Understanding dense hydrogen at planetary conditions

ABSTRACT Materials at high pressures and temperatures are of great interest for planetary science and astrophysics, warm dense-matter physics and inertial confinement fusion research.

Planetary structure models rely on an understanding of the behaviour of elements and their mixtures under conditions that do not exist on Earth; at the same time, planets serve as natural

laboratories for studying materials at extreme conditions. The topic of dense hydrogen is timely given the recent accurate measurements of the gravitational fields of Jupiter and Saturn, the

current and upcoming progress in shock experiments, and the advances in numerical simulations of materials at high pressure. In this Review we discuss the connection between modelling

planetary interiors and the high-pressure physics of hydrogen and helium. We summarize key experiments and theoretical approaches for determining the equation of state and phase diagram of

hydrogen and helium. We relate this to current knowledge of the internal structures of Jupiter and Saturn, and discuss the importance of high-pressure physics to their characterization. KEY

POINTS * Modelling planetary interiors relies on a profound knowledge of the behaviour of materials at high pressures and temperatures. For the gas giant planets, these materials are

hydrogen and helium. * Progress in high-pressure experiments using diamond anvil cells and shock waves is critical for understanding hydrogen under extreme conditions and for calibrating

theoretical models * Simulations of hydrogen at high pressure are essential to understand fundamental physical problems such as its rich phase diagram; assist the experimental realization

and interpretation of new materials; and predict its behaviour for parameters at which experiments cannot be performed. * Jupiter and Saturn are expected to have complex interiors in which

hydrogen metallizes and helium separates from hydrogen. The full understanding of these processes is still a major challenge in high-pressure physics. * Although the structure and evolution

of gas giant planets are dominated by hydrogen and helium, the planets contain other, heavier elements and can have complex interiors that include composition gradients and inhomogeneous

regions. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution ACCESS OPTIONS Access through your institution Access Nature

and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any time Learn more Subscribe to this journal Receive 12 digital issues

and online access to articles $99.00 per year only $8.25 per issue Learn more Buy this article * Purchase on SpringerLink * Instant access to full article PDF Buy now Prices may be subject

to local taxes which are calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in * Learn about institutional subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT

BEING VIEWED BY OTHERS EVIDENCE OF HYDROGEN−HELIUM IMMISCIBILITY AT JUPITER-INTERIOR CONDITIONS Article 26 May 2021 STRUCTURE AND DENSITY OF SILICON CARBIDE TO 1.5 TPA AND IMPLICATIONS FOR

EXTRASOLAR PLANETS Article Open access 27 April 2022 IMPLICATIONS OF THE IRON OXIDE PHASE TRANSITION ON THE INTERIORS OF ROCKY EXOPLANETS Article 11 February 2021 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). ADS  Google Scholar  * Wigner,

E. & Huntington, H. B. On the possibility of a metallic modification of hydrogen. _J. Chem. Phys._ 3, 764–770 (1935). ADS  Google Scholar  * Helled, R., Anderson, J. D., Podolak, M.

& Schubert, G. Interior models of Uranus and Neptune. _Astrophys. J._ 726, 15 (2011). ADS  Google Scholar  * Ashcroft, N. W. Metallic hydrogen: a high-temperature superconductor? _Phys.

Rev. Lett._ 21, 1748–1749 (1968). ADS  Google Scholar  * Babaev, E., Sudbø, A. & Ashcroft, N. A superconductor to superfluid phase transition in liquid metallic hydrogen. _Nature_ 431,

666 (2004). ADS  Google Scholar  * Goncharov, A. Phase diagram of hydrogen at extreme pressures and temperatures; updated through 2019 (Review article). _Low Temp. Phys._ 46, 97–103 (2020).

ADS  Google Scholar  * Weir, S., Mitchell, A. & Nellis, W. Metallization of fluid molecular hydrogen at 140 GPa (1.4 Mbar). _Phys. Rev. Lett._ 76, 1860 (1996). ADS  Google Scholar  *

Goncharov, A. F., Mazin, I. I., Eggert, J. H., Hemley, R. J. & Mao, H.-k Invariant points and phase transitions in deuterium at megabar pressures. _Phys. Rev. Lett._ 75, 2514–2517

(1995). ADS  Google Scholar  * Dias, R. P. & Silvera, I. F. Observation of the Wigner–Huntington transition to metallic hydrogen._Science_ 355, 715–718 (2017). ADS  Google Scholar  *

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).

ADS  Google Scholar  * Deemyad, S. & Silvera, I. F. Melting line of hydrogen at high pressures. _Phys. Rev. Lett._ 100, 155701 (2008). ADS  Google Scholar  * Dzyabura, V., Zaghoo, M.

& Silvera, I. F. Evidence of a liquid–liquid phase transition in hot dense hydrogen. _Proc. Natl Acad. Sci. USA_ 110, 8040–8044 (2013). ADS  Google Scholar  * Zaghoo, M., Salamat, A.

& Silvera, I. F. Evidence of a first-order phase transition to metallic hydrogen. _Phys. Rev. B_ 93, 155128 (2016). ADS  Google Scholar  * 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). ADS  Google Scholar  * Dubrovinsky, L. et al. The

most incompressible metal osmium at static pressures above 750 gigapascals. _Nature_ 525, 226–229 (2015). ADS  Google Scholar  * Loubeyre, P., Occelli, F. & Dumas, P. Synchrotron

infrared spectroscopic evidence of the probable transition to metal hydrogen. _Nature_ 577, 631–635 (2020). ADS  Google Scholar  * Goncharov, A. F. & Struzhkin, V. V. Comment on

‘‘Observation of the Wigner–Huntington transition to metallic hydrogen’’. _Science_ 357, eaam9736 (2017). Google Scholar  * Liu, X.-D. & Dalladay-Simpson, P. & Howie, R. T. & Li,

B. & Gregoryanz, E. Comment on ‘‘Observation of the Wigner–Huntington transition to metallic hydrogen”. _Science_ 357, eaan2286 (2017). Google Scholar  * Loubeyre, P., Occelli, F. &

Dumas, P. Comment on: ‘‘Observation of the Wigner–Huntington transition to metallic hydrogen’’. Preprint at http://arxiv.org/abs/1702.07192 (2017). * Eremets, M. & Drozdov, A. Comments

on the claimed observation of the Wigner–Huntington transition to metallic hydrogen. Preprint at https://arxiv.org/abs/1702.05125 (2017). * Geng, H. Y. Public debate on metallic hydrogen to

boost high pressure research. _Matter Radiat. Extremes_ 2, 275 (2018). Google Scholar  * Silvera, I. & Dias, R. Response to comment on ‘‘Observation of the Wigner–Huntington transition

to metallic hydrogen”. _Science_ 357, eaan1215 (2017). Google Scholar  * Silvera, I. & Dias, R. Response to critiques on observation of the Wigner–Huntington transition to metallic

hydrogen. Preprint at http://arxiv.org/abs/1703.0306 (2017). * Howie, R. T., Dalladay-Simpson, P. & Gregoryanz, E. Raman spectroscopy of hot hydrogen above 200 GPa. _Nat. Mater._ 14,

495–499 (2015). ADS  Google Scholar  * Dalladay-Simpson, P., Howie, R. T. & Gregoryanz, E. Evidence for a new phase of dense hydrogen above 325 gigapascals. _Nature_ 529, 63–67 (2016).

ADS  Google Scholar  * Eremets, M., Troyan, I. & Drozdov, A. Low temperature phase diagram of hydrogen at pressures up to 380 GPa. A possible metallic phase at 360 GPa and 200 K.

Preprint at http://arxiv.org/abs/1601.04479 (2016). * Dias, R. P., Noked, O. & Silvera, I. F. Quantum phase transition in solid hydrogen at high pressure. _Phys. Rev. B_ 100, 184112

(2019). ADS  Google Scholar  * Eremets, M. I., Drozdov, A. P., Kong, P. & Wang, H. Semimetallic molecular hydrogen at pressure above 350 GPa. _Nat. Phys._ 15, 1246–1249 (2019). Google

Scholar  * Gregoryanz, E. et al. Everything you always wanted to know about metallic hydrogen but were afraid to ask. _Matter Radiat. Extremes_ 5, 038101 (2020). Google Scholar  * Dias, R.

P. & Silvera, I. F. Observation of the Wigner–Huntington transition to metallic hydrogen. _Science_ 355, 715–718 (2017). ADS  Google Scholar  * Nellis, W. _Ultracondensed Matter by

Dynamic Compression_ (Cambridge Univ. Press, 2017). * Nellis, W. J. Dense quantum hydrogen. _Low Temp. Phys._ 45, 294–296 (2019). ADS  Google Scholar  * Knudson, M. et al. Direct observation

of an abrupt insulator-to-metal transition in dense liquid deuterium. _Science_ 348, 1455–1460 (2015). ADS  Google Scholar  * Celliers, P. M. et al. Insulator–metal transition in dense

fluid deuterium. _Science_ 361, 677–682 (2018). ADS  Google Scholar  * Mochalov, M. A. et al. Quasi-isentropic compressibility of deuterium at a pressure of ~12 TPa. _JETP Lett._ 107,

168–174 (2018). ADS  Google Scholar  * Brygoo, S. et al. Analysis of laser shock experiments on precompressed samples using a quartz reference and application to warm dense hydrogen and

helium. _J. Appl. Phys._ 118, 195901 (2015). ADS  Google Scholar  * Miller, J. E. et al. Streaked optical pyrometer system for laser-driven shock-wave experiments on omega. _Rev. Sci.

Instrum._ 78, 034903 (2007). ADS  Google Scholar  * Knudson, M. D. & Desjarlais, M. P. High-precision shock wave measurements of deuterium: evaluation of exchange-correlation functionals

at the molecular-to-atomic transition. _Phys. Rev. Lett._ 118, 035501 (2017). ADS  Google Scholar  * Knudson, M. D. et al. Probing the interiors of the ice giants: shock compression of

water to 700 GPa and 3.8 G/cm3. _Phys. Rev. Lett._ 108, 091102 (2012). ADS  Google Scholar  * Millot, M. et al. Nanosecond X-ray diffraction of shock-compressed superionic water ice.

_Nature_ 569, 251 (2019). ADS  Google Scholar  * Eremets, M. I. & Trojan, I. Evidence of maximum in the melting curve of hydrogen at megabar pressures. _JETP Lett._ 89, 174–179 (2009).

ADS  Google Scholar  * Subramanian, N., Goncharov, A. F., Struzhkin, V. V., Somayazulu, M. & Hemley, R. J. Bonding changes in hot fluid hydrogen at megabar pressures. _Proc. Natl Acad.

Sci. USA_ 108, 6014–6019 (2011). ADS  Google Scholar  * Zha, C.-s, Liu, H., Tse, J. S. & Hemley, R. J. Melting and high _P_−_T_ transitions of hydrogen up to 300 GPa. _Phys. Rev. Lett._

119, 075302 (2017). Google Scholar  * Zha, C.-S., 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). ADS  Google Scholar  * Mott, N. F. The transition to the metallic state. _Phil. Mag._ 6, 287–309 (1961). ADS  Google Scholar  * Ohta, K. et al. Phase

boundary of hot dense fluid hydrogen. _Sci. Rep._ 5, 16560 (2015). ADS  Google Scholar  * Ross, M., Ree, F. & Young, D. The equation of state of molecular hydrogen at very high density.

_J. Chem. Phys._ 79, 1487–1494 (1983). ADS  Google Scholar  * Saumon, D., Chabrier, G. & Van Horn, H. An equation of state for low-mass stars and giant planets. _Astrophys. J. Suppl.

Ser._ 99, 713 (1995). ADS  Google Scholar  * Chabrier, G., Mazevet, S. & Soubiran, F. A new equation of state for dense hydrogen–helium mixtures. _Astrophys. J._ 872, 51 (2019). ADS 

Google Scholar  * Ross, M. Linear-mixing model for shock-compressed liquid deuterium. _Phys. Rev. B_ 58, 669–677 (1998). ADS  Google Scholar  * Kerley, G. I. Equations of state for hydrogen

and deuterium. Sandia National Laboratories report SAND 2003–3613 (SAND, 2003). * Caillabet, L., Mazevet, S. & Loubeyre, P. Multiphase equation of state of hydrogen from ab initio

calculations in the range 0.2 to 5 g/cc up to 10 eV. _Phys. Rev. B_ 83, 094101 (2011). ADS  Google Scholar  * Militzer, B. & Hubbard, W. B. Ab initio equation of state for

hydrogen–helium mixtures with recalibration of the giant-planet mass–radius relation. _Astrophys. J._ 774, 148 (2013). ADS  Google Scholar  * Militzer, B. Equation of state calculations of

hydrogen–helium mixtures in solar and extrasolar giant planets. _Phys. Rev. B_ 87, 014202 (2013). ADS  Google Scholar  * Becker, A. et al. Ab initio equations of state for hydrogen (H-REOS.

3) and helium (He-REOS. 3) and their implications for the interior of brown dwarfs. _Astrophys. J. Suppl. Ser._ 215, 21 (2014). ADS  Google Scholar  * Brush, S., Sahlin, H. & Teller, E.

Monte Carlo study of a one-component plasma. I. _J. Chem. Phys._ 45, 2102–2118 (1966). ADS  Google Scholar  * Morales, M. A., McMahon, J. M., Pierleoni, C. & Ceperley, D. M. Nuclear

quantum effects and nonlocal exchange-correlation functionals applied to liquid hydrogen at high pressure. _Phys. Rev. Lett._ 110, 065702 (2013). ADS  Google Scholar  * Allen, M. P. &

Tildesley, D. J. _Computer Simulation of Liquids_ (Clarendon, 1987). * Pierleoni, C., Ceperley, D. M. & Holzmann, M. Coupled electron–ion Monte Carlo calculations of dense metallic

hydrogen. _Phys. Rev. Lett._ 93, 146402 (2004). ADS  Google Scholar  * Payne, M. C., Teter, M. P., Allan, D. C., Arias, T. A. & Joannopoulos, J. D. Iterative minimization techniques for

ab initio total-energy calculations: molecular dynamics and conjugate gradients. _Rev. Mod. Phys._ 64, 1045–1097 (1992). ADS  Google Scholar  * Alavi, S.Book review: _Ab initio Molecular

Dynamics. Basic Theory and Advanced Methods_. By Dominik Marx and Jürg Hutter. _Angew. Chem. Int. Ed._ 48, 9404–9405 (2009). Google Scholar  * Andersen, H. C. Molecular dynamics simulations

at constant pressure and/or temperature. _J. Chem. Phys._ 72, 2384–2393 (1980). ADS  Google Scholar  * Martyna, G. J., Tobias, D. J. & Klein, M. L. Constant pressure molecular dynamics

algorithms. _J. Chem. Phys._ 101, 4177–4189 (1994). ADS  Google Scholar  * Bussi, G., Donadio, D. & Parrinello, M. Canonical sampling through velocity rescaling. _J. Chem. Phys._ 126,

014101 (2007). ADS  Google Scholar  * Ceperley, D. M. & Alder, B. J. Ground state of solid hydrogen at high pressures. _Phys. Rev. B_ 36, 2092–2106 (1987). ADS  Google Scholar  * Cao, J.

& Voth, G. A. The formulation of quantum statistical mechanics based on the Feynman path centroid density. I. Equilibrium properties. _J. Chem. Phys._ 100, 5093–5105 (1994). ADS  Google

Scholar  * Ceperley, D. M. Path integrals in the theory of condensed helium. _Rev. Mod. Phys._ 67, 279–355 (1995). ADS  Google Scholar  * Pierleoni, C., Morales, M. A., Rillo, G., Holzmann,

M. & Ceperley, D. M. Liquid–liquid phase transition in hydrogen by coupled electron–ion Monte Carlo simulations. _Proc. Natl Acad. Sci. USA_ 113, 4953–4957 (2016). ADS  Google Scholar 

* Car, R. & Parrinello, M. Unified approach for molecular dynamics and density-functional theory. _Phys. Rev. Lett._ 55, 2471–2474 (1985). ADS  Google Scholar  * Hohenberg, P. &

Kohn, W. Inhomogeneous electron gas. _Phys. Rev._ 136, B864–B871 (1964). ADS  MathSciNet  Google Scholar  * Kohn, W. & Sham, L. J. Self-consistent equations including exchange and

correlation effects. _Phys. Rev._ 140, A1133–A1138 (1965). ADS  MathSciNet  Google Scholar  * Burke, K. Perspective on density functional theory. _J. Chem. Phys._ 136, 150901 (2012). ADS 

Google Scholar  * Cohen, A. J., Mori-Sánchez, P. & Yang, W. Challenges for density functional theory. _Chem. Rev._ 112, 289–320 (2011). Google Scholar  * Perdew, J. P., Burke, K. &

Ernzerhof, M. Generalized gradient approximation made simple. _Phys. Rev. Lett._ 77, 3865–3868 (1996). ADS  Google Scholar  * Scandolo, S. Liquid–liquid phase transition in compressed

hydrogen from first-principles simulations. _Proc. Natl Acad. Sci. USA_ 100, 3051–3053 (2003). ADS  Google Scholar  * Lorenzen, W., Holst, B. & Redmer, R. First-order liquid–liquid phase

transition in dense hydrogen. _Phys. Rev. B_ 82, 195107 (2010). ADS  Google Scholar  * Vorberger, J., Tamblyn, I., Militzer, B. & Bonev, S. A. Hydrogen–helium mixtures in the interiors

of giant planets. _Phys. Rev. B_ 75, 024206 (2007). ADS  Google Scholar  * Tamblyn, I. & Bonev, S. A. Structure and phase boundaries of compressed liquid hydrogen. _Phys. Rev. Lett._

104, 065702 (2010). ADS  Google Scholar  * 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). ADS  Google Scholar  * Bonev, S., Schwegler, E., Galli, G. & Ogitsu, T. A quantum fluid of metallic

hydrogen suggested by first-principles calculations. _Nature_ 431, 669 (2004). ADS  Google Scholar  * Pickard, C. J. & Needs, R. J. Structure of phase III of solid hydrogen. _Nat. Phys._

3, 473 (2007). Google Scholar  * Liu, H., Zhu, L., Cui, W. & Ma, Y. Room-temperature structures of solid hydrogen at high pressures. _J. Chem. Phys._ 137, 074501 (2012). ADS  Google

Scholar  * Magda˘u, I. B. & Ackland, G. J. Identification of high-pressure phases III and IV in hydrogen: simulating Raman spectra using molecular dynamics. _Phys. Rev. B_ 87, 174110

(2013). ADS  Google Scholar  * Pickard, C. J., Martinez-Canales, M. & Needs, R. J. Density functional theory study of phase IV of solid hydrogen. _Phys. Rev. B_ 85, 214114 (2012). ADS 

Google Scholar  * Naumov, I. I., Hemley, R. J., Hoffmann, R. & Ashcroft, N. Chemical bonding in hydrogen and lithium under pressure. _J. Chem. Phys._ 143, 064702 (2015). ADS  Google

Scholar  * Monserrat, B. et al. Structure and metallicity of phase V of hydrogen. _Phys. Rev. Lett._ 120, 255701 (2018). ADS  Google Scholar  * Morales, M. A. et al. Phase separation in

hydrogen–helium mixtures at Mbar pressures. _Proc. Natl Acad. Sci. USA_ 106, 1324–1329 (2009). ADS  Google Scholar  * Lorenzen, W., Holst, B. & Redmer, R. Demixing of hydrogen and helium

at megabar pressures. _Phys. Rev. Lett._ 102, 115701 (2009). ADS  Google Scholar  * Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. _Phys.

Rev. A_ 38, 3098–3100 (1988). ADS  Google Scholar  * Monserrat, B., Ashbrook, S. E. & Pickard, C. J. Nuclear magnetic resonance spectroscopy as a dynamical structural probe of hydrogen

under high pressure. _Phys. Rev. Lett._ 122, 135501 (2019). ADS  Google Scholar  * Monserrat, B., Needs, R. J., Gregoryanz, E. & Pickard, C. J. Hexagonal structure of phase III of solid

hydrogen. _Phys. Rev. B_ 94, 134101 (2016). ADS  Google Scholar  * Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. _J. Chem. Phys._

118, 8207–8215 (2003). ADS  Google Scholar  * Dion, M., Rydberg, H., Schröder, E., Langreth, D. C. & Lundqvist, B. I. Van der Waals density functional for general geometries. _Phys. Rev.

Lett._ 92, 246401 (2004). ADS  Google Scholar  * Lee, K., Murray, É. D., Kong, L., Lundqvist, B. I. & Langreth, D. C. Higher-accuracy van der Waals density functional. _Phys. Rev. B_

82, 081101 (2010). ADS  Google Scholar  * Azadi, S. & Ackland, G. J. The role of van der Waals and exchange interactions in high-pressure solid hydrogen. _Phys. Chem. Chem. Phys._ 19,

21829–21839 (2017). Google Scholar  * Knudson, M. D., Desjarlais, M. P., Preising, M. & Redmer, R. Evaluation of exchange-correlation functionals with multiple-shock conductivity

measurements in hydrogen and deuterium at the molecular-to-atomic transition. _Phys. Rev. B_ 98, 174110 (2018). ADS  Google Scholar  * Azadi, S. & Foulkes, W. M. C. Fate of density

functional theory in the study of high-pressure solid hydrogen. _Phys. Rev. B_ 88, 014115 (2013). ADS  Google Scholar  * 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). ADS  Google Scholar  * Clay, R. C. et al. Benchmarking

exchange-correlation functionals for hydrogen at high pressures using quantum Monte Carlo. _Phys. Rev. B_ 89, 184106 (2014). ADS  Google Scholar  * Schöttler, M. & Redmer, R. Ab initio

calculation of the miscibility diagram for hydrogen–helium mixtures. _Phys. Rev. Lett._ 120, 115703 (2018). ADS  Google Scholar  * Rillo, G., Morales, M. A., Ceperley, D. M. & Pierleoni,

C. Optical properties of high-pressure fluid hydrogen across molecular dissociation. _Proc. Natl Acad. Sci. USA_ 116, 9770–9774 (2019). ADS  Google Scholar  * Foulkes, W. M. C., Mitas, L.,

Needs, R. J. & Rajagopal, G. Quantum Monte Carlo simulations of solids. _Rev. Mod. Phys._ 73, 33–83 (2001). ADS  Google Scholar  * Clay, R. C. III, Holzmann, M., Ceperley, D. M. &

Morales, M. A. Benchmarking density functionals for hydrogen–helium mixtures with quantum Monte Carlo: energetics, pressures, and forces. _Phys. Rev. B_ 93, 035121 (2016). ADS  Google

Scholar  * Chen, J., Ren, X., Li, X.-Z., Alfè, D. & Wang, E. On the room-temperature phase diagram of high pressure hydrogen: an ab initio molecular dynamics perspective and a diffusion

Monte Carlo study. _J. Chem. Phys._ 141, 024501 (2014). ADS  Google Scholar  * Azadi, S., Monserrat, B., Foulkes, W. M. C. & Needs, R. J. Dissociation of high-pressure solid molecular

hydrogen: a quantum Monte Carlo and anharmonic vibrational study. _Phys. Rev. Lett._ 112, 165501 (2014). ADS  Google Scholar  * Drummond, N. D. et al. Quantum Monte Carlo study of the phase

diagram of solid molecular hydrogen at extreme pressures. _Nat. Commun._ 6, 7794 (2015). ADS  Google Scholar  * Azadi, S., Singh, R. & Kühne, T. D. Nuclear quantum effects induce

metallization of dense solid molecular hydrogen. _J. Comput. Chem._ 39, 262–268 (2018). Google Scholar  * Attaccalite, C. & Sorella, S. Stable liquid hydrogen at high pressure by a novel

ab initio molecular-dynamics calculation. _Phys. Rev. Lett._ 100, 114501 (2008). ADS  Google Scholar  * Mazzola, G., Yunoki, S. & Sorella, S. Unexpectedly high pressure for molecular

dissociation in liquid hydrogen by electronic simulation. _Nat. Commun._ 5, 3487 (2014). ADS  Google Scholar  * Mazzola, G., Zen, A. & Sorella, S. Finite-temperature electronic

simulations without the Born–Oppenheimer constraint. _J. Chem. Phys._ 137, 134112 (2012). ADS  Google Scholar  * Zen, A., Luo, Y., Mazzola, G., Guidoni, L. & Sorella, S. Ab initio

molecular dynamics simulation of liquid water by quantum Monte Carlo. _J. Chem. Phys._ 142, 144111 (2015). ADS  Google Scholar  * Mazzola, G. & Sorella, S. Accelerating ab initio

molecular dynamics and probing the weak dispersive forces in dense liquid hydrogen. _Phys. Rev. Lett._ 118, 015703 (2017). ADS  Google Scholar  * 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). ADS  Google Scholar  * Morales, M. A.,

Pierleoni, C. & Ceperley, D. M. Equation of state of metallic hydrogen from coupled electron–ion Monte Carlo simulations. _Phys. Rev. E_ 81, 021202 (2010). ADS  Google Scholar  *

Tubman, N. M., Liberatore, E., Pierleoni, C., Holzmann, M. & Ceperley, D. M. Molecular–atomic transition along the deuterium Hugoniot curve with coupled electron–ion Monte Carlo

simulations. _Phys. Rev. Lett._ 115, 045301 (2015). ADS  Google Scholar  * Luo, Y., Zen, A. & Sorella, S. Ab initio molecular dynamics with noisy forces: validating the quantum Monte

Carlo approach with benchmark calculations of molecular vibrational properties. _J. Chem. Phys._ 141, 194112 (2014). Google Scholar  * Lin, F. et al. Electrical conductivity of high-pressure

liquid hydrogen by quantum Monte Carlo methods. _Phys. Rev. Lett._ 103, 256401 (2009). ADS  Google Scholar  * Mazzola, G. & Sorella, S. Distinct metallization and atomization

transitions in dense liquid hydrogen. _Phys. Rev. Lett._ 114, 105701 (2015). ADS  Google Scholar  * Zaghoo, M., Husband, R. J. & Silvera, I. F. Striking isotope effect on the

metallization phase lines of liquid hydrogen and deuterium. _Phys. Rev. B_ 98, 104102 (2018). ADS  Google Scholar  * Davis, P. et al. X-ray scattering measurements of dissociation-induced

metallization of dynamically compressed deuterium. _Nat. Commun._ 7, 11189 (2016). ADS  Google Scholar  * 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). ADS  Google Scholar  * Clay, R. C., Desjarlais, M. P. & Shulenburger, L.

Deuterium Hugoniot: pitfalls of thermodynamic sampling beyond density functional theory. _Phys. Rev. B_ 100, 075103 (2019). ADS  Google Scholar  * 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). ADS  Google Scholar  * Holzmann, M. et

al. Theory of finite size effects for electronic quantum Monte Carlo calculations of liquids and solids. _Phys. Rev. B_ 94, 035126 (2016). ADS  Google Scholar  * Cheng, B., Mazzola, G. &

Ceriotti, M. Evidence for supercritical behavior of high-pressure liquid hydrogen. Preprint at http://arxiv.org/abs/1906.03341 (2019). * Soubiran, F. & Militzer, B. Miscibility

calculations for water and hydrogen in giant planets. _Astrophys. J._ 806, 228 (2015). ADS  Google Scholar  * Wilson, H. F. & Militzer, B. Rocky core solubility in Jupiter and giant

exoplanets. _Phys. Rev. Lett._ 108, 111101 (2012). ADS  Google Scholar  * Ancilotto, F., Chiarotti, G. L., Scandolo, S. & Tosatti, E. Dissociation of methane into hydrocarbons at extreme

(planetary) pressure and temperature. _Science_ 275, 1288–1290 (1997). ADS  Google Scholar  * Chau, R., Hamel, S. & Nellis, W. J. Chemical processes in the deep interior of Uranus.

_Nat. Commun._ 2, 203 (2011). ADS  Google Scholar  * Cytter, Y. et al. Transition to metallization in warm dense helium–hydrogen mixtures using stochastic density functional theory within

the Kubo–Greenwood formalism. _Phys. Rev. B_ 100, 195101 (2019). ADS  Google Scholar  * Loubeyre, P., Le Toullec, R. & Pinceaux, J. P. Binary phase diagrams of H2–He mixtures at high

temperature and high pressure. _Phys. Rev. B_ 36, 3723–3730 (1987). ADS  Google Scholar  * Loubeyre, P., Letoullec, R. & Pinceaux, J. A new determination of the binary phase diagram of

H2–He mixtures at 296 K. _J. Phys. Condens. Matter_ 3, 3183 (1991). ADS  Google Scholar  * Lim, J. & Yoo, C.-S. Phase diagram of dense H2−He mixtures: evidence for strong chemical

association, miscibility, and structural change. _Phys. Rev. Lett._ 120, 165301 (2018). ADS  Google Scholar  * Turnbull, R. et al. Reactivity of hydrogen–helium and hydrogen–nitrogen

mixtures at high pressures. _Phys. Rev. Lett._ 121, 195702 (2018). ADS  Google Scholar  * Stevenson, D. J. & Salpeter, E. E. The dynamics and helium distribution in hydrogen–helium fluid

planets. _Astrophys. J. Suppl._ 35, 239–261 (1977). ADS  Google Scholar  * Stevenson, D. J. & Salpeter, E. E. The phase diagram and transport properties for hydrogen–helium fluid

planets. _Astrophys. J. Suppl._ 35, 221–237 (1977). ADS  Google Scholar  * Morales, M. A. et al. Phase separation in hydrogen–helium mixtures at Mbar pressures. _Proc. Natl Acad. Sci. USA_

106, 1324–1329 (2009). ADS  Google Scholar  * Soubiran, F., Mazevet, S., Winisdoerffer, C. & Chabrier, G. Optical signature of hydrogen–helium demixing at extreme density–temperature

conditions. _Phys. Rev. B_ 87, 165114 (2013). ADS  Google Scholar  * Guillot, T. The interiors of giant planets: models and outstanding questions. _Annu. Rev. Earth Planet. Sci._ 33, 493–530

(2005). ADS  Google Scholar  * Fortney, J. J. et al. in _Saturn in the 21st Century_ (eds. Baines, K.,Flasar, F.,Krupp, N. & Stallard, T.) p. v (Cambridge Univ. Press, 2018). *

Militzer, B., Soubiran, F., Wahl, S. M. & Hubbard, W. Understanding Jupiter’s interior. _J. Geophys. Res. Planet._ 121, 1552–1572 (2016). ADS  Google Scholar  * Helled, R. & Guillot,

T. _Internal Structure of Giant and Icy Planets: Importance of Heavy Elements and Mixing_, 44 (Springer, 2018). * Helled, R. _The Interiors of Jupiter and Saturn_, 175 (Oxford Univ. Press,

2018). * Leconte, J. & Chabrier, G. A new vision of giant planet interiors: impact of double diffusive convection. _Astron. Astrophys._ 540, A20 (2012). ADS  Google Scholar  * Leconte,

J. & Chabrier, G. Layered convection as the origin of Saturn’s luminosity anomaly. _Nat. Geosci._ 6, 347–350 (2013). ADS  Google Scholar  * Debras, F. & Chabrier, G. New models of

Jupiter in the context of Juno and Galileo. _Astrophys. J._ 872, 100 (2019). ADS  Google Scholar  * Vazan, A., Helled, R. & Guillot, T. Jupiter’s evolution with primordial composition

gradients. _Astron. Astrophys_. 610, L14 (2018). * Marley, M. S., Gómez, P. & Podolak, M. Monte Carlo interior models for Uranus and Neptune. _J. Geophys. Res._ 100, 23349–23354 (1995).

ADS  Google Scholar  * Podolak, M., Podolak, J. I. & Marley, M. S. Further investigations of random models of Uranus and Neptune. _Planet. Space. Sci._ 48, 143–151 (2000). ADS  Google

Scholar  * Helled, R., Schubert, G. & Anderson, J. D. Empirical models of pressure and density in Saturn’s interior: implications for the helium concentration, its depth dependence, and

Saturn’s precession rate. _Icarus_ 199, 368–377 (2009). ADS  Google Scholar  * Guillot, T. & Gautier, D. in _Treatise on Geophysics._ 2nd edn. Volume 10, 529–557

https://www.elsevier.com/books/treatise-on-geophysics/schubert/978-0-444-53802-4 (2015). * Helled, R. et al. in _Protostars and Planets_ VI (eds Beuther, H. et al.) 643 (2014). * Fortney, J.

J. & Hubbard, W. B. Phase separation in giant planets: inhomogeneous evolution of Saturn. _Icarus_ 164, 228–243 (2003). ADS  Google Scholar  * Mankovich, C., Fortney, J. J. & Moore,

K. L. Bayesian evolution models for Jupiter with helium rain and double-diffusive convection. _Astrophys. J._ 832, 113 (2016). ADS  Google Scholar  * Vazan, A., Helled, R., Podolak, M.

& Kovetz, A. The evolution and internal structure of Jupiter and Saturn with compositional gradients. _Astrophys. J._ 829, 118 (2016). ADS  Google Scholar  * Püstow, R., Nettelmann, N.,

Lorenzen, W. & Redmer, R. H/He demixing and the cooling behavior of Saturn. _Icarus_ 267, 323–333 (2016). ADS  Google Scholar  * Debras, F. & Chabrier, G. New models of Jupiter in

the context of Juno and Galileo. _Astrophys. J._ 872, 100 (2019). ADS  Google Scholar  * Bolton, S. J. et al. Jupiter’s interior and deep atmosphere: the initial pole-to-pole passes with the

Juno spacecraft. _Science_ 356, 821–825 (2017). ADS  Google Scholar  * Iess, L. et al. Measurement of Jupiter’s asymmetric gravity field. _Nature_ 555, 220–222 (2018). ADS  Google Scholar 

* Wahl, S. M. et al. Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core. _Geophys. Res. Lett._ 44, 4649–4659 (2017). ADS  Google Scholar 

* Nettelmann, N. Low- and high-order gravitational harmonics of rigidly rotating Jupiter. _Astron. Astrophys._ 606, A139 (2017). ADS  Google Scholar  * Guillot, T. et al. A suppression of

differential rotation in Jupiter’s deep interior. _Nature_ 555, 227–230 (2018). ADS  Google Scholar  * Helled, R. & Stevenson, D. The fuzziness of giant planets’ cores. _Astrophys. J.

Lett._ 840, L4 (2017). ADS  Google Scholar  * Iess, L. et al. Measurement and implications of Saturn’s gravity field and ring mass. _Science_ 364, aat2965 (2019). ADS  Google Scholar  *

Militzer, B., Wahl, S. & Hubbard, W. B. Models of Saturn’s interior constructed with an accelerated concentric Maclaurin spheroid method. _Astrophys. J_. 879, 78 (2019). * Helled, R.

& Guillot, T. Interior models of Saturn: including the uncertainties in shape and rotation. _Astrophys. J._ 767, 113 (2013). ADS  Google Scholar  * Galanti, E. et al. Saturn’s deep

atmospheric flows revealed by the Cassini Grand Finale gravity measurements. _Geophys. Res. Lett._ 46, 616–624 (2019). ADS  Google Scholar  * Fuller, J. Saturn ring seismology: evidence for

stable stratification in the deep interior of Saturn. _Icarus_ 242, 283–296 (2014). ADS  Google Scholar  * Helled, R. _The Interiors of Jupiter and Saturn_, 175 (Oxford Univ. Press, 2018). *

Lühr, H., Wicht, J., Gilder, S. A. & Holschneider, M. _Magnetic Fields in the Solar System_, Vol. 448 (Springer, 2018). * French, M. et al. Ab initio simulations for material properties

along the Jupiter adiabat. _Astrophys. J. Suppl._ 202, 5 (2012). ADS  Google Scholar  * Liu, J., Goldreich, P. M. & Stevenson, D. J. Constraints on deep-seated zonal winds inside

Jupiter and Saturn. _Icarus_ 196, 653–664 (2008). ADS  Google Scholar  * Cao, H. & Stevenson, D. J. Zonal flow magnetic field interaction in the semi-conducting region of giant planets.

_Icarus_ 296, 59–72 (2017). ADS  Google Scholar  * Gastine, T., Wicht, J., Duarte, L. D. V., Heimpel, M. & Becker, A. Explaining Jupiter’s magnetic field and equatorial jet dynamics.

_Geophys. Res. Lett._ 41, 5410–5419 (2014). ADS  Google Scholar  * Jones, C. A. A dynamo model of Jupiter’s magnetic field. _Icarus_ 241, 148–159 (2014). ADS  Google Scholar  * Wicht, J.,

Gastine, T., Duarte, L. D. V. & Dietrich, W. Dynamo action of the zonal winds in Jupiter. _Astron. Astrophys._ 629, A125 (2019). ADS  Google Scholar  * Duer, K., Galanti, E. & Kaspi,

Y. Analysis of Jupiter’s deep jets combining Juno gravity and time-varying magnetic field measurements. _Astrophys. J. Lett._ 879, L22 (2019). ADS  Google Scholar  * Connerney, J. E. P. et

al. A new model of Jupiter’s magnetic field from Juno’s first nine orbits. _Geophys. Res. Lett._ 45, 2590–2596 (2018). ADS  Google Scholar  * Moore, K. M. et al. A complex dynamo inferred

from the hemispheric dichotomy of Jupiter’s magnetic field. _Nature_ 561, 76–78 (2018). ADS  Google Scholar  * Dougherty, M. K. et al. Cassini magnetometer observations during Saturn orbit

insertion. _Science_ 307, 1266–1270 (2005). ADS  Google Scholar  * Dougherty, M. K. et al. Saturn’s magnetic field from the Cassini Grand Finale orbits. In _AGU Fall Meeting Abstracts_, Vol.

2017, U22A-02 (2017). * Cao, H. et al. The landscape of Saturn’s internal magnetic field from the Cassini Grand Finale. _Icarus_ 344, 113541 (2020). Google Scholar  * Cao, H., Russell, C.

T., Wicht, J., Christensen, U. R. & Dougherty, M. K. Saturn’s high degree magnetic moments: evidence for a unique planetary dynamo. _Icarus_ 221, 388–394 (2012). ADS  Google Scholar  *

Drozdov, A., Eremets, M., Troyan, I., Ksenofontov, V. & Shylin, S. Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system. _Nature_ 525, 73–76

(2015). ADS  Google Scholar  * Liu, H., Naumov, I. I., Hoffmann, R., Ashcroft, N. & Hemley, R. J. Potential high-_T_c superconducting lanthanum and yttrium hydrides at high pressure.

_Proc. Natl Acad. Sci. USA_ 114, 6990–6995 (2017). ADS  Google Scholar  * Nellis, W. J. et al. Equation of state data for molecular hydrogen and deuterium at shock pressures in the range

2–76 GPa (20–760 kbar). _J. Chem. Phys._ 79, 1480–1486 (1983). ADS  Google Scholar  * Holmes, N. C., Ross, M. & Nellis, W. J. Temperature measurements and dissociation of

shock-compressed liquid deuterium and hydrogen. _Phys. Rev. B_ 52, 15835–15845 (1995). ADS  Google Scholar  * Collins, G. W. et al. Measurements of the equation of state of deuterium at the

fluid insulator–metal transition. _Science_ 281, 1178 (1998). ADS  Google Scholar  * Belov, S. I. et al. Shock compression of solid deuterium. _J. Exp. Theor. Phys. Lett._ 76, 433–435

(2002). Google Scholar  * Boriskov, G. V. et al. Shock-wave compression of solid deuterium at a pressure of 120 GPa. _Dokl. Phys._ 48, 553–555 (2003). ADS  Google Scholar  * Grishechkin, S.

K. et al. Experimental measurements of the compressibility, temperature, and light absorption in dense shock-compressed gaseous deuterium. _J. Exp. Theor. Phys. Lett._ 80, 398–404 (2004).

Google Scholar  * Knudson, M. D. et al. Principal Hugoniot, reverberating wave, and mechanical reshock measurements of liquid deuterium to 400 GPa using plate impact techniques. _Phys. Rev.

B_ 69, 144209 (2004). ADS  Google Scholar  * Hicks, D. G. et al. Laser-driven single shock compression of fluid deuterium from 45 to 220 GPa. _Phys. Rev. B_ 79, 014112 (2009). ADS  Google

Scholar  * Loubeyre, P. et al. Extended data set for the equation of state of warm dense hydrogen isotopes. _Phys. Rev. B_ 86, 144115 (2012). ADS  Google Scholar  * Miguel, Y., Guillot, T.

& Fayon, L. Jupiter internal structure: the effect of different equations of state. _Astron. Astrophys._ 596, A114 (2016). ADS  Google Scholar  Download references ACKNOWLEDGEMENTS The

authors thank the anonymous referees for comments that helped to improve the manuscript. The authors also acknowledge support from W. Nellis, F. Soubrian, S. Sorella, D. Stevenson, N.

Nettelmann, J. J. Fortney, Y. Miguel, S. Müller, C. Valletta and A. Cumming. R.H. acknowledges support from the Swiss National Science Foundation (SNSF grant 200020_188460) and thanks the

members of the Juno science team for discussions. R.R. acknowledges support by the Deutsche Forschungsgemeinschaft via the projects FOR 2440 and SPP 1992. AUTHOR INFORMATION AUTHORS AND

AFFILIATIONS * Institute for Computational Science, Center for Theoretical Astrophysics and Cosmology, University of Zurich, Zurich, Switzerland Ravit Helled * IBM Quantum, IBM Research —

Zurich, Rüschlikon, Switzerland Guglielmo Mazzola * Institut für Physik, Universität Rostock, Rostock, Germany Ronald Redmer Authors * Ravit Helled View author publications You can also

search for this author inPubMed Google Scholar * Guglielmo Mazzola View author publications You can also search for this author inPubMed Google Scholar * Ronald Redmer View author

publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS All authors contributed to all aspects of this article. CORRESPONDING AUTHOR Correspondence to Ravit

Helled. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature remains neutral with regard to

jurisdictional claims in published maps and institutional affiliations. RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Helled, R., Mazzola, G. &

Redmer, R. Understanding dense hydrogen at planetary conditions. _Nat Rev Phys_ 2, 562–574 (2020). https://doi.org/10.1038/s42254-020-0223-3 Download citation * Accepted: 20 July 2020 *

Published: 01 September 2020 * Issue Date: October 2020 * DOI: https://doi.org/10.1038/s42254-020-0223-3 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this

content: Get shareable link Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative