CALCULATION OF ELECTRON-TRANSFER RATE CONSTANTS IN THE INVERTED REGION FROM ABSORPTION-SPECTRA

Nanosecond transient absorption spectroscopy was used to measure back-electron-transfer rate constants k(b) in the series [(4,4'-(X)(2)bpy(.-))Re-I(CO)(3)(py-PTZ(.+))](+) with X = CO(2)Et, C(O)NEt(2), H, Me, MeO, NH2 and also the 2,2'-bipyrazine (bpz) and 3,4,7,8-tetramethyl- 1,10-phenanthroline (Me(4)phen) complexes in propylene carbonate (PC). These states are formed following Re-I --> (4,4'-(X)(2)bpy) excitation and -PTZ --> Re-II electron transfer. The reactions occur in the Marcus inverted region and In k(b) varies linearly with Delta G(O) as predicted by the energy gap law. In the complexes with X = Me, MeO, and Me(4)phen, weak, ground-state absorption bands corresponding to ligand-to-ligand charge transfer (LLCT) transitions between py-PTZ and 4,4'-(X)(2)bpy or Me(4)phen 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 H-ab are 44 cm(-1) (X = Me), 51 cm(-1) (X = MeO), and 61 cm(-1) (Me(4)phen) with lambda(0)' = 0.4 eV in PC. lambda(0)' is the sum of the solvent reorganizational energy and the coupled low frequency vibrations treated classically. By combining H-ab, lambda(0)' and kinetic' parameters obtained in the kinetic study, it is possible to calculate k(b) 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., k(b) = 3.1 X 10(7) s(-1), kb(calc) = 3.0 x 10(8) s(-1) 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.