The Pascal Triangle connection between Dunham and Simons-Pan-Finlan diatomic potential energy functions

摘要

The polynomial forms of the Dunham and Simons-Parr-Finlan (SPF) interatomic potential energy functions are commonly used for quantifying the bond-stretching and bond compression potential energy Due to the limitations of the Dunham and SPF potential functions for r > 2R and r < 0.5R respectively, where r = internuclear distance and R = equilibrium bond length, two sets of converting functions are proposed Each set of converting function enables the coefficients of one potential function to be converted to those of the other potential function so that when the limitations of one potential function is encountered, one may continue the theoretical model using the other potential function The converting functions were obtained by imposing Maclaurin series expansion on both potential functions, followed by comparison of terms It is herein shown that the converting functions take on the form of binomial coefficients - thereby allowing the converting functions to be schematically represented using the Pascal Triangle The use of Pascal Triangle is convenient and is therefore advantageous especially for generating the converting functions up to very high orders. Illustrations on the conversion of Dunham to SPF coefficients and vice versa reveal good agreement.