IR and Raman spectroscopy. Peter Hildebrandt

Transcription

1 IR and Raman spectroscopy Peter Hildebrandt

2 Content 1. Basics of vibrational spectroscopy 2. pecial approaches 3. Time-resolved methods

3 1. Basics of vibrational spectroscopy 1.1. Molecular vibrations and normal modes 1.2. Normal mode analysis 1.3. Probing molecular vibrations Fourier-transform infrared spectroscopy Raman spectroscopy 1.4. Infrared intensities 1.5. Raman intensities

4 1.1. Molecular vibrations and normal modes IR and Raman spectroscopy - vibrational spectroscopy: probing well-defined vibrations of atoms within a molecule iebert & 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?

5 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 (A 1g ): 3062 cm (E 1u ): 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.

6 Determination of normal modes a problem of classical physics Approach: Point masses connected with springs Harmonic motion 1.1. Molecular vibrations and normal modes iebert & 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

7 1.2. Normal mode analysis A. Describing the movement of the atoms in terms of mass-weighted Cartesian displacement coordinates x i e.g. x i = x i a i (i: all atoms) y i z i Mass-weighted Cartesian displacement coordinates iebert & Hildebrandt, 2007) q 1 m1 x1 q2 m1 y1 q3 m1 z q 1 4 m2 x2 etc.

8 1.2. Normal mode analysis B. Expressing the kinetic and potential energy kinetic energy T T 1 2 3N 2 q i i1 potential energy V for small displacements (harmonic approximation) V 1 2 3N i, j1 f ij q i q j Total energy: E T V Newton s equation of motion 0 q j 3N i, j1 f ij q i

9 C. olving the eigenwert problem et of 3N linear second-order differential equations q i A i 1/ 2 cos t ecular determinant: 1.2. Normal mode analysis 3N 0 f A A i1 ij i j f 11 - f 12 f 13.. f 1,3N 0 = f 21 f 22 - f 23.. f 2,3N f 31 f 23 f f 3,3N f 3N,1 f 3N,2 f 3N,3.. f 3N,3N - 3N solutions, 3N frequencies Removal of 6 solutions für f ij =0 (translation, rotation) 3N-6 non-zero solutions for frequencies

10 D. Coordinate transformation: Cartesian coordinates to normal coordinates Q k 3N i1 l ki x i 1.2. Normal mode analysis One normal mode accounts for one normal mode unique relationship! implifies the mathematical and theoretical treatment of molecular vibrations but is not illustrative! Intuitive coordinates internal coordinates: tretching Bending Out-of-plane deformation Torsion

11 E. olving the eigenwert problem 1.2. Normal mode analysis Constructing the G- und F-Matrix and inserting into Newton s equation of motion G t, t N 1 1 m s t, s t`, G F 1 0 Example: three-atomic molecule 1 3 r 13 r 12 2 G-Matrix known, if the structure is known olving the FG-matrix leads to (3N-6) solutions F-Matrix a priori unknown

12 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 olving the normal mode problem

13 1.2. Normal mode analysis sample presumed structure experimental spectra geometry optimization spectra calculation comparison poor agreement: new structure assumption good agreement: presumed structure is the true one

14 1.3. Probing molecular vibrations Infrared spectroscopy direct absorption of photons Raman spectroscopy inelastic scattering of photons iebert & Hildebrandt, 2007)

15 1.3. Probing molecular vibrations Infrared spectroscopy direct absorption of photons Raman spectroscopy inelastic scattering of photons white light white light n 0 0 n h n n : normal mode frequency

16 Fourier-Transform IR spectroscopy detected intensity interferogram: I=f(x) Fourier transformation spectrum: I = f()

17 Raman pectroscopy cw laser from nm pulsed laser from nm

18 1.4. Infrared intensities m n z y x 2 ) ( xyz mn mn Q k I * 0 * 0 N k n k m k x n m x x mn Q Q n x m x mn ˆ * k N i k x x x Q Q = 0, orthogonality 0, if dipole moment varies with Q k 0, if m = n 1

19 r 1.5. Raman intensities Oszillating EM radiation induces dipole in the molecule E0 cos2 t ind E E 0 xyz m Raman intensity I mn ( Q ) E k ind 2 mn xyz mn 2 xyz 2 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

20 2. pecial approaches 2.1. IR difference spectroscopy 2.2. Resonance Raman spectroscopy 2.3. urface enhanced (resonance) Raman and infrared absorption spectroscopy 2.4. Limitations of urface enhanced vibrational spectroscopies and how to overcome them 2.5. ERR and EIRA spectroelectrochemistry

21 2. pecial 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

22 2.1. IR difference spectroscopy A historical example: Bacteriorhodopsin N + [Lys] h BR 570 K 590 H iebert et al IR difference spectra: structural changes induced by a reaction

23 2.2. Resonance Raman spectroscopy Raman vs. resonance Raman electronically excited state Resonance Raman (RR): enhancement of the vibrational bands of a chromophore upon excitation in resonance with an electronic transition 0 0 n 0 0 n h n h n electronic ground state

24 2.2. Resonance Raman spectroscopy Resonance Raman intensities E r I mn ( Q ) E k mn 2 xyz 2 Raman intensity 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 G approximation for strong transitions m n for 0 EG 1 M EG, M EG, m r r n xyz mn h r EG 0 ir

25 2.2. Resonance Raman spectroscopy 1 M EG, M EG, m r r n xyz mn h r EG 0 ir Non-zero Franck-Condon factor products only for modes including coordinates with an excited state displacement iebert & Hildebrandt, 2007) xyz mn i i EG 0 M EG, r M EG, EG s 0 k k r

26 2.2. Resonance Raman spectroscopy bacteriorhodopsin resonant excitation nm non-resonant excitation x N + [Lys] H Resonance Raman selectively probes the vibrational bands of a chromophore in a macromolecular matrix / cm -1 / cm -1 Althaus et al. 1995

27 2.3. urface 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 (ER) effect. ER-active systems: - Electrochemically roughened electrodes - Colloidal metal particles - Evaporated (sputtered) or (electro-)chemically deposited metal films

28 2.3. urface enhanced Raman and IR effect Theorie - ER: 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 tot ( 0 ) E0 ( 0 ) Eind ( 0 ) E ind ( 0 ) Total electric field E 0 ( 0 ) F E E0 ( 0 ) Eind ( 0 ) ( 0 ) 1 2g E ( ) Enhancement factor for the field at the incident frequency

29 2.3. urface enhanced Raman and IR effect The magnitude of the enhancement depends on the frequency-dependent dielectric properties of the metal ~ r ( 0 ) 1 ~ g 0 ~ r ( 0 ) ( ) 2 r 0 complex dielectric constant ~ ( ) r 0 re ( 0 ) i n 2 solv im ( ) 0 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 E Ra ( 0 k ) ince the intensity is proportional to the square of the electric field strength, the ER enhancement factor is given by: F 1 2g 1 g 2 ER ( 0 k ) 0 2 Ra Total enhancement ca. 1o

30 2.3. urface enhanced Raman and IR effect ERR and EIRA: all photophysical processes at metal surfaces can be enhanced via the frequencydependent electric field enhancement combination of RR and ER: surface enhanced resonance Raman ERR: excitation in resonance with both an electronic transition of the adsorbate and the surface plasmon eigenfrequency of the metal ingle-molecule sensitivity! IR - Absorption: surface enhanced infrared absorption EIRA enhancement of the incident electric field in the infrared! (Au, Ag) E tot ( 0 ) E0 ( 0 ) Eind ( 0 ) Total electric field Total enhancement thus ca. less than the square root of the ER effect:

31 2.3. urface enhanced Raman and IR effect enhancement Calculations of the enhancement factor for various geometric shapes (Ag)

32 2.3. urface enhanced Raman and IR effect iebert & Hildebrandt, 2007) Distance-dependence of the ER and EIRA effect F F ER EIRA a ( d) FER (0) a d 12 a ( d) FEIRA (0) a d 6 ERR EIRA iebert & Hildebrandt, 2007)

33 2.4. Limitations of urface enhanced vibrational spectroscopies and how to overcome them Plasmon resonance of polydisperse nanostructures Ag Au Preferred spectral range for combining RR and ER But: Au displays a much broader electrochemical potential range and is chemically more stable

34 2.4. Limitations of urface enhanced vibrational spectroscopies Layered hybrid devices Electrochemical roughening of Ag electrode Coating by a dielectric layer (AM, io 2 ) Deposition of a metal film or semiconductor film (Au, Pt, TiO 2 ) -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

35 2.4. Limitations of urface enhanced vibrational spectroscopies Layered hybrid devices

36 2.4. Limitations of urface enhanced vibrational spectroscopies Layered hybrid devices

37 2.4. Limitations of urface enhanced vibrational spectroscopies Layered devices Distance-dependence of the enhancement experimental theoretical Ag 25 Ag-spacer-Au 20 Cyt 413 nm g Ag r/r

38 2.4. Limitations of urface enhanced vibrational spectroscopies Layered devices Potential application for in-situ studies in heterogeneous catalysis

39 2.5. ERR and EIRA spectroelectrochemistry probing electron transfer processes EIRA ERR iebert & Hildebrandt, 2007) iebert & Hildebrandt, 2007)

40 Electrostatic (CO 2-, PO 3 2-, NH 3+ ) Hydrophobic (e.g. CH 3 ) Mixed AMs (e.g. OH/CH 3 ) Polar (e.g. OH) O N H Covalent (cross linking) O O N Coordinative (e.g. Py) Immobilization of cytochrome c on membrane models ERR: applicable to proteins bound to biocompatibly coated metal surfaces 2.5. ERR and EIRA spectroelectrochemistry

41 2.5. ERR and EIRA spectroelectrochemistry Example: redox processes of cytochrome c Potential-dependent ERR measurements to probe the redox equilibrium of the immobilised protein Met Fe 2+ His Met Fe 3+ His

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43 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 ERR and EIRA spectroscopy 3.6. Time-resolved techniques - summary

44 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 IR > 1 ms Rapid scan > 100 fs timulated Raman Very demanding set-up > 10 ns tep scan > 100 fs transient absorption Very demanding set-up

45 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

46 3.2. Time-resolved pump-probe Raman spectroscopy Pump-probe experiments with cw excitation Time resolution t s v for s min dlaser t 100ns min

47 3.2. Time-resolved pump-probe Raman spectroscopy Pump-probe experiments with pulsed excitation Time resolution t s c for s 1mm min t min 3 ps

48 3.2. Time-resolved pump-probe Raman spectroscopy ensory rhodopsin II from Natronobacterium pharaonis

49 3.2. Time-resolved pump-probe Raman spectroscopy ensory rhodopsin II from Natronobacterium pharaonis Challenge: Time-resolved approach must cover a dynamic range of more than six decades Gated-cw pump probe experiments

50 3.2. Time-resolved pump-probe Raman spectroscopy pump iebert & Hildebrandt, 2007) probe

51 3.2. Time-resolved pump-probe Raman spectroscopy Intensity / a.u. NpRII 500 M Wavenumbers / cm -1

52 3.2. Time-resolved pump-probe Raman spectroscopy Intensity / a.u. M 400 formation Intensity / a.u. M 400 decay δ/μs δ/μs Intensity / a.u. M 400 kinetics ame results as for transient absorption spectroscopy δ/μs

53 3.3. Time-resolved IR techniques - Rapid scan measuring consecutive interferograms (ca. 10 ms) - tep scan Measuring signal decays after each mirror step (< 100 ns) iebert & Hildebrandt, 2007)

54 3.3. Time-resolved IR techniques Example: photocycle of bacteriorhodopsin Gerwert et al.)

55 3.3. Time-resolved IR techniques Example: photocycle of bacteriorhodopsin Gerwert et al.)

56 3.4. Rapid mixing techniques and time-resolved spectroscopy Rapid mixing of components A and B with t mix ms.... A mixing chamber B... and monitoring the reaction using the...

57 3.4. Rapid mixing techniques and time-resolved spectroscopy...stopped-flow method time resolution: t = t mix + A mixing chamber B observation stop rapid scan RR and FT IR ( = 10 ms)... continuous-flow method time resolution: t = t mix + with... freeze-quench method time resolution: t = t mix + t cool with t cool 2 ms A mixing chamber B A mixing chamber B s s observation RR spectroscopy ( min < t mix ) RR spectroscopy isopentane -120 o C

58 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 Conc H 2 O-Fe His-Fe-His H 2 O-Fe-His His-Fe-His 0.0 U log (time) H 2 O F His H 2 O Fe Met His His His Rousseau et al His partially unfolded folded

59 3.5. Potential-jump time-resolved ERR and EIRA 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 ERR or step-scan or rapid scan EIRA - time resolution limited by the reorganisation of the electrical double layer

60 3.5. Potential-jump time-resolved ERR and EIRA spectroscopy Example: interfacial redox process of cytochrome c one-step relaxation process B1 red Met Fe 2+ His B1 ox Met Fe 3+ His

61 3.5. Potential-jump time-resolved ERR and EIRA spectroscopy Example: interfacial redox process of cytochrome c one-step relaxation process B1 red Met Fe 2+ His B1 ox Met Fe 3+ His

62 3.5. Potential-jump time-resolved ERR and EIRA spectroscopy -turn III aa Protein structural changes monitored by EIRA spectroscopy Lys 72,73 Lys 86,87 heme Amide I band changes of the -turn III segment occur simultaneously with electron transfer

63 3.6. Time-resolved techniques summary RR IR Photoinduced processes Pump-probe cw (> 100 ns) pulsed (> 10 ps) rapid scan (> 10 ms) step scan (> 100 ns) Photoreceptors Ligand binding bimolecular reactions with caged compounds RR Bimolecular reactions cw (> 100 s) Protein folding Rapid mixing Enzymatic reactions IR rapid scan (> 10 ms) Ligand binding ERR EIRA Potential-dependent processes at electrodes Potential-jump cw (> 10 s) rapid scan (> 10 ms) step scan (> 10 s) Re-orientation Conformational transitions electron transfer

64 Literature Most of the figures shown in this presentation have been taken from this book