2. Applying the model to polyatomic molecules

2.1 Counting the fundamental vibrations of a molecule

The various bonds in a molecule can be treated as harmonic oscillators, but $\nu =\frac{1}{2\text{π}c}\sqrt{\frac{k}{\mu }}$ -type expressions that neglect the influence of neighboring groups are not very accurate. They are still very useful for calculating frequency changes associated with small structural modifications (isotopic substitution, etc.).

In the case of a non-rectilinear molecule of n atoms, there are 3n degrees of freedom (3 coordinates per atom) corresponding to 3n-6 vibratory motions...