Possible universal scaling properties of potential-energy curves for diatomic molecules

Abstract

The hypothesis is tested that ground-state potential-energy curves for neutral, bound diatomic molecules are universal scaled versions of one another in the sense of Ferrante, Smith, and Rose [Phys. Rev. Lett. 50, 1385 (1983)]. Let ε=[E(R)-E(∞)]/$D_e$ and s=(R-$R_e$)/$R_e$ be reduced energy and displacement variables, where $R_e$ and $D_e$ are the equilibrium distance and dissociation energy. The hypothesis is that ε=F(κs), where F(t) is a universal function and κ is a species-dependent parameter. By analysis of the data for 150 molecules the hypothesis is shown to be only moderately well satisfied if F(t) is taken to be a different characteristic function for each pair of columns in the Periodic Table, less well satisfied with F(t) completely universal. If F(t) is taken to be a single-parameter function, a much improved fit of almost all data is obtained. The second derivative at t=0, F’ ’(0), may be taken equal to 2 without loss of generality. Values of the third and fourth derivatives at t=0, F’ ’ ’(0) and $F^{\mathrm{iv}\mathrm{}\left(0\right)\mathrm{}}$, are given for the various cases. The standard formula for κ is ($k_e$ $R_e^2$/2$D_e$ ${)}^{1/2}$.