Importance of Quadratic Force Constants in Fermi Resonance

If the intramolecular potential energy is written in internal valence coordinates, the transformation to normal coordinates is nonlinear. Consequently both the quadratic and cubic valence-coordinate force constants contribute to the cubic normal-coordinate force constant which is the coefficient of the Fermi—Dennison resonance operator. The contributions of the quadratic force constants have been evaluated in some simple cases; they appear to be more important than the cubic internal-coordinate force constants. Anharmonicity enters mainly through the cubic stretch—bend—bend interaction force constant.