Including the Dispersion Attraction into Structure-Adapted Fast Multipole Expansions for MD Simulations

Molecular dynamics (MD) simulations of protein–solvent systems, which are modeled by polarizable or nonpolarizable all-atom force fields and are enclosed by periodic boundaries, require accurate and efficient algorithms for the computation of the long-range interactions. A possible choice is the fast structure-adapted multipole method called SAMM_<i>p</i>/RF (Lorenzen et al. <i>J. Chem. Theory Comput.</i> <b>2012</b>, <i>8</i>, 3628–3636). It is based on <i>p</i>th order Cartesian Taylor expansions of the electrostatic interactions, on an adaptive and hierarchical decomposition of a macromolecular simulation system into a quaternary tree of nested atom clusters, and on a reaction field (RF) correction originating from a distant dielectric continuum. Here, we substantially extend this method by adding <i>q</i>th order Taylor expansions of the dispersion attraction and by formulating an interaction acceptance criterion for cluster–cluster interactions, which is based on substance-specific accuracy estimates. As a result, we obtain with the default expansion orders (<i>p</i>,<i>q</i>) = (4,1) a family of MD algorithms SAMM_4,1^χ, which comprises carefully balanced compromises χ between accuracy and efficiency ranging from “accurate” (χ = a) to “fast” (χ = f). Issues of accuracy and efficiency are discussed by sample simulations of liquid water and methanol using simple nonpolarizable and complex polarizable model potentials. Here, it is shown that the computational effort scales linearly with the number <i>N</i> of atoms. For a complex polarizable water model, these simulations also show that SAMM_4,1^χ is by factors between 2 (χ = a) and 5 (χ = f) faster than its predecessor SAMM₄. Other benefits, which arise in simulations employing polarizable force fields with a high degree of local complexity, are also discussed