Raman SpectroscopyTheory and Aplications

Dr. Florian Paulat(Lehnert Laboratory)

Paulat, F.; Praneeth, V. K. K.; Lehnert, N. Inorg. Chem. 2006, 45, 2835-2856

Historical background

• 1920s: Prediction of inelasticscattering of light by molecules(Kramers, Heisenberg and Dirac)• 1928: First report of inelasticscattering in water and alcoholvapors by Raman & KrishnanTechnical limitation: light source• 1960s: Development of Laser as intense monochromatic light sources

OutlineAssembly of a Raman spectrometer

1) Theoretical background of:

Nonresonance Raman spectroscopy

Resonance Raman (rR) spectroscopy A-,B- and C-Term enhancement mechanism

2) Resonance Raman spectroscopy of metalloporphyrins

Electronic structure of metalloporphyrins

Assignment of vibrational modes using DFT and

rR spectroscopy

Identification of electronic transitions using rR spectroscopy

Raman spectrometer

1) Nonresonance Raman

• ~ 0.1 % is elastically (Rayleigh) and ~ 0.0001-0.00001 % inelasticallyscattered (Raman: Stokes; Anti-Stokes) LASER!• IR: one photon direct absorption of light in IR region• Raman: two photons UV, Vis and NIR excitation• Stokes more intense than anti-Stokes (Boltzmann distribution)

Resonance Raman (rR) theory

01

|m> 0|n> 1

Excited state |e>

Ground state |g>

|>

• Harmonic potentials• Intensity of a Raman line isproportional to 2

• Polarizability: = A + B + C What is the meaning of thedifferent mechanisms? Following: Vibronic treatment of Albrecht: Starting from thequantum theoretical dispersionequation, using the Herzberg-Teller formalism he derived equations forA-, B- and C-Term enhancement.Q

(a) Tang, Albrech in Raman Spectroscopy, Vol. 2, Plenum Press, New York, 1970. (b) Albrecht, J. Chem. Phys. 1961, 34, 1476.

rR – Enhancement Mechanism(A-Term)

iEEEnmge

Amge 0,,

2

• In resonance: Ee,v – Eg,m ≈ E0

• A proport. to electronic transition moment squared intenseelectronic transition (dipole allowed) • Vibrational overlap integrals (Franck-Condon factor):a) = 0 for identical potential curves and b) ≠ 0 only if displacement of potential curves (Q>0) only totallysymmetric modes (A1g) Albrecht, 1961

rR – Enhancement Mechanism(B-Term)

s j j

j

se

j

nQmgsge

mQngsge

E

sheDB

,

• Vibronic coupling of another excited state |s> with the resonant excited state |e>• Energetic separation of |e> and |s> must be small• Both transition dipole moments from |g> to |e> and |s> must be nonvanishing excited states must belong to allowed electronic transitions• <|Qj|m,n> connect |g> and |e> vibrational levels that differ by one quantum; when they are multiplied by Franck-Condon factors having same quantum numbers, the nominator does not! vanish even if there is no excited-state displacement Q (totally) and nontotally symmetric modes are enhanced via B-Term• Which modes are enhanced? group theory (direct product)

Albrecht, 1961

rR – Enhancement Mechanism(C-Term)

nQQmC • Numerator contains two Q-dependent integrals, which connectvibrational levels of |g> and |e> differing by one quantum

What kind of modes are enhanced byC-Term?

Overtones (02)!!!

Albrecht, 1961

2) Resonance Raman Spectroscopyof [Fe(TPP)Cl]

Optimized structure (B3LYP/LanL2DZ)

Vibrational Assignment: • 78 Atoms 3N-6 = 228 vibrations!!!• What tools to solve problem?- DFT calculations- Polarized rR spectroscopy (D4h

apply to the [M(TPP)] vibrations of[M(TPP)(Cl)])

Nonresonance Raman Spectrumof [Fe(TPP)Cl] (exc. = 1064 nm)

0.00

0.01

0.02

0.03

1363

1597

1574

1554

1495

1467

1371

1275

1233

1072

1030

1006

994

886

Inte

nsity

0.000

0.005

0.010

0.015

407

247

390

379

257

199

2000 1750 1500 1250 1000 750 500

0

1000

2000

3000

1274

1124 89

81008

1018

1649

.1

1054

1398

1649

.6

1598

1533

1508

1379

1260

Wavenumbers (cm-1)

500 400 300 200

0

30

60

90

251

241

202

388

419

Wavenumbers (cm-1)

calculated

measured

Depolarization ratio

Y

X

Z

Ez

LaserSample parallel

larperpendicu

II

0 < < ¾ polarized (p; A1g

vibrations)

= ¾ depolarized (dp; B1g

and B2g vibrations)

> ¾ anomalous Polarization (ap; A2g vibrations; in nonresonanceRaman forbidden!)

Polarized nonresonance Raman Spectrum of [Fe(TPP)Cl] (exc. = 1064 nm)

2000 1800 1600 1400 1200 1000 800 600 400 200

0.000

0.004

0.008

0.012

0.016

0.000

0.004

0.008

0.012

0.016

LM: C

H2C

l 2

p

LM: C

H2C

l 2

pp

dp

p

dp

p

dp

p

Inte

nsity

Wavenumbers (cm-1)

Electronic structure of [Fe(TPP)Cl]: Gouterman model

400 600 800

0

20000

40000

60000

80000

100000

120000

647.

1

568.

2

514.

5

454.

5

/ c

m-1 m

ol-1 L

Wavelength (nm)

Soret

Qv

Q

Electronic structure of [Fe(TPP)Cl]: Gouterman model

Qv

Q

A1u< 79>HOMO

A2u< 81>

Eg< 82/83>LUMO

Electronic structure of [Fe(TPP)Cl]: Gouterman model

400 600 800

0

20000

40000

60000

80000

100000

120000

647.

1

568.

2

514.

5

454.

5

/ c

m-1 m

ol-1 L

Wavelength (nm)

Both excited states have Eu

symmetry (a1u x eg = a2u x eg = Eu) Strong CI leads to large splitting Soret and Q-band

Qv: Vibronic mixing between Soret and Q excited states: Whichvibrations are active? Eu x Eu = (A1g) + B1g + B2g + A2g

Distance between Q and Qv?

Soret

Qv

Q

Polarized rR spectroscopy of Metalloporphyrins

A-Term: totally symmetric modes A1g vibrations

A-Term proport. to <e||g>2 A-Term is dominant for intenseelectronic transitions

B-Term: vibronic coupling nontotally symmetric modes whichare active in mixing |e> with |s> B1g, B2g and A2g

Metalloporphyrin: In Soret resonance enhancement of A1g

Metalloporphyrin: In Q resonance (vibronic mixing with Soretexcited state) enhancement of B1g, B2g and A2g modes

But: Q band is relative intense additional A-Term enhancement of A1g

Polarized rR spectrum (Soret) of [Fe(TPP)Cl] at exc. = 454.5 nm

500 1000 1500 20000

4000

8000

12000

16000

20000

Inte

nsity

Wavenumbers (cm-1)

500 1000 1500 20000

4000

8000

12000

16000

20000

p

259

p

887

p

723

p

639

p

572

p

1552

p

1598

p

1006

p10

73p

1235

p

1452

p

1364

p

391

only A1g vibrations

rR: excitation profile [Fe(TPP)Cl]

30000 25000 20000 150000

2

4

6

8

sym(C-Cm) + (C

-C

)

= 1556 cm-1 (A1g)

Rel

. int

ensi

ty

wavenumbers (cm-1)Symmetry?

Polarized rR spectrum (Qv) of [Fe(TPP)Cl] at exc. = 514.5 nm

1300 1400 1500 1600 1700

0

15000

30000

45000

60000

0

15000

30000

45000

60000

p

1594

dp

1576

p

1553

ap

1517

dp

1492

dp

1369

p

1362

ap

1334Inte

nsitä

t

Wellenzahl / cm-1Wavenumbers (cm-1)

Inte

nsity

polarized, depolarizedand anomalous polarizedbands

Anomalous Polarization

1934 Placzek: Theoretical Prediction of anomalous polarization

1972 Spiro and Strekas:almost 40 years later: firstexperimental determination of this effect: found in the resonanceRaman spectra (depolarizedmeasurements) of hemoglobin and cytochrome C

T. G. Spiro, T. C. Strekas, Proc. Nat. Acad. Sci. 1972, Vol. 69 (No. 9), 2622-2626.

Polarized rR spectrum (Q) of [Fe(TPP)Cl] at exc. = 568.2 nm

800 1000 1200 1400 1600

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000dp

1578

p

1557

ap

1522

dp

1496

dp

1373

p

1366

ap13

37

dp

1278

dp12

67

dp

1080p

1073

dp10

18p

1006

p

995

dp

851

ap

831

Inte

nsitä

t

Wellenzahl / cm-1Wavenumbers (cm-1)

Inte

nsity

polarized, depolarizedand anomalous polarizedbands

[Fe(TPP)Cl]: rR spectrum with excitationin ? exc. = 647.1 nm

low energy: anomalouspolarized bands: out-of-plane vibrations of thephenylrings

500 1000 1500 2000

10000

20000

30000

40000

50000

60000

70000

10000

20000

30000

40000

50000

60000

70000

ap

1722

p

1165

dp

1577ap

1522

ap

1515dp

1494

dp

1371

p

1363

ap

1335

p

dpp

ap10

2710

1510

0699

9

ap

943

dp

850

ip

830

p

779

ap

762

ap

554

inte

nsity

wavenumbers [cm-1]

1200 1210 1220 1230 1240 125010000

20000

30000

40000

50000

ap

1231

ap

1224

ap

1217

different enhancementcompared to excitationin Q What is the nature of this electronictransition?

TD-DFT calculationsand MCD Spectra haveto be analyzed in detail!

Gouterman: porphyrin(a1u/a2u) d transition (again Eu symmetry strong CI withSoret and or Q (if near in energy)? TDDFT: very very complicated!!!)

Summary (rR of Metalloporphyrins)

Complete assignment of the nonresonance and resonance Raman spectra of [Fe(TPP)Cl] using DFT and polarized Raman

Assignment of additional vibrations which are not present in thenonresonance case

Resonance enhancement is related to the nature of the excited electronic transition Polarized resonance Raman assists in assigning electronic absorption bands

Identification of anomalous polarized bands (A2g) which are a probe forvibronic mixing

Resonance enhancement very different for Soret, Q/Qv and ~680nm bands

What is the nature of the ~680nm feature? Gouterman: porphyrin(a1u/a2u) d transition

Paulat, F.; Praneeth, V. K. K.; Lehnert, N. Inorg. Chem. 2006, 45, 2835-2856.

Available wavelengths for rR in the Lehnert group

400 600 800

0

20000

40000

60000

80000

100000

120000

647.

1

568.

2

514.

5

/ c

m-1 m

ol-1 L

Wavelength (nm)

488.

0

457.

9

413.

1

351.

0