Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces
Abstract
Though density-functional-theory-based first-principles methods have the potential to provide the accuracy and computational efficiency required for this task, recent benchmarking in hydrogen has shown that achieving this accuracy requires a judicious choice of functional, and a quantification of the errors introduced. In this work, we present a quantum Monte Carlo (QMC) -based benchmarking study of a wide range of density functionals for use in hydrogen-helium mixtures at thermodynamic conditions relevant for Jovian planets. Not only do we continue our program of benchmarking energetics and pressures, but we deploy QMC-based force estimators and use them to gain insight into how well the local liquid structure is captured by different density functionals. We find that TPSS, BLYP, and vdW-DF are the most accurate functionals by most metrics, and that the enthalpy, energy, and pressure errors are very well behaved as a function of helium concentration. Beyond this, we highlight and analyze the major error trends and relative differences exhibited by the major classes of functionals, and we estimate the magnitudes of these effects when possible
- Authors:
-
- Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Physics; Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Univ. of Grenoble (France)
- Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Physics
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Univ. of Illinois at Urbana-Champaign, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1325453
- Alternate Identifier(s):
- OSTI ID: 1235751; OSTI ID: 1241957; OSTI ID: 1358610
- Report Number(s):
- LLNL-JRNL-676457
Journal ID: ISSN 2469-9950; PRBMDO; KC0202030; ERKCK03
- Grant/Contract Number:
- AC05-00OR22725; AC52-07NA27344; NA0001789; NA0002911
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 93; Journal Issue: 3; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Clay, Raymond C., Holzmann, Markus, Ceperley, David M., and Morales, Miguel A. Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces. United States: N. p., 2016.
Web. doi:10.1103/PhysRevB.93.035121.
Clay, Raymond C., Holzmann, Markus, Ceperley, David M., & Morales, Miguel A. Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces. United States. https://doi.org/10.1103/PhysRevB.93.035121
Clay, Raymond C., Holzmann, Markus, Ceperley, David M., and Morales, Miguel A. Tue .
"Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces". United States. https://doi.org/10.1103/PhysRevB.93.035121. https://www.osti.gov/servlets/purl/1325453.
@article{osti_1325453,
title = {Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces},
author = {Clay, Raymond C. and Holzmann, Markus and Ceperley, David M. and Morales, Miguel A.},
abstractNote = {Though density-functional-theory-based first-principles methods have the potential to provide the accuracy and computational efficiency required for this task, recent benchmarking in hydrogen has shown that achieving this accuracy requires a judicious choice of functional, and a quantification of the errors introduced. In this work, we present a quantum Monte Carlo (QMC) -based benchmarking study of a wide range of density functionals for use in hydrogen-helium mixtures at thermodynamic conditions relevant for Jovian planets. Not only do we continue our program of benchmarking energetics and pressures, but we deploy QMC-based force estimators and use them to gain insight into how well the local liquid structure is captured by different density functionals. We find that TPSS, BLYP, and vdW-DF are the most accurate functionals by most metrics, and that the enthalpy, energy, and pressure errors are very well behaved as a function of helium concentration. Beyond this, we highlight and analyze the major error trends and relative differences exhibited by the major classes of functionals, and we estimate the magnitudes of these effects when possible},
doi = {10.1103/PhysRevB.93.035121},
journal = {Physical Review B},
number = 3,
volume = 93,
place = {United States},
year = {Tue Jan 19 00:00:00 EST 2016},
month = {Tue Jan 19 00:00:00 EST 2016}
}
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Works referenced in this record:
Defining and cataloging exoplanets: the exoplanet.eu database
journal, July 2011
- Schneider, J.; Dedieu, C.; Le Sidaner, P.
- Astronomy & Astrophysics, Vol. 532
Thermodynamics and phase separation of dense fully ionized hydrogen-helium fluid mixtures
journal, November 1975
- Stevenson, D. J.
- Physical Review B, Vol. 12, Issue 10
An Equation of State for Low-Mass Stars and Giant Planets
journal, July 1995
- Saumon, D.; Chabrier, G.; van Horn, H. M.
- The Astrophysical Journal Supplement Series, Vol. 99
Hydrogen-Helium Mixtures at Megabar Pressures: Implications for Jupiter and Saturn
journal, November 1991
- Klepeis, J. E.; Schafer, K. J.; Barbee, T. W.
- Science, Vol. 254, Issue 5034
Miscibility of Hydrogen and Helium under Astrophysical Conditions
journal, March 1995
- Pfaffenzeller, O.; Hohl, D.; Ballone, P.
- Physical Review Letters, Vol. 74, Issue 13
Demixing of Hydrogen and Helium at Megabar Pressures
journal, March 2009
- Lorenzen, Winfried; Holst, Bastian; Redmer, Ronald
- Physical Review Letters, Vol. 102, Issue 11
Metallization in hydrogen-helium mixtures
journal, December 2011
- Lorenzen, Winfried; Holst, Bastian; Redmer, Ronald
- Physical Review B, Vol. 84, Issue 23
Phase separation in hydrogen-helium mixtures at Mbar pressures
journal, January 2009
- Morales, M. A.; Schwegler, E.; Ceperley, D.
- Proceedings of the National Academy of Sciences, Vol. 106, Issue 5
Hydrogen-helium demixing from first principles: From diamond anvil cells to planetary interiors
journal, May 2013
- Morales, Miguel A.; Hamel, Sebastien; Caspersen, Kyle
- Physical Review B, Vol. 87, Issue 17
The phase diagram and transport properties for hydrogen-helium fluid planets
journal, October 1977
- Stevenson, D. J.; Salpeter, E. E.
- The Astrophysical Journal Supplement Series, Vol. 35
The dynamics and helium distribution in hydrogen-helium fluid planets
journal, October 1977
- Stevenson, D. J.; Salpeter, E. E.
- The Astrophysical Journal Supplement Series, Vol. 35
Phase separation in giant planets: inhomogeneous evolution of Saturn
journal, July 2003
- Fortney, Jonathan J.; Hubbard, William B.
- Icarus, Vol. 164, Issue 1
Inhomogeneous Models of Jupiter and Saturn: Inhomogeneous Models of Jupiter and Saturn
journal, January 2015
- Nettelmann, N.
- Contributions to Plasma Physics, Vol. 55, Issue 2-3
Nuclear Quantum Effects and Nonlocal Exchange-Correlation Functionals Applied to Liquid Hydrogen at High Pressure
journal, February 2013
- Morales, Miguel A.; McMahon, Jeffrey M.; Pierleoni, Carlo
- Physical Review Letters, Vol. 110, Issue 6
Towards a predictive first-principles description of solid molecular hydrogen with density functional theory
journal, May 2013
- Morales, Miguel A.; McMahon, Jeffrey M.; Pierleoni, Carlo
- Physical Review B, Vol. 87, Issue 18
Benchmarking exchange-correlation functionals for hydrogen at high pressures using quantum Monte Carlo
journal, May 2014
- Clay, Raymond C.; Mcminis, Jeremy; McMahon, Jeffrey M.
- Physical Review B, Vol. 89, Issue 18
Molecular to Atomic Phase Transition in Hydrogen under High Pressure
journal, March 2015
- McMinis, Jeremy; Clay, Raymond C.; Lee, Donghwa
- Physical Review Letters, Vol. 114, Issue 10
Distinct Metallization and Atomization Transitions in Dense Liquid Hydrogen
journal, March 2015
- Mazzola, Guglielmo; Sorella, Sandro
- Physical Review Letters, Vol. 114, Issue 10
Dissociation of High-Pressure Solid Molecular Hydrogen: A Quantum Monte Carlo and Anharmonic Vibrational Study
journal, April 2014
- Azadi, Sam; Monserrat, Bartomeu; Foulkes, W. M. C.
- Physical Review Letters, Vol. 112, Issue 16
Quantum Monte Carlo study of the phase diagram of solid molecular hydrogen at extreme pressures
journal, July 2015
- Drummond, N. D.; Monserrat, Bartomeu; Lloyd-Williams, Jonathan H.
- Nature Communications, Vol. 6, Issue 1
Fate of density functional theory in the study of high-pressure solid hydrogen
journal, July 2013
- Azadi, Sam; Foulkes, W. M. C.
- Physical Review B, Vol. 88, Issue 1
Ab initiomolecular dynamics for liquid metals
journal, January 1993
- Kresse, G.; Hafner, J.
- Physical Review B, Vol. 47, Issue 1, p. 558-561
Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium
journal, May 1994
- Kresse, G.; Hafner, J.
- Physical Review B, Vol. 49, Issue 20, p. 14251-14269
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
journal, July 1996
- Kresse, G.; Furthmüller, J.
- Computational Materials Science, Vol. 6, Issue 1, p. 15-50
Projector augmented-wave method
journal, December 1994
- Blöchl, P. E.
- Physical Review B, Vol. 50, Issue 24, p. 17953-17979
Generalized Gradient Approximation Made Simple
journal, October 1996
- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
journal, September 2009
- Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola
- Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502
Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
journal, April 2008
- Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gábor I.
- Physical Review Letters, Vol. 100, Issue 13
More accurate generalized gradient approximation for solids
journal, June 2006
- Wu, Zhigang; Cohen, R. E.
- Physical Review B, Vol. 73, Issue 23
A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions
journal, November 2006
- Zhao, Yan; Truhlar, Donald G.
- The Journal of Chemical Physics, Vol. 125, Issue 19, Article No. 194101
Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids
journal, September 2003
- Tao, Jianmin; Perdew, John P.; Staroverov, Viktor N.
- Physical Review Letters, Vol. 91, Issue 14
Higher-accuracy van der Waals density functional
journal, August 2010
- Lee, Kyuho; Murray, Éamonn D.; Kong, Lingzhu
- Physical Review B, Vol. 82, Issue 8
Van der Waals density functional: An appropriate exchange functional
journal, April 2010
- Cooper, Valentino R.
- Physical Review B, Vol. 81, Issue 16
Exchange functional that tests the robustness of the plasmon description of the van der Waals density functional
journal, January 2014
- Berland, Kristian; Hyldgaard, Per
- Physical Review B, Vol. 89, Issue 3
Chemical accuracy for the van der Waals density functional
journal, December 2009
- Klimeš, Jiří; Bowler, David R.; Michaelides, Angelos
- Journal of Physics: Condensed Matter, Vol. 22, Issue 2
Efficient pseudopotentials for plane-wave calculations
journal, January 1991
- Troullier, N.; Martins, José Luriaas
- Physical Review B, Vol. 43, Issue 3
Hybrid algorithms in quantum Monte Carlo
journal, December 2012
- Kim, Jeongnim; Esler, Kenneth P.; McMinis, Jeremy
- Journal of Physics: Conference Series, Vol. 402
Alleviation of the Fermion-Sign Problem by Optimization of Many-Body Wave Functions
journal, March 2007
- Umrigar, C. J.; Toulouse, Julien; Filippi, Claudia
- Physical Review Letters, Vol. 98, Issue 11
Computational Methods in Coupled Electron-Ion Monte Carlo Simulations
journal, September 2005
- Pierleoni, Carlo; Ceperley, David M.
- ChemPhysChem, Vol. 6, Issue 9
Accurate, Efficient, and Simple Forces Computed with Quantum Monte Carlo Methods
journal, January 2005
- Chiesa, Simone; Ceperley, D. M.; Zhang, Shiwei
- Physical Review Letters, Vol. 94, Issue 3
Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms
journal, June 2001
- Lin, C.; Zong, F. H.; Ceperley, D. M.
- Physical Review E, Vol. 64, Issue 1
Works referencing / citing this record:
Nuclear quantum effects induce metallization of dense solid molecular hydrogen
journal, November 2017
- Azadi, Sam; Singh, Ranber; Kühne, Thomas D.
- Journal of Computational Chemistry, Vol. 39, Issue 5
Extent of Fock-exchange mixing for a hybrid van der Waals density functional?
journal, May 2018
- Jiao, Yang; Schröder, Elsebeth; Hyldgaard, Per
- The Journal of Chemical Physics, Vol. 148, Issue 19
Quantum Monte Carlo assessment of density functionals for π -electron molecules: ethylene and bifuran
journal, August 2018
- Ospadov, Egor; Rothstein, Stuart M.; Baer, Roi
- Molecular Physics, Vol. 117, Issue 17
Theory of finite size effects for electronic quantum Monte Carlo calculations of liquids and solids
journal, July 2016
- Holzmann, Markus; Clay, Raymond C.; Morales, Miguel A.
- Physical Review B, Vol. 94, Issue 3
First-principles prediction of the softening of the silicon shock Hugoniot curve
journal, September 2016
- Hu, S. X.; Militzer, B.; Collins, L. A.
- Physical Review B, Vol. 94, Issue 9
Quantum molecular dynamics study on the proton exchange, ionic structures, and transport properties of warm dense hydrogen-deuterium mixtures
journal, June 2018
- Liu, Lei; Li, Zhi-Guo; Dai, Jia-Yu
- Physical Review E, Vol. 97, Issue 6
Nuclear Quantum Effects Induce Metallization of Dense Solid Molecular Hydrogen
preprint, January 2017
- Azadi, Sam; Singh, Ranber; Kühne, T. D.
- arXiv
QMCPACK : An open source ab initio Quantum Monte Carlo package for the electronic structure of atoms, molecules, and solids
text, January 2018
- Kim, Jeongnim; Baczewski, Andrew; Beaudet, Todd D.
- arXiv
Extent of Fock-exchange mixing for a hybrid van der Waals density functional?
text, January 2018
- Jiao, Yang; Schröder, Elsebeth; Hyldgaard, Per
- arXiv