Ab initio based calculations of electron-transfer rates in metalloproteins.

A long-standing challenge in electron-transfer theory is to compute accurate rates of long-distance reactions in proteins. We describe an ab initio Hartree-Fock approach to compute electronic-coupling interactions and electron-transfer rates in proteins that allows the favorable comparison with experiment. The method includes the following key features; each is essential for reliable rate computations: (1) summing contributions over multiple tunneling pathways, (2) averaging couplings over thermally accessible protein conformations, (3) describing donor and acceptor electronic structure explicitly, including solvation effects, and averaging coupling over multiple energy-level crossings of the nearly degenerate donor-acceptor ligand-field states, and (4) eliminating basis set artifacts associated with diffuse basis functions. The strong dependence of coupling on donor-acceptor distance and on pathway interferences causes large variations of the computed electron-coupling values with protein geometry, and the strongest coupled conformers dominate the electron-transfer rate. As such, averaging over thermally accessible conformers of the protein and of the redox cofactors is essential. This approach was tested on six ruthenium-modified azurin derivatives using the high temperature nonadiabatic rate expression and compared with simpler pathways, average barrier, and semiempirical INDO models. Results of ab initio Hartree-Fock calculations with a split-valence basis set are in good agreement with the experimental rates. Predicted rates in the longer-distance derivatives are underestimated by 3-8-fold. This analysis indicates that the key ingredients needed for quantitatively reliable protein electron-transfer rate calculations are accessible.