The criteria that determines whether a particular transition is allowed, or forbidden are known as selection rules . Allowed transitions conform to the selection rules, forbidden transitions do not.
Forbidden bands are missing from the spectrum or appear in it with very low intensity
Born-Oppenheimer approximation:
Since the nuclei are so much more massive than the electrons, they must accordingly have much smaller velocities.
Nuclear motion includes the vibration and rotation movement. This separation of electronic and nuclear motion is known as the Born-Oppenheimer approximation. As a result, the total wavefunction can be separated into electronic, vibrational, and rotational parts.
Δ E = Δ E electronic
+ Δ E vibration
+ Δ E rotation
1.
Δ E electronic
> Δ E vibration
> Δ E rotation

E electronic

1000 *

E vibration

1 000 000*

E rotation
SelectionRules04 1

Figure.1. Superposition principle. Imperfect parabolas for ground, E
0
and excited, E
1
electronic states. Horizontal lines are vibrational energy levels.
Vertical blue line: absorption of a matching photon. Vertical green line: emission of a matching photon.
Transition Integral
In order to obtain the strength of interaction that causes a transition between two states, the transition dipole moments used rather than the dipole moment.
In quantum mechanics the basis for a spectroscopic selection rule is the value of the transition moment integral .
 f, i
 
final
initial d

0 2.
where ψ final
and ψ initial
are the wave functions of the two states involved in the transition and µ f,i
is the transition moment. If the value of this integral is zero the transition is forbidden.
If

has a nonzero value than the particular transition can be detected by f, i optical spectroscopy. Eq. 2. refers separately to electronic or vibration or rotation transition.
The intensities of spectroscopic transitions are proportional to the transition integral.
 
 r where e is the elementary charge. Now,
 f, i
 
  final r
 initial d
3.
Electronic transitions and their energetics.
Ultraviolet and visible radiation interacts with matter which causes electronic transitions (promotion of electrons from the ground state to a high energy state).
The ultraviolet region falls in the range between ≈190-380 nm, the visible region falls between ≈380-750 nm.
Calculate the energy of 285 nm photon ( c = 3 10 8 m/s, h = 6,63 10 -34 Js). Using the Planck equation

  


4.
SelectionRules04 2

hc = 6,63 10 -34
E
Js

3 10 8 m/s = 1.989 10 -25 Jm
 h
   h

 c
285

1 .
989
2 .
85


10
10

25

7

6.97
9

10 19 J
6.97 10 -19 J for a single photon, for one mole of photon it is: 419.7 kJ/mol.
The mean wavelength in visible is 565 nm. The energy of 565 nm photons is
E
 h
   h
 c

565

1 .
989

10

25
5 .
65

10

7

3.52

10
19
J the energy of one mole of photon is 211.7 kJ/mol.
Figure 2. Energy level diagram of different electronic transitions
SelectionRules04 3

Figure.3. Allowed electronic transitions.
One can observe from Fig 3. the charge density difference between wave functions Ψ final
Ψ initial
.
Measured transitions
Figure 4. Absorption spectrum of buta-1,3-diene.
The Fig. 4. shows a simple UV-visible absorption spectrum for buta-1,3-diene
SelectionRules04 4

CH
2
=CH-CH=CH
2
. Absorbance is just a measure of the amount of light absorbed in buta-1,3-diene, there are no non-bonding electrons. That means that the only electron jumps taking place are from

bonding to

anti-bonding orbitals.
Figure 5.
The absorbance spectrum of an important biological molecule called nicotinamide adenine dinucleotide, abbreviated NAD + .
This compound absorbs light in the UV range due to the presence of conjugated

-bonding systems.
Vibrations, selection rule (physical)
2
2
SelectionRules04 5

Figure 6. The normal vibrations of carbon dioxide.
The asymmetric stretch and the bends are the vibration types having dipole moment changing, and producing electromagnetic radiation. The radiation generated interacts with outer field.
The value of μ changes with the Q (coordinate) of the mode.
So selection rule for vibration is: dμ

0 dQ where Q is the coordinate of the vibration.
For a diatomic: Q = R (bond length)
A homonuclear diatomic (N
2
) is IR inactive . A heteronuclear diatomic is IR active .
Rotations
Pure rotation spectra can be observed in the microwave region of electromagnetic radiation.
Selection rule:
The physical requirement for observation of a pure rotational spectrum is an existing permanent dipole.
There is no dipole moment change when rotation axis coincides the direction of the bond.
SelectionRules04 6

A rotating HCl about an axis perpendicular to its bond produces an oscillating dipole .
A rotating N
2
about an axis perpendicular to its bond produces no oscillating dipole .
SelectionRules04 7