## Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo

## Abstract

We propose an algorithm for accurate, systematic, and scalable computation of interatomic forces within the auxiliary-field quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the method for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. We then perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient approach for geometry optimization and molecular dynamics within AFQMC.

- Authors:

- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23187-8795, USA

- Publication Date:

- Research Org.:
- College of William and Mary, Williamsburg, VA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1540205

- Alternate Identifier(s):
- OSTI ID: 1436372

- Grant/Contract Number:
- SC0001303; Grant no. DE-SC0001303

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 148; Journal Issue: 18; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Chemistry; Physics

### Citation Formats

```
Motta, Mario, and Zhang, Shiwei. Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo. United States: N. p., 2018.
Web. doi:10.1063/1.5029508.
```

```
Motta, Mario, & Zhang, Shiwei. Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo. United States. doi:10.1063/1.5029508.
```

```
Motta, Mario, and Zhang, Shiwei. Mon .
"Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo". United States. doi:10.1063/1.5029508. https://www.osti.gov/servlets/purl/1540205.
```

```
@article{osti_1540205,
```

title = {Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo},

author = {Motta, Mario and Zhang, Shiwei},

abstractNote = {We propose an algorithm for accurate, systematic, and scalable computation of interatomic forces within the auxiliary-field quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the method for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. We then perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient approach for geometry optimization and molecular dynamics within AFQMC.},

doi = {10.1063/1.5029508},

journal = {Journal of Chemical Physics},

number = 18,

volume = 148,

place = {United States},

year = {2018},

month = {5}

}

*Citation information provided by*

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Web of Science

Works referenced in this record:

##
NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations

journal, September 2010

- Valiev, M.; Bylaska, E. J.; Govind, N.
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