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(A1g): 3062 cm-1
14(E1u): 1037 cm-1
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
coordinates
q1  m1 x1
q 2  m1 y1
q3  m1 z1
Siebert &
Hildebrandt, 2007)
q 4  m2 x 2
etc.
1.2. Normal mode analysis
B. Expressing the kinetic and potential energy
kinetic energy T
1 3N 2
T   qi
2 i 1
potential energy V for small
displacements (harmonic
approximation)
1 3N
V   f ij qi q j
2 i , j 1
Total energy:
Newton´s equation
of motion
E  T V
3N
0  q j   f ij qi
i , j 1
1.2. Normal mode analysis
C. Solving the eigenwert problem
Set of 3N linear second-order differential equations

q i  Ai cos 1 / 2 t  

3N
0   f ij Ai  A j 
i 1
Secular determinant:
0=
f11-
f12
f13
…..
f1,3N
f21
f22-
f23
…..
f2,3N
f31
f23
f33-
…..
f3,3N
f3N,2
f3N,3
…..
f3N,3N-
…
f3N,1
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
i 1
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
st , st `,
m
 1 
Gt , t ´  
G  F 1  0
1
Example: three-atomic molecule
r13
3

r12
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
presumed structure
experimental
spectra
geometry
optimization
spectra
calculation
poor agreement:
new structure assumption
comparison
good agreement:
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
direct absorption of photons
Raman spectroscopy
inelastic scattering of photons
0
white
light
white light
― n
n : normal mode frequency
0 ― n
h n
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 mn (Qk )   mn xyz
2
 mn x
 mn x  
0
x
  x


k 1  Qk

  m* Qk  n
0
 0, if dipole
moment varies
with Qk
 0, if m
=n1
 n 
*
m
3 N 6
  m* ˆ x  n
= 0,
orthogonality
x   
0
x
3 N 6

i 1
  x

 Qk

 Qk
0
1.5. Raman intensities
r
Oszillating EM radiation
induces dipole in the
molecule
m
Raman intensity
 
E  E0 cos2 0 t 
 ind
 xyz

 E
 
I mn (Qk )  
ind 2
mn xyz
 

2
mn xyz
2
E
n
Calculating the scattering tensor by second–order perturbation theory
 
xyz mn
m M r r M  n
1  m M  r r M n
  

h r   r  n  0  ir
 r  n   0  ir




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
13
BR 570
Siebert et al. 1985
h
+
N
[Lys]
H
K 590
IR difference spectra: structural changes induced by a reaction
2.2. Resonance Raman spectroscopy
Raman
vs.
Resonance Raman (RR):
 enhancement of the
vibrational bands of a
chromophore upon
excitation in resonance
with an electronic
transition
resonance Raman
electronically excited state
0
0 ― n
0
h n
electronic ground state
0 ― n
h n
2.2. Resonance Raman spectroscopy
Resonance Raman intensities
E
r
I mn (Qk )  
 
xyz mn

approximation for
strong transitions
2
E
Raman intensity
m M r r M  n
1  m M  r r M n



h r   r  n  0  ir
 r  n   0  ir
m
G

2
mn xyz
for 0  EG
n
 
xyz mn

1  M EG ,  M EG , m r r n 





h r 
 EG  0  ir





2.2. Resonance Raman spectroscopy
 
xyz mn

1  M EG ,  M EG , m r r n 





h r 
 EG  0  ir

Non-zero Franck-Condon factor
products only for modes including
coordinates with an excited state
displacement
Siebert &
Hildebrandt, 2007)
 
xyz mn

M EG ,  M EG , s k
 EG   0  ir  EG   0   k  ir 
2.2. Resonance Raman spectroscopy
bacteriorhodopsin
1000
500
resonant excitation
1500
nm
non-resonant excitation
x 300
15
13
+
N
[Lys]
H
Resonance Raman
selectively probes the
vibrational bands of a
chromophore in a
macromolecular matrix
800
1000
1200
1400
1600
1500
1600
1700
 / cm-1
 / cm-1
Althaus et al. 1995
1800
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

Induces an electric field in the metal E ( )
ind



Etot ( 0 )  E0 ( 0 )  Eind ( 0 )

E0 ( 0 )
0
Total electric field


E 0 ( 0 )  Eind ( 0 )
FE ( 0 ) 
 1  2g0

E 0 ( 0 )
Enhancement factor for the
field at the incident frequency
2.3. Surface enhanced Raman and IR effect
The magnitude of the enhancement depends on the frequency-dependent dielectric properties of
the metal
~r ( 0 )  1
g0  ~
 r ( 0 )  2
~r ( 0 )
 re ( 0 )  i im ( 0 )
~
 r ( 0 ) 
2
n solv
complex dielectric constant
If real part  -2 and imaginary part  0,
largest enhancement
In a similar way, one may derive a field enhancement for the Raman scattered light

which depends on E ( )
tot
0
Since the intensity is proportional to the square of the electric field strength, the
SER enhancement factor is given by:
FSER ( 0   k )  1  2 g 0 1  2 g Ra 
2
Total enhancement ca. 1o5 - 106

E Ra ( 0   k )
2.3. Surface enhanced Raman and IR effect
SERR and SEIRA:

all photophysical processes at metal surfaces can be enhanced via the frequencydependent 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
enhancement
2.3. Surface enhanced Raman and IR effect
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
 a 
FSER (d )  FSER (0)  

ad 
SEIRA
12
 a 
FSEIRA (d )  FSEIRA (0)  

ad 
6
SERR
Siebert &
Hildebrandt, 2007)
2.4. Limitations of Surface enhanced vibrational spectroscopies
… and how to overcome them
Plasmon resonance of polydisperse nanostructures
Ag
Preferred spectral range for
combining RR and SER
Au
But: Au displays a much
broader electrochemical
potential range and is
chemically more stable
2.4. Limitations of Surface enhanced vibrational spectroscopies
Layered hybrid devices
Electrochemical roughening of Ag
electrode
Coating by a dielectric layer (SAM,
SiO2)
Deposition of a metal film or
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
Cyt
413 nm
g0
15
10
Ag
5
0
0.6
0.8
1.0
r/R
1.2
1.4
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“
Electrostatic (CO2-, PO32-, NH3+)
S
S
S
S
S
S
S
S
Hydrophobic (e.g. CH3)
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
Covalent (cross linking)
Mixed SAMs (e.g. OH/CH3)
S
S
S
S
S
S
S
S
Polar (e.g. OH)
H
N
O
Coordinative (e.g. Py)
S
S
S
S
S
S
S
S
N
O
O
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
Fe 2+
Fe 3+
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:
Resonance Raman
IR
Time scale Method
comments
> 100 ns
Cw excitation
Low photon flux
> 10 ps
Pulsed excitation
High photon flux
> 100 fs
Stimulated Raman
Very demanding
set-up
> 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
Time
resolution
t 
s
v
for
smin  d laser
t min  100ns
3.2. Time-resolved pump-probe Raman spectroscopy
Pump-probe experiments with pulsed excitation
Time
resolution
t 
s
c
for
smin  1mm
t min  3 ps
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 &
Hildebrandt, 2007)
probe
Intensity / a.u.
3.2. Time-resolved pump-probe Raman spectroscopy
NpSRII500
1500
M400
1520 1540
1560 1580
1600 1620
Wavenumbers / cm
-1
1640 1660
1680
Intensity / a.u.
Intensity / a.u.
3.2. Time-resolved pump-probe Raman spectroscopy
M400 formation
10
20
30
40
50
60
70
80
0
500
1000
δ /μ s
Intensity / a.u.
0
M400 decay
100
2000
2500
3000
δ /μ s
Same results as for
transient absorption
spectroscopy
M400 kinetics
101
1500
102
103
104
δ/μs
105
106
107
3500
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 .....
.
A
mixing
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
B
A
observation
stop
rapid scan RR and FT IR ( = 10 ms)
... continuous-flow method
time resolution: t = tmix +  with
.... freeze-quench method
time resolution: t = tmix + tcool with tcool  2 ms
mixing
chamber
mixing
chamber
B
A
s
s
observation
 RR spectroscopy (min < tmix)
B
A
 RR spectroscopy
isopentane
-120oC
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
Conc.
0.8
0.6
0.4
H2O-Fe
H2O-Fe-His
0.2
His-Fe-His
His-Fe-His
0.0
U
-4
-3 -2 -1
log (time)
F
H2O
H2O
Met
Fe
His
His
His
His
Rousseau et al. 1998
partially
unfolded
folded
His
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
Fe 2+
Fe 3+
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
Fe 2+
Fe 3+
His
His
3.5. Potential-jump time-resolved SERR and SEIRA spectroscopy
-turn III
aa 67-70
Protein structural changes monitored
by SEIRA spectroscopy
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
IR
RR
Photoinduced
processes
Pump-probe
Bimolecular reactions
Rapid mixing
SEIRA
rapid scan (> 10 ms)
step scan (> 100 ns)
cw (> 100 s)
rapid scan (> 10 ms)
IR
SERR
cw (> 100 ns)
pulsed (> 10 ps)
Potential-dependent
processes at
electrodes
Potential-jump
cw (> 10 s)
rapid scan (> 10 ms)
step scan (> 10 s)
Photoreceptors
Ligand binding
bimolecular reactions
with caged compounds
Protein folding
Enzymatic reactions
Ligand binding
Re-orientation
Conformational
transitions
electron transfer
Literature
Most of the figures shown in this presentation have been taken from this book