Efficient solution of Poisson's equation using discrete variable representation basis sets for Car-Parrinello ab initio molecular dynamics simulations with cluster boundary conditions.

An efficient computational approach to perform Car-Parrinello ab initio molecular dynamics (CPAIMD) simulations under cluster (free) boundary conditions is presented. The general approach builds upon a recent real-space CPAIMD formalism using discrete variable representation (DVR) basis sets [Y. Liu et al., Phys. Rev. B 12, 125110 (2003); H.-S. Lee and M. E. Tuckerman, J. Phys. Chem. A 110, 5549 (2006)]. In order to satisfy cluster boundary conditions, a DVR based on sinc functions is utilized to expand the Kohn-Sham orbitals and electron density. Poisson's equation is solved in order to calculate the Hartree potential via an integral representation of the 1/r singularity. Excellent convergence properties are achieved with respect to the number of grid points (or DVR functions) and the size of the simulation cell. A straightforward implementation of the present approach leads to near linear scaling [O(N(4/3))] of the computational cost with respect to the system size (N) for the solution of Poisson's equation. The accuracy and stability of CPAIMD simulations based on sinc DVR are tested for a model problem as well as for N(2) and a water dimer.