Application of density functional theory to large systems: Implementation of the continuous fast multipole method and investigation of models of pentacoordinate phosphorus

Abstract

The density functional package DeFT is used for systems with a large number of charge distributions, and the bottleneck of the computation is the evaluation of two-electron integrals. Previously, it scaled quadratically with system size. A particular strategy, called the continuous fast multipole method, has been implemented in DeFT and combined with traditional methods for evaluating the two-electron integrals. The result is a code which scales linearly with system size and is able to treat larger systems. The Continuous Fast Multipole Method (CFMM) uses the divide-and-conquer strategy to approximate the pairwise potentials between continuous charge distributions. Pairwise potentials are computed using the direct method if they are within a defined distance of one another; and are approximated by a multipolar expansion if they are not. The algorithm involves successive subdivisions of the simulation space until the desired precision is reached, which reduces the number of pairwise potentials evaluated. For large systems, this algorithm scales linearly with the number of charge distributions. Enzyme-catalyzed phosphoryl transfer reactions have many applications in biological systems. It has been shown in previous investigations that phosphoryl transfer in enzymes proceeds via a pentacoordinate phosphorus intermediate. Few theoretical investigations have been conducted on this class of enzymes due to the large number of atoms treated quantum mechanically. In this investigation, models of the pentacoordinate phosphorus intermediate are investigated with density functional methods. Comparison of the results of calculations using the VSXC functional with experiment and perturbation theory are employed to validate its use in investigations of phosphoryl transfer reactions.