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

**Teik-Cheng
Lim
**

__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 *a*_{2}.
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 *a*_{2}<0
and *a*_{2}>0 respectively.

**Keywords**:
interatomic potentials, Maclaurin series, parametric connections