Ellipsoidal delocalization of tunneling electrons in long-range electron transfer proteins

A formulation of long-range electronic coupling in electron transfer protei ns based on the wave function tails of the donor and acceptor states is pre sented. These wave function tails, calculated by the IAL Hamiltonian method for cytochrome c and cytochrome c peroxidase, decay exponentially with dis tance and have falloff rates in the experimentally observed range. Analytic al derivatives of the electronic coupling energy with regard to the energie s and interactions of the orbitals of the intervening medium provide a deta iled picture of the region of the protein important in the electron transfe r process. These electronic coupling energy derivatives are calculated for the long-range zinc porphyrin to ruthenium coupling in ruthenated cytochrom e c. The region of importance for long-range electron transfer is demonstra ted mathematically to approximate an ellipsoid of revolution with the donor and acceptor as foci, The ellipsoidal region has the interesting feature t hat its minor axis grows as the square root of the donor-acceptor distance in the Limit of long-range electron transfer.