Electronic coupling between heme electron-transfer centers and its decay with distance depends strongly on relative orientation

A method for calculating the electron-transfer matrix element V-RP using density functional theory KohnSham orbitals is presented and applied to heme dimers of varying relative orientation. The electronic coupling decays with increased iron separation according to V-RP = V-RP(0) exp(-Br/2) with a distance dependence parameter beta approximate to 2 angstrom(-1) for hemes with parallel porphyrins and either 1.1 or 4.0 angstrom(-1) when the porphyrin planes are perpendicular, depending on the alignment of the iron d(pi) orbital. These findings are used to interpret the observed orientation of the hemes in tetraheme redox proteins such as Flavocytochrome c(3) fumarate reductase (Ifc(3), PDB code 1QJD) of Shewanella frigidimarina, another flavocytochrome from the same bacterium (Fcc(3), 1E39) and a small tetraheme cytochrome of Shewanella oneidensis strain MR1 (1M1P). Our results show that shifting and rotating the hemes controls the adiabaticity of the three electron hopping steps.