Theoretical Study of Electron Transfer in Ferrocytochromes

Abstract

A series of calculations is reported of the superexchange electronic matrix element between donor and acceptor states in photoinduced long-distance electron-transfer reactions in seven Ru-modified proteins: Ru(bpy)_2im-(HisX)-cyt c, where X = 33, 39, 58, 62, 66, 72, 79. Calculated results are compared with experimental data. The model used for the calculation includes a detailed description of the donor and acceptor wave functions in terms of ligand field theory. The intervening protein medium is treated within the extended Hiickel theory. It is found that the symmetry and spatial properties of the donor/acceptor wave functions impose certain selection rules on the pathways used in electron transfer. Some paths through σ bonds are not allowed due to the symmetry requirement, for example. Also, the influence of the spatial mutual orientation of the donor and acceptor orbitals in the protein on the rates of electron transfer is analyzed. It is found that there is a strong stereochemical effect in this type of reaction. The mutual orientation of the orbitals is an important factor which determines the reaction rate, in addition to such factors as distance between donor and acceptor and concrete chemical structure of the protein matrix discussed before in the literature. In the calculations, a new method of transition amplitudes is applied. The method can be used for proteins and other large systems involving several thousand atoms. Numerically, the new method reduces the calculation of the electronic coupling between donor and acceptor to the problem of finding iteratively the minimum of a multidimensional parabola, and avoids the diagonalization of the Hamiltonian matrix.