A methodology to obtain accurate potential energy Functions for diatomic systems: mathematical point of view

Authors

DOI:

https://doi.org/10.22481/intermaths.v4i1.12921

Keywords:

Mathematical Analysis, Analytical potential energy functions, Born-Oppenheimer Approximation, Dunham coefficients, Morse-type potential

Abstract

The mathematics used in physical chemistry has changed greatly in the past forty years and it will certainly continue to change more quickly. Theoretical chemists and physicists must have an acquaintance with abstract mathematics if they are to keep up with their field, as the mathematical language in which it is expressed changes. Thinking about it, in this article, we want to show some of the most important concepts of Mathematical Analysis involved in obtaining analytical functions to represent the potential energy interaction for diatomic systems. A basic guide for the construction of a potential based on Dunham's coefficients and an example of a new potential obtained from this methodology is also presented.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Author Biographies

Judith de Paula Araújo, Instituto Federal Sudeste de Minas Gerais, Juiz de Fora - MG, Brasil

Judith P. Araújo nasceu no Brasil e formou-se em Matemática (2008) na Universidade Federal de São Carlos (UFSCar), São Paulo, Brasil. Durante 2009-2011, ela completou seu mestrado em Matemática na Universidade Estadual Paulista (UNESP), São Paulo, Brasil. Em 2021 concluiu seu doutorado em Física Atômica e Molecular na Universidade Federal de Juiz de Fora, Minas Gerais, Brasil. Atualmente é professora do Departamento de Matemática do Instituto Federal do Sudeste de Minas Gerais, Juiz de Fora, Minas Gerais, Brasil.

Maikel Y. Ballester, Universidade Federal de Juiz de Fora, Juiz de Fora - MG, Brasil

Maikel Y. Ballester nasceu em Cuba. Ele recebeu seu BSc e MSc em Física Nuclear no Instituto Superior de Ciências e Tecnologias Nucleares, Havana. Em 2008 concluiu o seu doutorado em Química Teórica na Universidade de Coimbra, Portugal. Atualmente é professor do Departamento de Física da Universidade Federal de Juiz de Fora, Minas Gerais, Brasil.

Mariana P. Martins, Instituto Federal Sudeste de Minas Gerais, Juiz de Fora - MG, Brasil

Mariana P. Martins nasceu no Brasil, e é uma estudante de Licenciatura em Matemática no Instituto Federal Sudeste de Minas Gerais, Juiz de Fora Minas Gerais. Atualmente ela é bolsista de iniciação científica sob orientação da Professora Judith de Paula Araújo.

Rafael P. Silva, Instituto Federal Sudeste de Minas Gerais, Juiz de Fora - MG, Brasil

Rafael P. Silva nasceu no Brasil, e é um estudante de Licenciatura em Física no Instituto Federal Sudeste de Minas Gerais, Juiz de Fora Minas Gerais. Atualmente ela é voluntário de iniciação científica sob orientação da Professora Judith de Paula Araújo.

Isadora G. Lugão, Instituto Federal Sudeste de Minas Gerais, Juiz de Fora - MG, Brasil

Isadora G. Lugão nasceu no Brasil e é aluna do curso de Licenciatura em Matemática do Instituto Federal Sudeste de Minas Gerais, Juiz de Fora Minas Gerais. Atualmente é bolsista de iniciação  científica sob orientação da professora Judith de Paula Araújo.

Ituen B. Okon, University of Uyo, Uyo, Nigéria

Ituen B. Okon nasceu na Nigéria. Ele recebeu seu BSc e MsC em Física na Universidade de Uyo e na Universidade de Ibadan, Nigéria, respectivamente. Em 2016 concluiu o seu doutorado em Física na Universidade de Ibadan, Nigéria. Atualmente é professor no Departamento de Física da Universidade de Uyo, Uyo, Akwa Ibom, Nigéria.

Clement A. Onate, Kogi State University, Anyigba, Nigéria

Clement A. Onate was born in Nigeria. He completed his Ph.D. degree in Quantum Information Theory from University of Benin, Nigeria. Currently, he is a professor at the Physics Department of the Kogi State University Anyiba, Nigeria.

References

J. N. Murrell and S. Carter and S. C. Farantos and P. Huxley and A. J. C. Varandas, Molecular Potential Energy Functions. New York: Wiley, 1977.

D. Marx and J. Hutter. Ab Initio Molecular Dynamics. New York,: Cambridge University Press, 2009.

J. P. Araújo and M. Y. Ballester, “A comparative review of 50 analytical representation of potential energy interaction for diatomic systems: 100 years of history”, International Journal of Quantum Chemistry, vol. 121, pp.e26808 1–102, 2021. https://doi.org/10.1002/qua.26808

E. L. Lima, Análise Real: Funções de uma variável, Rio de Janeiro: IMPA, 2008.

J. L. Dunham, “The Energy Levels of a Rotating Vibrator ”, Physical Review, vol. 41, pp.721–731, 1932. https://doi.org/10.1103/PhysRev.41.721

P. M. Morse, “Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels”, Physical Review, vol. 34, pp.57–64, 1929. https://doi.org/10.1103/PhysRev.34.57

J. P. Araújo and M. D. Alves and R. S. da Silva and M. Y. Ballester, “A comparative study of analytic representations of potential energy curves for O2, N2, and SO in their ground electronic states”, Journal of Molecular Modeling, vol. 25, pp.1–17,2019. https://doi.org/10.1007/s00894-019-4079-3

J. N. Murrell and K. S. Sorbie, “New Analytic Form for the Potential Energy Curves of Stable Diatomic States”, Journal of the Chemical Society, Faraday Transactions 2, vol.70, pp.1552–1556, 1974. https://doi.org/10.1039/F29747001552

P. Huxley and J. N. Murrell, “Ground-state Diatomic Potentials”,Journal of the Chemical Society, Faraday Transactions 2, vol. 79, pp.323–328, 1983. DOI https://doi.org/10.1039/F29837900323

Y. P. Varshni, “Comparative Study of Potential Energy Functions for Diatomic Systems”, Reviews of Modern Physics, vol. 29, pp.664–682, 1957. https://doi.org/10.1103/RevModPhys.29.664

I. N. Levine, “Accurate Potential Energy Function for Diatomic Molecules”, The Journal of Chemical Physics, vol.45, pp.827–828, 1966. https://doi.org/10.1063/1.1727689

H. M. Hulburt and J. O. Hirschfelder, `‘Potential Energy Functions for Diatomic Molecules ”textitThe Journal of Chemical Physics, vol. 9, pp. 61–69, 1941. https://doi.org/10.1063/1.1750827

A. J. C. Varandas and J. D. da Silva, “Potential model for diatomic molecules including the united-atom limit and its use in a multiproperty fit for argon”,Journal of the Chemical Society, Faraday Transactions, vol. 88, pp. 941–954, 1992. https://doi.org/10.1039/FT9928800941

A. Aguado and M. Paniagua, “A new functional form to obtain analytical potentials of triatomic molecules”, The Journal of Chemical Physics, vol. 96, pp. 1265–1275, 1992. https://doi.org/10.1063/1.462163

R. Rydberg, “Graphische Darstellung einiger bandenspektroskopischer Ergebnisse”, Zeitschrift für Physik, vol. 73, pp. 376–385, 1932. https://doi.org/10.1007/BF01341146

O. Z. Klein, “Zur Berechnung von Potentialkurven für zweiatomige Moleküle mit Hilfe von Spektraltermen”, Zeitschrift für Physik, vol. 76, pp. 226–2355, 1932. https://doi.org/10.1007/BF01341814

A. L. G. Rees, “The calculation of potential-energy curves from band-spectroscopic data”, Proceedings of the Physical Society of London A, vol. 59, pp. 998–1008,1947. https://doi.org/10.1088/0959-5309/59/6/310

A. C. Hurley, “Equivalence of RydbergKleinRees and Simplified Dunham Potentials”, The Journal of Chemical Physics, vol.36, pp.1117–1118, 1962. http://dx.doi.org/10.1063/1.1732678

J. F. Ogilvie and D. Koo, “Dunham potential energy coefficients of the hydrogen halides and carbon monoxide”,Journal of Molecular Spectroscopy, vol. 61, pp. 332–336, 1976. https://doi.org/10.1016/0022-2852(76)90323-4

J. F. Ogilvie, “Dunham energy parameters of isotopic carbon monoxide, hydrogen halide, and hydroxyl radical molecules”, Journal of Molecular Spectroscopy, vol. 69, pp.169–172, 1978. https://doi.org/10.1016/0022-2852(78)90056-5

J. P. Araújo and M. Y. Ballester, “New generalized potential energy function for diatomic systems”, Physica Scripta, vol. 96, pp.125407 1-10, 2021. https://doi.org/10.1088/1402-4896/ac3150

Downloads

Published

2023-06-30

How to Cite

de Paula Araújo, J., Ballester, M. Y., Martins, M. P., Silva, . R. P., Lugão, . I. G., Okon, I. B., & Onate, . C. A. (2023). A methodology to obtain accurate potential energy Functions for diatomic systems: mathematical point of view. INTERMATHS, 4(1), 9-24. https://doi.org/10.22481/intermaths.v4i1.12921

Issue

Vol. 4 No. 1 (2023)

Section

Artigos

License

Copyright (c) 2023 INTERMATHS

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  • Responsibility: The scientific content and the opinions expressed in the manuscript are the sole responsibility of the author(s).
  • Copyrights: INTERMATHS. 
  • All content of Revista INTERMATHS/INTERMATHS journal is licensed under a Creative Commons - Atribuição 4.0 Internacional

Licença Creative Commons