Coupled Electron-Ion Monte Carlo Study of High Pressure Hydrogen

Abstract

We propose to apply ab-initio methods to study the physics of hydrogen at high pressure, a long standing problem in condensed matter physics. The problem is particularly challenging since several energy scales are relevant (electronic correlations, zero-point energy for the protons, energy difference between several crystal structures) in the region of phase diagram where most of the interesting physics occurs (molecular dissociation, melting of molecular and monoatomic crystals, metal-insulator transition). Recently we have developed a new ab-initio simulation method particularly suitable for attacking this problem: the Coupled Electron Ion Monte Carlo Method (CEIMC). At variance with the standard ab-initio methods based on Density Functional Theory (DFT), in CEIMC we employ ground state Quantum Monte Carlo (QMC) to solve the electronic problem, and classical or Path Integral MC to sample the protons configurational space. CEIMC is therefore expected to be more accurate than DFT based methods, in particular close to molecular dissociation a process which DFT does not describe accurately enough. Recent improvements in trial wave functions employed in CEIMC allow to perform an accurate and systematic investigation of the physics of hydrogen. We have already computed the Equation of State (EOS) in the range of pressure 2 Mbars# P #20 Mbars and temperatures 2000K# T #10000 K and compared the results with prediction from the so called, Born-Oppenheimer molecular dynamics (BOMD). The aim of the present project is to continue the systematic exploration of high pressure hydrogen, in particular we want to perform:

1. a more refined study of the molecular dissociation regime in the fluid phase. We have already evidence that the dissociation process is very sensitive to the particular methods applied. We have found noticeable differences using two different DFT methods within BOMD (different pseudopotentials). It is therefore crucial to obtain predictions from an independent and accurate method such as CEIMC.

2. an accurate determination of the melting line of both molecular and atomic hydrogen. It has been speculated that the molecular crystal has a reentrant melting line and that the transition from the molecular crystal at lower pressure to the atomic crystal at higher pressure occurs through a low temperature liquid phase stabilized by the zero-point energy of protons. We intend to explore this phenomenology and clarify which of the possible proposed scenarios is more realistic.