Thermodynamic properties of diatomic molecules systems under anharmonic Eckart potential

TL;DR

This paper derives thermodynamic properties of diatomic molecules modeled with anharmonic potentials, connecting Eckart and Morse potentials, and compares theoretical predictions with molecular data.

Contribution

It provides analytical expressions for thermodynamic quantities of diatomic molecules using Eckart potential and compares results with Morse potential models.

Findings

Exact partition function and thermodynamic functions derived

Comparison shows differences between GMP and Morse potential predictions

Results applicable to heteronuclear diatomic molecules like HCl

Abstract

Due to one of the most representative contributions to the energy in diatomic molecules being the vibrational, we consider the generalized Morse potential (GMP) as one of the typical potential of interaction for one-dimensional microscopic systems, which describes local anharmonic effects. From Eckart potential (EP) model, it is possible to find a connection with the GMP model, as well as obtain the analytical expression for the energy spectrum because it is based on $S\,O\left(2,1\right)$ algebras. In this work we find the macroscopic properties such as vibrational mean energy $U$, specific heat $C$, Helmholtz free energy $F$ and entropy $S$ for a heteronuclear diatomic system, along with the exact partition function and its approximation for the high temperature region. Finally, we make a comparison between the graphs of some thermodynamic functions obtained with the GMP and the Morse potential (MP) for $H\,Cl$ molecules.