Vibrational model for electron transfer in the limit of small activation barriers

Abstract

Electron transfer (ET) is treated as a vibrational quantum mechanical problem in a symmetric Born–Oppenheimer (BO) biparabolic potential of Marcus type, where the distance between the energy minima is given by the reorganization energy λ and force constant k. The interaction is characterized by a gap Δ at the avoided crossing. Nonadiabaticity is accounted for by including the correction terms of the Born–Oppenheimer approximation. The energy splitting ΔE12=E2−E1 between the two lowest energy eigenvalues is related to the rate of ET in a wave packet model. For large Δ and λ, ΔE12 becomes the frequency of the promoting vibrational mode, independent of Δ. The theory is illustrated by internal ET in symmetric positive molecular ions with two double bonds, separated by single bonds. Completely delocalized ionization is obtained in the conjugated case when only one single bond separates the double bonds. More than one separating bond leads to mode softening and partial localization, whereas a completely localized, ionized double bond is obtained if many single bonds separate the double bonds. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 211–220, 2000