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A Modern Approach for the Identification of the Classical and Modified Generalized Morse Potential

[ Vol. 10 , Issue. 2 ]

Author(s):

Samuel A. Surulere*, Micheal Y. Shatalov, Andrew C.P.G. Mkolesia and Igor Fedotov   Pages 142 - 151 ( 10 )

Abstract:


Introduction: This paper proposes an approach for parameter estimation of the Classical and Generalized Morse Potential functions. A new potential which is a modification of the Generalized Morse Potential was proposed as parameter estimates yielded complex conjugate roots using gold atom for simulation.

Methods: Existing methods of parameter estimation requires the provision of initial guess values of which convergence to the optimal solution is not always guaranteed. This makes provision of initial guess values that guarantees convergence to the optimum solution more of an art than a science. The proposed objective least squares function method does not require the provision of initial guess values and it involves the minimization of two formulated objective functions using the differential numerical approach and least squares method. The built-in “Minimize” function of Mathematica® is also used to minimize the formulated objective function. Potential energy curves were constructed by fitting estimated parameter values to experimental data sets of the gold atom using values of the proposed approach and Mathematica® for performance evaluation. Errors of each constructed potential energy curves were simulated.

Results: It was observed that the errors were very small for both the Classical and Modified Generalized Morse Potential.

Conclusion: Hence the approximations of the proposed approach are very good.

Keywords:

Parameter estimation, least squares, objective functions, potential energy curves, objective least squares function, Morse Potential.

Affiliation:

Department of Mathematics and Statistics, Tshwane University of Technology, P/Bag X380, Pretoria 0001, Department of Mathematics and Statistics, Tshwane University of Technology, P/Bag X380, Pretoria 0001, Department of Mathematics and Statistics, Tshwane University of Technology, P/Bag X380, Pretoria 0001, Department of Mathematics and Statistics, Tshwane University of Technology, P/Bag X380, Pretoria 0001

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