Toward an improved control of the fixed-node error in quantum Monte Carlo: The case of the water molecule

TL;DR

This paper demonstrates that using systematically improved selected CI nodes in quantum Monte Carlo calculations can effectively control the fixed-node error, leading to highly accurate estimates of the water molecule's ground-state energy.

Contribution

It introduces a systematic approach to controlling fixed-node errors in QMC by employing selected CI nodes without re-optimizing the wavefunction.

Findings

Achieved the most accurate theoretical energy for water to date.

Fixed-node energy decreases with larger basis sets and approaches the CBS limit.

Selected CI nodes provide a deterministic way to improve fixed-node accuracy.

Abstract

All-electron Fixed-node Diffusion Monte Carlo (FN-DMC) calculations for the nonrelativistic ground-state energy of the water molecule at equilibrium geometry are presented. The determinantal part of the trial wavefunction is obtained from a perturbatively selected Configuration Interaction calculation (CIPSI method) including up to about 1.4 million of determinants. Calculations are made using the cc-pCV$n$Z family of basis sets, with $n$=2 to 5. In contrast with most QMC works no re-optimization of the determinantal part in presence of a Jastrow is performed. For the largest cc-pCV5Z basis set the lowest upper bound for the ground-state energy reported so far of -76.43744(18) is obtained. The fixed-node energy is found to decrease regularly as a function of the cardinal number $n$ and the Complete Basis Set limit (CBS) associated with {\it exact nodes} is easily extracted. The resulting energy of -76.43894(12) -in perfect agreement with the best experimentally derived value- is the most accurate theoretical estimate reported so far. We emphasize that employing selected CI nodes of increasing quality in a given family of basis sets may represent a simple, deterministic, reproducible, and systematic way of controlling the fixed-node error in DMC.