A new framework for electron-transfer calculations -: Beyond the Pathways-like models

We present a framework for analyzing and understanding the underlying mechanisms for the electron-transfer (ET) tunneling matrix element. Four principal issues that could not be addressed by the Pathways-like models are investigated: sensitivity to the choice of the Hamiltonian, effects of the interference among pathways. sensitivity to the bridge coordinates, and effects of the bridge motion. Our framework classifies the orbital interactions by using the overlap-coupling (S-H) maps and identifies the dominant pathways, as well as interference among them, mediated by these different classes of interactions. This strategy provides a clear view of how structural motifs of the bridge control T-DA and identifies, even without performing the dynamical calculations, the situations where T-DA is highly sensitive to the structural details and thermal motion. Even though the details of the interference mechanism depend on the choice of the Hamiltonian, the qualitative features obtained by this framework should not be sensitive to it as long as all relevant interactions have been included. The framework thus opens theoretical insight into ET and provides new tools for experimental design.