An iterative method is developed to generalize the original pathway model which identifies not simply the strongest pathway involved in the protein-mediation of electron transfer matrix elements but all the relevant ones. The generalized pathway model is a semianalytical, nonperturbative, and computationally tractable method that allows detail investigation of the electron tunneling propagation in the protein medium for any one-electron Hamiltonian, and to examine structure-function relationships in multiple pathway regimes that may be induced by hydrogen bond and through-space contacts in the folded protein structure. This method enables an understanding of how details of the 3-D protein structures control the tunneling process, and whether pathway interference in the protein structural motifs causes substantial deviation from standard pathway analysis.
Articles you may be interested inComparative study of perturbative methods for computing electron transfer tunneling matrix elements with a nonorthogonal basis set 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.J. Chem. Phys. 95 (2). 15
We consider the problem of building an effective Hamiltonian in a subset 𝒫 of the full Hilbert space in the case where there is an overlap between the states in 𝒫 and the states in its complement 𝒬. In this case the projectors onto these subspaces are non-Hermitian and one has various possible effective Hamiltonians. We show how these can be constructed directly from the Schrödinger equation and relate them to projections of the Green function operator. In the context of a simple electron-transfer model we discuss the dependence of the matrix elements of the effective Hamiltonians on the distance between orbitals and on the choice of the tunneling energy parameter. We also investigate with what accuracy the effective Hamiltonians estimate the exact eigenenergies of the problem.
We develop nonorthogonal projectors, called Löwdin projectors, to construct an effective donor-acceptor system composed of localized donor (D) and acceptor (A) states of a long-distance electron transfer problem. When these states have a nonvanishing overlap with the bridge states these projectors are non-Hermitian and there are various possible effective two-level systems that can be built. We show how these can be constructed directly from the Schrödinger or Dyson equation projected onto the D-A subspace of the Hilbert space and explore these equations to determine the connection between Hamiltonian and Green function partitioning. We illustrate the use of these effective two-level systems in estimating the electron transfer rate in the context of a simple electron transfer model.
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