Thermodynamic Properties of Diatomic Molecules from the Frost-Musulin Potential

TL;DR

This paper develops an analytical quantum-statistical model for diatomic molecules using the Frost-Musulin potential, accurately predicting thermodynamic properties and identifying limitations at high temperatures.

Contribution

It introduces a validated bound-state approach combined with the Pekeris representation to compute thermodynamic observables for diatomic molecules.

Findings

Accurately reproduces energy level ordering and thermodynamic quantities.

Captures Gibbs free energy deviation with high quantitative accuracy.

Identifies the regime where the model's limitations become significant.

Abstract

In this study, we present a quantum-statistical analysis of H$_2$ and LiH diatomic molecules within the Frost--Musulin potential framework. By combining the analytical bound-state approach to the radial Schr\"odinger problem with the near-equilibrium Pekeris representation, we obtain a validated rotation-vibration spectrum that reproduces a physically consistent ordering of energy levels. These bound states are subsequently combined with standard translational and rotational ideal gas contributions to construct the total partition function and the corresponding thermodynamic observables of the ground state. The resulting formulation captures the Gibbs free energy deviation function for both molecules with high quantitative accuracy and provides chemically plausible trends for heat capacity and enthalpy increase over a wide temperature range. At the same time, residual errors become increasingly pronounced in derivative-sensitive quantities, particularly at high temperatures; this indicates that the dominant limitations now stem not from the local bound-state spectrum itself, but from the neglect of inelastic rotational, continuity contributions and dynamics close to dissociation. Consequently, the present results define the potential model as a compact and analytically tractable representation of the bound region, recovering a significant portion of the observed thermochemistry whilst also delineating the regime where more comprehensive molecular statistical mechanics is required.