CHEM 515 Spectroscopy Vibrational Spectroscopy II

2 Vibrations of Polyatomic Molecules N particles have 3N degrees of freedom (x, y and z for each). Three degrees of freedom are translations. –T X = X 1 + X 2 +…+X N –T Y = Y 1 + Y 2 +…+Y N –T Z = Z 1 + Z 2 +…+Z N

3 Vibrations of Polyatomic Molecules N particles have 3N degrees of freedom (x, y and z for each). Three degrees of freedom are rotations about x, y and z axes. R X, R Y, and R z. For linear molecules, only two rotational axes will represent degrees of freedom.

4 Vibrations of Polyatomic Molecules N particles have 3N degrees of freedom (x, y and z for each). The rest of degrees of freedom are vibrations. Number of vibrations are: –3N – 6 for nonlinear molecules. –3N – 5 for linear molecules.

5 Classical Picture of Vibrational Motions in Molecules Classically, polyatomic molecules can be considered as a set of coupled harmonic oscillators. Atoms are shown as balls connected with each other by Hooke’s law springs.

6 Classical Picture of Vibrational Motions in Molecules Stronger forces between O and H atoms are represented by strong springs (resistance to stretching the bonds). Weaker force between H atoms is represented by weaker spring (resistance to increase of decrease of the HOH angle “bending of the angle”)

7 Normal Modes of Vibrations The collective motion of the atoms, sometimes called Lissajous motion, in a molecule can be decomposed into normal modes of vibration within the harmonic approximation.

8 Normal Modes of Vibrations The normal modes are mutually orthogonal. That is they represent linearly independent motions of the nuclei about the center-of-mass of the molecule. For CO 2 molecule, number of vibrations = 3N – 5 = four vibrations.

9 Normal Modes in Water Molecule For H 2 O molecule, number of vibrations = 3N – 6 = three vibrations. Liberation motions are the x, y and z rotations.

10 Vibrational Energy levels for H 2 O

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