Thermodynamic properties of some diatomic molecules confined by an harmonic oscillating system

In this study, the one-dimensional Schrödinger equation with harmonic oscillator is solved within the formalism of proper quantization rule and obtain the energy levels. By employing Hellmann–Feynman theorem, the expectation value for the square of position x 2 is evaluated and thereafter derived an expression for the diamagnetic susceptibility. Furthermore, using the energy levels equation, the expressions for the partition function, thermodynamic properties and the Massieu function were obtained. Using the spectroscopic parameters for the selected diatomic molecules, some graphs were plotted and reported. The graphical results show that diamagnetic susceptibility depends on the atomic number ( z ), and number of states n and that molecules in the ground state experienced the strongest effect of diamagnetic susceptibility. It was also found that the thermodynamic properties of some diatomic molecules depend not just on temperature but also on the vibrational frequencies ( ω ) and the number of states ( n ). The number of accessible vibrational states depends on temperature and the masses of the molecules. The heaviest molecule has the highest accessible vibrational state.