Phase Diagram of Hydrogen and a Hydrogen-Helium Mixture at Planetary Conditions by Quantum Monte Carlo Simulations

Abstract

Understanding planetary interiors is directly linked to our ability of simulating exotic quantum mechanical systems such as hydrogen (H) and hydrogen-helium (H-He) mixtures at high pressures and temperatures 1 . Equations of State (EOSs) tables based on Density Functional Theory (DFT), are commonly used by planetary scientists, although this method allows only for a qualitative description of the phase diagram 2 , due to an incomplete treatment of electronic interactions 3 . Here we report Quantum Monte Carlo (QMC) molecular dynamics simulations of pure H and H-He mixture. We calculate the first QMC EOS at 6000 K for an H-He mixture of a proto-solar composition, and show the crucial influence of He on the H metallization pressure. Our results can be used to calibrate other EOS calculations and are very timely given the accurate determination of Jupiter's gravitational field from the NASA Juno mission and the effort to determine its structure 4 .Since a few decades the link between the uncertainty of the H EOS and the internal structure of Jupiter (and other gaseous planets) has been investigated and many efforts to model Jupiter's interior have been carried 1,5-7 . The computation of an EOS from first principles requires to solve a many-body quantum mechanical problem, a task which is beyond the currently available theoretical and computational capabilities. In practice, we must resort to several approximations. The first is to decouple the ionic and electronic problems and consider the ions as classical or quantum particles, determining their motion by following the Born-Oppenheimer potential energy surface. The second approximation concerns the description of the electronic interaction and the exchange one, due to the Pauli exclusion principle.The standard approach to EOS calculations relies on Density Functional Theory (DFT), which targets the tridimensional electronic density rather than the (N e electrons) many-body wave-function. Its success and simplicity have lead to a widespread application in materials science and to the development of several software packages which allow fast and reproducible calculations 8 . Although DFT is formally exact, the explicit functional form to describe the exchange and correlation (XC) effects between electrons remains approximated 3 . Indeed, a systematic and efficient route to improve XC functional is still lacking. Therefore, in practical solid state calculations, benchmarks against experimental data, are often required to validate the XC functional used to describe the system in a satisfactory manner.Dense hydrogen systems, both in the low temperature solid and in the liquid phase remain a challenge to DFT simulations due to the interplay of strong correlation and non-covalent interactions between the atoms. DFT calculations with different functionals produce different results with the expected metallization pressure varying over a range of 100-200 GPa (Fig. 1) 12,13 . Since experimental data are limited, it is not possible to identify a posteriori the best functional...

Metastable molecular fluid hydrogen at high pressures

“…[26] While most theoretical works suggest that it is a first-order transition, [1][2][3][4][5][6][7][8][9][10] there is an uncertainty in the experimental verification. [26] While most theoretical works suggest that it is a first-order transition, [1][2][3][4][5][6][7][8][9][10] there is an uncertainty in the experimental verification.…”

“…[1][2][3][4][5][6][7][8][9][10][11] The methods also include density functional theory (DFT), [12] path-integral molecular dynamics (PIMD) based on DFT, coupled electron-ion Monte Carlo (CEIMC), [13] and the quantum Monte Carlo molecular dynamics (QMCMD). [1][2][3][4][5][6][7][8][9][10][11] The methods also include density functional theory (DFT), [12] path-integral molecular dynamics (PIMD) based on DFT, coupled electron-ion Monte Carlo (CEIMC), [13] and the quantum Monte Carlo molecular dynamics (QMCMD).…”

“…It is also noted in refs. [19] The molecular simulation studies [1][2][3][4][5]7] do not deal with the metastable region. According to refs.…”

Molecular Simulation of Covalent Bond Dynamics in Liquid Silicon

“…These liquids play important roles in fuel cells, catalysis, and electrochemistry, where the dynamic covalent bonds are expected to play an importance role in chemical reactivity 20 . Many of these liquids are also found in planetary cores 16,[21][22][23][24][25] and understanding their structure and dynamics is of importance to planetary and geophysical sciences.…”

Benchmarking vdW‐DF first‐principles predictions against Coupled Electron–Ion Monte Carlo for high‐pressure liquid hydrogen

“…At the same time, the simple electronic structure of hydrogen makes it the ideal candidate for developing new first‐principles methods based on more fundamental many‐body theories such as those based on quantum Monte Carlo (QMC) techniques. Two similar methods have appeared in the last decade and were applied to study compressed hydrogen: the Coupled Electron–Ion Monte Carlo (CEIMC) and the quantum Monte Carlo molecular dynamics (QMCMD) . They are both based on solving the electronic problem by ground‐state QMC methods but differ in the way they sample the nuclear configuration space .…”