Vibration—Rotation Interaction in Symmetric-Top Molecules and the Splitting between A1 and A2 Levels

Abstract

The main purpose of this paper is to reformulate the theory of vibration—rotation interaction in symmetric‐top molecules in a way which is more accessible to practicing spectroscopists than the current contact transformation formalism. Also it is pointed out that the many accurately measured l‐type doubling constants can provide information on the cubic as well as the quadratic potential constants. In Sec. I, analytical expressions for the splitting between the A₁ and the A₂ rovibrational states are derived starting from the Wilson—Howard equation. Although the result agrees with Grenier—Besson's formula, the method of derivation is new in the following three points: (1) The scheme of orders of magnitude of the terms appearing in the rovibrational Hamiltonian has been made in a definite way. (2) Symmetry considerations and the relations between various rovibrational constants have been fully used in the derivation. (3) The standard perturbation method is used instead of the contact transformation. In order to facilitate the understanding of the perturbation procedure, ``interaction diagrams'' are introduced and fully used. In Sec. II, several discussions of the l‐type doubling of symmetric rotors are given. First a physical interpretation of the l‐type doubling is discussed in Sec. II. A, and then the existence of a close analogy between the treatments of vibration—rotation interaction and vibronic interaction is pointed out in Sec. II. B. The above arguments lead to the conclusion that, because of certain anharmonic vibrational terms, the average structure of a symmetric‐top molecule in the first excited state of a degenerate vibration is no longer symmetric. An interpretation of this effect is presented. Finally it is emphasized that the observed l‐type doubling constants provide information on the anharmonic potential constants which are not obtainable from α. A numerical example for the NH₃ molecule is given and it is shown that the anharmonic vibrational contribution to the l‐type doubling is in fact large.