Abstract
Hydrogen, the simplest and most abundant element in the Universe, develops a remarkably complex behaviour upon compression1. Since Wigner predicted the dissociation and metallization of solid hydrogen at megabar pressures almost a century ago2, several efforts have been made to explain the many unusual properties of dense hydrogen, including a rich and poorly understood solid polymorphism1,3,4,5, an anomalous melting line6 and the possible transition to a superconducting state7. Experiments at such extreme conditions are challenging and often lead to hard-to-interpret and controversial observations, whereas theoretical investigations are constrained by the huge computational cost of sufficiently accurate quantum mechanical calculations. Here we present a theoretical study of the phase diagram of dense hydrogen that uses machine learning to ‘learn’ potential-energy surfaces and interatomic forces from reference calculations and then predict them at low computational cost, overcoming length- and timescale limitations. We reproduce both the re-entrant melting behaviour and the polymorphism of the solid phase. Simulations using our machine-learning-based potentials provide evidence for a continuous molecular-to-atomic transition in the liquid, with no first-order transition observed above the melting line. This suggests a smooth transition between insulating and metallic layers in giant gas planets, and reconciles existing discrepancies between experiments as a manifestation of supercritical behaviour.
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Data availability
The data supporting the findings of this study are available within the paper, and all input files that are necessary to reproduce the reported results are included in Supplementary Information. All data generated for the study are available upon request from the corresponding author, and the MLP for hydrogen constructed here are available at https://github.com/BingqingCheng/MLP-highP-H.
References
McMahon, J. M., Morales, M. A., Pierleoni, C. & Ceperley, D. M. The properties of hydrogen and helium under extreme conditions. Rev. Mod. Phys. 84, 1607–1653 (2012).
Wigner, E. & Huntington, H. B. On the possibility of a metallic modification of hydrogen. J. Chem. Phys. 3, 764–770 (1935).
Howie, R. T., Guillaume, C. L., Scheler, T., Goncharov, A. F. & Gregoryanz, E. Mixed molecular and atomic phase of dense hydrogen. Phys. Rev. Lett. 108, 125501 (2012).
Zha, C., Liu, Z., Ahart, M., Boehler, R. & Hemley, R. J. High-pressure measurements of hydrogen phase IV using synchrotron infrared spectroscopy. Phys. Rev. Lett. 110, 217402 (2013).
Dalladay-Simpson, P., Howie, R. T. & Gregoryanz, E. Evidence for a new phase of dense hydrogen above 325 gigapascals. Nature 529, 63–67 (2016).
Bonev, S. A., Schwegler, E., Ogitsu, T. & Galli, G. A quantum fluid of metallic hydrogen suggested by first-principles calculations. Nature 431, 669–672 (2004).
Ashcroft, N. W. Metallic hydrogen: a high-temperature superconductor? Phys. Rev. Lett. 21, 1748–1749 (1968).
Guillot, T. The interiors of giant planets: models and outstanding questions. Annu. Rev. Earth Planet. Sci. 33, 493–530 (2005).
Hubbard, W. B. & Militzer, B. A preliminary Jupiter model. Astrophys. J. 820, 80 (2016).
Celliers, P. M. et al. Insulator-metal transition in dense fluid deuterium. Science 361, 677–682 (2018).
Knudson, M. D. et al. Direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium. Science 348, 1455–1460 (2015).
Ohta, K. et al. Phase boundary of hot dense fluid hydrogen. Sci. Rep. 5, 16560 (2015).
McWilliams, R. S., Dalton, D. A., Mahmood, M. F. & Goncharov, A. F. Optical properties of fluid hydrogen at the transition to a conducting state. Phys. Rev. Lett. 116, 255501 (2016).
Zaghoo, M., Salamat, A. & Silvera, I. F. Evidence of a first-order phase transition to metallic hydrogen. Phys. Rev. B 93, 155128 (2016).
Zaghoo, M. & Silvera, I. F. Conductivity and dissociation in liquid metallic hydrogen and implications for planetary interiors. Proc. Natl Acad. Sci. USA 114, 11873–11877 (2017).
Scandolo, S. Liquid–liquid phase transition in compressed hydrogen from first-principles simulations. Proc. Natl Acad. Sci. USA 100, 3051–3053 (2003).
Morales, M. A., Pierleoni, C., Schwegler, E. & Ceperley, D. M. Evidence for a first-order liquid–liquid transition in high-pressure hydrogen from ab initio simulations. Proc. Natl Acad. Sci. USA 107, 12799–12803 (2010).
Lorenzen, W., Holst, B. & Redmer, R. First-order liquid–liquid phase transition in dense hydrogen. Phys. Rev. B 82, 195107 (2010).
Delaney, K. T., Pierleoni, C. & Ceperley, D. M. Quantum Monte Carlo simulation of the high-pressure molecular-atomic crossover in fluid hydrogen. Phys. Rev. Lett. 97, 235702 (2006).
Mazzola, G., Helled, R. & Sorella, S. Phase diagram of hydrogen and a hydrogen–helium mixture at planetary conditions by quantum Monte Carlo simulations. Phys. Rev. Lett. 120, 025701 (2018).
Vorberger, J., Tamblyn, I., Militzer, B. & Bonev, S. A. Hydrogen–helium mixtures in the interiors of giant planets. Phys. Rev. B 75, (2007).
Geng, H. Y., Wu, Q., Marqués, M. & Ackland, G. J. Thermodynamic anomalies and three distinct liquid–liquid transitions in warm dense liquid hydrogen. Phys. Rev. B 100, 134109 (2019).
Clay, R. C. III et al. Benchmarking exchange-correlation functionals for hydrogen at high pressures using quantum Monte Carlo. Phys. Rev. B 89, 184106 (2014).
Behler, J. & Parrinello, M. Generalized neural network representation of high-dimensional potential energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).
Magdău, I. B., Marqués, M., Borgulya, B. & Ackland, G. J. Simple thermodynamic model for the hydrogen phase diagram. Phys. Rev. B 95, 094107 (2017).
Loubeyre, P., Occelli, F. & Dumas, P. Synchrotron infrared spectroscopic evidence of the probable transition to metal hydrogen. Nature 577, 631–635 (2020).
Pickard, C. J. & Needs, R. J. Ab initio random structure searching. J. Phys. Condens. Matter 23, 053201 (2011).
Pickard, C. J. & Needs, R. J. Structure of phase III of solid hydrogen. Nat. Phys. 3, 473 (2007).
Monserrat, B., Needs, R. J., Gregoryanz, E. & Pickard, C. J. Hexagonal structure of phase III of solid hydrogen. Phys. Rev. B 94, 134101 (2016).
Zha, C., Liu, H., Tse John, S. & Hemley, R. J. Melting and high P–T transitions of hydrogen up to 300 GPa. Phys. Rev. Lett. 119, 075302 (2017).
Anisimov, M. A. et al. Thermodynamics of fluid polyamorphism. Phys. Rev. X 8, 011004 (2018).
Laio, A. & Parrinello, M. Escaping free energy minima. Proc. Natl Acad. Sci. USA 99, 12562–12566 (2002).
Soper, A. K. & Ricci, M. A. Structures of high-density and low-density water. Phys. Rev. Lett. 84, 2881 (2000).
Acknowledgements
We are thankful to G. Ackland, H. Geng. and R. Redmer, who shared their AIMD trajectories for us to benchmark the MLP. We thank S. Sorella for providing the VMC training dataset. We acknowledge D. Frenkel, B. Monserrat, M. Casula, A. M. Saitta, R. Helled, G. Carleo and S. Sorella for discussions. B.C. acknowledges funding from the Swiss National Science Foundation (project P2ELP2-184408), resources provided by the Cambridge Tier-2 system funded by EPSRC Tier-2 capital grant EP/P020259/1 and by CSCS under project ID s957. G.M. acknowledges financial support from the Swiss National Science Foundation through grant number 200021-179312. C.J.P. is supported by the Royal Society through a Royal Society Wolfson Research Merit award and the EPSRC through grant EP/P022596/1. M.C. acknowledges funding from the Swiss National Science Foundation (project 200021-182057).
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B.C., G.M. and M.C. conceptualized the research; B.C., C.J.P. and M.C. performed the research and analysed the data; B.C., G.M., C.J.P. and M.C. wrote the paper.
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Supplementary information
Supplementary Information
This file contains Supplementary Methods, a detailed description of results not reported in the main text and additional analysis. It contains Supplementary Figures 1-19.
Supplementary Data
This zipped folder contains three machine learning potentials for high pressure hydrogen based on PBE DFT, BLYP DFT and VMC, as well as all necessary simulation input files.
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Cheng, B., Mazzola, G., Pickard, C.J. et al. Evidence for supercritical behaviour of high-pressure liquid hydrogen. Nature 585, 217–220 (2020). https://doi.org/10.1038/s41586-020-2677-y
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DOI: https://doi.org/10.1038/s41586-020-2677-y
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