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Title: Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo

Abstract

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.

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
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  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1480630
Alternate Identifier(s):
OSTI ID: 1480165
Grant/Contract Number:  
AC05-00OR22725
Resource 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)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

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., 2018. Web. doi:10.1063/1.5040584.
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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. https://doi.org/10.1063/1.5040584
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Archibald, Richard K., Krogel, Jaron T., and Kent, Paul R. C. Sun . "Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo". United States. https://doi.org/10.1063/1.5040584. https://www.osti.gov/servlets/purl/1480630.
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@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 = {Sun Oct 28 00:00:00 EDT 2018},
month = {Sun Oct 28 00:00:00 EDT 2018}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1063/1.5040584
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Cited by: 8 works
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Figures / Tables:

FIG. 1 FIG. 1: Depiction of the proposed optimization process, beginning with the initial domain, QMC evaluation of LHC samples, GP approximation as given in Eq. 4, and finally estimation of minimum and new search domain, such that $Ω$i+1 $\subset$ $Ω$i. The process is halted when the predicted minimum energies and configurationmore » parameters are sufficiently converged.« less
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    Structural, electronic, and magnetic properties of bulk and epitaxial LaCoO 3 through diffusion Monte Carlo
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