An efficient real space multigrid OM/MM electrostatic coupling

A popular strategy for simulating large systems where quantum chemical effects are important is the use of mixed quantum mechanical/molecular mechanics methods (QM/MM). While the cost of solving the Schrodinger equation in the QM part is the bottleneck of these calculations, evaluating the Coulomb interaction between the QM and the MM part is surprisingly expensive. In fact it can be just as time-consuming as solving the QM part. We present here a novel real space multigrid approach that handles Coulomb interactions very effectively and implement it in the CP2K code. This novel scheme cuts the cost of this part of the calculation by 2 orders of magnitude. The method does not need very fine-tuning or adjustable parameters, and it is quite accurate, leading to a dynamics with very good energy conservation. We exemplify the validity of our algorithms with simulations of water and of a zwitterionic dipeptide solvated in water.