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

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

The dominant cost in accurate quantum/mol. mechanics calcns. is the recalcn. of the wavefunction of the active (QM) part of the system in the field of the MM solvent or 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 QM/MM interaction, particularly in the most important case of polar solvents, is electrostatic, and the calcns. can be greatly accelerated if the precalcd. electrostatic response of the QM system is used instead of recalcg. its wavefunction. We represent the elec. potential of the solvent within the QM solute as a linear combination of sine functions. This is very stable numerically, unlike the common multipole expansion. The response of the QM system to the spatially modulated elec. potential components is the generalized multipole polarizability (GMP). It is calcd. anal. before the simulation run. By using time-dependent instead of static polarizabilities, the d.-d. response function (polarization propagator) χ(r, r ',w) can also be calcd. Tests show that the total energies from GMP calcns. agree with full QM/MM to ∼0.05 kcal/mol, and run ∼104 times faster. 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 course-grained methods 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 SN2 reactions in water, to the hydration of 5-Br-uracil, and to NMR spectra in aq. solns.