The transfer of atoms, ions and molecular groups in solution. Part 1.—Models and limits

Abstract

The theory of the activated complex, as formulated by Marcus, is applied to the transfer in condensed phases of atoms, ions and molecular groups. Particular attention is given to reactions which take place in the diabatic limit. A Born–Oppenheimer–Holstein separation is developed in order to separate the degrees of freedom of the reactive subsystem from those of the environment; perturbations which can drive the reaction in the diabatic limit are identified. An analysis of a simple system is carried out. The system is two-dimensional and consists of a lithium cation which migrates (via activation) from one site of solvation to another. The development of the paper and the examination of the simple, ideal system reveal the following. First, diabatic transfers can occur only over short distances for the tunnelling (vibrational overlap guarantees this result). Secondly, if the reaction follows a completely adiabatic path, the migrating species will occupy a position of stable mechanical equilibrium in the transition state. Thirdly, if the reaction is diabatic, the migrating species adiabatically follows a path to the initial state for the tunnel transfer; the work of creating the initial state enters the expression for the energy of activation, as is well known. Finally, it is possible, in terms of the specific development of the paper, to formulate either an optimal or Monte Carlo method for determining the configuration and energy of the transition state. An optimal method for investigating the transition state can use a minimum number of molecules of solvent. This particular development draws a close parallel to the work of Glyde on the self-diffusion of solid argon.