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A quantum fluid of metallic hydrogen suggested by first-principles calculations


It is generally assumed1,2,3 that solid hydrogen will transform into a metallic alkali-like crystal at sufficiently high pressure. However, some theoretical models4,5 have also suggested that compressed hydrogen may form an unusual two-component (protons and electrons) metallic fluid at low temperature, or possibly even a zero-temperature liquid ground state. The existence of these new states of matter is conditional on the presence of a maximum in the melting temperature versus pressure curve (the ‘melt line’). Previous measurements6,7,8 of the hydrogen melt line up to pressures of 44 GPa have led to controversial conclusions regarding the existence of this maximum. Here we report ab initio calculations that establish the melt line up to 200 GPa. We predict that subtle changes in the intermolecular interactions lead to a decline of the melt line above 90 GPa. The implication is that as solid molecular hydrogen is compressed, it transforms into a low-temperature quantum fluid before becoming a monatomic crystal. The emerging low-temperature phase diagram of hydrogen and its isotopes bears analogies with the familiar phases of 3He and 4He (the only known zero-temperature liquids), but the long-range Coulomb interactions and the large component mass ratio present in hydrogen would result in dramatically different properties9.

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Figure 1: Snapshots from two-phase MD simulations at P = 130 GPa and temperatures below and above the melting temperature.
Figure 2: Melt curve of hydrogen predicted from first-principles MD.
Figure 3: Difference of the specific volumes (ΔV) and enthalpies (ΔH) between the liquid and solid phases at the melting temperatures determined from the two-phase simulations.
Figure 4: The probability distribution of MLWF spreads21 at T = 700 K and P = 50 (black curves), 130 (red curves) and 200 GPa (green curves).


  1. Wigner, E. & Huntington, H. B. On the possibility of metallic modifications of hydrogen. J. Chem. Phys. 3, 764–770 (1935)

    Article  ADS  CAS  Google Scholar 

  2. Ashcroft, N. W. Metallic hydrogen: A high temperature superconductor? Phys. Rev. Lett. 21, 1748–1799 (1968)

    Article  ADS  CAS  Google Scholar 

  3. Mao, H. K. & Hemley, R. J. Ultrahigh-pressure transitions in solid hydrogen. Rev. Mod. Phys. 66, 671–692 (1994)

    Article  ADS  CAS  Google Scholar 

  4. Brovman, E. G., Kagan, Yu. & Kholas, A. Properties of metallic hydrogen under pressure. Sov. Phys. JETP 35, 783–792 (1972)

    ADS  Google Scholar 

  5. Ashcroft, N. W. The hydrogen liquids. J. Phys. Condens. Matter 12, A129–A137 (2000)

    Article  ADS  CAS  Google Scholar 

  6. Diatschenko, V. et al. Melting curves of molecular hydrogen and molecular deuterium under high pressures between 20 and 373 K. Phys. Rev B 32, 381–389 (1985)

    Article  ADS  CAS  Google Scholar 

  7. Datchi, F., Loubeyre, P. & LeToullec, R. Extended and accurate determination of the melting curves of argon, helium, ice (H2O) and hydrogen (H2). Phys. Rev. B 61, 6535–6546 (2000)

    Article  ADS  CAS  Google Scholar 

  8. Gregoryanz, E., Goncharov, A. F., Matsuishi, K., Mao, H.-k. & Hemley, R. J. Raman spectroscopy of hot dense hydrogen. Phys. Rev. Lett. 90, 175701 (2003)

    Article  ADS  Google Scholar 

  9. Ashcroft, N. W. Hydrogen at high density. J. Phys. A 36, 6137–6147 (2003)

    Article  ADS  CAS  Google Scholar 

  10. Jayaraman, J., Newton, R. C. & McDonough, J. M. Phase relations, resistivity, and electronic structure of cesium at high pressure. Phys. Rev. 159, 527–533 (1967)

    Article  ADS  CAS  Google Scholar 

  11. Scandolo, S. Liquid–liquid phase transition in compressed hydrogen from first-principles simulations. Proc. Natl Acad. Sci. USA 100, 3051–3053 (2003)

    Article  ADS  CAS  Google Scholar 

  12. Kechin, V. V. Melting of metallic hydrogen at high pressure. JETP Lett. 79, 46–49 (2004)

    Article  ADS  Google Scholar 

  13. Morris, J. R., Wang, C. Z., Ho, K. M. & Chan, C. T. Melting line of aluminum from simulations of coexisting phases. Phys. Rev. B 49, 3109–3115 (1994)

    Article  ADS  CAS  Google Scholar 

  14. Ogitsu, T., Schwegler, E., Gygi, F. & Galli, G. Melting of lithium hydride under pressure. Phys. Rev. Lett. 91, 175502 (2003)

    Article  ADS  Google Scholar 

  15. Alfe, D. First-principles simulations of direct coexistence of solid and liquid aluminum. Phys. Rev. B 68, 064423 (2003)

    Article  ADS  Google Scholar 

  16. Bonev, S. A., Militzer, B. & Galli, G. Ab initio simulations of dense liquid deuterium: Comparison with gas-gun shock-wave experiments. Phys. Rev. B 69, 104101 (2004)

    Article  Google Scholar 

  17. Chacham, H., Zhu, X. & Louie, S. G. Pressure-induced insulator-metal transitions in solid xenon and hydrogen: A first-principles quasiparticle study. Phys. Rev. B 46, 6688–6699 (1992)

    Article  ADS  CAS  Google Scholar 

  18. Hemley, R. J. et al. Equation of state of solid hydrogen and deuterium from single-crystal x-ray diffraction to 26.5 GPa. Phys. Rev. B 42, 6458–6470 (1990)

    Article  ADS  CAS  Google Scholar 

  19. Nagao, K., Bonev, S. A., Bergara, A. & Ashcroft, N. W. Enhanced Friedel structure and proton pairing in dense solid hydrogen. Phys. Rev. Lett. 90, 035501 (2003)

    Article  ADS  Google Scholar 

  20. Yoshida, T. & Kamakura, S. Liquid-solid transitions in systems of soft repulsive forces. Prog. Theor. Phys. 52, 822–838 (1972)

    Article  ADS  Google Scholar 

  21. Marzari, N. & Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847–12856 (1997)

    Article  ADS  CAS  Google Scholar 

  22. Souza, I., Martin, R. M., Marzari, N., Zhao, X. & Vanderbilt, D. Wannier-functional description of the electronic polarization and infrared absorption of high-pressure hydrogen. Phys. Rev. B 62, 15505–15519 (2000)

    Article  ADS  CAS  Google Scholar 

  23. Izvekov, S., Parrinello, M., Burnham, C. J. & Voth, G. A. Effective force fields for condensed phase systems from ab initio molecular dynamics simulations: A new method for force-matching. J. Chem. Phys. 120, 10896–10913 (2004)

    Article  ADS  CAS  Google Scholar 

  24. Hemley, R. J., Soos, Z. G., Hanfland, M. & Mao, H. K. Charge-transfer states in dense hydrogen. Nature 369, 384–387 (1994)

    Article  ADS  CAS  Google Scholar 

  25. Moshary, F., Chen, N. H. & Silvera, I. F. Pressure dependence of the vibron in H2, HD, and D2: Implications for inter- and intramolecular forces. Phys. Rev. B 48, 12613–12619 (1993)

    Article  ADS  CAS  Google Scholar 

  26. Loubeyre, P., Occelli, F. & LeToullec, R. Optical studies of solid hydrogen to 320 GPa and evidence for black hydrogen. Nature 416, 613–617 (2002)

    Article  ADS  CAS  Google Scholar 

  27. Car, R. & Parrinello, M. Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 2471–2474 (1985)

    Article  ADS  CAS  Google Scholar 

  28. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996)

    Article  ADS  CAS  Google Scholar 

  29. Steinhardt, P. J., Nelson, D. R. & Ronchetti, M. Bond-orientational order in liquids and glasses. Phys. Rev. B 28, 784–805 (1983)

    Article  ADS  CAS  Google Scholar 

  30. Kechin, V. V. Melting curve equations at high temperature. Phys. Rev. B 65, 052102 (2001)

    Article  ADS  Google Scholar 

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We thank S. Izvekov for providing the force-matching routines that were used in the analysis shown in the inset of Fig. 4, and F. Gygi for many discussions. This work was performed under the auspices of the US Department of Energy at the University of California/Lawrence Livermore National Laboratory.

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Correspondence to Stanimir A. Bonev.

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Bonev, S., Schwegler, E., Ogitsu, T. et al. A quantum fluid of metallic hydrogen suggested by first-principles calculations. Nature 431, 669–672 (2004).

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