Calculation of centrifugal distortion constants for diatomic molecules from RKR potentials

Expressions are developed for computing the centrifugal distortion constants D_v, H_v, and L_v directly from the Rydberg-Klein-Rees rotationless potential of a diatomic molecule. These expressions involve summations over integrals of the wavefunctions of all neighboring vibrational levels. Application is made to the X¹Σ⁺ state of CO and the $\text{X}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state of O₂. In these applications, we have neglected the contributions of the continuum wavefunctions. For higher vibrational levels, particularly those near the dissociation limit, this approximation would be expected to fail. For the lowest vibrational levels of an electronic state, this method gives the same results for D_v, H_v, and L_v as the Dunham relations. However, for intermediate vibrational levels the present method is an improvement since expressions for only a few coefficients of the Dunham expansion are available. The use of D_v and H_v values calculated from Rydberg-Klein-Rees potentials in an iterative improvement of the reduction of spectroscopic data is described.