Electron tunneling pathways in proteins: A method to compute tunneling matrix elements in very large systems

Abstract

A tight-binding Hamiltonian and Dyson’s equation method are described that allow the computation of the tunneling matrix elements between electron donor and acceptor sites in a protein. The method is exact and computationally tractable. The Green’s function matrix elements of the bridge are computed using a strategy that builds up the bridge one orbital at a time, allowing inclusion of all orbitals on proposed tunneling pathways and elsewhere. The tunneling matrix element is determined directly from the bridge Green’s function. A simple representation of a helical protein segment is used to illustrate the method and its ability to include contributions from high-order backscattering and multiple pathway interference in the donor–acceptor coupling.