New Distributed Multipole Metdhods for Accurate Electrostatics in Large-Scale Biomolecular Simulations

Abstract

It has long been known that accurate electrostatics is a key issue for improving current force fields for large-scale biomolecular simulations. Typically, this calls for an improved and more accurate description of the molecular electrostatic potential, which eliminates the artifacts associated with current point charge-based descriptions. In turn, this involves the partitioning of the extended molecular charge distribution, so that charges and multipole moments can be assigned to different atoms. As an alternate to current approaches, we have investigated a charge partitioning scheme that is based on the maximally-localized Wannier functions. This has the advantage of partitioning the charge, and placing it around the molecule in a chemically meaningful manner. Moreover, higher order multipoles may all be calculated without any undue numerical difficulties. In order to deal with the extra computational costs, we have developed an efficient Cartesian formalism for the treatment of higher order multipoles. The Ewald ‘direct sum’ is evaluated through a McMurchie-Davidson formalism. The ‘reciprocal sum’ has been implemented in three different ways: using an Ewald scheme, a Particle Mesh Ewald (PME) method and a multigrid-based approach. Even though the use of the McMurchie-Davidson formalism considerably reduces the cost of the calculation with respect to the standard matrix implementation of multipole interactions, the calculation in direct space remains expensive. When most of the calculation is moved to reciprocal space via the PME method, the cost of a calculation where all multipolar interactions (up to hexadecapolehexadecapole) are included is only about 8.5 times more expensive than a regular AMBER 7 implementation with only charge-charge interactions. The multigrid implementation is slower but shows very promising results for parallelization.