Multipolar Ewald methods, 1: Theory, accuracy, and performance

Timothy J. Giese, Maria T. Panteva, Haoyuan Chen, Darrin M. York

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)436-450
Number of pages15
JournalJournal of Chemical Theory and Computation
Issue number2
StatePublished - Feb 10 2015

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Physical and Theoretical Chemistry


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