Quantum Monte Carlo Simulation of the High-Pressure Molecular-Atomic Crossover in Fluid Hydrogen

A first-order liquid-liquid phase transition in high-pressure hydrogen between molecular and atomic fluid phases has been predicted in computer simulations using ab initio molecular dynamics approaches. However, experiments indicate that molecular dissociation may occur through a continuous crossover rather than a first-order transition. Here we study the nature of molecular dissociation in fluid hydrogen using an alternative simulation technique in which electronic correlation is computed within quantum Monte Carlo methods, the so-called coupled electron-ion Monte Carlo method. We find no evidence for a first-order liquid-liquid phase transition.

Figure 1

VMC and RQMC total energies for five different crystal configurations at two different densities (left graphs $V=9.42\mathrm{a}.\mathrm{u}./\mathrm{\text{atom}}$ or $r_s=1.31$; right graphs $V=33.51\mathrm{a}.\mathrm{u}./\mathrm{\text{atom}}$ or $r_s=2.0$) using a number of different Slater-Jastrow wave functions. Configuration 1 is molecular, 2–5 are nonmolecular. Owing to the variational principle, a lower energy implies a better wave function. DFT-LDA and bare electron-proton bands (see text) provide the best and most transferable orbitals for the Slater determinant. Gaussian for configuration 1 refers to localized molecular orbitals.

Figure 2

Proton-proton correlation functions for CEIMC simulations in the canonical ensemble with 32 atoms at $T=2000\mathrm{K}$. The BO energies are computed with VMC (left pane) or RQMC (right pane) and the wave function is a Slater-Jastrow type with bare electron-proton bands (see text). Gray lines are simulations initially prepared with a molecular fluid and black with an atomic fluid. Hysteresis is evident. $P_{\mathrm{at}}$ and $P_m$ are the computed pressures for simulations prepared with an atomic and a molecular fluid, respectively. All correlation functions are plotted to the same scale.

Figure 3

Molecular order parameter [$\lambda$ in Eq. (2)] evaluated for simulation results from Fig. 2. Two curves are obtained for each method from different initial conditions (see text). VMC (dashed lines) simulations indicate an irreversible, weakly first-order phase transition for molecular dissociation in the fluid with increasing or decreasing pressure. This picture is compatible with conclusions from CPMD DFT-LDA. Accurate RQMC (solid lines) simulations find a reversible crossover.

Figure 4

Demonstration of finite-size errors in VMC pair-correlation functions (upper pane). Solid lines are 32-atom simulations, dashed are 54 atoms. Gray lines are simulations started from a molecular fluid and black are from an atomic fluid. Quoted pressures are for simulations started from a molecular fluid. RQMC (lower pane) simulations show small finite-size errors.

Figure 5

Proton-proton correlation functions for simulations at $T=1500\mathrm{K}$. Black lines are simulations prepared with an atomic fluid, gray are prepared with a molecular fluid. The simulations demonstrate an irreversible transition with hysteresis for VMC. Left pane: VMC; right pane: RQMC.