Compact and Flexible Basis Functions for Quantum Monte Carlo Calculations

TL;DR

This paper introduces reoptimized primitive Gaussian exponents and Gauss-Slater basis functions to create more compact and accurate basis sets for quantum Monte Carlo calculations, especially for excited states and larger molecules.

Contribution

It presents novel reoptimization techniques and new basis functions that improve efficiency and accuracy in quantum Monte Carlo molecular calculations.

Findings

Reoptimized primitive exponents lead to more compact basis sets.

Gauss-Slater functions improve energy and local energy fluctuations.

Basis size reduction enables larger molecule simulations.

Abstract

Molecular calculations in quantum Monte Carlo frequently employ a mixed basis consisting of contracted and primitive Gaussian functions. While standard basis sets of varying size and accuracy are available in the literature, we demonstrate that reoptimizing the primitive function exponents within quantum Monte Carlo yields more compact basis sets for a given accuracy. Particularly large gains are achieved for highly excited states. For calculations requiring non-diverging pseudopotentials, we introduce Gauss-Slater basis functions that behave as Gaussians at short distances and Slaters at long distances. These basis functions further improve the energy and fluctuations of the local energy for a given basis size. Gains achieved by exponent optimization and Gauss-Slater basis use are exemplified by calculations for the ground state of carbon, the lowest lying excited states of carbon with $^5S^o$, $^3P^o$, $^1D^o$, $^3F^o$ symmetries, carbon dimer, and naphthalene. Basis size reduction enables quantum Monte Carlo treatment of larger molecules at high accuracy.