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IR and Raman Spectroscopy

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IR and Raman Spectroscopy 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 Q m k n k 1 k 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 E0 ( 0 ) Eind ( 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.
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