Approximate Treatment of the Effect of Centrifugal Distortion on the Rotational Energy Levels of Asymmetric-Rotor Molecules

Abstract

A first-order treatment yields the relation W=W0+A1W02+A2W0J(J+1)+A3J2(J+1)2+A4J(J+1)〈Pz2〉+A5〈Pz4〉+A6W0〈Pz2〉for the rotational energy W of a nonrigid asymmetric rotor. The A's are constants independent of the rotational quantum numbers (J, K−1, K+1) while W0 is the rigid-rotor energy. Pz is the operator for the component of angular momentum along the axis of quantization. Formulas are given for 〈Pz2〉 and 〈Pz4〉, based on continued fractions, as well as expansions useful for nearly symmetric cases. As a special case, the corrections are derived for transitions between the components of asymmetry doublets.