Determination of Centrifugal Distortion Coefficients of Asymmetric-Top Molecules

TLDR

The rotational Hamiltonian of an asymmetric‑top molecule in a given vibrational state contains more parameters than can be determined from observed energy levels. The study investigates whether the Hamiltonian reduction can be performed generally. The authors apply a unitary transformation to reduce the Hamiltonian to a symmetric‑D2 form with only (n+1) independent terms of degree n for even n, and ΔK = 0, ±2 selection rules, making it suitable for fitting observed energies. The reduced Hamiltonian contains one fewer quartic coefficient than previously used, and this case is examined in detail.

Abstract

The rotational Hamiltonian of an asymmetric-top molecule in a given vibrational state, obtained by the usual vibrational perturbation treatment, contains more parameters than can be determined from the observed energy levels. This Hamiltonian is therefore transformed by means of a unitary transformation to a reduced Hamiltonian which is suitable for fitting to observed energies. The unitary transformation can be chosen so that the reduced Hamiltonian has the following properties: (i) It is totally symmetric in the point group D2, regardless of the symmetry of the molecule; (ii) It contains only (n+1) independent terms of total degree n in the components of the total angular momentum, for each even value of n; (iii) Its matrix elements in a symmetric-top basis satisfy the selection rule ΔK=0, ±2. This paper is concerned mainly with the possibility of carrying out this reduction in general. However, the reduced Hamiltonian described above contains one less quartic coefficient than has been used previously, and this particular case is discussed in more detail.