Solvent Boundary Potentials for Hybrid QM/MM Computations Using Classical Drude Oscillators: A Fully Polarizable Model.

Accurate quantum mechanical/molecular mechanical (QM/MM) treatments should account for MM polarization and properly include long-range electrostatic interactions. We report on a development that covers both these aspects. Our approach combines the classical Drude oscillator (DO) model for the electronic polarizability of the MM atoms with the generalized solvent boundary Potential (GSBP) and the solvated macromolecule boundary potential (SMBP). These boundary potentials (BP) are designed to capture the long-range effects of the outer region of a large system on its interior. They employ a finite difference approximation to the Poisson-Boltzmann equation for computing electrostatic interactions and take into account outer-region bulk solvent through a polarizable dielectric continuum (PDC). This approach thus leads to fully polarizable three-layer QM/MM-DO/BP methods. As the mutual responses of each of the subsystems have to be taken into account, we propose efficient schemes to converge the polarization of each layer simultaneously. For molecular dynamics (MD) simulations using GSBP, this is achieved by considering the MM polarizable model as a dynamical degree of freedom, and hence contributions from the boundary potential can be evaluated for a frozen state of polarization at every time step. For geometry optimizations using SMBP, we propose a dual self-consistent field approach for relaxing the Drude oscillators to their ideal positions and converging the QM wave function with the proper boundary potential. The chosen coupling schemes are evaluated with a test system consisting of a glycine molecule in a water ball. Both boundary potentials are capable of properly reproducing the gradients at the inner-region atoms and the Drude oscillators. We show that the effect of the Drude oscillators must be included in all terms of the boundary potentials to obtain accurate results and that the use of a high dielectric constant for the PDC does not lead to a polarization catastrophe of the DO models. Optimum values for some key parameters are discussed. We also address the efficiency of these approaches compared to standard QM/MM-DO calculations without BP. In the SMBP case, computation times can be reduced by around 40% for each step of a geometry optimization, with some variation depending on the chosen QM method. In the GSBP case, the computational advantages of using the boundary potential increase with system size and with the number of MD steps.