Improved energy equations and thermal functions for diatomic molecules: a generalized fractional derivative approach

• DOI: 10.1007/s00894-024-06208-4
• Publication Date: 2024-11-27T07:22:51Z
• Authors: E. S. Eyube; C. R. Makasson; E. Omugbe; C. A. Onate; E. P. Inyang; A. M. Tahir; J. U. Ojar; S. D. Najoji
• Keywords: Diatomic molecule; Derivative (finance)

Abstract Due to the need for accurate analysis of interactions in diatomic molecules using analytical models, this work develops expressions for ro-vibrational energy models embedding fractional parameters. These expressions are derived by solving the Schrödinger equation for a variant of the Tietz potential using the generalized fractional Nikiforov-Uvarov solution method and a Pekeris-type approximation scheme. The canonical partition function for the system is employed to formulate thermodynamic models, including Helmholtz free energy, mean thermal energy, entropy, and isochoric heat capacity. The analytical equations are applied to diatomic molecules such as CO (X (C(2) 1 Π u), and NaK (c 3 ∑ +). The percentage average absolute deviations for the pure vibrational energies of these molecules are 0.2185%, 0.0630%, 0.6984%, 0.0975%, 0.7433%, 0.1988%, 0.1684%, and 0.2645%, relative to the experimental data. The study reveals a linear decrease in Helmholtz free energy and an initial increase in heat capacity as the temperature of the system rises. The results obtained are consistent with existing literature on diatomic systems.