Recurrence relations for the Dunham coefficients and analytic expressions of the diagonal radial matrix elements for an anharmonic oscillator

Analytic recurrence relations for the calculation of the Yun Dunham coefficients are established, thereby allowing to generate all the set of the Yun from the Yu0 coefficients. Then, expressions for diagonal radial matrix elements of any power of the internuclear displacement from equilibrium in an arbitrary vibration–rotation level of the 1Σ-state diatomic molecule follow in terms of Yu0 only. As an illustrative application, all the set of Yun coefficients previously published are found again by using the computer algebraic manipulation language reduce. A number of diagonal matrix elements of CO, HBr, and HCl have been symbolically computed and compared with previous available results.