Theory and mechanism of electron transfer in a condensed medium at high temperatures with allowance for change in vibrational frequencies

Abstract

An expression for electron transfer rate has been obtained through the solution of a time wave equation by the variational method by defining the wave function as a linear combination of functions corresponding to electron localization on the donor and on the acceptor. A dependence of electron transfer on temperature, on the electronic and vibrational characteristics of the system has been derived. An activation energy temperature-variation effect has been obtained. It has been proved that many-electron transfers are impossible.

Medium Effects on Charge Transfer in Metal Complexes

“…ln 124) Charge Even with the apparent agreement with eq 124, the underlying analysis is not sufficient to explain the H 2 O/D 2 O kinetic isotope effect of ∼2 in Figure 3C. The data in D 2 O fall on the correlation line for the nonhydroxylic solvents.…”

“…Frequency changes in the solvent modes (and lowfrequency vibrations) are included in ∆G°(see section II.H). 8,[115][116][117][121][122][123][124] In the classical limit with pω j , k B T and λ ) λ i + λ o : 8,43 The classical result works reasonably well for metal complexes where the reaction barrier is dominated by coupled low-frequency metal-ligand vibrations and the solvent. [8][9][10][11][12][13]77,[125][126][127][128][129][130] With one coupled medium-or high-frequency mode (or averaged mode), only the v ) 0 vibrational level is appreciably populated at room temperature (pω .…”

The Golden Rule. Application for fun and profit in electron transfer, energy transfer, and excited-state decay

“…Frequency changes in the coupled solvent modes (and low-frequency vibrations) are included in DG 0 ET . 35,49,75,76,[80][81][82][83] In the classical limit with ho j { k B T and l = l i + l o , 39,[84][85][86] the rate constant can be written as,…”

Estimation of the solvent reorganization energy and the absolute energy of solvation of charge-transfer states from their emission spectra

“…Further development of ET theories that considered different force constants for the (AD)*/solvent and (A ∑ -D ∑ + )/solvent interactions (and weighting factors of the thermal population of these states) sought to provide a better understanding of the ET processes and, in particular, on the temperature effects. 40,71, 72 For instance, Hupp et al 40 showed that the DS associated to the change in the solvation of the reactant and product states is given approximately by:…”