Section 6Raman Scattering

(lecture 10)

Quantum theoryof atoms / molecules

Previously: QuantumMechanics

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 alsobe scattered (approx. 1 in 107 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 same

state (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 << l scatters with an intensity:

2

2

0 4 2

polarizabilityno. of scatterers

distancescatterer - observer

wavelength

4

5 times more effectivefor 400nm than 600nmHence the sky is blue!

(and sunsets red)

n.b.,

Nobel Prize 1904(physics)

Nobel Prize 1930(physics)

6.3 Inelastic (Raman) Scattering

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

n0 – nt

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

n0 + nt

The strongest scattering is Rayleigh scatterSt

oke

s

An

ti-S

toke

s

Ray

leig

h

n0 + nt

n0

n

n0 – nt

n0

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

Virtual state

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]

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 rotation results in rotational transitions

Sto

kes

An

ti-S

toke

s

Ray

leig

h

n0

J

J + 2

J – 2

Effective two-photon process and

Specific Selection Rule:

J

Rayleigh

Stokes lines

Anti-Stokes lines

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:

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 6B between n0 and 1st lines of

each branch lines in each branch of equal spacing = 4B

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

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 transitionsconnect levels of the same symmetry.

For the same reason, alternate lies are completely missing in the Raman spectra of16O2 and C16O2.(if the level doesn’t exist one can’t 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.

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 (x2, xy, etc.)

CO2: Dh

RamanActive

RamanInactive

RamanInactive

IRActive

IRActive

IRInactiveg

u

u

6.7 The Rule of Mutual Exclusion

In the case of CO2 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 whichstates:

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

Dh

Raman Raman Infra Red

Infra RedRaman

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 (we -2wexe)