Taming the fixed-node error in diffusion Monte Carlo via range separation

TL;DR

This paper introduces a method combining density-functional theory and wave function theory via range separation to produce accurate, compact trial wave functions for diffusion Monte Carlo, reducing fixed-node errors and computational cost.

Contribution

The study presents RS-DFT-CIPSI, a novel approach that yields lower fixed-node energies with fewer determinants by integrating short-range DFT with selected CI, mimicking short-range correlation effects.

Findings

RS-DFT-CIPSI produces more compact trial wave functions than traditional CIPSI.

Using a fixed range separation parameter effectively cancels errors in atomization energies.

The method performs well on the Gaussian-1 benchmark set for large molecules.

Abstract

By combining density-functional theory (DFT) and wave function theory (WFT) via the range separation (RS) of the interelectronic Coulomb operator, we obtain accurate fixed-node diffusion Monte Carlo (FN-DMC) energies with compact multi-determinant trial wave functions. In particular, we combine here short-range exchange-correlation functionals with a flavor of selected configuration interaction (SCI) known as \emph{configuration interaction using a perturbative selection made iteratively} (CIPSI), a scheme that we label RS-DFT-CIPSI. One of the take-home messages of the present study is that RS-DFT-CIPSI trial wave functions yield lower fixed-node energies with more compact multi-determinant expansions than CIPSI, especially for small basis sets. Indeed, as the CIPSI component of RS-DFT-CIPSI is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points, the number of determinants in the trial wave function required to reach a given accuracy is significantly reduced as compared to a conventional CIPSI calculation. Importantly, by performing various numerical experiments, we evidence that the RS-DFT scheme essentially plays the role of a simple Jastrow factor by mimicking short-range correlation effects, hence avoiding the burden of performing a stochastic optimization. Considering the 55 atomization energies of the Gaussian-1 benchmark set of molecules, we show that using a fixed value of $\mu=0.5$~bohr$^{-1}$ provides effective error cancellations as well as compact trial wave functions, making the present method a good candidate for the accurate description of large chemical systems.