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Title: Deuterium Hugoniot: Pitfalls of thermodynamic sampling beyond density functional theory

Abstract

Outstanding problems in the high-pressure phase diagram of hydrogen have demonstrated the need for more accurate ab initio methods for thermodynamic sampling. One promising method that has been deployed extensively above 100 GPa is coupled electron-ion Monte Carlo (CEIMC), which treats the electronic structure with quantum Monte Carlo (QMC). However, CEIMC predictions of the deuterium principal Hugoniot disagree significantly with experiment, overshooting the experimentally determined peak compression density by 7% and lower temperature gas-gun data by well over 20%. By deriving an equation relating the predicted Hugoniot density to underlying equation of state errors, we show that QMC and many-body methods can easily spoil the error cancellation properties inherent in the Rankine-Hugoniot relation, and very likely suffer from error addition. By cross validating QMC based on systematically improvable trial functions against post-Hartree-Fock many-body methods, we find that these methods introduce errors of the right sign and magnitude to account for much of the observed discrepancy between CEIMC and experiment. In conclusion, we stress that this is not just a CEIMC problem, but that thermodynamic sampling based on other many-body methods is likely to experience similar difficulties.

Authors:
 [1];  [1];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Pulsed Power Sciences Center
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1574698
Alternate Identifier(s):
OSTI ID: 1546843
Report Number(s):
SAND-2019-9668J
Journal ID: ISSN 2469-9950; PRBMDO; 678577
Grant/Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 100; Journal Issue: 7; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Clay, III, Raymond C., Desjarlais, Michael P., and Shulenburger, Luke. Deuterium Hugoniot: Pitfalls of thermodynamic sampling beyond density functional theory. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.100.075103.
Clay, III, Raymond C., Desjarlais, Michael P., & Shulenburger, Luke. Deuterium Hugoniot: Pitfalls of thermodynamic sampling beyond density functional theory. United States. doi:10.1103/PhysRevB.100.075103.
Clay, III, Raymond C., Desjarlais, Michael P., and Shulenburger, Luke. Thu . "Deuterium Hugoniot: Pitfalls of thermodynamic sampling beyond density functional theory". United States. doi:10.1103/PhysRevB.100.075103.
@article{osti_1574698,
title = {Deuterium Hugoniot: Pitfalls of thermodynamic sampling beyond density functional theory},
author = {Clay, III, Raymond C. and Desjarlais, Michael P. and Shulenburger, Luke},
abstractNote = {Outstanding problems in the high-pressure phase diagram of hydrogen have demonstrated the need for more accurate ab initio methods for thermodynamic sampling. One promising method that has been deployed extensively above 100 GPa is coupled electron-ion Monte Carlo (CEIMC), which treats the electronic structure with quantum Monte Carlo (QMC). However, CEIMC predictions of the deuterium principal Hugoniot disagree significantly with experiment, overshooting the experimentally determined peak compression density by 7% and lower temperature gas-gun data by well over 20%. By deriving an equation relating the predicted Hugoniot density to underlying equation of state errors, we show that QMC and many-body methods can easily spoil the error cancellation properties inherent in the Rankine-Hugoniot relation, and very likely suffer from error addition. By cross validating QMC based on systematically improvable trial functions against post-Hartree-Fock many-body methods, we find that these methods introduce errors of the right sign and magnitude to account for much of the observed discrepancy between CEIMC and experiment. In conclusion, we stress that this is not just a CEIMC problem, but that thermodynamic sampling based on other many-body methods is likely to experience similar difficulties.},
doi = {10.1103/PhysRevB.100.075103},
journal = {Physical Review B},
number = 7,
volume = 100,
place = {United States},
year = {2019},
month = {8}
}

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Works referenced in this record:

High-Precision Shock Wave Measurements of Deuterium: Evaluation of Exchange-Correlation Functionals at the Molecular-to-Atomic Transition
journal, January 2017


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
  • DOI: 10.1103/PhysRevLett.77.3865

P y SCF: the Python-based simulations of chemistry framework : The PySCF program
journal, September 2017

  • Sun, Qiming; Berkelbach, Timothy C.; Blunt, Nick S.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 1
  • DOI: 10.1002/wcms.1340

Using perturbatively selected configuration interaction in quantum Monte Carlo calculations
journal, September 2013

  • Giner, Emmanuel; Scemama, Anthony; Caffarel, Michel
  • Canadian Journal of Chemistry, Vol. 91, Issue 9
  • DOI: 10.1139/cjc-2013-0017

Absolute Equation of State Measurements on Shocked Liquid Deuterium up to 200 GPa (2 Mbar)
journal, January 1997


Molecular-Atomic Transition along the Deuterium Hugoniot Curve with Coupled Electron-Ion Monte Carlo Simulations
journal, July 2015


First Principles Methods: A Perspective from Quantum Monte Carlo
journal, December 2013

  • Morales, Miguel; Clay, Raymond; Pierleoni, Carlo
  • Entropy, Vol. 16, Issue 1
  • DOI: 10.3390/e16010287

Quantum Monte Carlo simulations of solids
journal, January 2001


Comparison between x-ray scattering and velocity-interferometry measurements from shocked liquid deuterium
journal, April 2013


From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999


Unexpectedly high pressure for molecular dissociation in liquid hydrogen by electronic simulation
journal, March 2014

  • Mazzola, Guglielmo; Yunoki, Seiji; Sorella, Sandro
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms4487

Liquid–liquid phase transition in hydrogen by coupled electron–ion Monte Carlo simulations
journal, April 2016

  • Pierleoni, Carlo; Morales, Miguel A.; Rillo, Giovanni
  • Proceedings of the National Academy of Sciences, Vol. 113, Issue 18
  • DOI: 10.1073/pnas.1603853113

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
  • DOI: 10.1088/0953-8984/22/2/022201

Laser-driven single shock compression of fluid deuterium from 45 to 220 GPa
journal, January 2009


Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 90, Issue 2
  • DOI: 10.1063/1.456153

Accelerating ab initio Molecular Dynamics and Probing the Weak Dispersive Forces in Dense Liquid Hydrogen
journal, January 2017


Coupled electron-ion Monte Carlo simulation of hydrogen molecular crystals
journal, March 2018

  • Rillo, Giovanni; Morales, Miguel A.; Ceperley, David M.
  • The Journal of Chemical Physics, Vol. 148, Issue 10
  • DOI: 10.1063/1.5001387

Phase transitions under shock-wave loading
journal, July 1977


The properties of hydrogen and helium under extreme conditions
journal, November 2012

  • McMahon, Jeffrey M.; Morales, Miguel A.; Pierleoni, Carlo
  • Reviews of Modern Physics, Vol. 84, Issue 4
  • DOI: 10.1103/RevModPhys.84.1607

Ab initiomolecular dynamics for liquid metals
journal, January 1993


Thermophysical properties of warm dense hydrogen using quantum molecular dynamics simulations
journal, May 2008


Towards a predictive first-principles description of solid molecular hydrogen with density functional theory
journal, May 2013


Evidence for a first-order liquid-liquid transition in high-pressure hydrogen from ab initio simulations
journal, June 2010

  • Morales, M. A.; Pierleoni, C.; Schwegler, E.
  • Proceedings of the National Academy of Sciences, Vol. 107, Issue 29
  • DOI: 10.1073/pnas.1007309107

Equation of State Measurements in Liquid Deuterium to 70 GPa
journal, November 2001


Benchmarking exchange-correlation functionals for hydrogen at high pressures using quantum Monte Carlo
journal, May 2014


Alleviation of the Fermion-Sign Problem by Optimization of Many-Body Wave Functions
journal, March 2007


Coupled-cluster theory in quantum chemistry
journal, February 2007


Optical Properties of Fluid Hydrogen at the Transition to a Conducting State
journal, June 2016


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
  • DOI: 10.1038/ncomms8794

Density-functional calculations of the liquid deuterium Hugoniot, reshock, and reverberation timing
journal, August 2003


Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants
journal, April 2003


General atomic and molecular electronic structure system
journal, November 1993

  • Schmidt, Michael W.; Baldridge, Kim K.; Boatz, Jerry A.
  • Journal of Computational Chemistry, Vol. 14, Issue 11, p. 1347-1363
  • DOI: 10.1002/jcc.540141112

Size Consistency Error in the Antisymmetric Geminal Power Wave Function can be Completely Removed
journal, November 2012


Higher-accuracy van der Waals density functional
journal, August 2010


Dissociation of High-Pressure Solid Molecular Hydrogen: A Quantum Monte Carlo and Anharmonic Vibrational Study
journal, April 2014


Comment on “Observation of the Wigner-Huntington transition to metallic hydrogen”
journal, August 2017

  • Liu, Xiao-Di; Dalladay-Simpson, Philip; Howie, Ross T.
  • Science, Vol. 357, Issue 6353
  • DOI: 10.1126/science.aan2286

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996


Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium
journal, May 1994


Free energy methods in coupled electron ion Monte Carlo
journal, December 2011


Coupled Electron-Ion Monte Carlo Calculations of Dense Metallic Hydrogen
journal, September 2004


Direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium
journal, June 2015


Self-consistent measurement of the equation of state of liquid deuterium
journal, March 2012


Accurate and simple analytic representation of the electron-gas correlation energy
journal, June 1992


Distinct Metallization and Atomization Transitions in Dense Liquid Hydrogen
journal, March 2015


Molecular to Atomic Phase Transition in Hydrogen under High Pressure
journal, March 2015


Fate of density functional theory in the study of high-pressure solid hydrogen
journal, July 2013


Geminal wave functions with Jastrow correlation: A first application to atoms
journal, October 2003

  • Casula, Michele; Sorella, Sandro
  • The Journal of Chemical Physics, Vol. 119, Issue 13
  • DOI: 10.1063/1.1604379

Conductivity and dissociation in liquid metallic hydrogen and implications for planetary interiors
journal, October 2017

  • Zaghoo, Mohamed; Silvera, Isaac F.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 45
  • DOI: 10.1073/pnas.1707918114

Observation of the Wigner-Huntington transition to metallic hydrogen
journal, January 2017


Towards an exact description of electronic wavefunctions in real solids
journal, December 2012

  • Booth, George H.; Grüneis, Andreas; Kresse, Georg
  • Nature, Vol. 493, Issue 7432
  • DOI: 10.1038/nature11770

QMCPACK : an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids
journal, April 2018

  • Kim, Jeongnim; Baczewski, Andrew D.; Beaudet, Todd D.
  • Journal of Physics: Condensed Matter, Vol. 30, Issue 19
  • DOI: 10.1088/1361-648X/aab9c3

Extension of the Hugoniot and analytical release model of α -quartz to 0.2–3 TPa
journal, July 2017

  • Desjarlais, M. P.; Knudson, M. D.; Cochrane, K. R.
  • Journal of Applied Physics, Vol. 122, Issue 3
  • DOI: 10.1063/1.4991814

Nuclear Quantum Effects and Nonlocal Exchange-Correlation Functionals Applied to Liquid Hydrogen at High Pressure
journal, February 2013


Shock compression of liquid deuterium up to 109 GPa
journal, March 2005


Iterative backflow renormalization procedure for many-body ground-state wave functions of strongly interacting normal Fermi liquids
journal, March 2015


Temperature measurements and dissociation of shock-compressed liquid deuterium and hydrogen
journal, December 1995


Multiphase equation of state of hydrogen from ab initio calculations in the range 0.2 to 5 g/cc up to 10 eV
journal, March 2011


Evidence of a first-order phase transition to metallic hydrogen
journal, April 2016