8/6/2019 Raman Scattering - Lecture 10

1/11

Section 6Raman Scattering

(lecture 10)

Quantum theoryof atoms / molecules

Previously: QuantumMechanics

Valence

Atomic and Molecular Spectroscopy

Raman ScatteringThe scattering processElastic (Rayleigh) and inelastic (Raman) scatteringSelection rules for Raman

Similarities and differences with dipole allowed absorption

8/6/2019 Raman Scattering - Lecture 10

2/11

6.1 ScatteringIn addition to being absorbed and emitted by atoms and molecules, photons may alsobe scattered (approx. 1 in 10 7 in a transparent medium). This is not due to defects ordust but a molecular effect which provides another way to study energy levels.

This scattering may be:

Elastic and leave the molecule in the samestate ( Rayleigh Scattering ) or

Inelastic and leave the molecule in a different quantum state ( Raman Scattering )

6.2 Rayleigh Scattering

Lord Rayleigh calculated that a dipole scatterer

8/6/2019 Raman Scattering - Lecture 10

3/11

6.3 Inelastic (Raman) Scattering

Energy exchange between the photon and molecule leads to inelastic scatter.

n 0 n t

In Raman Scattering the scattered photon hasdifferent energy (frequency, wavelength) than theincident photon:

Stokes lines are those in which the photon haslost energy to the molecule

Anti-Stokes lines are those in which the photonhas gained energy from the molecule

n 0 + n t

The strongest scattering is Rayleigh scatter

S t o k e s

A n t i

- S t o k e s

R a y

l e i g h

n 0 + n t

n 0

n

n 0 n t

n 0

Since molecular energy levels are quantised thisproduces discrete lines from which we can gain infoon the molecule itself.

Virtual state

8/6/2019 Raman Scattering - Lecture 10

4/11

6.4 Raman Scattering selection rules

Scattering is not an oscillating dipole phenomenon! (no TDM)

ind The presence of an electric field E induces apolarization in an atom/ molecule given by

polarizability

If the field is oscillating (e.g., photon) 0ind n

In atoms the polarizability is isotropic, and the atom acts like an antenna and re-radiates at the incident frequency Rayleigh Scattering only

In molecules the polarizability may be anisotropic, and depends on the rotationaland 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]

8/6/2019 Raman Scattering - Lecture 10

5/11

6.5 Rotational Raman

6.5.1 Linear Molecules : The polarizability tensor is anisotropic ( || )

As a molecule rotates the polarizability presented to the E field changes:the induced dipole is modulated by rotationresults in rotational transitions

S t o k e s

A n t i

- S t o k e s

R a y

l e i g h

n 0

J

J + 2

J 2

Effective two-photon process and

Specific Selection Rule:

J

Rayleigh

Stokes lines

Anti-Stokes lines

Even non-polar molecules (O 2, N2, CO2) exhibit rotational Raman Spectra

8/6/2019 Raman Scattering - Lecture 10

6/11

6.5.1 Rotational Raman spectra

J

Assuming a rigid rotor: F ( J ) = B J ( J +1)

Stokes lines are observed at:

0 0n n n J J J

and Anti- Stokes lines at:

0 0n n n J J J - 2

i.e.,a gap of 6 B between n 0 and 1 st lines of each branchlines in each branch of equal spacing = 4 B

n.b. 1st Anti-Stokes line is J = 2

8/6/2019 Raman Scattering - Lecture 10

7/11

6.5.1 Example Rotational Raman spectra

H2Stokes

Anti-Stokes

3:1 intensity alternation observed due tonuclear spin-statistics (3 times as manyortho -H2 levels (odd J ) as para -H2 (even J ))

Spectrum allowed because all transitions

connect levels of the same symmetry.

For the same reason, alternate lies are completely missing in the Raman spectra of 16O2 and C 16O2.(if the level doesnt exist one cant see transitions to and from it)

Likewise the 14N2 Raman spectrum shows 2:1 aternations

In deducing B from spacings, beware the possibility of missing lines in the spectrum.

8/6/2019 Raman Scattering - Lecture 10

8/11

6.6 Vibrational Raman

Gross Selection Rule : The polarizability must change during the vibration

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

6.6.1 Diatomics:

6.6.2 Polyatomics:

Need to check each normal mode against thegross selection rule:

RamanActive

RamanActive

RamanActive

H2O

0q

In practice this means the normal mode must transform with the same symmetry asthe quadratic forms (x 2, xy, etc .)

8/6/2019 Raman Scattering - Lecture 10

9/11

CO2: D h

RamanActive

RamanInactive

RamanInactive

IRActive

IRActive

IRInactiveg

u

u

8/6/2019 Raman Scattering - Lecture 10

10/11

6.7 The Rule of Mutual Exclusion

In the case of CO 2 it is not coincidence that those modes which are Raman active areIR 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 Raman Infra Red

Infra RedRaman

8/6/2019 Raman Scattering - Lecture 10

11/11

6.8 Vibration-Rotation Raman

In the same way that rotational transitions accompany vibrational absorptions sorotational structure is observed in high resolution Raman spectra.

Vibrational / Rotational Ramanspectrum of CO.

The Q-branch identifies thevibrational spacing ( w e -2w exe)