Dissociation Energy and Long-Range Potential of Diatomic Molecules from Vibrational Spacings of Higher Levels

Abstract

An expression is derived which relates the distribution of vibrational levels near the dissociation limit $D$ of a given diatomic species to the nature of the long‐range interatomic potential, in the region where the latter may be approximated by ${\mathrm{D\hspace{0.17em}-\hspace{0.17em}C}}_n{\mathrm{\hspace{0.17em}/\hspace{0.17em}R}}^n$ . Fitting experimental energies directly to this relationship yields values of $D$ , $n$ , and $C_n$ . This procedure requires a knowledge of the relative energies and relative vibrational numbering for at least four rotationless levels lying near the dissociation limit. However, it requires no information on the rotational constants or on the number and energies of the deeply bound levels. $D$ can be evaluated with a much smaller uncertainty than heretofore obtainable from Birge–Sponer extrapolations. The formula predicts the energies of all vibrational levels lying above the highest one measured, with uncertainties no larger than that of the binding energy of the highest level. The validity of the method is tested with model potentials, and its usefulness is demonstrated by application to the precise data of Douglas, Mo/ller, and Stoicheff for the $B^3{\Pi }_{\text{0u}}^{+}$ state of Cl₂.