ELSEVIER 14 February 1997 Chemical Physics Letters 265 (1997) 643-648 CHEMICAL PHYSICS LETTERS On the non-orthogonal basis set calculations of the bridge-mediated electronic matrix elements Alexei A. Stuchebrukhov Department of Chemistry, University of California, Davis, CA 95616, USA Received 5 November1996; in final form 9 December 1996 Abstract A simple derivation of the tunneling superexchange matrix element for long-distance electron transfer reactions is presented. Non-orthogonality (overlaps) of the donor and acceptor orbitals and the bridging orbitals are explicitly taken into account. (~) 1997 Elsevier Science B.V. 1. Introduction In theory of long-distance electron transfer reactions, the expression for the superexchange tunneling matrix element is usually derived by using an approximate perturbative method, which assumes a weak coupling between donor and acceptor states and the states of the bridging intervening medium [ l-15 ]. All the interactions in the bridge, on the other hand, can be taken into account exactly within the Green function formalism. In most of the previous papers (one of the exceptions is Newton's work, e.g. Ref. [ 10]), in the perturbative treatment of the coupling of donor and acceptor states and the bridge, an additional simplified assumption is made that the donor and acceptor states are orthogonal to the subspace of states of the bridge. In fact, this assumption is a consequence of writing the total Hamiltonian of the system in the usual form as a sum of the bridge Hamiltonian, Hamiltonians of donor and acceptor complexes, and their interaction [ 15]. Since the total Hamiltonian of the zeroth-order system (without interaction) is hermitian, in this approach the subspace of the states of donor and acceptor complexes turns out to be automatically orthogonal to the subspace of the bridge. Formally neglecting the overlap (non-orthogonality) of donor and acceptor orbitals and those of the bridge, the effective couplings VDb and VAb are introduced, assuming that the overlap effects are taken into account in the magnitude of Vob and VAb. This approximation, however, can be improved. In a recent paper [9], Beratan and co-workers have generalized the treatment and included explicitly the overlap effects of the donor and acceptor orbitals and the bridge in couplings VDb and VAb. In their derivation Green's function and L6wdin partitioning methods were used. In this paper we show how to derive the appropriate expression for the superexchange tunneling matrix element using a different and somewhat simpler method than those used in Ref. [9]. One of the conclusions of Ref. [9] was that the Green function method and the L6wdin partitioning method give different formal expressions for the effective two-state Hamiltonian when a non-orthogonal basis set is used in the calculations. Since the effective coupling should be independent of the method used to derive it, the 0009-2614/97/$17.00 Copyright(~) 1997 Elsevier Science B.V. All rights reserved. PII S0009-2614(96) 01487-X