Optimization of atomic coordinates and lattice parameters remains a significant challenge to the wide use of stochastic electronic structure methods such as quantum Monte Carlo (QMC). Measurements of the forces and stress tensor by these methods contain statistical errors, challenging conventional gradient-based numerical optimization methods that assume deterministic results. Additionally, forces are not yet available for some methods, wavefunctions, and basis sets and when available may be expensive to compute to sufficiently high statistical accuracy near energy minima, where the energy surfaces are flat. Here, we explore the use of Gaussian process based techniques to sample the energy surfaces and reduce sensitivity to the statistical nature of the problem. We utilize Latin hypercube sampling, with the number of sampled energy points scaling quadratically with the number of optimized parameters. Furthermore, we show these techniques may be successfully applied to systems consisting of tens of parameters, demonstrating QMC optimization of a benzene molecule starting from a randomly perturbed, broken symmetry geometry.

- Publication Date:

- Grant/Contract Number:
- AC05-00OR22725

- Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 149; Journal Issue: 16; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

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

- Sponsoring Org:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS

- OSTI Identifier:
- 1480630

- Alternate Identifier(s):
- OSTI ID: 1480165

```
Archibald, Richard K., Krogel, Jaron T., and Kent, Paul R. C..
```*Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo*. United States: N. p.,
Web. doi:10.1063/1.5040584.

```
Archibald, Richard K., Krogel, Jaron T., & Kent, Paul R. C..
```*Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo*. United States. doi:10.1063/1.5040584.

```
Archibald, Richard K., Krogel, Jaron T., and Kent, Paul R. C.. 2018.
"Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo". United States.
doi:10.1063/1.5040584.
```

```
@article{osti_1480630,
```

title = {Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo},

author = {Archibald, Richard K. and Krogel, Jaron T. and Kent, Paul R. C.},

abstractNote = {Optimization of atomic coordinates and lattice parameters remains a significant challenge to the wide use of stochastic electronic structure methods such as quantum Monte Carlo (QMC). Measurements of the forces and stress tensor by these methods contain statistical errors, challenging conventional gradient-based numerical optimization methods that assume deterministic results. Additionally, forces are not yet available for some methods, wavefunctions, and basis sets and when available may be expensive to compute to sufficiently high statistical accuracy near energy minima, where the energy surfaces are flat. Here, we explore the use of Gaussian process based techniques to sample the energy surfaces and reduce sensitivity to the statistical nature of the problem. We utilize Latin hypercube sampling, with the number of sampled energy points scaling quadratically with the number of optimized parameters. Furthermore, we show these techniques may be successfully applied to systems consisting of tens of parameters, demonstrating QMC optimization of a benzene molecule starting from a randomly perturbed, broken symmetry geometry.},

doi = {10.1063/1.5040584},

journal = {Journal of Chemical Physics},

number = 16,

volume = 149,

place = {United States},

year = {2018},

month = {10}

}

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