Generalized multipole polarizabilities and their use in ultrafast QM/MM simulations

by Janowski, Tomasz; Wolinski, Krzysztof; Pulay, Peter

The dominant cost in quantum mechanics/mol. mechanics (QM/MM) calcns. is the recalcn. of the wavefunction of the active (QM) part of the system in the field of the MM solvent or in protein environment. The flexibility of the environment requires a large no. (~104) of snapshots from the solvent ensemble, and this in turn needs ~106-108 Monte Carlo (MC) or mol. dynamics steps to guarantee that the individual snapshots are uncorrelated. The dominant contribution to the QM/MM interactions, particularly in the most important case of polar solvents, is electrostatic, and the calcns. can be greatly accelerated if electrostatic response of the QM system is precalcd. and then reused, instead of recalcg. its wavefunction. We represent the electrostatic potential of the solvent within the QM solute by a linear fit using a "basis set" of sine functions. The response of the QM system to these spatially modulated elec. potential components is the generalized multipole polarizability (GMP). It is calcd. anal. before the simulation run. In the actual simulation the QM energy evaluations are replaced by numerically fast operations requiring only two matrix-vector products per each MC step. Addnl. vectorization can be implemented which results in total speedups more than four orders of magnitude (~104), compared to the full QM/MM evaluation of the interaction energy. As an addnl. benefit the d.-d. response function (polarization propagator) can be calcd. Test simulations show that the total energies from GMP calcns. agree with full QM/MM to ~0.05 kcal/mol. Generalized multipole polarizabilities do not suffer from divergence problems and the QM energy is very accurately recovered even for MM charges penetrating the electronic charge d. of the QM system. Anal. derivs., which require spatially modulated analogs of IR and Raman intensities, were implemented. Their use should lead to further substantial savings. Our method can be considered as an accurate version of the coarse-grained method of Morita and Kato (JACS 1997), and Hu and Yang (Annu Rev Phys Chem 2008). Our GMP method, part of the PQS suite, has been applied to Monte Carlo simulations of the positional preferences of halide ions in nanodroplets, to the hydration of 5-Br-uracil, and to NMR spectra in aq. solns. Sym. SN2 reactions in water involving exchange of identical halide ions have been used as a platform to assess the importance of the QM polarizability on the resulting free energies.