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

Autor: Eyube ES; Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria. edwineyubes@mau.edu.ng., Makasson CR; Department of Science Laboratory Technology, School of Science and Technology, Adamawa State Polytechnic, P.M.B. 2146, Yola, Adamawa State, Nigeria., Omugbe E; Department of Physics, University of Agriculture and Environmental Sciences, P.M.B. 1038, UmuagwoOwerri, Imo State, Nigeria., Onate CA; Physics Program, College of Agriculture, Engineering and Science, Bowen University, Iwo, Osun State, Nigeria., Inyang EP; Department of Physics, National Open University of Nigeria, Jabi-Abuja, Nigeria., Tahir AM; Department of Science Laboratory Technology, School of Science and Technology, Adamawa State Polytechnic, P.M.B. 2146, Yola, Adamawa State, Nigeria., Ojar JU; Department of Science Laboratory Technology, Adamawa State College of Agriculture, P.O. Box 2088, Ganye, Adamawa State, Nigeria., Najoji SD; Department of Science Laboratory Technology, School of Science and Technology, The Federal Polytechnic, P.M.B. 1006, Damaturu, Yobe State, Nigeria.
Jazyk: angličtina
Zdroj: Journal of molecular modeling [J Mol Model] 2024 Nov 27; Vol. 30 (12), pp. 419. Date of Electronic Publication: 2024 Nov 27.
DOI: 10.1007/s00894-024-06208-4
Abstrakt: Context: This work presents analytical expressions for ro-vibrational energy models of diatomic molecules by introducing fractional parameters to improve molecular interaction analysis. Thermodynamic models, including Helmholtz free energy, mean thermal energy, entropy, and isochoric heat capacity, are formulated for diatomic molecules such as CO (X 1 ∑ + ), Cs 2 (3 3 ∑ g + ), K 2 (X 1 ∑ g + ), 7 Li 2 (6 1 Π u ), 7 Li 2 (1 3 Δ g ), Na 2 (5 1 Δ g ), Na 2 (C(2) 1 Π u ), and NaK (c 3 ∑ + ). The incorporation of fractional parameters improves predictive accuracy for vibrational energies, as shown by reductions in percentage average absolute deviations from 0.5511 to 0.2185% for CO. Findings indicate a linear decrease in Helmholtz free energy and an initial increase in heat capacity with rising temperature, providing valuable insights for characterizing materials and optimizing molecular processes in chemistry, material science, and chemical engineering. The results obtained show strong agreement with established theoretical predictions and experimental data, validating the robustness and applicability of the proposed models.
Methods: The energy equations are derived by solving the radial Schrödinger equation for a variant of the Tietz potential using the generalized fractional Nikiforov-Uvarov (GFNU) method in addition to a Pekeris-type approximation for the centrifugal term. The canonical partition function is derived using the modified Poisson series formula, which serves as a basis for calculating other thermodynamic functions. All computations are carried out using MATLAB programming software.
Competing Interests: Declarations. Ethics approval: Not applicable. Consent to participate: Not applicable. Consent for publication: Not applicable. Competing interests: The authors declare no competing interests. Final version of the manuscript: All authors approved the final version of the manuscript submitted.
(© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)
Databáze: MEDLINE
Externí odkaz: