lectures in spectroscopy raman spectroscopy

Introduction Rotational Raman Vibrational Raman Raman spectrometer

Lectures in Spectroscopy

Raman Spectroscopy

K. Sakkaravarthi

Department of PhysicsNational Institute of Technology

Tiruchirappalli – 620 015Tamil Nadu

India

[email protected]

K. Sakkaravarthi Lectures in Spectroscopy 1/28


My sincere acknowledgments toFundamentals of Molecular Spectroscopy, 4th Ed.,C.N. Banwell, McGraw-Hill, New York (2004).

Molecular Structure and Spectroscopy,G. Aruldhas, Prentice Hall of India, New Delhi (2002).

Introduction to Atomic Spectra,E. H. White, McGraw-Hill, New York (2005).

Many other free & copyright internet resources.



1 IntroductionRaman Scattering

2 Rotational Raman spectroscopyLinear MoleculesSymmetric Top Molecules

3 Vibrational Raman spectroscopyVibrational RamanVibrational+Rotational RamanMutual ExclusionHyper-Raman scattering

4 Raman spectrometer



Scattering in MoleculesInteraction of photons (ν0) with molecules:(i) Elastic (Rayleigh) scattering: Most molecules.

(ii) Inelastic (Raman) scattering: Very few moleculesFrequency/Energy shift (1928: CV Raman & KS Krishnan)

Raman ScatteringLower freq. (ν = ν −∆ν) ⇒ Stoke’s lines.Higher freq. (ν = ν + ∆ν) ⇒ Anti-Stoke’s lines.Raman shift ∆ν (around 10− 4, 000 cm−1).Original freq. ν ⇒ Rayleigh lines.



Classical Theory: Raman ScatteringMolecule in electric field ’E’:Electric field of radiation distorts the electron distribution.Polarization of charged particles P = αE,α: Polarizability of the molecule.For an incident radiation of freq. ν0,change in electric field E = E0 cos(2πν0t).Vibrational motion of the moleculeQ = Q0 cos(2πνmt),for normal coordinate Q with vibrational freq. νm.Polarizability due to vibrations/rotationsα = α0 +

(∂α∂Q

)0Q+ · · ·H.O.

Effective Polarization:P =

[α0 +

(∂α∂Q

)0Q0 cos(2πνmt)

]E0 cos(2πν0t.



Classical Theory: Raman Scattering...⇒ P = α0E0 cos(2πν0t)

+12

(∂α∂Q

)0Q0E0[cos 2π(ν0 + νm)t+ cos 2π(ν0 − νm)t].

First term: original freq. ν0 (Rayleigh line)Second term: higher freq. ν0 + νm (Raman anti-Stokes line)Third term: lower freq. ν0 − νm (Raman Stokes line)

Change in polarizability for CO2

symmetric stretch bend asymmetric stretch.

Symmetric vibrations: Raman active (but IR inactive)Asymmetric vibrations: very weak in Raman (negligibly small)



Quantum Theory: Raman ScatteringDrawback in classical theory: Gave frequency shifts,but not able to find intensities.Duality: Radiation as particle/photon & wave.Molecules interact with photon/particle hν0.Moves to virtual state by absorbing some energy. &Return to original state by emitting radiation.No. photon scattering ∝ Size of bonds.Mostly, frequency of emitted radiation is same to thefrequency of incident radiation: Rayleigh/elastic scattering.Small fraction of radiation with high/low frequency thanincident frequency (gains/looses energy): Raman scattering.If molecule gains energy, scattered photon freq. ν0 − νm:Stokes linesIf molecule looses energy, scattered photon freq. ν0 + νm:anti-Stokes lines.



Quantum Theory: Raman Scattering...Intensity depends on initial population.Power Ps = I0 × σR (Incident Int. & Raman cross-section)Boltzmann distribution ⇒ Is

Ias= exp hνm

kT .

(or) IsIas

= (ν0−νm)4

(ν0+νm)4exp hνm

kT



Rotational Raman spectroscopy

Linear MoleculesRotational energy changes due to Raman scattering!

Rotational energy εJ = BJ(J + 1) cm−1, J = 0, 1, 2, ...

Selection rule ∆J = 0,±2 !Jump in the level due to additional scattered energy.(Symmetry of the polarizability: end-over-end rotations)Rotational energy change ν̄ = ∆εJ = εJ+2 − εJ = B(4J + 6).When molecules gains energy or scattered photon loosesenergy ⇒ Stokes lines with lower frequencies than ν̄0.Freq. of Stokes spectral lines ν̄ = ν̄0 −B(4J + 6).When molecules looses energy or scattered photon gainsenergy ⇒ anti-Stokes lines with higher frequencies than ν̄0.Freq. of anti-Stokes spectral lines ν̄ = ν̄0 +B(4J + 6).Freq. of Raman spectra ν̄ = ν̄0 ±B(4J + 6), J = 0, 1, 2, · · ·



Rotational Raman spectra for Linear Molecules



Symmetric Top Molecules

Rotational energy εJK = BJ(J + 1) + (A−B)K2 cm−1,Here J = 0, 1, 2, ..., K = 0,±1,±2, ...

Selection rule ∆K = 0 & ∆J = 0,±1,±2 !!Jump in the level due to additional scattered energy.(Rotation about molecular axis & its perpendicular axis)Rotational energy changeν̄ = ∆εR = εJ+1 − εJ = 2B(J + 1) (for ∆J = 1: R branch)ν̄ = ∆εS = εJ+2 − εJ = B(4J + 6) (for ∆J = 2: S branch)Two Frequency bands for Raman lines:ν̄R = ν̄0 ± 2B(J + 1) cm−1.ν̄S = ν̄0 ±B(4J + 6) cm−1.Spectral lines spacing: 2B for R branch Raman lines.Spectral lines spacing: 4B for S branch Raman lines.



Rotational Raman spectra for Symmetric Top molecule



Vibrational Raman spectroscopy

Vibrational Raman spectraDegrees of freedom (normal modes): Anharmonicvibrations.Vibrational energy εv =

(v + 1

2

)ν̄e −

(v + 1

2

)2xe ν̄e cm−1.

Here v = 0, 1, 2, ... (ν̄e equilibrium oscillation freq.)Selection rule ∆v = ±1,±2,±3, ...!!!Jump in the level due to additional scattered energy.Raman spectra are very weak, so only ∆v = ±1.(overtones, combination & hot bands are negligible)Vibrational energy change ∆ε = ε1 − ε0 = ν̄e(1− 2xe) cm−1.Freq. of Raman lines ν̄ = ν̄0 ± ν̄e(1− 2xe) cm−1.Population in v ≥ 1 is very less, so anti-Stokes lines arevery weak than Stokes lines.



Vibrational+Rotational Raman spectraEnergy for Raman spectra with vibration+rotationεJv =

(v + 1

2

)ν̄e −

(v + 1

2

)2xe ν̄e +BJ(J + 1) cm−1.

Here v = 0, 1, 2, ... & J = 0, 1, 2, ...

Selection rule ∆v = ±1 & ∆J = 0,±2!

For ∆v = 1 & ∆J = 0: Q branch Stokes lines∆ε = ν̄e(1− 2xe) cm−1 ν̄Q = ν̄0 − ν̄e(1− 2xe) cm−1.

For ∆v = 1 & ∆J = 2: S branch Stokes lines∆εJv = ν̄e(1− 2xe) +B(4J + 6) cm−1

ν̄S = ν̄0 − ν̄e(1− 2xe)−B(4J + 6) cm−1.

For ∆v = 1 & ∆J = −2: O branch Stokes lines∆εJv = ν̄e(1− 2xe)−B(4J + 6) cm−1

ν̄S = ν̄0 − ν̄e(1− 2xe) +B(4J + 6) cm−1.



Rotational+Vibrational structure of Raman Stokes lines ofdiatomic molecule with vibrational frequency ν̄e(1− 2xe).



Mutual Exclusion: Raman spectraRaman scattering & IR: two different processes.

Some molecular vibrations are active in both IR & Raman.Several vibrations can be active either in Raman or IR.

Molecules with centre of symmetry: Raman active(polarizability), IR inactive (no change in dipole moment)⇒ Mutual exclusion

Molecules without centre of symmetry shall be active inboth IR & Raman.



Comparison: IR and Raman transitions!



IR and Raman offers complementary techniques!



Hyper-Raman scattering (HRS) effectA modified version of Raman scattering!Inelastic second harmonic scattering of photons.

Sum frequency generation: A coherent process involvingtwo incident fields (with frequencies ν1 & ν2 and wavevectors k1 & k2) produce a single field with frequencyν1 + ν2 and wave vector k1 + k2.Hyper-Rayleigh scat.: Elastic scat. for ν1 = ν2 & k1 = k2.Hyper-Raman scattering: Inelastic form of Hyper-Rayleighscattering!!



Hyper-Raman scattering (HRS) effect...Hyper-Raman scattering: Inelastic scattering of incidentphotons (with frequency ν1 = ν2 = ν) into photons of twodifferent frequencies 2ν ±∆ν!!

HRS Stokes lines: νS = ν1 + ν2 −∆ν.HRS anti-Stokes lines: νAS = ν1 + ν2 + ∆ν.∆ν depends on the usual scattering of molecular vibrations.

HRS effect is usually very weak, but has aspects whichmake it interesting for Raman spectroscopy.HRS can provide vibrational information on moleculeswhere ordinary Raman Scattering is suppressed due tosymmetry issues.



Basic Raman spectrometer



Schematic: Basic Raman spectrometer



Basic Raman spectrometer



Raman spectrometerSeveral variants of Raman spectrometers...To enhance the sensitivity (ex. surface-enhanced Raman),improve the spatial resolution (Raman microscopy),very specific information (resonance Raman), etc.

Spontaneous Raman spectroscopySurface-enhanced Raman spectroscopy (SERS)Resonance Raman spectroscopySurface-enhanced resonance Raman spectroscopy (SERRS)Angle-resolved Raman spectroscopyTransmission Raman spectroscopyTip-enhanced Raman spectroscopy (TERS)Stand-off remote Raman

Many hand-held Raman spectrometers!K. Sakkaravarthi Lectures in Spectroscopy 25/28


Few Applications of Raman spectra



SummaryFrom the present series of lectures, we have learned theprinciple, explicit description and detailed analyses oftransitions in molecules due to Raman scattering byincluding the vibrational and rotational effects!



Thank You


lectures in spectroscopy raman spectroscopy

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