Knowledge Bank

A simple semiclassical quadrature procedure has been developed for calculating the diatomic molecule centrifugal distortion constants associated with a given potential energy curve. Unlike other methods, it is just as reliable for levels lying near dissociation as for those at the potential minimum. Consideration of the method shows that distortion constants of levels lying near dissociation depend mainly on the long-range inverse-power tail of the potential $V(R)=D=Cn/Rn$, and simple analytic expressions characterising the near-dissociation behaviour of the constants have been developed. In particular, the coefficient of $[J(J+1)]k$ in the expression for the rotational energy is proportional to $(vD-v)2n/(n-2)-2k$, where $vD$ is the vibrational quantum number at dissociation and the proportionality constant depends only on n , $Cn$ and the reduced mass $\mu$. Applications and implications of these results are discussed.