A planarity relation for sextic centrifugal distortion constants

The relations between the molecular parameters of a planar molecule are used to derive a planarity relation for the sextic centrifugal distortion constants from the recently published expressions [Aliev and Watson, J. Mol. Spectrosc.61, 29 (1976)]. This relation, which contains only the rotational constants and the quartic and sextic distortion constants, is strictly valid only for the equilibrium constants, but will be useful as a constraint in the fitting of rotational energies if the experimental error is larger than the vibrational defect. The planarity relation is compared with the observed constants for the SO₂, O₃, NO₂, H₂O, and H₂S molecules. There appears to be a significant defect for SO₂ and for H₂O and its isotopes. The defect for SO₂ may be too large to be genuine, and possibly results from truncation of the Hamiltonian at the sextic terms.