Knowledge Bank

At long range, the interaction potential for a diatomic molecule may be written as a sum of inverse power terms: $V(R)=D\Sigma Cm/Rm$, where the contributing values of m are determined by the nature of the atomic dissociation products and the symmetry of the molecular electronic state. Values of the potential coefficients $Cm$ (together with the dissociation limit D) may be determined from experiment in one of two wasys: (i) RKR turning points may be fitted directly to the above $expression,1-3$ or (ii) the energies of the levels closest to dissociation may be fitted to the limiting near-dissociation theory expression $G(v)=D-X0(n)(vD-v)2n/(n-2)$ to yield values of D and of the leading inverse power coefficient, 1, 4 However, parameters obtained from the former approach are very highly correlated, sometimes having sufficiently large statistical uncertainties to make their values virtually meaningless, while the latter approach is limited by the fact that it takes account of only the leading inverse-power potential term. The present paper describes a generalized near-dissociation theory approach which can take account of as many terms as desired in the long-range potential, and is basd on fits to experimental vibrational energies and $Bv$ values. The interparameter correlation associated with this new approach is much smaller than for the turning point fits, and the uncertainties in the input data (G(v)'s and $Bv\prime s$ rather than RKR turning points) may be properly estimated and taken into account.