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.

The calculation of ro-vibrational energies, franck-condon factors and r-centroids for Yttrium/Scandium oxides in D-dimension

“…The equation (30) is known in the literature as the Deng-Fan potential function [32]. By using Lambert function as z = w(z)e w( z) [33], the screening parameter α is expressed in the following form: When the literature is scanned, it is seen that ro-vibrational energies are calculated for many diatomic molecules by using different potential functions [34][35][36][37][38][39][40][41][42][43]. In this study, taking = a q e r e and the screening parameter as in equation ( 32), Deng-fan potential given by equation (30) will be considered in D-Dimensional (D 3).…”

A method for predicting the entropy and Gibbs free energy of ICl and BrCl gases based on an improved Hulburt-Hirschfelder potential

“…It can be seen from table 2 that the average absolute deviation of the thermodynamic quantities of ICl and BrCl molecules calculated based on the IHH potential model are all smaller than those of the HH and Morse potentials, which demonstrates that the potential energy data predicted by the IHH potential energy model are found to be more accurate compared with HH and Morse models. To compare with existing literature results, table 2 also lists the average absolute deviation obtained by other models that are the IQSO model [13] and the RSO model [15]. The results clearly demonstrate that on the scale of the 1% error limit of the NIST experimental data, the IHH potential energy model can successfully predict both the reduced molar Gibbs free energy and molar entropy data for ICl molecule and is more accurate than that obtained by IQSO model, and is as effective as the RSO model in predicting both cases for BrCl molecule.…”

“…Recently, Habibinejad et al [12] have solved the Schrödinger equation with the improved deformed exponential-type potential (IDEP) and have obtained the energy spectra of the model using the Greene-Aldrich approximation and a coordinate transformation, with the classical partition function obtained, the explicit expressions of Gibbs free energy and enthalpy are derived and are successfully applied to four diatomic molecules. Eyube et al used the improved q-deformed Scarf II oscillator (IQSO) [13], the improved generalized Pöschl-Teller (IGPT) potential [14], the reparameterized Scarf oscillator (RSO) [15] and the specialized Pöschl-Teller (SPT) potential [16] to derive the analytical equations of molar entropy and Gibbs free energy, which are verified by the applications for several diatomic molecules in a wild temperature range up to 6000 K.…”

“…The study of the thermodynamic properties of diatomic molecules gas has attracted great attention in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. It is applicable in the fields of material science, engineering science, chemical engineering, food chemistry, medicine and agriculture.…”

Energy eigenvalues and finite-temperature magnetization for the improved Scarf II potential in the presence of external magnetic and Aharonov-Bohm flux fields

“…The equation for pure vibrational state energies obtained for the ISPEF has been used to analyze the energy states of diatomic molecules [ 11 ]. Thermo-chemical equations of substances have also been reported with various formulations of the ISPEF [ 8 , 50 ].…”