Possible universal scaling properties of potential-energy curves for diatomic molecules
- 1 January 1985
- journal article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 31 (1), 1-4
- https://doi.org/10.1103/physreva.31.1
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(∞)]/ and s=(R-)/ be reduced energy and displacement variables, where and 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 , are given for the various cases. The standard formula for κ is ( /2 .
Keywords
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