Assessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters

TL;DR

This study compares the accuracy of diffusion Monte Carlo and density functional theory in calculating the energetics of small water clusters, demonstrating DMC's superior precision and potential as a benchmark for larger water systems.

Contribution

It provides a detailed error analysis of DMC and DFT for water clusters, highlighting DMC's higher accuracy and suggesting its use for benchmarking larger water systems.

Findings

DMC is more accurate than DFT for water cluster energetics.

Many DFT functionals exhibit significant beyond-2-body errors.

Correcting 1- and 2-body errors improves DFT accuracy, but some functionals still underperform.

Abstract

We present a detailed study of the energetics of water clusters (H$_2$O)$_n$ with $n \le 6$, comparing diffusion Monte Carlo (DMC) and approximate density functional theory (DFT) with well converged coupled-cluster benchmarks. We use the many-body decomposition of the total energy to classify the errors of DMC and DFT into 1-body, 2-body and beyond-2-body components. Using both equilibrium cluster configurations and thermal ensembles of configurations, we find DMC to be uniformly much more accurate than DFT, partly because some of the approximate functionals give poor 1-body distortion energies. Even when these are corrected, DFT remains considerably less accurate than DMC. When both 1- and 2-body errors of DFT are corrected, some functionals compete in accuracy with DMC; however, other functionals remain worse, showing that they suffer from significant beyond-2-body errors. Combining the evidence presented here with the recently demonstrated high accuracy of DMC for ice structures, we suggest how DMC can now be used to provide benchmarks for larger clusters and for bulk liquid water.