Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

TL;DR

This paper introduces a stochastic sampling method in quantum Monte Carlo that accurately computes molecular properties like nuclear forces and dipole moments, achieving results close to experimental data.

Contribution

It extends full configuration interaction quantum Monte Carlo to include analytic nuclear forces and molecular properties using a replica ensemble approach.

Findings

Accurate sampling of reduced density matrices achieved

Close agreement with experimental molecular properties obtained

Method applicable to a broad range of molecular calculations

Abstract

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first, and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality, and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation.