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 Kohn-Sham orbitals is presented and applied to heme dimers of varying relative orientation. The electronic coupling decays with increased iron separation according to V_RP = V₀^RP exp(-βr/2) with a distance dependence parameter β ≈ Å^-1 for hemes with parallel porphyrins and either 1.1 or 4.0 Å^-1 when the porphyrin planes are perpendicular, depending on the alignment of the iron d_π orbital. These findings are used to interpret the observed orientation of the hemes in tetraheme redox proteins such as Flavocytochrome c₃ fumarate reductase (Ifc ₃, PDB code 1QJD) of Shewanella frigidimarina, another flavocytochrome from the same bacterium (Fcc₃, 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.