Ambiguities in the semiclassical assignment of the asymmetric rotor rotational quantum numbers

The semiclassical quantization of the rigid asymmetric rotor is revisited in the context of classical inelastic collisions. It is shown that the standard bin histogram method, widely used in quasiclassical trajectory calculations involving linear target molecules, cannot be generalized to the case of asymmetric top molecules owing to ambiguities in the assignment of the final classical action to a particular rotational quantum state. These ambiguities result from pairs of states which are indistinguishable within the bin histogram approach at all the common levels of semiclassical theory. A single value of the classical action can thus correspond to two different quantum states, preventing the distinction between these states in the calculation of rotational cross sections. Our results are illustrated for the rotational states J=1-4 of the water molecule at its equilibrium geometry.