Analytic gradient for the QM/MM-Ewald method using charges derived from the electrostatic potential: Theory,...

We report an implementation of periodic boundary conditions for mixed quantum mechanics/molecular mechanics (QM/MM) simulations, in which atomic partial charges are used to represent periodic images of the QM region. These charges are incorporated into the Fock matrix in a manner that preserves the variational nature of the self-consistent field procedure, and their interactions with the MM charges are summed using the conventional Ewald technique. To ensure that the procedure is stable in arbitrary basis sets, the atomic charges are derived by least-squares fit to the electrostatic potential generated by the QM region. We formulate and implement analytic energy gradients for the QM/MM-Ewald method and demonstrate that stable molecular dynamics simulations are thereby obtained. As a proof-of-concept application, we perform QM/MM simulations of a hydrated electron in bulk liquid water at the level of Hartree-Fock theory plus empirical dispersion. These simulations demonstrate that the "cavity model" of the aqueous electron, in which the spin density of the anionic defect is localized within an excluded volume in the liquid, is stable at room temperature on a time scale of at least several picoseconds. These results validate cavity-forming pseudopotential models of e^-(aq) that have previously been derived from static-exchange Hartree-Fock calculations, and cast doubt upon whether non-cavity-forming pseudopotentials are faithful to the underlying Hartree-Fock calculation from which they were obtained.