An efficient algorithm for multipole energies and derivatives based on spherical harmonics and extensions to particle mesh Ewald.
Next-generation molecular force fields deliver accurate descriptions of non-covalent interactions by employing more elaborate functional forms than their predecessors. Much work has been dedicated to improving the description of the electrostatic potential (ESP) generated by these force fields. A common approach to improving the ESP is by augmenting the point charges on each center with higher-order multipole moments. The resulting anisotropy greatly improves the directionality of the non-covalent bonding, with a concomitant increase in computational cost. In this work, we develop an efficient strategy for enumerating multipole interactions, by casting an efficient spherical harmonic based approach within a particle mesh Ewald (PME) framework. Although the derivation involves lengthy algebra, the final expressions are relatively compact, yielding an approach that can efficiently handle both finite and periodic systems without imposing any approximations beyond PME. Forces and torques are readily obtained, making our method well suited to modern molecular dynamics simulations.
Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA.
Andrew C
AC
Simmonett
Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA.
Frank C
FC
Pickard
Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA.
Henry F
HF
Schaefer
Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA.
Bernard R
BR
Brooks
D000465:Algorithms; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D008968:Molecular Conformation; D009716:Numerical Analysis, Computer-Assisted; D010316:Particle Size; D055672:Static Electricity