# Magnitude of pseudopotential localization errors in fixed node diffusion quantum Monte Carlo

## TL;DR

This paper investigates the magnitude of pseudopotential localization errors in fixed node diffusion quantum Monte Carlo, showing that these errors can be significant and proposing methods to reduce them through improved Jastrow factors.

## Contribution

The study demonstrates that localization errors in DMC can be large for heavy elements and introduces a metric for Jastrow sensitivity to guide pseudopotential design.

## Key findings

- Localization errors can reach about 1 eV for cerium atoms.
- Energy minimized Jastrow factors with three-body terms effectively reduce errors.
- Locality approximation generally yields smaller localization errors than T-moves.

## Abstract

Growth in computational resources has lead to the application of real space diffusion quantum Monte Carlo (DMC) to increasingly heavy elements. Although generally assumed to be small, we find that when using standard techniques the pseudopotential localization error can be large, on the order of an electron volt for an isolated cerium atom. We formally show that localization error can be reduced to zero with improvements to the Jastrow factor alone and we define a metric of Jastrow sensitivity that may be useful in the design of pseudopotentials. We employ an extrapolation scheme to extract the bare fixed node energy and estimate the localization error in both the locality approximation and the T-moves schemes for the Ce atom in charge states 3+ and 4+. The locality approximation exhibits the lowest Jastrow sensitivity and generally smaller localization errors than T-moves, although the locality approximation energy approaches the localization free limit from above/below for the 3+/4+ charge state. We find that energy minimized Jastrow factors including three-body electron-electron-ion terms are the most effective at reducing localization error for both the locality approximation and T-moves. Less complex or variance minimized Jastrows are generally less effective. Our results suggest that further improvements to Jastrow factors and trial wavefunction forms will be necessary to reduce localization errors to chemical accuracy in calculations of heavy elements.