On the universality of spectroscopic constants of diatomic molecules

We show, through a machine learning approach, that the equilibrium distance, harmonic vibrational frequency, and binding energy of diatomic molecules are universally related. In particular, the relationships between spectroscopic constants are valid independently of the molecular bond. However, they depend strongly on the group and period of the constituent atoms. As a result, we show that by employing the group and period of atoms within a molecule, the spectroscopic constants are predicted with an accuracy of $\lesssim 5\mathrm{\%}$. Finally, the same universal relationships are satisfied when spectroscopic constants from {\it ab initio} and density functional theory (DFT) electronic structure methods are employed.