Boundary based on exchange symmetry theory for multilevel simulations. II. Multiple time scale approach

The QM/MM BEST method presented in the first article of this series [M. Shiga and M. Masia, J. Chem. Phys. 139, 044120 (2013)] has been applied herein to simulate the whole series of hydrated alkali ions. In this article we show how to overcome the sampling bottleneck for QM/MM simulations by using our method with multiple time scale algorithm (MTS-BEST). We extend the use of MTS-BEST to ab initio QM/MM path integral molecular dynamics simulations, thus demonstrating that one could obtain a complete quantum description of the primary subsystem based on first principles. We highlight that the MTS-BEST approach could be generally applied to hybrid multiscale simulation of diffusive systems, thus extending its relevance to a broad class of simulation techniques beyond QM/MM. We show that it is important to account for electron correlation to better reproduce the hydration structural properties such as the ion-water radial distribution functions, and the anisotropic angular distributions around the ion.