Models for Quantum Effects in Electron Transfer:  Co(Cp)2+|V(CO)6-

Abstract

We model the absolute electron transfer (ET) rate and the vibrational quantum effects on ET rate previously observed experimentally for the ion pair complex Co(Cp)2+|V(CO)6-. We find that the absolute rate and vibrational rate effects cannot be predicted by the standard ET methods. In this work we analyze new resonance Raman, absorption, and infrared spectra and combine these results with density functional (DFT) quantum calculations of structure, vibrational modes, and solvent effects to predict absolute electron-transfer rates and vibrational quantum effects for ET. Related DFT calculations on Na+|V(CO)6- are used to support a spectroscopic identification of the ion pair geometry. The ET is from the radical pair state reached by charge-transfer absorption of the ion pair Co(Cp)2+|V(CO)6-. The weak coupling rate model based on the golden rule model of ET predicts absolute ET rates that are 135 times too large. From our DFT calculations on Co(Cp)2|V(CO)6 we conclude that a small Jahn−Teller geometry change in both radicals can reduce the orbital overlap and electronic coupling in the radical pair state so that the effective coupling matrix element is much smaller than the 417 cm-1 inferred from the absorption spectrum. A new study of the electronic coupling versus geometry is required to test this suggestion versus the possibility that the weak coupling model is inappropriate for our molecule. The standard model, which emphasizes totally symmetric vibrations, also cannot explain prior experimental ET rates for quantum populations (v = 0, 1, 2) in the nontotally symmetric CO stretching mode. These rate effects likely involve a fast IVR conversion from totally symmetric vibrations to IR active CO stretching motions followed by ET. The vibrational quantum effect on ET probably is caused by a breakdown in the Condon approximation, where an increase in the quantum number of vibration increases the electronic coupling matrix element. The models suggest a number of new experiments to probe the mechanism of ET in weak coupled molecules.