Energetics and partition function of H$_3^+$ molecular ion

TL;DR

This paper uses path integral Monte Carlo simulations to compute the thermodynamic properties of H$_3^+$, providing new insights into its energetics and dissociation behavior at planetary-relevant temperatures.

Contribution

It introduces the first comprehensive quantum statistical analysis of H$_3^+$, including a new analytical partition function model and extension of ab initio methods beyond Born--Oppenheimer approximation.

Findings

Calculated total energy, partition function, free energy, entropy, and heat capacity of H$_3^+$.

Described temperature and density-dependent dissociation and ionization processes.

Provided a new analytical model for the molecular partition function.

Abstract

Full $NVT$ quantum statistics of the H$_3^+$ ion is simulated at low densities using the path integral Monte Carlo approach. For the first time, the molecular total energy, partition function, free energy, entropy and heat capacity are evaluated in temperatures relevant for planetary atmospheric physics. Temperature and density dependent dissociation recombination reaction balance of the molecule and its fragments above 4000 K is described, and also, the density dependence of thermal ionization above $10 000$ K is demonstrated. We introduce a new well-behaving analytical model for the molecular partition function of the H$_3^+$ ion for the temperature range below dissociation and fit the parameters to the energetics from our simulations. The approach presented here can be regarded as an extension of the traditional {\it ab initio} quantum chemistry beyond the Born--Oppenheimer approximation to description of nonadiabatic phenomena, and even further, account of nuclear quantum dynamics.