Knowledge Bank

An analytic recursion relation for the calculation of expectation values of any power of the internuclear displacement from equilibrium in an arbitrary vibration-rotation level of $1\Sigma$-state diatomic molecules is derived via an iterative solution of the hypervirial theorem. Explicit results, more accurate than those previously published, are given for the first six powers of the displacement along with numerical results for $H2$ and HCl to illustrate the accuracy obtained.