A Coupled Polarization-Matrix Inversion and Iteration Approach for Accelerating the Dipole Convergence in a Polarizable Potential Function

Abstract

A coupled polarization-matrix inversion and iteration (CPII) method is described to achieve and accelerate the convergence of induced dipoles for condensed phase systems employing polarizable intermolecular potential functions (PIPF). The present PIPF is based on the Thole interaction dipole model in which all atomic pair interactions are considered, including those that are directly bonded covalently. Although induced dipoles can be obtained both by inverting a 3N x 3N polarization-matrix where N is the number of polarizable sites, or by a direct iterative approach, the latter approach is more efficient computationally for large systems in molecular dynamics simulations. It was found that induced dipole moments failed to converge in the direct iterative approach if 1-2, 1-3, and 1-4 intramolecular interactions are included in the Thole model. However, it is necessary to include all intramolecular interactions in the Thole model to yield the correct molecular anisotropic polarizability tensor. To solve this numerical stability problem, we reformulated the Thole interaction dipole model in terms of molecular block matrices, which naturally leads to a coupled, preconditioning algorithm that involves a polarization-matrix inversion term to account for intramolecular interactions, and an iterative procedure to incorporate the mutual polarization effects between different molecules. The CPII method is illustrated by applying to cubic boxes of water and NMA molecules as well as an alanine pentapeptide configuration, and it was shown that the CPII method can achieve convergence for the dipole induction polarization rapidly in all cases, whereas the direct iterative approach failed to reach convergence in these cases. In addition, the CPII reduces the overall computational costs by decreasing the number of iteration steps in comparison with the direct iteration approach in which intramolecular bonded interactions are excluded to ensure that induced dipole convergence is obtained.