Higher-order vibration-rotation energies of the X 3 molecule

Higher-order vibration-rotation perturbation calculations are presented for the X ₃ molecular model, employing a sequential contact transformation procedure. The calculations are simpler than for a general molecule because the principal Coriolis interaction is diagonal in the quantum numbers ( V₁, V₂). Most of the terms of the effective Hamiltonian that depend on quartic or lower potential constants are evaluated, including the vibrational dependence of the quartic centrifugal and Coriolis constants. The inertial and centrifugal planarity defects are proportional to ( V₂ + 1). To a good approximation, the energies are diagonal in the quantum number G = | k - l₂| and are given by a secular equation of dimension ( V₂ + 1) or lower. Explicit rotational energy level formulas are given for the vibrational states with any value of V₁ and with V₂ = 0 or 1.