Correlation diagrams between the free-rotor and the hindered rotor states of a diatomic molecule: energy levels and transition moments obtained by numerical integration of the schrödinger equation

Abstract

We present a numerical technique for the direct calculation of the rotational eigenvalues and transition moments of a rigid diatomic 1Σ rotor in an external axially-symmetric potential. Because this technique does not require an expansion in spherical harmonics, the wavefunctions and energy eigenvalues are obtained without having to perform integrals over the potential energy function, or having to calculate (and truncate) a Hamiltonian matrix. We use our technique to show the effect of the external field on the molecular spectra and present correlation diagrams of energy levels and transition moments between high barrier and free-rotor limits. The case of double minima potential energy functions, including those with inequivalent minima, is presented. The general features of the rotational states and transition probabilities of rotors in such potential energy functions is explored to serve as a guide for future experimental work. The presentation of the technique and of the intricacies of the energy levels and transition moments of the double minima potential energy functions is intentionally pedagogical.