An efficient linear-scaling electrostatic coupling for treating periodic boundary conditions in QM/MM simulations

A new linear-scaling method based on a multigrid approach to treat long-range electrostatic interactions in hybrid quantum mechanics/molecular mechanics (QM/MM) simulations is described. The scheme has been implemented in the context of a QM calculation based on density functional theory (DFT). The method is tested on an analytical model to validate the new algorithm. Two realistic problems in alpha-quartz crystals and a zwitterionic dipeptide (GLYALA) in water have been chosen as further tests. Results from QM/MM calculations with periodic boundary conditions (PBC) show that the use of PBC is essential when studying highly ordered crystal structures, unless a carefully designed MM crystal is used for the calculation. With a general shaped MM subsystem, the absence of PBC leads to an incorrect description of Kohn-Sham band gaps and charge density. The present method allows periodic boundary conditions to be used in molecular simulations of biological and material science systems.