Free Energy Perturbation Calculations with Combined QM/MM Potentials Complications, Simplifications, and Applications to Redox Potential Calculations

Abstract

The present work deals with a formal discussion on complications associated with using combined quantum mechanical and molecular mechanical (QM/MM) potentials in free energy perturbation simulations. Because quantum mechanical potentials are not trivially separable and because of the difficulty associated with QM calculations for “fractional” electronic Hamiltonians, conventional computational strategies cannot be straightforwardly applied to free energy simulations with QM/MM potentials. Here, we propose a unique coupling scheme, termed the “dual-topology-single-coordinate” scheme, in which the two chemical states are forced to adopt the same set of Cartesian coordinates during the perturbation simulation; the method is exact because the free energy difference is independent of the coupling path, although a formal proof is also given. The scheme combines the merits of the conventional dual- and single-topology approaches: both coupling potential and free energy derivative are straightforward to compute ...