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Abstract
Most of the previous work on the theory of thermally assisted hopping between localized electronic states has assumed a perfect Debye phonon spectrum. The purpose of the present contribution is to consider the influence of impurity phonon modes, including local modes, on the electronic jump rate. In this paper we develop a very general formalism which is not only ideal for studying this particular problem but which may provide a useful alternative to existing multiphononjump-rate theories. A numerical investigation into the effect of impurity phonon modes on the hopping rate is pursued in the accompanying paper.