1. Infra-Red (IR) Spectroscopy Vibrational spectroscopyor
Vibrational spectroscopy
Applied Chemistry
Course: CHY101

2. Electromagnetic Radiation
Frequency ()
Wavelength ()
Radio-waves
Region
Microwaves
Infra-red
Visible
Ultra-violet
X-ray Region
-ray Region
Frequency (HZ)
Wavelength
10m – 1 cm
1 cm – 100µm
100µm – 1µm
700 – 400 nm nm
10nm – 100pm
100pm –
1 pm
NMR, ESR
Rotational
Spectroscopy
Vibrational spectroscopy
Electronic
Spec.
Energy
0.001 – 10 J/mole
Order of some 100 J/mole
Some 104 J/mole
Some 100
kJ/mole
Some 100s
J/mole
UHF TV, cellular, telephones.
(300 MHz and 3 GHz)
Table lamp,
Tube light (400 nm -800 nm or 400–790 THz)
Sun Lamp
X-ray
FM Radio, VHF TV.
AM Radio
Microwave ovens,
Police radar, satellite stations-- (3 to 30 GHz)

3. Electromagnetic Radiation

4. The interaction of radiation with matter

6. Hook’s Law Hook’s Law, F = - k x F is the restoring force
x is the displacement from equilibrium
k is the force constant
The restoring force proportional to the displacement of particle from its equilibrium position and the force constant k of the spring.

7. Vibrational spectra: Harmonic oscillator model
The Simple Harmonic Oscillator Model: H2 molecule H1
H2’
H2” E1 E2
req
In this case, energy curve is parabolic,
E = k (r – req)2 1 2

8. Vibrational spectra: Harmonic oscillator model
The Simple Harmonic Oscillator Model: H2 molecule H1
H2’
H2” E1 E2
req
The compression & extension of a bond (like a spring) obeys Hooke’s Law,
f is the restoring force
k is the force constant
In this case, energy curve is parabolic,
E = k (r – req)2 1 2

9. Anharmonic oscillator model
The actual potential energy of an anharmonic oscillator fits the parabolic function fairly well only near the equilibrium internuclear distance.
The Morse potential function more closely resembles the potential energy of an anharmonic oscillator model.
Deq
req
Fig. The energy diagram of molecule’s vibrational model showing an (a) ideal diatomic or (b) anharmonic diatomic oscillator.

11. Vibrational spectra: Harmonic oscillator model
Oscillation Frequency,
k is the force constant
 = reduced mass,
Vibrational frequency only dependent on the mass of the system and the force constant .
From Schrodinger equation, Vibrational energies for simple harmonic oscillator,

12. Vibrational spectra: Harmonic oscillator model
Oscillation Frequency,
k is the force constant
 = reduced mass,
The vibrational frequency is increasing with:
increasing force constant k ( = increasing bond strength)
decreasing atomic mass
• Example: k cc > k c=c > k c-c

13. Infrared Spectroscopy
POSITION
REDUCED MASS
BOND STRENGTH
(STIFFNESS)
LIGHT ATOMS
HIGH FREQUENCY
STRONG BONDS
The vibrational frequency is increasing with:
• increasing force constant k (= increasing bond strength)
• decreasing atomic mass

14. Vibrational spectra: Anharmonic oscillator model
Vibrational energies for simple harmonic oscillators,
……… A
Vibrational energies for anharmonic oscillators,
……… B

15. Different types of Energy
Connecting macroscopic thermodynamics to a molecular understanding requires that we understand how energy is distributed on a molecular level.
ATOMS:
The electrons: Electronic energy. Increase the energy of one (or more) electrons in the atom.
Nuclear motion: Translational energy. The atom can move around (translate) in space.
MOLECULES:
The electrons: Electronic energy. Increase the energy of one (or more) electrons in the molecule.
Nuclear motion:
Translational energy. The entire molecule can translate in space.
Vibrational energy. The nuclei can move relative to one another.
Rotational energy. The entire molecule can rotate in space.

16. N2
Figure 8.2

17. CO2
Figure 8.2

18. Molecular vibrations
How many vibrations are possible (= fundamental vibrations)?
A molecule has as many degrees of freedom as the total degree of freedom of its individual atoms.
Each atom has three degrees of freedom (corresponding to the Cartesian coordinates), thus in an N-atom molecule there will be 3N degree of freedom.
In molecules, movements of the atoms are constrained by interactions through chemical bonds.

19. Molecular vibrations
Figure 8.1

20. Molecular vibrations
Figure 8.1

21. Fundamental Vibrations
Molecular vibrations
Translation - the movement of the entire molecule while the positions of the atoms relative to each other remain fixed: 3 degrees of translational freedom.
Rotational transitions – interatomic distances remain constant but the entire molecule rotates with respect to three mutually perpendicular axes: 3 rotational freedom (nonlinear), 2 rotational freedom (linear).
Fundamental Vibrations
Vibrations – relative positions of the atoms change while the average position and orientation of the molecule remain fixed.

22. Molecular vibrations

23. Stretching and Bending
Types of Molecular Vibrations: Vibrations fall into the basic categories of stretching and bending.
Stretching vibration involves a continuous change in the inter-atomic distance along the axis of the bond between two atoms.
Bending vibrations are characterized by a change in the angle between two bonds and are of four types: scissoring, rocking, wagging, and twisting.

24. Stretching Vibration

25. Bending Vibration

26. H2O: Stretching and Bending Vibrations
Bending is easier than stretching -- happens at lower energy (lower wavenumber)
Bond Order is reflected in ordering -- triple > double > single (energy)
with single bonds easier than double easier than triple bonds
Heavier atoms move slower than lighter ones