Extensive Study of Modern Approaches Used in Identifying the Buckingham Potential

Abstract

This paper presents two mathematical approaches of estimating unknown parameters of the Buckingham potential. Two functional forms of the potential was investigated owing to the complexities and difficulties arising from the original Buckingham potential. These complexities are due to the combination of both powers and an exponent in mathematical representation of the potential. Hence, we decided to consider approximating the parameters of the simpler form, widely known as the modified Buckingham potential. The method of least squares (differential and integral methods) were used to estimate the potential parameters and the calculation of the optimized values of the constructed goal function were included in the paper. The calculated estimates showed reasonable agreement with experimental datasets of copper atoms over a large vicinity of the interatomic potential distance. This conclusion was reached through the graphical analysis of potential energy curves and through the error between the respective curves. Optimized goal function values were used to compare the efficiency of the methods.