IR and Raman spectroscopy
Peter Hildebrandt Content 1. Basics of vibrational spectroscopy 2. Special approaches 3. Time-resolved methods 1. Basics of vibrational spectroscopy 1.1. Molecular vibrations and normal modes 1.2. Normal mode analysis 1.3. Probing molecular vibrations 1.3.1. Fourier-transform infrared spectroscopy 1.3.2. Raman spectroscopy 1.4. Infrared intensities 1.5. Raman intensities 1.1. Molecular vibrations and normal modes
IR and Raman spectroscopy - vibrational spectroscopy: probing well-defined vibrations of atoms within a molecule
Siebert & Hildebrandt, 2007) Motions of the atoms in a molecule are not random! well-defined number of vibrational degrees of freedom 3N-6 and 3N-5 for non-linear and linear molecules, respectively
What controls the molecular vibrations and how are they characterized? 1.1. Molecular vibrations and normal modes Definition of the molecular vibrations: Eigenwert problem normal modes for a non-linear N-atomic molecule: 3N-6 normal modes
example: benzene
in each normal mode: all atoms vibrate with the same frequency but different amplitudes
-1 -1 1(A1g): 3062 cm 14(E1u): 1037 cm
Thus: normal modes are characterised by frequencies (given in cm-1) and the extent by which individual atoms (or coordinates) are involved. 1.1. Molecular vibrations and normal modes Determination of normal modes – a problem of classical physics
Approach: Point masses connected with springs Harmonic motion
Siebert & Hildebrandt, 2007)
Crucial parameters determining the normal modes: - Geometry of the molecule (spatial arrangement of the spheres) - strength of the springs (force constants)
very sensitive fingerprint of the molecular structure 1.2. Normal mode analysis
A. Describing the movement of the atoms in terms of mass-weighted Cartesian displacement coordinates
xi
e.g. xi = xi –ai (i: all atoms) yi
zi
Mass-weighted Cartesian displacement Siebert & coordinates Hildebrandt, 2007)
q1 m1 x1 q2 m1 y1 q3 m1 z1 q4 m2 x2 etc. 1.2. Normal mode analysis
B. Expressing the kinetic and potential energy
3N kinetic energy T 1 2 T qi 2 i1
potential energy V for small 1 3N displacements (harmonic V fij qiq j approximation) 2 i, j1
Total energy: E T V
Newton´s equation 3N of motion 0 qj fij qi i, j1 1.2. Normal mode analysis
C. Solving the eigenwert problem Set of 3N linear second-order differential equations 3N 1/ 2 0 f A A qi Ai cos t ij i j i1 Secular determinant:
f11- f12 f13 ….. f1,3N
f21 f22- f23 ….. f2,3N
0 = f31 f23 f33- ….. f3,3N …
f3N,1 f3N,2 f3N,3 ….. f3N,3N-
3N solutions, 3N frequencies
Removal of 6 solutions für fij=0 (translation, rotation) 3N-6 non-zero solutions for frequencies 1.2. Normal mode analysis D. Coordinate transformation: Cartesian coordinates to normal coordinates
3N Qk lki xi i1 One normal mode accounts for one normal mode – unique relationship! Simplifies the mathematical and theoretical treatment of molecular vibrations but is not illustrative!
Intuitive coordinates – internal coordinates:
Stretching Bending Out-of-plane deformation Torsion 1.2. Normal mode analysis
E. Solving the eigenwert problem
Constructing the G- und F-Matrix and inserting into Newton´s equation of motion
N 1 1 Gt,t´ st, st`, G F 0 1 m
Example: three-atomic molecule 1
r r12 13 3 2
G-Matrix known, if the structure is known
Solving the FG-matrix leads to (3N-6) solutions
F-Matrix a priori unknown 1.2. Normal mode analysis
Main problem: How to determine the force constant matrix? Quantum chemical calculations
Objectives of the theoretical treatment of the vibrational problem: Calculating vibrational spectra rather than analysing vibrational spectra Comparing the experimental vibrational spectra with spectra calculated for different structures
Quantum chemical methods Optimizing the geometry for a molecule Calculating the force field Solving the normal mode problem 1.2. Normal mode analysis
sample
experimental presumed structure spectra
geometry optimization
spectra calculation comparison
poor agreement: good agreement: new structure assumption presumed structure is the true one 1.3. Probing molecular vibrations
Infrared spectroscopy direct absorption of photons
Raman spectroscopy inelastic scattering of photons
Siebert & Hildebrandt, 2007) 1.3. Probing molecular vibrations
Infrared spectroscopy Raman spectroscopy direct absorption of photons inelastic scattering of photons
0 0 ― n white white light light ― n h n
n : normal mode frequency 1.3.1. Fourier-Transform IR spectroscopy
detected intensity interferogram: I=f(x)
Fourier transformation
spectrum: I = f() 1.3.2. Raman Spectroscopy
cw laser from 240 – 1064 nm pulsed laser from 180 – 1064 nm 1.4. Infrared intensities z
m
x n y I (Q ) 2 mn k mn xyz 3N 6 0 * x * Q mn x x m n m k n k 1 Qk 0 * mn x m ˆ x n = 0, 0, if dipole 0, if m orthogonality moment varies = n 1 with Qk 3N 6 0 x Q x x Q k i1 k 0 1.5. Raman intensities
r Oszillating EM radiation E E0 cos2 0t induces dipole in the molecule ind xyz E 2 m ind 2 2 Raman intensity Imn (Qk ) mn xyz mn xyz E n
Calculating the scattering tensor by second–order perturbation theory 1 m M r r M n m M r r M n xyz mn h r r n 0 ir r n 0 ir 2. Special approaches 2.1. IR difference spectroscopy 2.2. Resonance Raman spectroscopy 2.3. Surface enhanced (resonance) Raman and infrared absorption spectroscopy 2.4. Limitations of Surface enhanced vibrational spectroscopies and how to overcome them 2.5. SERR and SEIRA spectroelectrochemistry 2. Special approaches
Intrinsic problem of Raman and IR spectroscopy: low sensitivity and selectivity
Therefore: - Resonance Raman spectroscopy - surface enhanced resonance Raman spectroscopy - IR difference spectroscopy - surface enhanced infrared absorption difference spectroscopy 2.1. IR difference spectroscopy A historical example: Bacteriorhodopsin
15 + [Lys] 13 N H h K BR 570 590
Siebert et al. 1985 IR difference spectra: structural changes induced by a reaction 2.2. Resonance Raman spectroscopy
Raman vs. resonance Raman Resonance Raman (RR): enhancement of the electronically excited state vibrational bands of a chromophore upon excitation in resonance with an electronic transition
― 0 n ― n 0 0 0
h n h n
electronic ground state 2.2. Resonance Raman spectroscopy
Resonance Raman intensities E r 2 2 Raman intensity Imn (Qk ) mn xyz E 1 m M r r M n m M r r M n xyz mn h r r n 0 ir r n 0 ir
m for G 0 EG n
1 M M m r r n approximation for EG, EG, xyz mn strong transitions h r EG 0 ir 2.2. Resonance Raman spectroscopy
1 M M m r r n EG, EG, xyz mn h r EG 0 ir
Non-zero Franck-Condon factor products only for modes including coordinates with an excited state displacement
Siebert & Hildebrandt, 2007) M M s EG , EG , k xyz mn EG 0 ir EG 0 k ir 2.2. Resonance Raman spectroscopy
bacteriorhodopsin
500 1000 1500 nm resonant excitation non-resonant excitation
x 300
15 + [Lys] 13 N H
Resonance Raman selectively probes the vibrational bands of a chromophore in a 800 1000 1200 1400 16001500 1600 1700 1800 macromolecular matrix / cm-1 / cm-1 Althaus et al. 1995 2.3. Surface enhanced (resonance) Raman and infrared absorption spectroscopy Observation: molecules adsorbed on rough (nm-scale) Ag or Au surface experience an enhancement of the Raman scattering – surface enhanced Raman (SER) effect.
SER-active systems: - Electrochemically roughened electrodes - Colloidal metal particles - Evaporated (sputtered) or (electro-)chemically deposited metal films 2.3. Surface enhanced Raman and IR effect
Theorie - SER:
Delocalised electrons in metals can undergo collective oscillations (plasmons) that can be excited by electromagnetic radiation
Eigenfrequencies of plasmons are determined by boundary conditions - Morphology - Dielectric properties
Upon resonant excitation, the oscillating electric field of the radiation field E0 ( 0 ) Induces an electric field in the metal Eind ( 0 ) Etot ( 0 ) E0 ( 0 ) Eind ( 0 ) Total electric field E ( ) E ( ) 0 0 ind 0 Enhancement factor for the FE ( 0 ) 1 2g 0 field at the incident frequency E0 ( 0 ) 2.3. Surface enhanced Raman and IR effect
The magnitude of the enhancement depends on the frequency-dependent dielectric properties of the metal ~ ( ) 1 r 0 ~ ( ) complex dielectric constant g 0 ~ r 0 r ( 0 ) 2
If real part -2 and imaginary part 0, ~ re ( 0 ) i im ( 0 ) r ( 0 ) 2 largest enhancement nsolv In a similar way, one may derive a field enhancement for the Raman scattered light ERa ( 0 k ) which depends on Etot ( 0 )
Since the intensity is proportional to the square of the electric field strength, the SER enhancement factor is given by:
2 FSER ( 0 k ) 1 2g0 1 2g Ra
Total enhancement ca. 1o5 -106 2.3. Surface enhanced Raman and IR effect
SERR and SEIRA: all photophysical processes at metal surfaces can be enhanced via the frequency- dependent electric field enhancement combination of RR and SER: surface enhanced resonance Raman – SERR: excitation in resonance with both an electronic transition of the adsorbate and the surface plasmon eigenfrequency of the metal Single-molecule sensitivity!
IR - Absorption: surface enhanced infrared absorption – SEIRA enhancement of the incident electric field in the infrared! (Au, Ag) Etot ( 0 ) E0 ( 0 ) Eind ( 0 ) Total electric field
Total enhancement thus ca. less than the square root of the SER effect:100 – 1000 2.3. Surface enhanced Raman and IR effect enhancement
Calculations of the enhancement factor for various geometric shapes (Ag) 2.3. Surface enhanced Raman and IR effect
Siebert & Hildebrandt, 2007)
Distance-dependence of the SER and SEIRA effect SEIRA 12 a FSER (d) FSER (0) a d
6 a SERR FSEIRA (d) FSEIRA (0) a d Siebert & Hildebrandt, 2007) 2.4. Limitations of Surface enhanced vibrational spectroscopies
… and how to overcome them
Plasmon resonance of polydisperse nanostructures
Ag Au
Preferred spectral range for But: Au displays a much combining RR and SER broader electrochemical potential range and is chemically more stable 2.4. Limitations of Surface enhanced vibrational spectroscopies
Layered hybrid devices
Electrochemical roughening of Ag Coating by a dielectric layer (SAM, Deposition of a metal film or
electrode SiO2) semiconductor film (Au, Pt, TiO2)
0.3 V -0.3 V
75 nm
Functionalisation of the outer metal layer for protein binding
Metal film: ca. 20 nm dielectric layer: 2 – 30 nm
Nanostructured Ag Ag 2.4. Limitations of Surface enhanced vibrational spectroscopies
Layered hybrid devices 2.4. Limitations of Surface enhanced vibrational spectroscopies
Layered hybrid devices 2.4. Limitations of Surface enhanced vibrational spectroscopies
Layered devices Distance-dependence of the enhancement
experimental theoretical
Ag
25 Ag-spacer-Au 20
15 0
g Cyt 10 413 nm 5 Ag
0 0.6 0.8 1.0 1.2 1.4 r/R 2.4. Limitations of Surface enhanced vibrational spectroscopies
Layered devices Potential application for in-situ studies in heterogeneous catalysis 2.5. SERR and SEIRA spectroelectrochemistry
probing electron transfer processes
SERR
SEIRA
Siebert & Hildebrandt, 2007)
Siebert & Hildebrandt, 2007) 2.5. SERR and SEIRA spectroelectrochemistry
SERR: applicable to proteins bound to biocompatibly coated metal surfaces
Immobilization of cytochrome c on “membrane models“
- 2- + Electrostatic (CO2 , PO3 , NH3 ) Hydrophobic (e.g. CH3) Polar (e.g. OH)
S S S S S S S S S S S S S S S S S S S S S S S S
Mixed SAMs (e.g. OH/CH3) Covalent (cross linking) Coordinative (e.g. Py)
S S S S S S S S S S S H N S S S S O N S S O S O S S S S S S 2.5. SERR and SEIRA spectroelectrochemistry Example: redox processes of cytochrome c
Potential-dependent SERR measurements to probe the redox equilibrium of the immobilised protein
Met Met Fe2+ Fe3+ His His
3. Time-resolved methods 3.1. Principles of time-resolved IR and RR experiments 3.2. Time-resolved pump-probe Raman spectroscopy with cw excitation 3.3. Time-resolved IR experiments 3.4. Rapid mixing techniques and time-resolved spectroscopy 3.5. Potential-jump time-resolved SERR and SEIRA spectroscopy 3.6. Time-resolved techniques -summary 3. Time-resolved methods
Principle approaches:
Time scale Method comments
Resonance Raman > 100 ns Cw excitation Low photon flux
> 10 ps Pulsed excitation High photon flux
> 100 fs Stimulated Raman Very demanding set-up IR > 1 ms Rapid scan
> 10 ns Step scan
> 100 fs transient absorption Very demanding set-up 3.1. Principles of time-resolved IR and RR experiments
Triggering the processes to be studied by light (photo-processes or photoinduced release of reactands) temperature, pressure, or potential jump rapid mixing with the reaction partner 3.2. Time-resolved pump-probe Raman spectroscopy
Pump-probe experiments with cw excitation
s Time t for smin dlaser tmin 100ns resolution v 3.2. Time-resolved pump-probe Raman spectroscopy
Pump-probe experiments with pulsed excitation
s Time t for s 1mm tmin 3ps resolution c min 3.2. Time-resolved pump-probe Raman spectroscopy
Sensory rhodopsin II from Natronobacterium pharaonis 3.2. Time-resolved pump-probe Raman spectroscopy
Sensory rhodopsin II from Natronobacterium pharaonis
Challenge: Time-resolved approach must cover a dynamic range of more than six decades
Gated-cw pump probe experiments 3.2. Time-resolved pump-probe Raman spectroscopy
pump
Siebert & probe Hildebrandt, 2007) 3.2. Time-resolved pump-probe Raman spectroscopy
NpSRII500
M400 Intensity / a.u.
1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 Wavenumbers / cm-1 3.2. Time-resolved pump-probe Raman spectroscopy
M400 formation M400 decay Intensity / a.u. Intensity / a.u.
0 10 20 30 40 50 60 70 80 0 500 1000 1500 2000 2500 3000 3500 δ/μs δ/μs
Same results as for transient absorption spectroscopy Intensity / a.u. M400 kinetics
100 101 102 103 104 105 106 107 δ/μs 3.3. Time-resolved IR techniques
- Rapid scan measuring consecutive interferograms (ca. 10 ms)
- Step scan Measuring signal decays after each mirror step (< 100 ns)
Siebert & Hildebrandt, 2007) 3.3. Time-resolved IR techniques
Example: photocycle of bacteriorhodopsin
Gerwert et al.) 3.3. Time-resolved IR techniques
Example: photocycle of bacteriorhodopsin
Gerwert et al.) 3.4. Rapid mixing techniques and time-resolved spectroscopy
Rapid mixing of components A and B with
tmix 0.1 - 5 ms ......
mixing A chamber B
.... and monitoring the reaction using the .... 3.4. Rapid mixing techniques and time-resolved spectroscopy
....stopped-flow method
time resolution: t = tmix +
mixing chamber
A B
observation
stop rapid scan RR and FT IR ( = 10 ms)
... continuous-flow method .... freeze-quench method time resolution: t = tmix + with time resolution: t = tmix + tcool with tcool 2 ms
mixing chamber mixing chamber A B A B
s s
observation
isopentane -120oC RR spectroscopy (min < tmix) RR spectroscopy 3.4. Rapid mixing techniques and time-resolved spectroscopy
Example: re-folding of cytochrome c rapid mixing of unfolded cytochrome c in GuHCl with a GuHCl-free solution continuous-flow method with RR detection
0.8 0.6
H2O-Fe H2O-Fe-His
Conc. 0.4 0.2 His-Fe-His His-Fe-His 0.0 UF-4 -3 -2 -1 log (time)
H2O
H2O Met Fe His His His His His partially folded unfolded Rousseau et al. 1998 3.5. Potential-jump time-resolved SERR and SEIRA spectroscopy
for probing the dynamics of interfacial processes
- Rapid potential jump to perturb the equilibrium of protein immobilised on an electrode - probing the relaxation process by TR SERR or step-scan or rapid scan SEIRA - time resolution limited by the reorganisation of the electrical double layer 3.5. Potential-jump time-resolved SERR and SEIRA spectroscopy
Example: interfacial redox process of cytochrome c
one-step relaxation process
B1red B1ox Met Met Fe2+ Fe3+ His His 3.5. Potential-jump time-resolved SERR and SEIRA spectroscopy
Example: interfacial redox process of cytochrome c
one-step relaxation process
B1red B1ox Met Met Fe2+ Fe3+ His His 3.5. Potential-jump time-resolved SERR and SEIRA spectroscopy
Protein structural changes monitored by SEIRA spectroscopy -turn III aa 67-70 Lys 86,87 Lys 72,73
heme
Amide I band changes of the -turn III segment 67-70 occur simultaneously with electron transfer 3.6. Time-resolved techniques – summary
RR Photoinduced cw (> 100 ns) Photoreceptors processes pulsed (> 10 ps) Ligand binding Pump-probe IR rapid scan (> 10 ms) bimolecular reactions with caged compounds step scan (> 100 ns)
RR Bimolecular reactions cw (> 100 s) Protein folding Rapid mixing Enzymatic reactions IR rapid scan (> 10 ms) Ligand binding
SERR Potential-dependent cw (> 10 s) Re-orientation processes at Conformational electrodes SEIRA rapid scan (> 10 ms) transitions Potential-jump step scan (> 10 s) electron transfer Literature
Most of the figures shown in this presentation have been taken from this book