New alternatives to the Lennard-Jones potential

We present a new method for approximating two-body interatomic potentials from existing ab initio data based on representing the unknown function as an analytic continued fraction. In this study, our method was first inspired by a representation of the unknown potential as a Dirichlet polynomial, i.e., the partial sum of some terms of a Dirichlet series. Our method allows for a close and computationally efficient approximation of the ab initio data for the noble gases Xenon (Xe), Krypton (Kr), Argon (Ar), and Neon (Ne), which are proportional to $$ and to a very simple $$ truncated continued fraction with integer coefficients and depending on $$ only, where n is a natural number (with $$ for Xe, $$ for Kr, $$ for Ar, and $$ for Neon). For Helium (He), the data is well approximated with a function having only one variable $$ with $$ and a truncated continued fraction with $$ (i.e., the third convergent of the expansion). Also, for He, we have found an interesting $$ result, a Dirichlet polynomial of the form $$ (with $$ all integers), which provides a surprisingly good fit, not only in the attractive but also in the repulsive region. We also discuss lessons learned while facing the surprisingly challenging non-linear optimisation tasks in fitting these approximations and opportunities for parallelisation.