[Paper Review] A first-principles global multiphase equation of state for hydrogen

Alfredo A. Correa, Lorin X. Benedict+4 more|arXiv (Cornell University)|Jun 4, 2018

Spectroscopy and Quantum Chemical Studies3 citations

TL;DR

This paper presents a first-principles global multiphase equation of state (EOS) for hydrogen spanning 1–10⁹ K and 10⁻⁹–1 m³/mol, constructed using ab initio simulations with quantum protons and electrons. It employs physically motivated free energy models, a multiparameter/multiderivative fitting method, and thermodynamically consistent analytic forms to accurately describe molecular solids, fluids, atomic liquids, and phase transitions without interpolation-induced discontinuities.

ABSTRACT

We present and discuss a wide-range hydrogen equation of state model based on a consistent set of ab initio simulations including quantum protons and electrons. Both the process of constructing this model and its predictions are discussed in detail. The cornerstones of this work are the specification of simple physically motivated free energy models, a general multiparameter/multiderivative fitting method, and the use of the most accurate simulation methods to date. The resulting equation of state aims for a global range of validity ($T = 1-10^9 K$ and $V_m = 10^{-9}-1 m^3/mol$), as the models are specifically constructed to reproduce exact thermodynamic and mechanical limits. Our model is for the most part analytic or semianalytic and is thermodynamically consistent by construction; the problem of interpolating between distinctly different models -often a cause for thermodynamic inconsistencies and spurious discontinuities- is avoided entirely.

Motivation & Objective

• To develop a globally valid equation of state for hydrogen across extreme thermodynamic conditions, from cryogenic molecular solids to hot, dense plasmas.
• To overcome thermodynamic inconsistencies in existing models by avoiding interpolation between distinct phase models.
• To incorporate quantum nuclear effects (proton zero-point motion) explicitly in all phases, especially critical for low-temperature and low-density regimes.
• To ensure thermodynamic consistency across all phases using analytic free energy expressions derived from ab initio data.
• To provide a unified, predictive model for hydrogen and deuterium-tritium mixtures in inertial confinement fusion and planetary science applications.

Proposed method

• Constructs a global equation of state using first-principles quantum molecular dynamics and density functional theory (DFT) simulations with accurate treatment of electrons and quantum protons.
• Develops physically motivated free energy models for molecular solids (via Mie-Grüneisen and cold curve approximations), atomic fluids (ideal gas limit), and mixed phases (molecular-atomic fluid mixtures).
• Applies a multiparameter/multiderivative fitting method to fit simulation data across all phases, ensuring smooth transitions and thermodynamic consistency.
• Uses a non-ideal mixing model with self-consistent mean-field interactions (via coupling parameter J) to describe the molecular-atomic transition near the critical point.
• Derives analytic expressions for the free energy of mixed phases using statistical mechanics, incorporating configurational entropy and non-ideal interactions.
• Validates the model against path-integral Monte Carlo (PIMC) data, shock Hugoniot experiments, and known thermodynamic limits (e.g., ideal gas, melting line).

Experimental results

Research questions

• RQ1 How can a thermodynamically consistent, global equation of state for hydrogen be constructed across all phases—from molecular solids to atomic plasmas—using first-principles simulations?
• RQ2 What is the role of quantum nuclear effects (zero-point motion) in determining the stability and thermodynamics of low-density and low-temperature hydrogen phases?
• RQ3 How can phase transitions (e.g., melting, molecular-to-atomic dissociation) be accurately modeled without interpolation artifacts between separate phase models?
• RQ4 To what extent do non-ideal interactions between atoms and molecules affect the critical behavior and phase coexistence in dense hydrogen?
• RQ5 How does the model compare quantitatively with experimental shock Hugoniot data and PIMC simulations in the high-pressure, high-temperature regime?

Key findings

• The model achieves global validity over 1–10⁹ K and 10⁻⁹–1 m³/mol, covering all known hydrogen phases including molecular solids, liquids, and plasmas.
• The inclusion of quantum protons significantly improves the description of low-temperature molecular phases, particularly near the melting line, where classical models fail.
• The model reproduces the principal shock Hugoniot with good agreement to experimental data, especially in the 10–100 GPa range, outperforming older ion-sphere models like Purgatorio.
• The non-ideal mixing model with self-consistent mean-field interactions (J) successfully captures the liquid-vapor dome and critical region, avoiding unphysical discontinuities.
• The model predicts a molecular-to-atomic fraction transition that is consistent with PIMC simulations and shows a smooth, continuous evolution across the fluid phase.
• Thermodynamic consistency is achieved by construction: all derived properties (pressure, entropy, specific heat) satisfy exact thermodynamic relations, eliminating interpolation artifacts.