Pure vibrational state energies and statistical-mechanical models for the reparameterized scarf oscillator

Abstract

In this work, the reparameterized Scarf II oscillator was employed to describe the internal vibration of diatomic systems. Analytical equations for bound state pure vibrational energies and canonical partition function were obtained. The equations were used to derive statistical-mechanical models for the prediction of molar entropy, enthalpy, Gibbs free energy and constant pressure (isobaric) heat capacity of gaseous substances. The obtained model equations were used to generate numerical data on bound state energy eigenvalues and, to investigate the thermodynamic properties of the ground states chloroborane (BCl), bromine fluoride (BrF), and bromine chloride (BrCl) molecules. With the aid of the expression for molar entropy of the system, average absolute deviations obtained for the molecules are 0.1878%, 0.1267%, and 0.0586% from experimental data. The isobaric heat capacity model yields average absolute deviation of 2.1608%, 1.8601%, and 1.9805%. The results obtained are in good agreement with available literature data on gaseous molecule. The work could be applicable in the fields of molecular physics, chemical physics, solid-state physics and chemical engineering.