Thermodynamic properties of diatomic molecule systems under SO(2,1)-anharmonic Eckart potential

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 a typical interaction for one-dimensional microscopic systems, which describes local anharmonic effects. From the Eckart potential (EP) model, it is possible to find a connection with the GMP model, as well as obtaining the analytical expression for the energy spectrum because it is based on SO(2,1) algebras. This gives the macroscopic properties such as vibrational mean energy U, specific heat C, Helmholtz free energy F, and entropy S for a heteronuclear diatomic system, as well as with the exact partition function and its approximation for the high temperature region. Finally, a comparison is made between the graphs of some thermodynamic functions obtained with the GMP and the Morse potential (MP) for HCl molecules.