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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