Computing energy fluctuations in diatomic molecules through thermodynamic properties using the partition function approach

This study presents a numerical and computational investigation into the energy fluctuations of three diatomic molecules—carbon monoxide (CO), hydrogen (H₂), and scandium hydride (ScH)— under a varying temperature parameter β based on two – dimension Schrödinger equation governed by Nikiforov – Uvarov Functional Analysis (NUFA) approach under the influence of magnetic field and magnetic flux. The numerical analysis indicates that when no external magnetic field is applied B = 0T and AB = 0, the energy spectrum experiences a slight increase. However, a higher energy spectrum is observed when an external field is introduced at ∅AB = 9 and B = 9 T. Examining the individual effects reveals that ∅AB = 9 and B = 0 T have a somewhat stronger impact on the energy spectrum compared to B = 0T, and ∅AB = 0 has a limited effect on the overall energy spectrum. Additionally, it was numerically demonstrated that the energy levels remain consistent across three diatomic molecules, regardless of changes in the magnetic quantum number. Furthermore, shifts were noted in orbitals (s, p, d, f), which are uniformly affected by external variables. The values of these orbitals decrease as the orbital quantum number (n) increases, following the expected sequence: s > p > d > f. Computational findings, derived from a thermodynamic approach using partition analysis, show a reduction in the partition function when plotted against temperature, influenced by the magnetic field and flux. It was also observed that both molecules exhibit heightened energy fluctuations as the magnetic field strength and flux increase. The study underscores the critical role of external magnetic factors in shaping molecular energy behaviour through entropy, internal energy, free energy, specific heat capacity and energy fluctuation across various temperature ranges.