High temperature melting of dense molecular hydrogen from machine-learning interatomic potentials trained on quantum Monte Carlo

Goswami, Shubhang; Jensen, Scott; Yang, Yubo; Holzmann, Markus; Pierleoni, Carlo; Ceperley, David M.

doi:10.1063/5.0250686

High temperature melting of dense molecular hydrogen from machine-learning interatomic potentials trained on quantum Monte Carlo

Journal Article · Wed Feb 05 00:00:00 EST 2025 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/5.0250686· OSTI ID:2561243

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University of Illinois Urbana-Champaign, IL (United States); University of Illinois
University of Illinois Urbana-Champaign, IL (United States)
Flatiron Institute, New York, NY (United States); Hofstra University, Hempstead, NY (United States)
Univ. Grenoble Alpes (France)
University of L’Aquila (Italy)

We present results and discuss methods for computing the melting temperature of dense molecular hydrogen using a machine learned model trained on quantum Monte Carlo data. In this newly trained model, we emphasize the importance of accurate total energies in the training. We integrate a two phase method for estimating the melting temperature with estimates from the Clausius–Clapeyron relation to provide a more accurate melting curve from the model. We make detailed predictions of the melting temperature, solid and liquid volumes, latent heat, and internal energy from 50 to 180 GPa for both classical hydrogen and quantum hydrogen. At pressures of roughly 173 GPa and 1635 K, we observe molecular dissociation in the liquid phase. Here, we compare with previous simulations and experimental measurements.

View Accepted Manuscript (DOE)

Research Organization:: University of Illinois Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE)

Grant/Contract Number:: SC0021177

OSTI ID:: 2561243

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 5 Vol. 162; ISSN 0021-9606

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

Country of Publication:: United States

Language:: English

References (57)

Benchmarking vdW-DF first-principles predictions against Coupled Electron-Ion Monte Carlo for high-pressure liquid hydrogen Gorelov, Vitaly; Pierleoni, Carlo; Ceperley, David M. Contributions to Plasma Physics, Vol. 59, Issue 4-5 https://doi.org/10.1002/ctpp.201800185	journal	February 2019
Trial wave functions for high-pressure metallic hydrogen Pierleoni, Carlo; Delaney, Kris T.; Morales, Miguel A. Computer Physics Communications, Vol. 179, Issue 1-3 https://doi.org/10.1016/j.cpc.2008.01.041	journal	July 2008
i-PI: A Python interface for ab initio path integral molecular dynamics simulations Ceriotti, Michele; More, Joshua; Manolopoulos, David E. Computer Physics Communications, Vol. 185, Issue 3 https://doi.org/10.1016/j.cpc.2013.10.027	journal	March 2014
LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales Thompson, Aidan P.; Aktulga, H. Metin; Berger, Richard Computer Physics Communications, Vol. 271 https://doi.org/10.1016/j.cpc.2021.108171	journal	February 2022
A comprehensive investigation on the accuracy and efficiency of methods for melting temperature calculation using molecular dynamics simulations Wang, Xinwei; Yang, Mengxin; Gai, Xiaoqian Journal of Molecular Liquids, Vol. 395 https://doi.org/10.1016/j.molliq.2023.123924	journal	February 2024
Anomalous Melting Behavior of Solid Hydrogen at High Pressures Liu, Hanyu; Hernández, Eduardo R.; Yan, Jun The Journal of Physical Chemistry C, Vol. 117, Issue 22 https://doi.org/10.1021/jp403885h	journal	May 2013
A quantum fluid of metallic hydrogen suggested by first-principles calculations Bonev, Stanimir A.; Schwegler, Eric; Ogitsu, Tadashi Nature, Vol. 431, Issue 7009 https://doi.org/10.1038/nature02968	journal	October 2004
Raman spectroscopy of hot hydrogen above 200 GPa Howie, Ross T.; Dalladay-Simpson, Philip; Gregoryanz, Eugene Nature Materials, Vol. 14, Issue 5 https://doi.org/10.1038/nmat4213	journal	February 2015
Understanding high pressure molecular hydrogen with a hierarchical machine-learned potential Zong, Hongxiang; Wiebe, Heather; Ackland, Graeme J. Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-18788-9	journal	October 2020
Ultrahigh-pressure isostructural electronic transitions in hydrogen Ji, Cheng; Li, Bing; Liu, Wenjun Nature, Vol. 573, Issue 7775 https://doi.org/10.1038/s41586-019-1565-9	journal	September 2019
Evidence for supercritical behaviour of high-pressure liquid hydrogen Cheng, Bingqing; Mazzola, Guglielmo; Pickard, Chris J. Nature, Vol. 585, Issue 7824 https://doi.org/10.1038/s41586-020-2677-y	journal	September 2020
On the Possibility of a Metallic Modification of Hydrogen Wigner, E.; Huntington, H. B. The Journal of Chemical Physics, Vol. 3, Issue 12 https://doi.org/10.1063/1.1749590	journal	December 1935
Liquid-solid transition in fully ionized hydrogen at ultra-high pressures Liberatore, Elisa; Pierleoni, Carlo; Ceperley, D. M. The Journal of Chemical Physics, Vol. 134, Issue 18 https://doi.org/10.1063/1.3586808	journal	May 2011
A comparison of methods for melting point calculation using molecular dynamics simulations Zhang, Yong; Maginn, Edward J. The Journal of Chemical Physics, Vol. 136, Issue 14 https://doi.org/10.1063/1.3702587	journal	April 2012
The isotropic intermolecular potential for H ₂ and D ₂ in the solid and gas phases Silvera, Isaac F.; Goldman, Victor V. The Journal of Chemical Physics, Vol. 69, Issue 9 https://doi.org/10.1063/1.437103	journal	November 1978
Theoretical calculation of thermodynamic properties and melting curves for hydrogen and deuterium Young, David A.; Ross, Marvin The Journal of Chemical Physics, Vol. 74, Issue 12 https://doi.org/10.1063/1.441058	journal	June 1981
Study of an F center in molten KCl Parrinello, M.; Rahman, A. The Journal of Chemical Physics, Vol. 80, Issue 2 https://doi.org/10.1063/1.446740	journal	January 1984
Direct evaluation of phase coexistence by molecular simulation via integration along the saturation line Kofke, David A. The Journal of Chemical Physics, Vol. 98, Issue 5 https://doi.org/10.1063/1.465023	journal	March 1993
Hydrogen at extreme pressures (Review Article) Goncharov, Alexander F.; Howie, Ross T.; Gregoryanz, Eugene Low Temperature Physics, Vol. 39, Issue 5 https://doi.org/10.1063/1.4807051	journal	May 2013
Coupled electron-ion Monte Carlo simulation of hydrogen molecular crystals Rillo, Giovanni; Morales, Miguel A.; Ceperley, David M. The Journal of Chemical Physics, Vol. 148, Issue 10 https://doi.org/10.1063/1.5001387	journal	March 2018
QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo Kent, P. R. C.; Annaberdiyev, Abdulgani; Benali, Anouar The Journal of Chemical Physics, Vol. 152, Issue 17 https://doi.org/10.1063/5.0004860	journal	May 2020
Evidence for a first-order liquid-liquid transition in high-pressure hydrogen from ab initio simulations Morales, M. A.; Pierleoni, C.; Schwegler, E. Proceedings of the National Academy of Sciences, Vol. 107, Issue 29 https://doi.org/10.1073/pnas.1007309107	journal	June 2010
Bonding changes in hot fluid hydrogen at megabar pressures Subramanian, N.; Goncharov, A. F.; Struzhkin, V. V. Proceedings of the National Academy of Sciences, Vol. 108, Issue 15 https://doi.org/10.1073/pnas.1102760108	journal	March 2011
Liquid–liquid phase transition in hydrogen by coupled electron–ion Monte Carlo simulations Pierleoni, Carlo; Morales, Miguel A.; Rillo, Giovanni Proceedings of the National Academy of Sciences, Vol. 113, Issue 18 https://doi.org/10.1073/pnas.1603853113	journal	April 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
Advanced capabilities for materials modelling with Quantum ESPRESSO Giannozzi, P.; Andreussi, O.; Brumme, T. Journal of Physics: Condensed Matter, Vol. 29, Issue 46 https://doi.org/10.1088/1361-648x/aa8f79	journal	October 2017
`QMCPACK` : an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids Kim, Jeongnim; Baczewski, Andrew D.; Beaudet, Todd D. Journal of Physics: Condensed Matter, Vol. 30, Issue 19 https://doi.org/10.1088/1361-648x/aab9c3	journal	April 2018
Training models using forces computed by stochastic electronic structure methods Ceperley, David M.; Jensen, Scott; Yang, Yubo Electronic Structure, Vol. 6, Issue 1 https://doi.org/10.1088/2516-1075/ad2eb0	journal	March 2024
Correlations in the Motion of Atoms in Liquid Argon Rahman, A. Physical Review, Vol. 136, Issue 2A https://doi.org/10.1103/physrev.136.a405	journal	October 1964
New Melting Law at High Pressures Kraut, Edgar A.; Kennedy, George C. Physical Review, Vol. 151, Issue 2 https://doi.org/10.1103/physrev.151.668	journal	November 1966
Density-functional exchange-energy approximation with correct asymptotic behavior Becke, A. D. Physical Review A, Vol. 38, Issue 6 https://doi.org/10.1103/physreva.38.3098	journal	September 1988
Melting curves of molecular hydrogen and molecular deuterium under high pressures between 20 and 373 K Diatschenko, V.; Chu, C. W.; Liebenberg, D. H. Physical Review B, Vol. 32, Issue 1 https://doi.org/10.1103/physrevb.32.381	journal	July 1985
Path-integral Monte Carlo calculation of the kinetic energy of condensed lithium Filippi, Claudia; Ceperley, David M. Physical Review B, Vol. 57, Issue 1 https://doi.org/10.1103/physrevb.57.252	journal	January 1998
Extended and accurate determination of the melting curves of argon, helium, ice ( H 2 O ) , and hydrogen ( H 2 ) Datchi, Frédéric; Loubeyre, Paul; LeToullec, René Physical Review B, Vol. 61, Issue 10 https://doi.org/10.1103/physrevb.61.6535	journal	March 2000
Transferable relativistic Dirac-Slater pseudopotentials Grinberg, Ilya; Ramer, Nicholas J.; Rappe, Andrew M. Physical Review B, Vol. 62, Issue 4 https://doi.org/10.1103/physrevb.62.2311	journal	July 2000
Melting curve equations at high pressure Kechin, Vladimir V. Physical Review B, Vol. 65, Issue 5 https://doi.org/10.1103/physrevb.65.052102	journal	December 2001
Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces Clay, Raymond C.; Holzmann, Markus; Ceperley, David M. Physical Review B, Vol. 93, Issue 3 https://doi.org/10.1103/physrevb.93.035121	journal	January 2016
Theory of finite size effects for electronic quantum Monte Carlo calculations of liquids and solids Holzmann, Markus; Clay, Raymond C.; Morales, Miguel A. Physical Review B, Vol. 94, Issue 3 https://doi.org/10.1103/physrevb.94.035126	journal	July 2016
Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms Lin, C.; Zong, F. H.; Ceperley, D. M. Physical Review E, Vol. 64, Issue 1 https://doi.org/10.1103/physreve.64.016702	journal	June 2001
Melting Line of Hydrogen at High Pressures Deemyad, Shanti; Silvera, Isaac F. Physical Review Letters, Vol. 100, Issue 15 https://doi.org/10.1103/physrevlett.100.155701	journal	April 2008
Nuclear Quantum Effects and Nonlocal Exchange-Correlation Functionals Applied to Liquid Hydrogen at High Pressure Morales, Miguel A.; McMahon, Jeffrey M.; Pierleoni, Carlo Physical Review Letters, Vol. 110, Issue 6 https://doi.org/10.1103/physrevlett.110.065702	journal	February 2013
Melting and High P − T Transitions of Hydrogen up to 300 GPa Zha, Chang-sheng; Liu, Hanyu; Tse, John S. Physical Review Letters, Vol. 119, Issue 7 https://doi.org/10.1103/physrevlett.119.075302	journal	August 2017
Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics Zhang, Linfeng; Han, Jiequn; Wang, Han Physical Review Letters, Vol. 120, Issue 14 https://doi.org/10.1103/physrevlett.120.143001	journal	April 2018
Energy Gap Closure of Crystalline Molecular Hydrogen with Pressure Gorelov, Vitaly; Holzmann, Markus; Ceperley, David M. Physical Review Letters, Vol. 124, Issue 11 https://doi.org/10.1103/physrevlett.124.116401	journal	March 2020
Stable Solid Molecular Hydrogen above 900 K from a Machine-Learned Potential Trained with Diffusion Quantum Monte Carlo Niu, Hongwei; Yang, Yubo; Jensen, Scott Physical Review Letters, Vol. 130, Issue 7 https://doi.org/10.1103/physrevlett.130.076102	journal	February 2023
Crystal Structure and Pair Potentials: A Molecular-Dynamics Study Parrinello, M.; Rahman, A. Physical Review Letters, Vol. 45, Issue 14 https://doi.org/10.1103/physrevlett.45.1196	journal	October 1980
Unified Approach for Molecular Dynamics and Density-Functional Theory Car, R.; Parrinello, M. Physical Review Letters, Vol. 55, Issue 22 https://doi.org/10.1103/physrevlett.55.2471	journal	November 1985
Isotopic shift of helium melting pressure: Path integral Monte Carlo study Boninsegni, M.; Pierleoni, C.; Ceperley, D. M. Physical Review Letters, Vol. 72, Issue 12 https://doi.org/10.1103/physrevlett.72.1854	journal	March 1994
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/physrevlett.77.3865	journal	October 1996
Raman Spectroscopy of Hot Dense Hydrogen Gregoryanz, Eugene; Goncharov, Alexander F.; Matsuishi, Kiyoto Physical Review Letters, Vol. 90, Issue 17 https://doi.org/10.1103/physrevlett.90.175701	journal	April 2003
Van der Waals Density Functional for General Geometries Dion, M.; Rydberg, H.; Schröder, E. Physical Review Letters, Vol. 92, Issue 24 https://doi.org/10.1103/physrevlett.92.246401	journal	June 2004
Accurate, Efficient, and Simple Forces Computed with Quantum Monte Carlo Methods Chiesa, Simone; Ceperley, D. M.; Zhang, Shiwei Physical Review Letters, Vol. 94, Issue 3 https://doi.org/10.1103/physrevlett.94.036404	journal	January 2005
Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces Behler, Jörg; Parrinello, Michele Physical Review Letters, Vol. 98, Issue 14 https://doi.org/10.1103/physrevlett.98.146401	journal	April 2007
The properties of hydrogen and helium under extreme conditions McMahon, Jeffrey M.; Morales, Miguel A.; Pierleoni, Carlo Reviews of Modern Physics, Vol. 84, Issue 4 https://doi.org/10.1103/revmodphys.84.1607	journal	November 2012
Insulator-metal transition in dense fluid deuterium Celliers, Peter M.; Millot, Marius; Brygoo, Stephanie Science, Vol. 361, Issue 6403 https://doi.org/10.1126/science.aat0970	journal	August 2018
Evidence of maximum in the melting curve of hydrogen at megabar pressures Eremets, M. I.; Trojan, I. A. JETP Letters, Vol. 89, Issue 4 https://doi.org/10.1134/s0021364009040031	journal	April 2009
Deep Potential: A General Representation of a Many-Body Potential Energy Surface Han, Jiequn; Zhang, Linfeng; Car, Roberto Communications in Computational Physics, Vol. 23, Issue 3 https://doi.org/10.4208/cicp.OA-2017-0213	journal	January 2018

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High temperature melting of dense molecular hydrogen from machine-learning interatomic potentials trained on quantum Monte Carlo

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