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Home , Infrared spectroscopy, Raman spectroscopy

IR and Raman

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 spectroscopy 1.3.2. 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 within a

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 , 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:

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   qi 2 i1

potential energy V for small 1 3N displacements (harmonic V   fij qiq j approximation) 2 i, j1

Total energy: E  T V

Newton´s equation 3N of motion 0  qj   fij qi i, j1 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 i1 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 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 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  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

Raman spectroscopy inelastic of photons

Siebert & Hildebrandt, 2007) 1.3. Probing molecular vibrations

Infrared spectroscopy Raman spectroscopy direct absorption of photons 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 from 240 – 1064 nm 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 i1  k 0 1.5. Raman intensities

  r Oszillating EM radiation E  E0 cos2 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  ir r  n  0  ir  2. Special approaches 2.1. IR difference spectroscopy 2.2. Raman spectroscopy 2.3. Surface enhanced (resonance) Raman and infrared 2.4. Limitations of Surface enhanced vibrational and how to overcome them 2.5. SERR and SEIRA 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 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  ir r  n  0  ir 

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  ir   2.2. Resonance Raman spectroscopy

 1  M M m r r n    EG, EG,  xyz mn   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)    M M s  EG , EG , k xyz mn  EG  0  ir EG  0  k  ir 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 – 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 in metals can undergo collective oscillations () 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 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 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 2.5. SERR and SEIRA spectroelectrochemistry

probing transfer processes

SERR

SEIRA

Siebert & Hildebrandt, 2007)

Siebert & Hildebrandt, 2007) 2.5. SERR and SEIRA spectroelectrochemistry

SERR: applicable to 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 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)  , 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 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 / 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) 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