Fixed-Node Diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions

TL;DR

This paper demonstrates that using selected configuration interaction trial wavefunctions in Fixed-Node Diffusion Monte Carlo significantly improves the potential energy curve of F2, achieving near-FCI quality with a systematic, automatic approach.

Contribution

The study introduces a systematic, automatic method to improve trial wavefunction nodes in FN-DMC using CIPSI-selected CI expansions, avoiding multi-parameter optimization.

Findings

FN-DMC energy curves with CIPSI trial wavefunctions are highly accurate.

The approach achieves near-FCI quality with a smaller basis set.

Systematic node improvement correlates with the number of selected determinants.

Abstract

The potential energy curve of the F$_2$ molecule is calculated with Fixed-Node Diffusion Monte Carlo (FN-DMC) using Configuration Interaction (CI)-type trial wavefunctions. To keep the number of determinants reasonable (the first and second derivatives of the trial wavefunction need to be calculated at each step of FN-DMC), the CI expansion is restricted to those determinants that contribute the most to the total energy. The selection of the determinants is made using the so-called CIPSI approach (Configuration Interaction using a Perturbative Selection made Iteratively). Quite remarkably, the nodes of CIPSI wavefunctions are found to be systematically improved when increasing the number of selected determinants. To reduce the non-parallelism error of the potential energy curve a scheme based on the use of a $R$-dependent number of determinants is introduced. Numerical results show that improved FN-DMC energy curves for the F$_2$ molecule are obtained when employing CIPSI trial wavefunctions. Using the Dunning's cc-pVDZ basis set the FN-DMC energy curve is of a quality similar to that obtained with FCI/cc-pVQZ. A key advantage of using selected CI in FN-DMC is the possibility of improving nodes in a systematic and automatic way without resorting to a preliminary multi-parameter stochastic optimization of the trial wavefunction performed at the Variational Monte Carlo level as usually done in FN-DMC.