Approximate Relationships Between the Generalized Morse and the Extended-Rydberg Potential Energy Functions

Teik-Cheng Lim
Faculty of Engineering, Nanoscience & Nanotechnology Initiative,National University of Singapore, S 117576, Republic of Singapore. E-mail: alan_tc_lim@yahoo.com

Abstract
Parameters of the Generalized Morse and the Extended-Rydberg potential functions are connected herein. Due to the existence of a polynomial portion in the latter, we apply the Maclaurin series expansion to the former to allow comparison of terms that lead to the parametric relationships. Two schemes for the parametric connections were developed in order to cater to two broad categories of the Extended-Rydberg parameters on the basis of the sign of a₂. In either case, it was shown that the curvatures at the minimum well-depth are equal, thereby indicating validity of the parametric connections for small distortion. Theoretical plots also reveal that, in the case of large interatomic distortion, the Generalized Morse approximation gives slight over-estimation and under-estimation to the Extended-Rydberg potential for a₂<0 and a₂>0 respectively.

Keywords: interatomic potentials, Maclaurin series, parametric connections