the where quantum channels dominate because of coupling with Hush analysis’ is labeled hv’ in Scheme 1. Since there is no medium-frequency ring stretching modes a t bpy and PTZ.4J2 In n-bond connection between the donor and the acceptor, the molar analyzing the available data, the classical result in eq 1 is not absorptivity of this band should be low. Absorption spectra of applicable but eqs 3 are. In principle, the parameters h w ~SM, , highly purified samples of [(4,4’-(Me)2bpy)Ke1(C0)3(py-PTZ)]+ X’O, and Eo are available by a Franck-Condon analysis of the and the model, [(4,4’-(Me)2bpy)Re1(CO)3(4-Etpy)]+, in P C are absorption band, but the Gaussian deconvolution procedure shown in Figure 2. For the -PTZ containing complex, a new, employed here distorts the band shape. Rather, it is possible to weak absorption feature appears at Amax 500 nm (2.0 X lo4 use 1‘0= 3200 cm-I and Hab= 44 cm-I from the spectral study, cm-1) as a low-energy tail on the usual Re1 bpy metal-toy = 0.54 and SM= 2.1 from the slope of the plot in Figure 1, ligand charge transfer (MLCT) band at A, 370 nm (Figure and ~ W M= 1350 cm-I (estimated from resonance Raman 2, inset). It obeys Beer’s law over the range 10-3-10-2 M. measurements) to calculate kb. By inserting these values into Absorption features of comparable molar absorptivities are also eqs 3, good agreement is found to exist between experimental found in PC solutions containing purified [(Me4phen)Re1(kob= 3.1 X lo7 s-I) and calculated values (kcalc= 3.0 X lo8 s-l) (CO),(py-PTZ)]+ and [ (4,4’-(MeO)2bpy)Re1(CO)3(py-FTZ)]+ for kb. There is similar good agreement for [(4,4’-(MeO)2bpy)but not in the corresponding 4-Etpy complexes.6 By Gaussian ReI(C0)3(py-PTZ)]+ (kob= 2.7 X lo7 s-I; kcalc= 2.9 X 108 s-I) = deconvolution of the low-energy spectrum in Figure 2, and [(Me4phen)Re1(CO)3(py-PTZ)]+ (kob= 3.6 X lo7 s-I; kcalc 1.99 X 104cm-l, tmax= 2.4 M-1 cm-1 and A;’/2 = 3.50 X 103cm-l = 3.0 X 108 s-I), by using the same procedure. for the low-energy ~ o m p o n e n t . Almost ~ the same values are Given the approximations involved, the agreement between obtained by subtracting the spectrum from that of the model theory and experiment is remarkable. It raises the possibility of compound and fitting the difference spectrum as a single Gaussian, using absorption band measurements routinely to calculate but either procedure is limited in its accuracy. electron transfer rate constants in the inverted region.lc’5J3 From the results of the bandshape analysis and eq 2, it is possible to calculate Hab. There is rotation around the -CH2- spacer to Acknowledgment. We acknowledge the National Science PTZ; the center-to-center distance for electron transfer can vary Foundation for financial support under Grant CHE-8806664. from -6 to -9 A.“ Back electron transfer, kb in Scheme 1, is N.E.K. acknowledges the Guggenheim Foundation for financial expected to be dominated by the close-contact distance in order support and Universidad Nacional de Tucumln and CONICET, to maximize electrostatic interactions and donor-acceptor elecArgentina, for a leave of absence. tronic coupling. By using this value and 1.99 X 104 cm-1 for the [(4,4‘-(X)2bpyo7~“(CO)~PY-PTZ)I+’
I” tIIko
=
--
--
Calculation of Electron-Transfer Rate Constants
References and Notes (1) (a) Hush, N. S. Prog. Inorg. Chem. 1967,8, 391. (b) Hush, N. S. Electrochim. Acta 1968.13, 1005. (c) Creutz, C. Prog. Inorg. Chem. 1983, 30, 1. (d) Hush, N. S.Coord. Chem. Rev. 1985, 64, 135. (2) (a) Marcus, R. A,; Sutin, N. Comm. Inorg. Chem. 1986,5,119. (b) Hupp, J.; Neyhart, G.; Meyer, T. J.; Kober, E. M. J. Phys. Chem. 1992, 96, 10820. (c) Schatz, G. C.; Ratner, M. A. Quantum Mechanics in Chemistry; Prentice-Hall: Englewood Cliffs, NJ, 1992; p 246. (3) (a) Creutz, C.; Kroger, P.; Matsubara, T.; Netzel, T. L.; Sutin, N. J. Am. Chem.Soc. 1979,101,5442. (b) Penfield,K. W.;Miller, J.R.;PaddonRow, M. N.; Cotsaris, E.; Oliver, A. M.; Hush, N. S.J . Am. Chem. SOC.1987, 109,5061. (c) Tominaga, K.; Kliner, D. A. V.; Johnson, A. E.; Levinger, N. E.; Barbara, P. F. J . Phys. Chem. 1993,98, 1228. (d) Nelsen, S.F.; Chang, H.; Wolff, J.; Adamus, J. J . Am. Chem. SOC.1993, 115, 12276. (e) Gould, I. R.; Noukakis, D.; Gomez-Jahn, L.; Young, R. H.; Goodman, J. L.; Farid, S.Chem. Phys. 1993, 176, 439. (f) Wynne, K.; Galli, C.; Hochstrasser, R. M. 1. Chem. Phys., submitted. (8) Myers,A.B. Chem. Phys. 1994,180,215. (h) Walker, G. C.; Akesson, E.; Johnson, A. E.; Levinger, N. E.; Barbara, P. F. J. Phys. Chem. 1992,96, 3728. Akesson, E.; Walker, G. C.; Barbara, P. F. J . Chem. Phys. 1991, 95, 4188. (4) (a) Chen, P.; Mecklenburg, S.L.; Meyer, T. J. J. Phys. Chem. 1993, 97, 13126. (b) Chen, P.; Mecklenburg, S.L.; Duesing, R.; Meyer, T. J. J. Phys. Chem. 1993,97,6811. (c) Chen, P.; Duesing, R.; Graff, D. K.; Meyer, T. J. J . Phys. Chem. 1991, 95, 5850. (d) Chen, P.; Duesing, R.; Tapolsky, G.; Meyer, T. J. J . Am. Chem. SOC.1989, I l l , 8305. (e) Chen, P.; Westmoreland, D.; Danielson, E.; Schanze, K. S.;Anthon, D.; Neveux, P. E., Jr.; Meyer, T. J. Inorg. Chem. 1987, 26, 1116. (5) (a) Kober, E. M.; Caspar, J. V.; Lumpkin, R. S.; Meyer, T. J. J . Phys. Chem. 1986, 90, 3722. (b) Caspar, J. V.; Sullivan, B. P.; Kober, E. M.; Meyer, T. J. Chem. Phys. Lett. 1982, 91, 91. (c) Englman, R.; Jortner, J. Mol. Phys. 1970, 18, 145. (d) Freed, K.; Jortner, J. 1970, 52, 6272.
The Journal of Physical Chemistry, Vol. 98, No. 36, 1994 8961 (6) In solutions containing 3 X 1Q3 M [(4,4’-(CH,)zbpy)ReI(CO)3(4Etpy)]+andO.l M (IO-MePTZ),anew,low-energyshoulderappearsat-500 nm. It increases in intensity with additional added IO-MePTZ and appears to be the outer-sphere equivalent of the transition hv’ in Scheme 1. (7) The program used for deconvolutionwas GRAMS/386. The fit was made to two Gaussian bands in the region 1.45 X 104-2.15 X 104 cm-1. The parameters obtained for band 2 were: vrmX = 2.70 X 104 cm-1, cm = 4.0 X 103 M-1 cm-1 and Ail,* = 3.86 X 103 cm-I. (8) Equations 3 assume thevalidity of the Condon approximation. It has been argued that &will be different in the optical and thermal experiments becauseof the different nuclear co$igurations involved for the two transition^.^ Since this effect depends on the extent of nuclear tunneling,lo Hab could be overestimated from the absorption measurement. (9) (a) Sutin,N. InElectron Tramferinlnorganic, OrganicandBiological Systems. Bolton, J. R., Mataga, N., McLendon, G., Eds.; Advances in Chemistry Series 228; American Chemical Society: Washington, DC, 1991; p 25. (b) Chou, M. H.; Creutz, C.; Sutin, N. Inorg. Chem. 1992,31, 2318. (10) Redi, M.; Hopfield, J. J. J . Chem. Phys. 1980, 72, 6651. (11) The calculated slope
is 1.9 with a1 = 2.5 A (-PTZ’+), a2 = 5.0 A [Re’ bpy’)], and r = 6 A. Including the pyridyl linker with -PTZ gives a1 = 4.0 and a calculated slope of 0.83. (12) Lipari, N. 0.; Rice, M. J.; Duke, C. B.; Bozio, R.; Girlando, A.; Pecile, C. Int. J . Quantum Chem., Quantum Chem. Symp. 1977, 11, 583. (13) (a) Meyer, T. J. Chem. Phys. Lett. 1979,64,417. (b) Curtis, J. C.; Meyer, T. J. J. Am. Chem. SOC.1978,100,6284.
A
