Construction of bound-state potential energy curves of diatomic molecules from spectroscopic data

Abstract

We propose a method for the construction of potential energy curves of diatomic molecules from spectroscopic data. It is based on perturbation theory and an appropriate numerical integration algorithm and corrects the potential energy function iteratively until the eigenvalues of the Schrödinger equation agree with the experimental energies. The method is stable and converges fast enough to allow one to adjust many potential parameters. We choose the eigenvalues of the Kratzer oscillator as experimental data to test both the performance of the method and the accuracy of the Dunham expansion about equilibrium. The Dunham expansion obtained from the spectrum has a range of utility which is remarkably larger than the radius of convergence of the Taylor expansion about equilibrium. We also apply the present method to the ground electronic state of the CO molecule and show that the Dunham expansion agrees with the RKR turning points. We discuss further applications of the method.