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

## Abstract

Growth in computational resources has lead to the application of real space diffusion quantum Monte Carlo 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 the 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+/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 the localization error for both the locality approximation and T-moves for the case of the Ce atom. Less complex or variance minimized Jastrows are generally less effective. Finally, ourmore »

- Authors:

- ORNL

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1376370

- Alternate Identifier(s):
- OSTI ID: 1365431

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 146; Journal Issue: 24; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Kent, Paul R., and Krogel, Jaron T.
```*Magnitude of pseudopotential localization errors in fixed node diffusion quantum Monte Carlo*. United States: N. p., 2017.
Web. doi:10.1063/1.4986951.

```
Kent, Paul R., & Krogel, Jaron T.
```*Magnitude of pseudopotential localization errors in fixed node diffusion quantum Monte Carlo*. United States. doi:10.1063/1.4986951.

```
Kent, Paul R., and Krogel, Jaron T. Thu .
"Magnitude of pseudopotential localization errors in fixed node diffusion quantum Monte Carlo". United States. doi:10.1063/1.4986951. https://www.osti.gov/servlets/purl/1376370.
```

```
@article{osti_1376370,
```

title = {Magnitude of pseudopotential localization errors in fixed node diffusion quantum Monte Carlo},

author = {Kent, Paul R. and Krogel, Jaron T.},

abstractNote = {Growth in computational resources has lead to the application of real space diffusion quantum Monte Carlo 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 the 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+/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 the localization error for both the locality approximation and T-moves for the case of the Ce atom. Less complex or variance minimized Jastrows are generally less effective. Finally, our results suggest that further improvements to Jastrow factors and trial wavefunction forms may be needed to reduce localization errors to chemical accuracy when medium core pseudopotentials are applied to heavy elements such as Ce.},

doi = {10.1063/1.4986951},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 24,

volume = 146,

place = {United States},

year = {2017},

month = {6}

}

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

##
General atomic and molecular electronic structure system

journal, November 1993

- Schmidt, Michael W.; Baldridge, Kim K.; Boatz, Jerry A.
- Journal of Computational Chemistry, Vol. 14, Issue 11, p. 1347-1363