Ellipsoidal Delocalization of Tunneling Electrons in Long-Range Electron Transfer Proteins

Abstract

A formulation of long-range electronic coupling in electron transfer proteins based on the wave function tails of the donor and acceptor states is presented. These wave function tails, calculated by the IAL Hamiltonian method for cytochrome c and cytochrome c peroxidase, decay exponentially with distance and have falloff rates in the experimentally observed range. Analytical derivatives of the electronic coupling energy with regard to the energies and interactions of the orbitals of the intervening medium provide a detailed picture of the region of the protein important in the electron transfer process. These electronic coupling energy derivatives are calculated for the long-range zinc porphyrin to ruthenium coupling in ruthenated cytochrome c. The region of importance for long-range electron transfer is demonstrated mathematically to approximate an ellipsoid of revolution with the donor and acceptor as foci. The ellipsoidal region has the interesting feature that its minor axis grows as the square root o...