Quantum mechanical analysis of cesium dimer, titanium hydride, and titanium carbide: Vibrational spectra, expectation values, and information-theoretic measures

This study explores quantum systems governed by a hybrid potential model that combines the Möbius square and screened Kratzer potentials (MSSKP). The Schrödinger Eq. was solved analytically using the parametric Nikiforov–Uvarov (pNU) method to investigate the quantum properties of heteronuclear diatomic molecules such as titanium hydride (TiH) and titanium carbide (TiC). Information-theoretic measures—namely, Shannon entropy and Fisher information—were employed to probe wavefunction delocalization and electron density localization, respectively. Expectation values were derived using the Hellmann–Feynman theorem. The results indicate that TiC exhibits stronger electron localization and covalent bonding compared to TiH. Moreover, the vibrational energy levels of the cesium dimer (Cs₂) were calculated and showed excellent agreement with experimental Rydberg–Klein–Rees (RKR) data. Comparative analysis revealed that the MSSKP outperforms the Morse and Manning–Rosen potentials, achieving a minimum mean absolute error (MAE) of 0.0234 cm⁻¹, compared to 0.2364 cm⁻¹ and 0.0517 cm⁻¹, respectively. This work underscores the synergy between quantum mechanical modeling and information theory, offering deeper insights into molecular structure, bonding, and quantum behavior relevant to quantum chemistry and nanophysics.