The Nikiforov-Uvarov method in the study of thermodynamic properties of the diatomic molecules

Abstract

Transition metal hydrides, including CrH and others, have a significant impact on chemical synthesis, serving as intermediates and in solid matrix samples for infrared spectroscopy. Moreover, the CuLi molecule provides insights into the bonding characteristics of mixed transition metal lithides. Additionally, the study of transition metal carbide molecules like TiC, NiC, and others is currently a highly active research area, driven by the necessity for accurate measurement of their chemical bonding. This thesis explores the solution of the Schr¨odinger equation for the Manning-Rosen potential alongside a class of Yukawa and the Hulth´en plus Yukawa potential models using the Nikiforov-Uvarov method. It obtains the energy eigenvalues and corresponding eigenfunctions in closed form. Subsequently, the partition function is computed, and various thermodynamic functions such as Helmholtz free energy, mean energy, entropy, and specific heat capacity of the system are evaluated. Furthermore, the Schr¨odinger equation for the Hulth´en plus Yukawa potential model is solved under the influence of magnetic and Aharonov-Bohm flux fields using the exact quantization rule. Closed-form expressions for the energy eigenvalues are derived and utilized to compute the partition function and other thermo-magnetic functions such as Helmholtz free energy, mean energy, entropy, specific heat, magnetization, and magnetic susceptibility for CuLi, CrH, and NiC diatomic molecules. These findings are relevant in condensed matter physics, chemical and molecular physics, and various other areas of physics.