Title: The integral-differential and integral approach for the estimation of the classical Lennard-Jones and Biswas-Hamann potentials

Authors: Samuel A. Surulere; Micheal Y. Shatalov; Andrew C. Mkolesia; Julius O. Ehigie

Addresses: Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, South Africa ' Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, South Africa ' Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, South Africa ' Department of Mathematics and Statistics, University of Lagos, Akoka, Nigeria

Abstract: Many well-known semiempirical potential energy functions have been used to construct potential energy curves from the physical or chemical properties of atoms. In this study, we identify the Lennard-Jones and Biswas-Hamann potential parameters and use these to calculate and reconstruct potential energy curves using experimental datasets of gold atom. Two different approaches are studied in detail. The Lennard-Jones potential yielded complex conjugate eigenvalues for both approaches. Numerical estimates proved the considered approaches gives better approximations as constructed and reconstructed potential energy curves were almost graphically indistinguishable.

Keywords: potential parameters; objective functions; potential energy curves; PECs; objective least squares function; ObLSf.

DOI: 10.1504/IJMMNO.2020.108612

International Journal of Mathematical Modelling and Numerical Optimisation, 2020 Vol.10 No.3, pp.239 - 254

Received: 13 Mar 2019
Accepted: 12 Aug 2019
Published online: 21 Jul 2020 *

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