Exact analytical expressions for diatomic rotational and centrifugal distortion constants for a Kratzer-Fues oscillator

The exact closed-form expression for the vibrational-rotational eigenvalues of the Kratzer-Fues oscillator served as the starting point for a derivation of exact analytical expressions for the rotational constant B_υ, and the set D_υ to S_υ of centrifugal distortion constants up to 11th-order. The derivations employed the MAPLE symbolic algebra coprocessor. The expressions for B_υ to S_υ were then employed in the calculation of a set of constants for a Kratzer-Fues potential with specified dissociation energy and equilibrium internuclear separation for a hypothetical diatomic molecule with a reduced mass of unity. The tabulated constants serve as a benchmark against which the reliability of various existing or future numerical methods for the determination of rotational and centrifugal distortion constants may be assessed. The near-dissociation behaviour of the calculated constants was also examined and is useful in predicting the behaviour of such constants for real electronic states having pure ionic long-range form.