Knowledge Bank

A new method for determining accurate internuclear potentials for diatomic molecules in $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}\Sigma$ states directly form spectroscopic measurements is described. The method employs an iterative solution of the radial wave equation in the least-squares adjustment of a nonlinear analytical potential function of the type \begin{equation}U(R)={\cal D}c[1-{e}^{-\beta(R)(R-R{e})}]^{2}\end{equation} where\begin{equation}\beta(R)=\beta_{0}+\beta_{1}(R-R_c)+\beta_{2}(R-R_e)^{2}\ldots\end{equation} The quantal eigenvalues of the variable-$\beta$ Morse oscillator in Eq. (1) represent the experimental data over wide ranges of $v$ and $J$ within the measurement accuracies. The method offers distinct advantages over the conventional RKR procedure, or even variational methods such as Inverse Perturbation Analysis (IPA). When data for several isotopomers are considered simultaneously, the method yields the Born--Oppenheimer potential and radial functions describing BornûOppenheimer breakdown effects. The method has been tested for several diatomic molecules for which accurate measurements of pure rotational and rotational-vibrational transitions are available; results are presented for HI/DI, HBr/DBr, CO, SiS, CS NaF and LiI.