Mathematical relationships for development of a molecular potential function converter

Abstract

This paper gives a short review on relating molecular potential functions within the same category of interatomic interactions. The bond-stretching potentials that were related include the harmonic, polynomial series and Morse functions. The bond-bending potentials that were connected involve the harmonic angle, polynomial angle series, harmonic cosine and Fourier series functions. The bond-twisting potentials that were related are the trigonometric series and the cosine power series functions. Finally, the non-bonded potentials that were connected include the Lennard-Jones type and the Exponential-6 functional forms. The above-mentioned relationships were previously obtained using mathematical methods such as Maclaurin's series expansions, trigonometric identities and elementary calculus. These relationships are tabulated in a concise manner in preparation for the development of a potential function converter software that enables a given molecular potential function to be converted to a different functional form. The software can be further utilized as an educational tool for displaying, in a graphical manner, the similarities and discrepancies in normalized molecular potential functions.