Potential Energy Functions for Diatomic Molecules

Abstract

The usual Morse functions are determined from the energy of dissociation, the equilibrium separation of the nuclei, and the fundamental vibration frequency. Two additional spectroscopic constants, ω_ex_e and α_e, are available for most of the common diatomic molecules and permit us to add a two‐parameter correction term to the Morse curve. Both the potential ${\text{V/D=(1−e}}^{\mathrm{-x}}{)}^2{\mathrm{+cx}}^3{\text{(1+bx)e}}^{\text{−2x}}$ and the extended Morse curve of the Coolidge, James and Vernon type, ${\mathrm{V/D=C}}_2{\text{(1−e}}^{\mathrm{-x}}{)}^2{\mathrm{+C}}_3{\text{(1−e}}^{\mathrm{-x}}{)}^3{\mathrm{+C}}_4{\text{(1−e}}^{\mathrm{-x}}{)}^4$ agree with accurate potentials in those cases where they are known. Here x = 2β(r—r_e)/r_e. The constants for the first of these potentials are easy to evaluate and are given for 25 common diatomic molecules. With only a few exceptions, the improved potentials lie above the Morse curves and the corrections for moderately large internuclear separations may amount to ten percent of the energy of dissociation. Our treatment is based on the work of Dunham and the analysis of Coolidge, James and Vernon.