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

Archibald, Richard K.; Krogel, Jaron T.; Kent, Paul R. C.

doi:10.1063/1.5040584

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

Journal Article · Sun Oct 28 00:00:00 EDT 2018 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.5040584· OSTI ID:1480630

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Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

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.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1480630

Alternate ID(s):: OSTI ID: 1480165

Journal Information:: Journal of Chemical Physics, Vol. 149, Issue 16; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 8 works

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References (44)

Solvent Effects on Excited-State Structures: A Quantum Monte Carlo and Density Functional Study Guareschi, Riccardo; Floris, Franca Maria; Amovilli, Claudio Journal of Chemical Theory and Computation, Vol. 10, Issue 12 https://doi.org/10.1021/ct500723s	journal	November 2014
Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo Motta, Mario; Zhang, Shiwei The Journal of Chemical Physics, Vol. 148, Issue 18 https://doi.org/10.1063/1.5029508	journal	May 2018
Monte-Carlo solution of Schrödinger's equation Grimm, R. C.; Storer, R. G. Journal of Computational Physics, Vol. 7, Issue 1 https://doi.org/10.1016/0021-9991(71)90054-4	journal	February 1971
Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space Booth, George H.; Thom, Alex J. W.; Alavi, Ali The Journal of Chemical Physics, Vol. 131, Issue 5 https://doi.org/10.1063/1.3193710	journal	January 2009
Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo Zen, Andrea; Luo, Ye; Mazzola, Guglielmo The Journal of Chemical Physics, Vol. 142, Issue 14 https://doi.org/10.1063/1.4917171	journal	April 2015
Construction of reactive potential energy surfaces with Gaussian process regression: active data selection Guan, Yafu; Yang, Shuo; Zhang, Dong H. Molecular Physics, Vol. 116, Issue 7-8 https://doi.org/10.1080/00268976.2017.1407460	journal	November 2017
Sequential Exploration of Complex Surfaces Using Minimum Energy Designs Joseph, V. Roshan; Dasgupta, Tirthankar; Tuo, Rui Technometrics, Vol. 57, Issue 1 https://doi.org/10.1080/00401706.2014.881749	journal	January 2015
Stochastic Coupled Cluster Theory Thom, Alex J. W. Physical Review Letters, Vol. 105, Issue 26 https://doi.org/10.1103/physrevlett.105.263004	journal	December 2010
Bayesian Treed Gaussian Process Models With an Application to Computer Modeling Gramacy, Robert B.; Lee, Herbert K. H. Journal of the American Statistical Association, Vol. 103, Issue 483 https://doi.org/10.1198/016214508000000689	journal	September 2008
General atomic and molecular electronic structure system Schmidt, Michael W.; Baldridge, Kim K.; Boatz, Jerry A. Journal of Computational Chemistry, Vol. 14, Issue 11, p. 1347-1363 https://doi.org/10.1002/jcc.540141112	journal	November 1993
The Design and Analysis of Computer Experiments Santner, Thomas J.; Williams, Brian J.; Notz, William I. Springer Series in Statistics https://doi.org/10.1007/978-1-4757-3799-8	book	January 2003
Bayesian calibration of computer models Kennedy, Marc C.; O'Hagan, Anthony Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 63, Issue 3 https://doi.org/10.1111/1467-9868.00294	journal	August 2001
Machine learning unifies the modeling of materials and molecules Bartók, Albert P.; De, Sandip; Poelking, Carl Science Advances, Vol. 3, Issue 12 https://doi.org/10.1126/sciadv.1701816	journal	December 2017
A Blocked Linear Method for Optimizing Large Parameter Sets in Variational Monte Carlo Zhao, Luning; Neuscamman, Eric Journal of Chemical Theory and Computation, Vol. 13, Issue 6 https://doi.org/10.1021/acs.jctc.7b00119	journal	May 2017
Correlated sampling in quantum Monte Carlo: A route to forces Filippi, Claudia; Umrigar, C. J. Physical Review B, Vol. 61, Issue 24 https://doi.org/10.1103/physrevb.61.r16291	journal	June 2000
Electronic quantum Monte Carlo calculations of atomic forces, vibrations, and anharmonicities Lee, Myung Won; Mella, Massimo; Rappe, Andrew M. The Journal of Chemical Physics, Vol. 122, Issue 24 https://doi.org/10.1063/1.1924690	journal	June 2005
A reactive potential for hydrocarbons with intermolecular interactions Stuart, Steven J.; Tutein, Alan B.; Harrison, Judith A. The Journal of Chemical Physics, Vol. 112, Issue 14 https://doi.org/10.1063/1.481208	journal	April 2000
Generalized Latin Hypercube Design for Computer Experiments Dette, Holger; Pepelyshev, Andrey Technometrics, Vol. 52, Issue 4 https://doi.org/10.1198/TECH.2010.09157	journal	November 2010
Energy-consistent pseudopotentials for quantum Monte Carlo calculations Burkatzki, M.; Filippi, C.; Dolg, M. The Journal of Chemical Physics, Vol. 126, Issue 23 https://doi.org/10.1063/1.2741534	journal	June 2007
Theory of reproducing kernels Aronszajn, N. Transactions of the American Mathematical Society, Vol. 68, Issue 3 https://doi.org/10.1090/s0002-9947-1950-0051437-7	journal	March 1950
Practical Schemes for Accurate Forces in Quantum Monte Carlo Moroni, S.; Saccani, S.; Filippi, C. Journal of Chemical Theory and Computation, Vol. 10, Issue 11 https://doi.org/10.1021/ct500780r	journal	October 2014
Electronic Structure Martin, Richard M. https://doi.org/10.1017/CBO9780511805769	book	January 2004
Computing forces with quantum Monte Carlo Assaraf, Roland; Caffarel, Michel The Journal of Chemical Physics, Vol. 113, Issue 10 https://doi.org/10.1063/1.1286598	journal	September 2000
Theoretical S ₁ ← S ₀ Absorption Energies of the Anionic Forms of Oxyluciferin by Variational Monte Carlo and Many-Body Green’s Function Theory Coccia, Emanuele; Varsano, Daniele; Guidoni, Leonardo Journal of Chemical Theory and Computation, Vol. 13, Issue 9 https://doi.org/10.1021/acs.jctc.7b00505	journal	August 2017
Optimizing the Energy with Quantum Monte Carlo: A Lower Numerical Scaling for Jastrow–Slater Expansions Assaraf, Roland; Moroni, S.; Filippi, Claudia Journal of Chemical Theory and Computation, Vol. 13, Issue 11 https://doi.org/10.1021/acs.jctc.7b00648	journal	October 2017
Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F. The Journal of Physical Chemistry, Vol. 98, Issue 45, p. 11623-11627 https://doi.org/10.1021/j100096a001	journal	November 1994
Ground State of Liquid ${He}^{4}$ McMillan, W. L. Physical Review, Vol. 138, Issue 2A https://doi.org/10.1103/physrev.138.a442	journal	April 1965
Accurate emulators for large-scale computer experiments Haaland, Ben; Qian, Peter Z. G. The Annals of Statistics, Vol. 39, Issue 6 https://doi.org/10.1214/11-aos929	journal	December 2011
Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo Thomas, Robert E.; Opalka, Daniel; Overy, Catherine The Journal of Chemical Physics, Vol. 143, Issue 5 https://doi.org/10.1063/1.4927594	journal	August 2015
Nexus: A modular workflow management system for quantum simulation codes Krogel, Jaron T. Computer Physics Communications, Vol. 198 https://doi.org/10.1016/j.cpc.2015.08.012	journal	January 2016
Quantum Monte Carlo Calculations for Minimum Energy Structures Wagner, Lucas K.; Grossman, Jeffrey C. Physical Review Letters, Vol. 104, Issue 21 https://doi.org/10.1103/physrevlett.104.210201	journal	May 2010
Geometries of low spin states of multi-centre transition metal complexes through extended broken symmetry variational Monte Carlo Barborini, Matteo; Guidoni, Leonardo The Journal of Chemical Physics, Vol. 145, Issue 12 https://doi.org/10.1063/1.4963015	journal	September 2016
Computing accurate forces in quantum Monte Carlo using Pulay’s corrections and energy minimization Casalegno, Mosé; Mella, Massimo; Rappe, Andrew M. The Journal of Chemical Physics, Vol. 118, Issue 16 https://doi.org/10.1063/1.1562605	journal	January 2003
Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code McKay, M. D.; Beckman, R. J.; Conover, W. J. Technometrics, Vol. 21, Issue 2 https://doi.org/10.1080/00401706.1979.10489755	journal	May 1979
Gaussian Processes for Machine Learning Rasmussen, Carl Edward; Williams, Christopher K. I. The MIT Press https://doi.org/10.7551/mitpress/3206.001.0001	book	January 2005
The Design and Analysis of Computer Experiments Santner, Thomas J.; Williams, Brian J.; Notz, William I. Springer Series in Statistics https://doi.org/10.1007/978-1-4939-8847-1	book	January 2018
Machine learning unifies the modeling of materials and molecules. Bartók, Albert P.; De, Sandip; Poelking, Carl Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.21944	text	January 2017
Generalized latin hypercube design for computer experiments Dette, Holger; Pepelyshev, Andrey Technische Universität Dortmund https://doi.org/10.17877/de290r-12659	text	January 2009
Electronic Structure Martin, Richard M. https://doi.org/10.1017/9781108555586	book	September 2020
A Blocked Linear Method for Optimizing Large Parameter Sets in Variational Monte Carlo Zhao, Luning; Neuscamman, Eric arXiv https://doi.org/10.48550/arxiv.1702.01481	preprint	January 2017
QMCPACK : An open source ab initio Quantum Monte Carlo package for the electronic structure of atoms, molecules, and solids Kim, Jeongnim; Baczewski, Andrew; Beaudet, Todd D. arXiv https://doi.org/10.48550/arxiv.1802.06922	text	January 2018
Alleviation of the Fermion-sign problem by optimization of many-body wave functions Umrigar, C. J.; Toulouse, Julien; Filippi, Claudia arXiv https://doi.org/10.48550/arxiv.cond-mat/0611094	text	January 2006
A Constrained Path Monte Carlo Method for Fermion Ground States Zhang, Shiwei; Carlson, J.; Gubernatis, J. E. arXiv https://doi.org/10.48550/arxiv.cond-mat/9607062	text	January 1996
Correlated sampling in quantum Monte Carlo: a route to forces Filippi, Claudia; Umrigar, C. J. arXiv https://doi.org/10.48550/arxiv.cond-mat/9911326	text	January 1999

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