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

A first‐order treatment yields the relation

$${\mathrm{W=W}}_0{\mathrm{+A}}_1{W}_0^2{\mathrm{+A}}_2{W}_0{\text{J(J+1)+A}}_3{J}^2{\text{(J+1)}}^2{\mathrm{+A}}_4\text{J(J+1)〈}{\mathbf{P}}_z^2{\mathrm{〉+A}}_5〈{\mathbf{P}}_z^4{\mathrm{〉+A}}_6{W}_0〈{\mathbf{P}}_z^2〉$$

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. P_z is the operator for the component of angular momentum along the axis of quantization. Formulas are given for 〈P_z²〉 and 〈P_z⁴〉, 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.