Extension of adaptive tree code and fast multipole methods to high angular momentum particle charge densities

Journal of Computational Chemistry  vol. 29  p. 1895-1904  DOI: 10.1002/jcc.20946
PMID/PMCID: PMC2716046 Published: 2008-09-01 

Timothy J. Giese [ ] , Darrin M. York [ ]

  View Full Article
 Download PDF


The development and implementation of a tree code (TC) and fast multipole method (FMM) for the efficient, linear-scaling calculation of long-range electrostatic interactions of particle distributions with variable shape and multipole character are described. The target application of these methods are stochastic boundary molecular simulations with polarizable force fields and/or combined quantum mechanical/molecular mechanical potentials. Linear-scaling is accomplished through the adaptive decomposition of the system into a hierarchy of interacting particle sets. Two methods for effecting this decomposition are evaluated: fluc-splitting and box-splitting, for which the latter is demonstrated to be generally more accurate. In addition, a generalized termination criterion is developed that delivers optimal performance at fixed error tolerance that, in the case of quadrupole-represented Drude water, effects a speed-up by a factor of 2–3 relative to a multipole-independent termination criteria. The FMM is shown to be ~2–3 times faster than the TC, independent of the system size and multipole order of the particles. The TC and FMM are tested for a variety of static and polarizable water systems, and for the the 70S ribosome functional complex containing an assembly of transfer and messenger RNAs.