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 (02)!!!
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