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Donor–acceptor symmetric and antisymmetric tunneling matrix elements: a pathway model investigation of protein electron transfer

  • P. C. P. de AndradeEmail author
  • J. C. O. Guerra
Original Paper

Abstract

In protein electron transfer reaction rate calculations, the electronic Hamiltonian is apportioned into donor–acceptor (DA) and protein bridge subspaces, and a two-state system is defined for the DA subspace. Löwdin partitioning is used to perform the two-state reductions necessary to compute the tunneling matrix element between D and A sites. Here, a method of performing donor and acceptor state analysis for a non-orthogonal basis set in both the weak and strong electronic coupling regimes is developed. The electron tunneling current and coupling are obtained in terms of DA symmetric and antisymmetric interatomic tunneling elements, and are then used to compare pathway models. These interatomic tunneling elements are both proportional to the Green’s function elements of the isolated protein bridge. To facilitate a perturbative treatment of antisymmetric interatomic tunneling currents, we found a well-known expression for the DA tunneling matrix element in terms of transformed Green’s function matrix elements of the isolated protein bridge. Also, the relationship of the tunneling matrix element to BO pathways is discussed using the symmetric interatomic coupling. Finally, the definition of the average interatomic and atomic pathway coupling allows us obtain the quantum interference between interatomic tunneling pathways.

Keywords

Two-state approximation for non-orthogonal basis set Protein electron transfer Pathway models 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade Federal de UberlândiaUberlândiaBrazil

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