CHEM%20515%20Spectroscopy

1
CHEM 515Spectroscopy

• 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.
• TX X1 X2 XN
• TY Y1 Y2 YN
• TZ Z1 Z2 ZN

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. RX, RY, and Rz .
• 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 Hookes 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 CO2 molecule, number of vibrations 3N 5
  four vibrations.

9
Normal Modes in Water Molecule

• For H2O molecule, number of vibrations 3N 6
  three vibrations.
• Liberation motions are the x, y and z rotations.

10
Vibrational Energy levels for H2O
11
(No Transcript)
12
(No Transcript)