Accurate analytic matrix elements for anharmonic oscillators using quantum mechanical commutator relations and sum rules

Abstract

An expression connecting the vibration‐rotation matrix elements of various powers of the internuclear displacement from equilibrium for ¹Σ‐state diatomic molecules is derived via quantum mechanical commutator relations. This expression can be solved by an iterative procedure and used to generate the diagonal elements. For off‐diagonal elements, additional information available through sum rules is necessary in order to obtain explicit results. To illustrate the power and accuracy of the present method, selected matrix elements of H₂ have been computed and will be compared with previous numerical results.