Calculation of electronic tunneling matrix element in proteins: Comparison of exact and approximate one-electron methods for Ru-modified azurin

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Abstract
In recent years several theoretical methods have been developed for evaluation of the magnitude of electronic coupling between distant donor and acceptor complexes mediated by a protein molecule. Most detailed studies have been carried out within the one-electron tight-binding (extended Hückel) approximation for electronic structure of the protein medium. In this paper different approximate and exact one-electron methods such as perturbation theory, exact diagonalization, and method of tunneling currents are reviewed and results of calculations are compared for three HisX-Ru-modified azurin molecules, where X=122, 124, and 126. These systems have been recently synthesized and studied experimentally by Gray and co-workers. The calculations show that perturbation theory results are in excellent agreement with exact calculations if the symmetry of the zeroth-order wave functions of the donor and acceptor metal ions are chosen correctly. A simple computational procedure for construction of such correct zeroth-order functions is proposed.