Direct Calculation of Electron Transfer Rates with the Binless Dynamic Histogram Analysis Method

Umbrella sampling molecular dynamics simulations are widely used to enhance sampling along the reaction coordinate of chemical reactions. The effect of the artificial bias can be removed using methods such as the Dynamic Weighted Histogram Analysis Method (DHAM), which in addition to the global free energy profile also provides kinetic information on barrier-crossing rates directly from the Markov matrix. Here we present a binless formulation of DHAM, which extends DHAM to high-dimensional and Hamiltonian-based biasing, allowing the study of electron transfer (ET) processes, where enhanced sampling is usually not possible based on simple geometric grounds. We show the capabilities of binless DHAM on examples such as aqueous ferrous-ferric ET and intramolecular ET in the radical anion of benzoquinone–tetrathiafulvalene–benzoquinone (Q-TTF-Q)–. From classical Hamiltonian-based umbrella sampling simulations and electronic coupling values from quantum chemistry calculations, binless DHAM provides ET rates for adiabatic and nonadiabatic ET reactions alike, in excellent agreement with experiment.