Thermomagnetic Models for the Improved Rosen–Morse Oscillator

This study solves the radial Schrödinger wave equation (RSWE) with the improved Rosen–Morse (IRM) potential constrained by an electromagnetic field. Energy eigenvalues are derived using the parametric Nikiforov–Uvarov method and Pekeris approximation. The internal partition function, isobaric molar heat capacity formula, and magnetization model are then deduced from the equation governing pure vibrational energy states. These analytical models are applied to several pure substances, specifically Br₂ (X ¹Σ_g⁺), BrF (X ¹Σ⁺), ICl (X ¹Σ_g⁺), and P₂ (X ¹Σ_g⁺) molecules. Numerical approximations of the energy eigenvalues for these molecules closely match their exact values. The isobaric molar heat capacity expression yields mean percentage absolute deviations of 1.6585%, 0.9162%, 1.2193%, and 0.7232% when compared against experimental data for Br₂ (X ¹Σ_g⁺), BrF (X ¹Σ⁺), ICl (X ¹Σ_g⁺), and P₂ (X ¹Σ_g⁺), respectively. These results align well with other heat capacity models in existing literature.