A methodology to obtain accurate potential energy Functions for diatomic systems: mathematical point of view

The mathematics used in physical chemistry has changed greatly in the past forty years and it will certainly continue to change more quickly. Theoretical chemists and physicists must have an acquaintance with abstract mathematics if they are to keep up with their field, as the mathematical language in which it is expressed changes. Thinking about it, in this article, we want to show some of the most important concepts of Mathematical Analysis involved in obtaining analytical functions to represent the potential energy interaction for diatomic systems. A basic guide for the construction of a potential based on Dunham's coefficients and an example of a new potential obtained from this methodology is also presented.