Comment on "Bound state solutions of Schrödinger equation with modified Mobius square potential (MMSP) and its...

Okorie et al. (J. Mol. Model. 24, 289 (2018)) obtained approximate bound-state energies for the Schrödinger equation with the so-called modified Mobius square potential (MMSP) by means of the Greene-Aldrich approximation and a modified factorization method. The resulting eigenvalues were subsequently employed for the calculation of vibrational thermodynamic functions. In this Comment, we examine the physical interpretation of the proposed potential and the consistency of the corresponding spectroscopic and thermodynamic results. The MMSP is analyzed through its asymptotic behaviour, stationary points, parameter dependence, and scaling properties. The validity of the Greene-Aldrich approximation and the derivation of the vibrational partition function are also examined. The analysis shows that the MMSP is singular at the origin and, for the parameter values employed by the authors, exhibits a maximum instead of a minimum, thus lacking the qualitative features required for the description of vibrational motion in a diatomic molecule. We further show that the model effectively depends on only two independent parameters, that the reported energy spectrum exhibits unphysical features, and that the proposed thermodynamic treatment contains several inconsistencies, including an arbitrary choice of the upper vibrational quantum number and an explicit dependence of the vibrational partition function on the rotational quantum number. These results indicate that neither the MMSP nor the associated thermodynamic analysis provides a physically consistent basis for molecular applications.