Vibrations of polyatomic molecules

We discussed vibrations in diatomic molecules, as we model it with harmonic oscillator model either in CM and QM. Eigenvalues were corresponding to vibrational levels of the molecule, since as a potential we use Hooke's Law and as the mass, the reduced mass. Both in FTIR (Infrared absorption spectroscopy) and Raman we have vibrational levels and we used harmonic oscillator model. Now we will talk about polyatomic molecules. Also remember, vibrational spectroscopy = raman spectroscopy + infrared absorption spectroscopy

In polyatomic molecules we have the sense of multibody systems with multiple springs. We have collective vibrations and multiple degrees of freedom. Main task in vibrational spectroscopy is to interpretate experimental vibrational spectral bands.
There are mainly two approaches:

Solving equations of mechanical movements: Molecular mechanics

Solving equations of quantum mechanics: Ab initio

MOLECULAR MECHANICS

There are 3N-6 vibrations in nonlinear polyatomic molecules. COME BACK.