The Integral-differential and Integral Approach for the Exact Solution of the Hybrid Functional Forms for Morse Potential

• Published in: IAENG international journal of applied mathematics 2020-06, Vol.50 (2), p.1-9
• Main Authors: A, Surulere S, Y, Shatalov M, C, Mkolesia A, N, Malange T, A, Adeniji A
• Format: Article
• Language: English
• Subjects: Computer simulation; Datasets; Diatomic molecules; Differential equations; Exact solutions; Gold; Integrals; Interatomic distance; Least squares; Morse potential; Parameter estimation; Parameter identification; Potential energy
• ISSN: 1992-9978; 1992-9986

The Morse potential, which is the most widely used potential in evaluating the vibrational energies of diatomic molecules, is studied and its unknown parameters were estimated in this paper. The integral-differential and integral approaches which are relatively more accurate approaches of the objective least squares function method were discussed and applied in this paper. The approaches were used to estimate the Classical and Generalized Morse potential parameters. The estimates obtained for the Classical Morse potential was used to obtain the Morse potential parameters. The approaches were used to identify new unknown parameters of the Classical and Generalized Morse potential. They were also used to approximate parameters which were fundamental to graphically identifying the potentials using potential energy curves. The approach consists of recognizing the functional form of the hybrid forms of the Morse potential as the solution of some second order ordinary differential equation with unknown parameters. Then constructing the first objective function and integrating once (for the integral-differential method) and twice (for the integral method). The second objective function is constructed from the functional forms of the Classical and Generalized Morse potential under paper. A matrix system with the unknown parameters is formulated and numerical simulation of the system is done using gold atom experimental data sets. The objective function values and reconstructed potential energy curves fitted to experimental data sets of gold atom shows high accuracy to the optimum solution when compared to the objective least squares function method. The estimated parameters approximates to the experimental data sets of gold atom through the range of interatomic distance.