Universal scaling of potential energy functions describing intermolecular interactions. I. Foundations and scalable forms of new generalized Mie, Lennard-Jones, Morse, and Buckingham exponential-6 potentials.

Based on the formulation of the analytical expression of the potential V(r) describing intermolecular interactions in terms of the dimensionless variables r* = r/r(m) and ɛ* = V/ɛ, where r(m) is the separation at the minimum and ɛ the well depth, we propose more generalized scalable forms for the commonly used Mie, Lennard-Jones, Morse, and Buckingham exponential-6 potential energy functions. These new generalized forms have an additional parameter from the original forms and revert to the original ones for some choice of that parameter. In this respect, the original forms of those potentials can be considered as special cases of the more general forms that are introduced. We also propose a scalable, non-revertible to the original one, 4-parameter extended Morse potential.