| Summary: | By employing the Pekeris-type approximation to deal with the centrifugal term, we study the thermodynamic properties and approximate analytical solutions of the Schrödinger equation with the exponential inversely quadratic plus improved deformed exponential-type potential using parametric Nikiforov–Uvarov method and hypergeometric functional analysis method. The complex eigen energy equation was presented in a closed and compact form and extended to study partition function and other thermodynamic properties. The total normalized wave functions were also obtained and expressed in terms of hypergeometric Jacobi polynomial. The mathematical accuracy of analytical calculation can be verified consistently by comparing numerical data and results of different arbitrarily l state. The potential also reduces to improved deformed exponential-type potential as a special case. We calculated energy spectra for some selected diatomic molecules namely: Silicon Flouride (SiF+ (X1∑+), Oxygen molecule O2+ (X2∏g), Nitrogen molecule, N2+ (X1∑g+), Sulphur chloride SCl and Rubidium hydride RbH using standard molecular spectroscopic constants as applied to the two methods. The results show that the energy eigenvalues for these selected diatomic molecules are in excellent agreement using the two methods and also increases with an increase in quantum state.
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