Calculation of electron transfer reorganization energies using the finite difference Poisson-Boltzmann model

A description is given of a method to calculate the electron transfer reorganization energy (lambda) in proteins using the linear or nonlinear Poisson-Boltzmann (PB) equation. Finite difference solutions to the linear PB equation are then used to calculate lambda for intramolecular electron transfer reactions in the photosynthetic reaction center from Rhodopseudomonas viridis and the ruthenated heme proteins cytochrome c, myoglobin, and cytochrome b and for intermolecular electron transfer between two cytochrome c molecules. The overall agreement with experiment is good considering both the experimental and computational difficulties in estimating lambda. The calculations show that acceptor/donor separation and position of the cofactors with respect to the protein/solvent boundary are equally important and, along with the overall polarizability of the protein, are the major determinants of lambda. In agreement with previous studies, the calculations show that the protein provides a low reorganization environment for electron transfer. Agreement with experiment is best if the protein polarizability is modeled with a low (<8) average effective dielectric constant. The effect of buried waters on the reorganization energy of the photosynthetic reaction center was examined and found to make a contribution ranging from 0.05 eV to 0.27 eV, depending on the donor/acceptor pair.