# Atom-in-jellium equations of state for cryogenic liquids

## TL;DR

This paper applies an efficient atom-in-jellium model to predict equations of state for cryogenic liquids nitrogen, oxygen, and fluorine, showing good agreement with experimental shock data and advanced simulations, and improving high-pressure predictions.

## Contribution

The study extends the atom-in-jellium EOS approach to cryogenic liquids, providing more accurate high-pressure models for nitrogen, oxygen, and fluorine compared to previous methods.

## Key findings

- EOS predictions align with shock data and PIMC simulations
- Systematic deviations from Thomas-Fermi EOS due to shell ionization
- Enhanced high-pressure accuracy for nitrogen and oxygen EOS

## Abstract

Equations of state (EOS) calculated from a computationally efficient atom-in-jellium treatment of the electronic structure have recently been shown to be consistent with more rigorous path integral Monte Carlo (PIMC) and quantum molecular dynamics (QMD) simulations of metals in the warm dense matter regime. Here we apply the atom-in-jellium model to predict wide-ranging EOS for the cryogenic liquid elements nitrogen, oxygen, and fluorine. The principal Hugoniots for these substances were surprisingly consistent with available shock data and Thomas-Fermi (TF) EOS for very high pressures, and exhibited systematic variations from TF associated with shell ionization effects, in good agreement with PIMC, though deviating from QMD and experiment in the molecular regime. The new EOS are accurate much higher in pressure than previous widely-used models for nitrogen and oxygen in particular, and should allow much more accurate predictions for oxides and nitrides in the liquid, vapor, and plasma regime, where these have previously been constructed as mixtures containing the older EOS.