Effective Rotation–Pseudorotation Hamiltonian forX3-Type Molecules: Application to theB̃–X̃Transition of Na3

Abstract

A formalism has been developed for rotation–pseudorotation energy levels ofX3-type molecules in orbitally nondegenerate electronic states (so that Jahn–Teller complications are absent). The formalism includes electron spin, but excludes nuclear spin effects. Correlation diagrams are presented connecting rotational energy levels in the high-barrier asymmetric-rotor limit to those in the low-barrier free-rotor quasi-symmetric-top limit. By applying the formalism to theB̃state of Na3, which exhibits nearly free pseudorotation, a global fit of 216B̃(u= 1)–X̃transitions to 15 molecular parameters was carried out, leading to a satisfactory standard deviation of 0.012 cm−1. (The lowerX̃state was treated as a rigid asymmetric rotor.) The fit contains manyj= 0 levels and somej= 1 levels, but only a fewj= 2 andj= 3 levels, wherejis the pseudorotation quantum number in theB̃state. Inclusion of traditional spin–rotation terms did not improve the fit, but a phenomenological term coupling electron spin to the pseudorotation angular momentum was able to account for the large spin splittings observed inj> 0 pseudorotational levels. Our ground state rotational constants are consistent with those determined by other workers from analysis of theÖX̃transition.