Raman Spectroscopy Theory and Aplications

Raman Spectroscopy Theory and Aplications Dr. Florian Paulat (Lehnert Laboratory) Paulat, F.; Praneeth, V. K. K.; Lehnert, N. Inorg. Chem. 2006, 45,...
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Raman Spectroscopy Theory 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 inelastic scattering of light by molecules (Kramers, Heisenberg and Dirac) • 1928: First report of inelastic scattering in water and alcohol vapors by Raman & Krishnan Technical limitation: light source • 1960s: Development of Laser as intense monochromatic light sources

Outline Assembly 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 % inelastically scattered (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 • Harmonic potentials

Excited state |e>

1 0 Ground state |g>

|n> 1 |m> 0

Q

• Intensity of a Raman line is proportional to 2 • Polarizability:  = A + B + C |>

 What is the meaning of the different mechanisms?  Following: Vibronic treatment of Albrecht: Starting from the quantum theoretical dispersion equation, using the Herzberg-Teller formalism he derived equations for A-, B- and C-Term enhancement.

(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)

A 

2

e g  m    n Ee,  E g ,m  E0  i

• In resonance: Ee,v – Eg,m ≈ E0 • A proport. to electronic transition moment squared  intense electronic 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 totally symmetric modes (A1g)

Albrecht, 1961

rR – Enhancement Mechanism (B-Term)  e hj s  B   D    Ee, s  s j 

 e  g  s  g  n    Qj m     e  g  s  g  m    Qj n 

    

• 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 • 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)

C  mQ    Q n • Numerator contains two Q-dependent integrals, which connect vibrational levels of |g> and |e> differing by one quantum

What kind of modes are enhanced by C-Term?

 Overtones (02)!!!

Albrecht, 1961

2) Resonance Raman Spectroscopy of [Fe(TPP)Cl]

Vibrational Assignment: • 78 Atoms  3N-6 = 228

Optimized structure (B3LYP/LanL2DZ)

vibrations!!! • What tools to solve problem? - DFT calculations - Polarized rR spectroscopy (D4h apply to the [M(TPP)] vibrations of [M(TPP)(Cl)])

Nonresonance Raman Spectrum of [Fe(TPP)Cl] (exc. = 1064 nm) 0.015

1495

0.010

379

1006

257

0.005

247

407

886

1072

1030

994

1233 1275

1467

1363

1597 1574

0.01

199

measured 1371

0.02

0.000

1598

419

0.00 3000

90

388

1649.6 1649.1

0 2000

1750

1500

1250

202

251

898

241

30

1018 1008

1054

1124

1274

1379

1533

1000

60

calculated

1260

1398

2000

1508

Intensity

390

1554

0.03

0

1000 -1

Wavenumbers (cm )

750

500

500

400

300

200 -1

Wavenumbers (cm )

Depolarization ratio 



Z

Sample

Ez Y

Laser 

I perpendicu lar I parallel

0 <  < ¾ polarized (p; A1g vibrations)

X





 = ¾ depolarized (dp; B1g and B2g vibrations)

> ¾ anomalous Polarization (ap; A2g vibrations; in nonresonance Raman forbidden!)

LM: CH2Cl2

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

Intensity

0.012

0.016

LM: CH2Cl2

0.016

dp p

0.008

p

p

p

p

0.012

0.008

dp dp 0.004

0.004

0.000

0.000

2000

1800

1600

1400

1200

1000

800 -1

Wavenumbers (cm )

600

400

200

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

647.1

568.2

514.5

Soret 100000

454.5

120000

Qv

-1

/ cm mol L

80000

-1

60000

40000

Q

20000

0 400

600

Wavelength (nm)

800

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

Qv

LUMO

Eg < 82/83>

Q

A 1u< 79>

HOMO

A2u< 81>

Electronic structure of [Fe(TPP)Cl]: Gouterman model 647.1

568.2

514.5

Soret 100000

454.5

120000

Qv

-1

/ cm mol L

80000

-1

60000

 Both excited states have Eu Q symmetry (a1u x eg = a2u x eg = Eu)  Strong CI leads to large splitting Wavelength (nm)  Soret and Q-band  Qv: Vibronic mixing between Soret and Q excited states: Which vibrations are active?  Eu x Eu = (A1g) + B1g + B2g + A2g 40000

20000

0

400

600

 Distance between Q and Qv?

800

Polarized rR spectroscopy of Metalloporphyrins 

A-Term: totally symmetric modes  A1g vibrations

A-Term proport. to 2  A-Term is dominant for intense electronic transitions

Metalloporphyrin: In Soret resonance enhancement of A1g 

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

Metalloporphyrin:  In Q resonance (vibronic mixing with Soret excited 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 20000

1552

p

only A1g vibrations

16000

p 1364

391

p

p

p 887

p p

723

4000

572 639

p 1598

p

p

p 1452

1006 1073

p

p 1235

8000

259

Intensity

12000

0 500

1000

1500 -1

Wavenumbers (cm )

2000

rR: excitation profile [Fe(TPP)Cl] 8

sym(C-Cm) + (C-C) -1

= 1556 cm (A1g)

Rel. intensity

6

4

2

0 30000

25000

20000

15000 -1

wavenumbers (cm )

Symmetry?

Polarized rR spectrum (Qv) of [Fe(TPP)Cl] at exc. = 514.5 nm polarized, depolarized and anomalous polarized bands

60000

p 1553

60000

45000

dp

ap

1492

1517

ap

1362 1369

30000

1576

dp

p dp

1334

30000

p 1594

Intensity Intensität

45000

15000

0 1300

15000

0 1400

1500

1600

-1 -1 Wavenumbers (cm ) Wellenzahl / cm

1700

Anomalous Polarization 



1934 Placzek: Theoretical Prediction of anomalous polarization

1972 Spiro and Strekas: almost 40 years later: first experimental determination of this effect: found in the resonance Raman spectra (depolarized measurements) 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

p

12000

1006 1018

1557

1496 1366 1373

12000 dp

dp p

10000 8000

dp dp ap 1337

ap

851

dp

6000

ap

6000 4000 2000

2000

0

0 800

18000 16000

p

1267 1278

8000

20000

14000

1080

p

p

dp

1073

10000

995

14000

831

Intensity Intensität

16000

dp

1578

polarized, depolarized and anomalous polarized bands

18000

4000

dp

1522

20000

1000

1200

Wavenumbers

1400 (cm-1) -1

Wellenzahl / cm

1600

[Fe(TPP)Cl]: rR spectrum with excitation in ? exc. = 647.1 nm 50000

ip

70000

1231

ap 1335

1217

60000

ap 1224

ap

40000

70000

830

ap

30000

60000

20000

1250

app

762 779

40000

ap dp

30000

p p

40000

dp

ap

1722

ap ap 943

20000

p

50000

1494 1515 1522 1577

1240

1363

1230

apap dp

1371

1220

850

1210

554

intensity

10000 1200

dp

dp

999 1006 1015 1027

p

1165

50000

10000

30000 20000 10000

500

1000

1500 -1

wavenumbers [cm ]

2000

 low energy: anomalous polarized bands: out-ofplane vibrations of the phenylrings  different enhancement compared to excitation in Q  What is the nature of this electronic transition?  TD-DFT calculations and MCD Spectra have to be analyzed in detail!

Gouterman: porphyrin(a1u/a2u)  d transition (again Eu symmetry  strong CI with Soret 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 the nonresonance 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 for vibronic 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.

647.1

568.2

514.5

488.0

100000

351.0

120000

457.9

413.1

Available wavelengths for rR in the Lehnert group

-1

/ cm mol L

80000

-1

60000

40000

20000

0 400

600

Wavelength (nm)

800

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