Download Section 6 Raman Scattering (lecture 10)

Section 6
Raman Scattering
(lecture 10)
Quantum theory
of atoms / molecules
Previously:
Quantum
Mechanics
Valence
Atomic and Molecular Spectroscopy
Raman Scattering




The scattering process
Elastic (Rayleigh) and inelastic (Raman) scattering
Selection rules for Raman
Similarities and differences with dipole allowed absorption
6.1 Scattering
In addition to being absorbed and emitted by atoms and molecules, photons may also
be scattered (approx. 1 in 107 in a transparent medium). This is not due to defects or
dust but a molecular effect which provides another way to study energy levels.
This scattering may be:
Elastic and leave the molecule in the same
state (Rayleigh Scattering) or
Inelastic and leave the molecule in a different
quantum state (Raman Scattering)
Nobel Prize 1904
(physics)
6.2 Rayleigh Scattering
Nobel Prize 1930
(physics)
Lord Rayleigh calculated that a dipole scatterer << l scatters with an intensity:
no. of scatterers

wavelength
polarizability
0
 2

4 2 

2

n.b.,
distance
scatterer - observer

4
5 times more effective
for 400nm than 600nm
Hence the sky is blue!
(and sunsets red)
6.3 Inelastic (Raman) Scattering
Energy exchange between the photon and molecule leads to inelastic scatter.
Anti-Stokes
Rayleigh
n0
Stokes
Virtual state
The strongest scattering is Rayleigh scatter
In Raman Scattering the scattered photon has
different energy (frequency, wavelength) than the
incident photon:
Stokes lines are those in which the photon has
lost energy to the molecule
n0 – nt
Anti-Stokes lines are those in which the photon
has gained energy from the molecule
n0 + nt
n0
n0 – nt
n0 + nt
n
Since molecular energy levels are quantised this
produces discrete lines from which we can gain info
on the molecule itself.
6.4 Raman Scattering selection rules
Scattering is not an oscillating dipole phenomenon! (no TDM)
The presence of an electric field E induces a
polarization in an atom/ molecule given by ind  
If the field is oscillating (e.g., photon) ind  
0
polarizability

n

In atoms the polarizability is isotropic, and the atom acts like an antenna and reradiates at the incident frequency – Rayleigh Scattering only
In molecules the polarizability may be anisotropic, and depends on the rotational
and vibrational coordinates. This can also give rise to Raman Scattering.
Gross Selection Rule:
To be Raman active a molecule must have anisotropic polarizability
[Less restrictive than the need for a dipole moment, symmetric molecules can be Raman active]
6.5 Rotational Raman
6.5.1 Linear Molecules: The polarizability tensor is anisotropic (  ||)
Specific Selection Rule:
Anti-Stokes
Rayleigh
n0
Stokes
As a molecule rotates the polarizability presented to the E field changes:
 the induced dipole is modulated by rotation
 results in rotational transitions
Effective two-photon process and
Stokes lines
J+2
J 
Anti-Stokes lines
J
J–2

Rayleigh
Even non-polar molecules (O2, N2, CO2) exhibit rotational Raman Spectra
6.5.1 Rotational Raman spectra
J 
Assuming a rigid rotor:

F(J) = BJ(J+1)
 Stokes lines are observed at:
n n 0 
  J     J  n
0


J



J -2

and Anti- Stokes lines at:
n n 0 
  J    J  n
0
n.b. 1st Anti-Stokes line is J = 2
i.e.,
 a gap of 6B between n0 and 1st lines of
each branch
 lines in each branch of equal spacing = 4B
6.5.1 Example Rotational Raman spectra
Stokes
H2
Anti-Stokes
3:1 intensity alternation observed due to
nuclear spin-statistics (3 times as many
ortho-H2 levels (odd J) as para-H2 (even J))
Spectrum allowed because all transitions
connect levels of the same symmetry.
Likewise the 14N2 Raman spectrum shows 2:1 aternations
For the same reason, alternate lies are completely missing in the Raman spectra of
16O and C16O .(if the level doesn’t exist one can’t see transitions to and from it)
2
2
In deducing B from spacings, beware the possibility of missing lines in the spectrum.
6.6 Vibrational Raman
 
Gross Selection Rule: The polarizability must change during the vibration 
 

q 0
In practice this means the normal mode must transform with the same symmetry as
the quadratic forms (x2, xy, etc.)
6.6.1 Diatomics:
Even homonuclear diatomics satisfy the gross selection rule and exhibit Raman spectra
Specific Selection Rule: Dv = ± 1 (+ Stokes, – Anti-Stokes)
n.b. Anti-Stokes rarely observed because v > 0 weakly populated
6.6.2 Polyatomics:
Need to check each normal mode against the
gross selection rule:
H2O
Raman
Active
Raman
Active
Raman
Active
CO2: Dh
IR
Inactive
Raman
Active
u
IR
Active
Raman
Inactive
u
IR
Active
Raman
Inactive
g


6.7 The Rule of Mutual Exclusion
In the case of CO2 it is not coincidence that those modes which are Raman active are
IR inactive and vice versa. This is an example of the rule of mutual exclusion which
states:
In a centrosymmetric molecule (i.e., one with a centre of inversion symmetry)
a vibrational mode may be either IR active or Raman active but not both.
acetylene
D h
Raman
Infra Red
Raman
Raman
Infra Red
6.8 Vibration-Rotation Raman
In the same way that rotational transitions accompany vibrational absorptions so
rotational structure is observed in high resolution Raman spectra.
Vibrational / Rotational Raman
spectrum of CO.
The Q-branch identifies the
vibrational spacing (we -2wexe)