Phaseless auxiliary-field quantum Monte Carlo calculations with planewaves and pseudopotentials--applications to atoms and molecules

TL;DR

This paper applies the phaseless auxiliary-field quantum Monte Carlo method with planewaves and pseudopotentials to study atomic and molecular energies, demonstrating its accuracy and convergence for second-row elements and dimers.

Contribution

It introduces a systematic implementation of AF QMC with planewaves and pseudopotentials, analyzing its accuracy and computational aspects for atoms and molecules.

Findings

Accurate dissociation and ionization energies for second-row atoms and dimers.

Demonstrated convergence behavior with respect to supercell size and planewave cutoff.

Validates the use of norm-conserving pseudopotentials in AF QMC calculations.

Abstract

The phaseless auxiliary-field quantum Monte Carlo (AF QMC) method [S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003)] is used to carry out a systematic study of the dissociation and ionization energies of second-row group 3A-7A atoms and dimers, Al, Si, P, S, Cl. In addition, the P_2 dimer is compared to the third-row As_2 dimer, which is also triply-bonded. This method projects the many-body ground state by means of importance-sampled random walks in the space of Slater determinants. The Monte Carlo phase problem, due to the electron-electron Coulomb interaction, is controlled via the phaseless approximation, with a trial wave function |Psi_T>. As in previous calculations, a mean-field single Slater determinant is used as |Psi_T>. The method is formulated in the Hilbert space defined by any chosen one-particle basis. The present calculations use a planewave basis under periodic boundary conditions with norm-conserving pseudopotentials. Computational details of the planewave AF QMC method are presented. The isolated systems chosen here allow a systematic study of the various algorithmic issues. We show the accuracy of the planewave method and discuss its convergence with respect to parameters such as the supercell size and planewave cutoff. The use of standard norm-conserving pseudopotentials in the many-body AF QMC framework is examined.