Scaling properties of diatomic potentials

The existence of a universal reduced potential valid for all diatomic molecules has been predicted on a theoretical basis and verified using Rydberg-Klein-Rees (RKR) potentials. The reduced RKR potentials for various molecules have been shown to coalesce into virtually a single curve when they are plotted against z=z₁ +(1/2(1-{}β₁{})z₁²+1)2 (β₂-(1/4β₁²-{}β₁{}+ 2)/3)z₁³, where z₁={}{Δ} (R/Rₑ-1) and βₗr=aₗ/Δˡ/2. The Morse curve [1-exp (-z)]²-1 is found to represent the universal curve well. Here R is the internuclear distance, {Δ} is the Sutherland parameter, and aₗ are the Dunham coefficients.