title: Multipolar Ewald methods, 1: theory, accuracy, and performance.
abstract: The Ewald, Particle Mesh Ewald (PME), and Fast Fourier–Poisson (FFP) methods are developed for systems composed of spherical multipole moment expansions. A unified set of equations is derived that takes advantage of a spherical tensor gradient operator formalism in both real space and reciprocal space to allow extension to arbitrary multipole order. The implementation of these methods into a novel linear-scaling modified “divide-and-conquer” (mDC) quantum mechanical force field is discussed. The evaluation times and relative force errors are compared between the three methods, as a function of multipole expansion order. Timings and errors are also compared within the context of the quantum mechanical force field, which encounters primary errors related to the quality of reproducing electrostatic forces for a given density matrix and secondary errors resulting from the propagation of the approximate electrostatics into the self-consistent field procedure, which yields a converged, variational, but nonetheless approximate density matrix. Condensed-phase simulations of an mDC water model are performed with the multipolar PME method and compared to an electrostatic cutoff method, which is shown to artificially increase the density of water and heat of vaporization relative to full electrostatic treatment.
authors.affiliation: Center for Integrative Proteomics Research, BioMaPS Institute for Quantitative Biology and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854-8087, United States
authors.forename: Timothy J
authors.initials: TJ
authors.lastname: Giese
authors.forename: Maria T
authors.initials: MT
authors.lastname: Panteva
authors.forename: Haoyuan
authors.initials: H
authors.lastname: Chen
authors.forename: Darrin M
authors.initials: DM
authors.lastname: York
mesh_terms: D011789:Quantum Theory; D055672:Static Electricity; D014835:Volatilization; D014867:Water / Q000737:chemistry*
chemical_list: D014867:Water