Quantum Monte Carlo with reoptimized perturbatively selected configuration-interaction wave functions

TL;DR

This paper investigates the use of reoptimized Jastrow-CIPSI wave functions in quantum Monte Carlo, demonstrating improved energy calculations and systematic convergence for first-row atoms through parameter reoptimization.

Contribution

It introduces a method combining CIPSI-selected determinants with reoptimization in QMC, enhancing accuracy and convergence of total energy calculations.

Findings

Reoptimization of determinants lowers both VMC and DMC energies.

Systematic convergence observed with increasing determinants.

Orbital reoptimization is crucial for accurate results with large basis sets.

Abstract

We explore the use in quantum Monte Carlo (QMC) of trial wave functions consisting of a Jastrow factor multiplied by a truncated configuration-interaction (CI) expansion in Slater determinants obtained from a CI perturbatively selected iteratively (CIPSI) calculation. In the CIPSI algorithm, the CI expansion is iteratively enlarged by selecting the best determinants using perturbation theory, which provides an optimal and automatic way of constructing truncated CI expansions approaching the full CI limit. We perform a systematic study of variational Monte Carlo (VMC) and fixed-node diffusion Monte Carlo (DMC) total energies of first-row atoms from B to Ne with different levels of optimization of the parameters (Jastrow parameters, coefficients of the determinants, and orbital parameters) in these trial wave functions. The results show that the reoptimization of the coefficients of the determinants in VMC (together with the Jastrow factor) leads to an important lowering of both VMC and DMC total energies, and to their monotonic convergence with the number of determinants. In addition, we show that the reoptimization of the orbitals is also important in both VMC and DMC for the Be atom when using a large basis set. These reoptimized Jastrow-CIPSI wave functions appear as promising, systematically improvable trial wave functions for QMC calculations.