In this research paper, the approximate bound state solutions and thermodynamic
properties of Schrӧdinger equation with modified exponential screened plus Yukawa
potential (MESPYP) were obtained with the help Greene–Aldrich approximation to
evaluate the centrifugal term. The Nikiforov–Uvarov (NU) method was used to obtain
the analytical solutions. The numerical bound state solutions of five selected diatomic
molecules, namely mercury hydride (HgH), zinc hydride (ZnH), cadmium hydride (CdH),
hydrogen bromide (HBr) and hydrogen fluoride (HF) molecules were also obtained.
We obtained the energy eigenvalues for these molecules using the resulting energy
eigenequation and total unnormalized wave function expressed in terms of associated
Jacobi polynomial. The resulting energy eigenequation was presented in a closed
form and applied to study partition function (Z) and other thermodynamic properties
of the system such as vibrational mean energy (U), vibrational specific heat capacity
(C), vibrational entropy (S) and vibrational free energy (F). The numerical bound state solutions were obtained from the resulting energy eigenequation for some orbital angular quantum number. The results obtained from the thermodynamic properties are in excellent agreement with the existing literature. All numerical computations were carried out using spectroscopic constants of the selected diatomic molecules with the help of MATLAB 10.0 version. The numerical bound state solutions obtained increases with an increase in quantum state