Perturbatively selected configuration-interaction wave functions for efficient geometry optimization in quantum Monte Carlo

TL;DR

This paper demonstrates that perturbatively selected configuration-interaction wave functions, combined with variational Monte Carlo, enable efficient and accurate geometry optimization of complex molecules like 1,3-trans-butadiene.

Contribution

It introduces a systematic and efficient approach using CIPSI-selected wave functions for geometry optimization in quantum Monte Carlo, outperforming traditional active space methods.

Findings

CIPSI selection yields better energies than conventional active space methods.

Accurate bond lengths are achieved with only a few thousand determinants.

The method converges to CCSD(T)-like accuracy for geometries.

Abstract

We investigate the performance of a class of compact and systematically improvable Jastrow-Slater wave functions for the efficient and accurate computation of structural properties, where the determinantal component is expanded with a perturbatively selected configuration interaction scheme (CIPSI). We concurrently optimize the molecular ground-state geometry and full wave function -- Jastrow factor, orbitals, and configuration interaction coefficients-- in variational Monte Carlo (VMC) for the prototypical case of 1,3-trans-butadiene, a small yet theoretically challenging $\pi$-conjugated system. We find that the CIPSI selection outperforms the conventional scheme of correlating orbitals within active spaces chosen by chemical intuition: it gives significantly better variational and diffusion Monte Carlo energies for all but the smallest expansions, and much smoother convergence of the geometry with the number of determinants. In particular, the optimal bond lengths and bond-length alternation of butadiene are converged to better than one m\AA\ with just a few thousand determinants, to values very close to the corresponding CCSD(T) results. The combination of CIPSI expansion and VMC optimization represents an affordable tool for the determination of accurate ground-state geometries in quantum Monte Carlo.