Planarity relations for the sextic centrifugal distortion constants of triangular triatomic molecules

Four linearly independent linear combinations of the ten sextic centrifugal distortion coefficients of triangular triatomic molecules are presented. These combinations are formed in such a way that the resulting expressions depend only on the equilibrium geometry and the harmonic force field parameters of the molecule, quantities which are ordinarily known to considerably better precision than the sextic constants. The relations obtained thus constitute a set of planarity constraints on the ten sextic coefficients which arise in connection with the Nielsen-Amat expansion of the Darling-Dennison Hamiltonian. The planarity expressions can be utilized to effect a reduction of the sextic portion of the Hamiltonian.