Fragment-based Quantum Mechanical/Molecular Mechanical Simulations of Thermodynamic and Kinetic Process of the Ru(2+)-Ru(3+) Self-Exchange Electron Transfer

A fragment-based fractional number of electron (FNE) approach, is developed to study entire electron transfer (ET) processes from the electron donor region to the acceptor region in condensed phase. Both regions are described by the density-fragment interaction (DFI) method while FNE as an efficient ET order parameter is applied to simulate the electron transfer process. In association with the QM/MM energy expression, the DFI-FNE method is demonstrated to describe ET processes robustly with the Ru(2+)-Ru(3+) self-exchange ET as a proof-of-concept example. This method allows for systematic calculations of redox free energies, reorganization energies, and electronic couplings, and the absolute ET rate constants within the Marcus regime.