An efficient hybrid orbital representation for quantum Monte Carlo calculations

Luo, Ye; Esler, Kenneth P.; Kent, Paul R.  C.; Shulenburger, Luke

doi:10.1063/1.5037094

Title: An efficient hybrid orbital representation for quantum Monte Carlo calculations

Journal Article · Tue Aug 28 00:00:00 EDT 2018 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.5037094· OSTI ID:1470876

^[1]; Esler, Kenneth P. ^[2];

^[3];

^[4]

Argonne National Lab. (ANL), Argonne, IL (United States). Argonne Leadership Computing Facility
Stone Ridge Technology, Bel Air, MD (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences. Computational Sciences and Engineering Division
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). HEDP Theory Dept.

The scale and complexity of the quantum system to which real-space quantum Monte Carlo (QMC) can be applied in part depends on the representation and memory usage of the trial wavefunction. B-splines, the computationally most efficient basis set, can have memory requirements exceeding the capacity of a single computational node. This situation has traditionally forced a difficult choice of either using slow internode communication or a potentially less accurate but smaller basis set such as Gaussians. In this paper, we introduce a hybrid representation of the single particle orbitals that combine a localized atomic basis set around atomic cores and B-splines in the interstitial regions to reduce the memory usage while retaining the high speed of evaluation and either retaining or increasing overall accuracy. We present a benchmark calculation for NiO demonstrating a superior accuracy while using only one eighth of the memory required for conventional B-splines. Finally, the hybrid orbital representation therefore expands the overall range of systems that can be practically studied with QMC.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525; AC02-06CH11357; AC05-00OR22725

OSTI ID:: 1470876

Alternate ID(s):: OSTI ID: 1467143; OSTI ID: 1467389; OSTI ID: 1470892; OSTI ID: 1473622

Report Number(s):: SAND-2018-4780J

Journal Information:: Journal of Chemical Physics, Vol. 149, Issue 8; ISSN 0021-9606

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

Country of Publication:: United States

Language:: English

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Cited by: 4 works

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References (47)

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
Linear-scaling quantum Monte Carlo technique with non-orthogonal localized orbitals Alfè, D.; Gillan, M. J. Journal of Physics: Condensed Matter, Vol. 16, Issue 25 https://doi.org/10.1088/0953-8984/16/25/l01	journal	June 2004
Boosting the accuracy and speed of quantum Monte Carlo: Size consistency and time step Zen, Andrea; Sorella, Sandro; Gillan, Michael J. Physical Review B, Vol. 93, Issue 24 https://doi.org/10.1103/physrevb.93.241118	journal	June 2016
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502 https://doi.org/10.1088/0953-8984/21/39/395502	journal	September 2009
A comparison between quantum chemistry and quantum Monte Carlo techniques for the adsorption of water on the (001) LiH surface Tsatsoulis, Theodoros; Hummel, Felix; Usvyat, Denis The Journal of Chemical Physics, Vol. 146, Issue 20 https://doi.org/10.1063/1.4984048	journal	May 2017
Diffusion quantum Monte Carlo study of the equation of state and point defects in aluminum Hood, Randolph Q.; Kent, P. R. C.; Reboredo, Fernando A. Physical Review B, Vol. 85, Issue 13 https://doi.org/10.1103/physrevb.85.134109	journal	April 2012
Kinetic energy classification and smoothing for compact B-spline basis sets in quantum Monte Carlo Krogel, Jaron T.; Reboredo, Fernando A. The Journal of Chemical Physics, Vol. 148, Issue 4 https://doi.org/10.1063/1.4994817	journal	January 2018
Investigation of a Quantum Monte Carlo Protocol To Achieve High Accuracy and High-Throughput Materials Formation Energies Saritas, Kayahan; Mueller, Tim; Wagner, Lucas Journal of Chemical Theory and Computation, Vol. 13, Issue 5 https://doi.org/10.1021/acs.jctc.6b01179	journal	April 2017
Shape and energy consistent pseudopotentials for correlated electron systems Trail, J. R.; Needs, R. J. The Journal of Chemical Physics, Vol. 146, Issue 20 https://doi.org/10.1063/1.4984046	journal	May 2017
Diffusion quantum Monte Carlo calculations of SrFeO ₃ and LaFeO ₃ Santana, Juan A.; Krogel, Jaron T.; Kent, Paul R. C. The Journal of Chemical Physics, Vol. 147, Issue 3 https://doi.org/10.1063/1.4994083	journal	July 2017
Noncovalent Interactions by Quantum Monte Carlo Dubecký, Matúš; Mitas, Lubos; Jurečka, Petr Chemical Reviews, Vol. 116, Issue 9 https://doi.org/10.1021/acs.chemrev.5b00577	journal	April 2016
Fast and accurate quantum Monte Carlo for molecular crystals Zen, Andrea; Brandenburg, Jan Gerit; Klimeš, Jiří Proceedings of the National Academy of Sciences, Vol. 115, Issue 8 https://doi.org/10.1073/pnas.1715434115	journal	February 2018
Fully Quantum Description of the Zundel Ion: Combining Variational Quantum Monte Carlo with Path Integral Langevin Dynamics Mouhat, Félix; Sorella, Sandro; Vuilleumier, Rodolphe Journal of Chemical Theory and Computation, Vol. 13, Issue 6 https://doi.org/10.1021/acs.jctc.7b00017	journal	May 2017
MnNiO ₃ revisited with modern theoretical and experimental methods Dzubak, Allison L.; Mitra, Chandrima; Chance, Michael The Journal of Chemical Physics, Vol. 147, Issue 17 https://doi.org/10.1063/1.5000847	journal	November 2017
Discovering correlated fermions using quantum Monte Carlo Wagner, Lucas K.; Ceperley, David M. Reports on Progress in Physics, Vol. 79, Issue 9 https://doi.org/10.1088/0034-4885/79/9/094501	journal	August 2016
Carbon nanotubes as excitonic insulators Varsano, Daniele; Sorella, Sandro; Sangalli, Davide Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-01660-8	journal	November 2017
Comparison of polynomial approximations to speed up planewave-based quantum Monte Carlo calculations Parker, William D.; Umrigar, C. J.; Alfè, Dario Journal of Computational Physics, Vol. 287 https://doi.org/10.1016/j.jcp.2015.01.037	journal	April 2015
Pseudopotentials for quantum Monte Carlo studies of transition metal oxides Krogel, Jaron T.; Santana, Juan A.; Reboredo, Fernando A. Physical Review B, Vol. 93, Issue 7 https://doi.org/10.1103/physrevb.93.075143	journal	February 2016
Electronic Structure Martin, Richard M. https://doi.org/10.1017/CBO9780511805769	book	January 2004
Evidence for stable square ice from quantum Monte Carlo Chen, Ji; Zen, Andrea; Brandenburg, Jan Gerit Physical Review B, Vol. 94, Issue 22 https://doi.org/10.1103/physrevb.94.220102	journal	December 2016
Quantitative estimation of localization errors of 3 d transition metal pseudopotentials in diffusion Monte Carlo Dzubak, Allison L.; Krogel, Jaron T.; Reboredo, Fernando A. The Journal of Chemical Physics, Vol. 147, Issue 2 https://doi.org/10.1063/1.4991414	journal	July 2017
Accelerating Quantum Monte Carlo Simulations of Real Materials on GPU Clusters Esler, Kenneth; Kim, Jeongnim; Ceperley, David Computing in Science & Engineering, Vol. 14, Issue 1 https://doi.org/10.1109/mcse.2010.122	journal	January 2012
Magnitude of pseudopotential localization errors in fixed node diffusion quantum Monte Carlo Krogel, Jaron T.; Kent, P. R. C. The Journal of Chemical Physics, Vol. 146, Issue 24 https://doi.org/10.1063/1.4986951	journal	June 2017
Diffusion Monte Carlo Perspective on the Spin-State Energetics of [Fe(NCH) ₆ ] ²⁺ Fumanal, Maria; Wagner, Lucas K.; Sanvito, Stefano Journal of Chemical Theory and Computation, Vol. 12, Issue 9 https://doi.org/10.1021/acs.jctc.6b00332	journal	August 2016
Accurate barrier heights using diffusion Monte Carlo Krongchon, Kittithat; Busemeyer, Brian; Wagner, Lucas K. The Journal of Chemical Physics, Vol. 146, Issue 12 https://doi.org/10.1063/1.4979059	journal	March 2017
Application of Diffusion Monte Carlo to Materials Dominated by van der Waals Interactions Benali, Anouar; Shulenburger, Luke; Romero, Nichols A. Journal of Chemical Theory and Computation, Vol. 10, Issue 8 https://doi.org/10.1021/ct5003225	journal	June 2014
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
Quantum Monte Carlo study of the energetics of the rutile, anatase, brookite, and columbite ${TiO}_{2}$ polymorphs Trail, John; Monserrat, Bartomeu; López Ríos, Pablo Physical Review B, Vol. 95, Issue 12 https://doi.org/10.1103/physrevb.95.121108	journal	March 2017
Continuum variational and diffusion quantum Monte Carlo calculations Needs, R. J.; Towler, M. D.; Drummond, N. D. Journal of Physics: Condensed Matter, Vol. 22, Issue 2 https://doi.org/10.1088/0953-8984/22/2/023201	journal	December 2009
Phase stability of TiO ₂ polymorphs from diffusion Quantum Monte Carlo Luo, Ye; Benali, Anouar; Shulenburger, Luke New Journal of Physics, Vol. 18, Issue 11 https://doi.org/10.1088/1367-2630/18/11/113049	journal	November 2016
Shape and energy consistent pseudopotentials for correlated electron systems Trail, John; Needs, Richard Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.9998	text	January 2017
Quantum Monte Carlo study of the energetics of the rutile, anatase, brookite, and columbite TiO$_{2}$ polymorphs Trail, John; Monserrat Sanchez, Bartomeu; López Ríos, P. Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.9937	text	January 2017
Advanced capabilities for materials modelling with Quantum ESPRESSO Unknown, (:Unkn) My University https://doi.org/10.34944/dspace/4844	text	January 2017
Phase Diagram of Hydrogen and a Hydrogen-Helium Mixture at Planetary Conditions by Quantum Monte Carlo Simulations Mazzola, Guglielmo; Helled, Ravit; Sorella, Sandro American Physical Society https://doi.org/10.5167/uzh-157116	text	January 2018
Phase diagram of hydrogen and a hydrogen-helium mixture at planetary conditions by Quantum Monte Carlo simulations Mazzola, Guglielmo; Helled, Ravit; Sorella, Sandro ETH Zurich https://doi.org/10.3929/ethz-b-000224874	text	January 2017
Electronic Structure Martin, Richard M. https://doi.org/10.1017/9781108555586	book	September 2020
Shock Response and Phase Transitions of MgO at Planetary Impact Conditions Root, Seth; Shulenburger, Luke; Lemke, Raymond W. arXiv https://doi.org/10.48550/arxiv.1502.00009	text	January 2015
Trail-Needs pseudopotentials in quantum Monte Carlo calculations with plane-wave/blip basis sets Drummond, N. D.; Trail, J. R.; Needs, R. J. arXiv https://doi.org/10.48550/arxiv.1607.01544	text	January 2016
Fully quantum description of the Zundel ion: combining variational quantum Monte Carlo with path integral Langevin dynamics Mouhat, Félix; Sorella, Sandro; Vuilleumier, Rodolphe arXiv https://doi.org/10.48550/arxiv.1701.03392	text	January 2017
Carbon nanotubes as excitonic insulators Varsano, Daniele; Sorella, Sandro; Sangalli, Davide arXiv https://doi.org/10.48550/arxiv.1703.09235	text	January 2017
Magnitude of pseudopotential localization errors in fixed node diffusion quantum Monte Carlo Krogel, Jaron T.; Kent, Paul R. C. arXiv https://doi.org/10.48550/arxiv.1703.10450	text	January 2017
Diffusion quantum Monte Carlo calculations of SrFeO${_3}$ and LaFeO${_3}$ Santana, Juan A.; Krogel, Jaron T.; Kent, Paul R. C. arXiv https://doi.org/10.48550/arxiv.1704.09008	text	January 2017
Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods Motta, Mario; Ceperley, David M.; Chan, Garnet Kin-Lic arXiv https://doi.org/10.48550/arxiv.1705.01608	text	January 2017
Advanced capabilities for materials modelling with Quantum ESPRESSO Giannozzi, P.; Andreussi, O.; Brumme, T. arXiv https://doi.org/10.48550/arxiv.1709.10010	text	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
An efficient localized basis set for quantum Monte Carlo calculations on condensed matter Alfè, D.; Gillan, M. J. arXiv https://doi.org/10.48550/arxiv.cond-mat/0407037	text	January 2004
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

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