Rigid bender model for the out-of-plane vibrations of C s and C2v tetra-atomic molecules

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Abstract
A formula for the evaluation of the mass‐weighted coordinate Q for out‐of‐plane bending which is applicable to Cs or C2v tetra‐atomic molecules has been derived. This formula is tested numerically against earlier, more approximate methods of determining Q. The effects of approximations for Q on the vibrational energy levels of a double minimum potential and on the determination of the equilibrium out‐of‐plane angle are examined. The present formula is exact within the rigid bender constraints and is more widely applicable than previously published methods.