Concepts and Methods of 2D Infrared Spectroscopy

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
1 Introduction......Page 13
1.1 Studying molecular structure with 2D IR spectroscopy......Page 15
1.1.1 2D IR spectrum of a single vibrational mode......Page 18
1.1.2 2D IR spectrum of two coupled vibrational modes......Page 20
1.2 Structural distributions and inhomogeneous broadening......Page 22
1.3.1 Spectral diffusion......Page 24
1.3.2 Chemical exchange......Page 25
1.4 Time domain 2D IR spectroscopy......Page 26
Exercises......Page 28
2.1 Eigenstates, coherences and the emitted field......Page 30
2.2 Bloch vectors and molecular ensembles......Page 35
2.3 Bloch vectors are a graphical representation of the density matrix......Page 39
2.4.1 Manipulating the density matrix......Page 43
2.4.2 Rotating wave approximation......Page 47
2.5 What is absorption?......Page 49
2.6 Designing multi-pulse experiments......Page 50
2.7 Selecting pathways by phase matching......Page 54
2.8 Selecting pathways by phase cycling......Page 56
2.9 Double sided Feynman diagrams: Rules......Page 58
Exercises......Page 59
3.1.1 Density matrix of a pure state......Page 60
3.2 Time dependent perturbation theory......Page 64
3.2.2 Perturbative expansion of the wavefunction......Page 66
3.2.3 Perturbative expansion of the density matrix......Page 68
3.2.4 Nonlinear polarization......Page 69
Exercises......Page 72
4.1 Linear spectroscopy......Page 73
4.2 Third-order response functions......Page 77
4.3 Time domain 2D IR spectroscopy......Page 81
4.3.1 2D IR spectrum of diagonal peaks......Page 84
Rephasing 2D IR spectra......Page 89
Non-rephasing 2D IR spectra......Page 91
Quasi-absorptive 2D IR spectra......Page 93
4.4 Frequency domain 2D IR spectroscopy......Page 94
4.5 Transient pump–probe spectroscopy......Page 96
Exercises......Page 98
5.1 Using polarization to manipulate the molecular response......Page 100
5.2 Diagonal peak, no rotations......Page 104
5.3 Cross-peaks and orientations of coupled transition dipoles......Page 105
5.4 Combining pulse polarizations: Eliminating diagonal peaks......Page 111
5.5 Including (or excluding) rotational motions......Page 112
5.6 Polarization conditions for higher-order pulse sequences......Page 118
Exercises......Page 120
6.1 Vibrational excitons......Page 121
6.1.1 Transforming the transition dipole matrix......Page 125
6.2.1 Linear absorption spectrum of a coupled dimer......Page 126
6.2.2 2D IR spectrum of a coupled dimer......Page 129
2D IR spectroscopy to determine molecular structures......Page 131
6.3.1 Linear chain of coupled oscillators......Page 132
6.3.2 Diagonal and off-diagonal disorder......Page 136
6.3.3 α-Helices......Page 137
6.4 Isotope labeling......Page 140
6.4.1 Strategies for isotope labeling......Page 142
6.5 Local mode transition dipoles......Page 145
6.6 Calculation of coupling constants......Page 146
6.6.1Comparison of the models and coupling maps......Page 148
6.7 Local versus normal modes......Page 149
6.8 Fermi resonance......Page 152
Exercises......Page 154
7.1 Microscopic theory of dephasing......Page 157
7.2 Correlation functions......Page 161
7.3 Homogeneous and inhomogeneous dynamics......Page 164
7.4 Nonlinear response......Page 167
7.4.1 2D lineshape of a two-level system......Page 168
7.4.2 2D IR lineshape of a vibrational transition\n\nω1 ω1......Page 170
7.4.3 Extracting spectral diffusion times from 2D IR spectra......Page 171
7.5 Photon echo peak shift experiments......Page 173
Exercises......Page 176
8.1 Population transfer......Page 178
8.2 Dynamic response functions......Page 184
8.3 Chemical exchange......Page 186
9.1 Frequency domain spectrometer designs......Page 188
9.2.1 Phase stability......Page 192
9.2.2 Achieving accurate time delays......Page 195
9.2.3 Phase matching geometry......Page 196
9.2.5 Signal detection and balanced heterodyne detection......Page 198
9.2.7 Optical densities......Page 200
9.2.8 Suppressing scatter and transient absorption signals......Page 201
9.3.1 Removing scatter and transient absorption background by phase cycling......Page 203
9.3.2 Phase cycling to extract the rephasing and non-rephasing spectra......Page 205
9.3.3 Rotating frame......Page 206
9.4 Phase control devices......Page 209
9.4.1 Photoelastic modulator and wobbling Brewster windows......Page 210
9.4.2 Pulse shaper......Page 211
Basic methods of collecting 2D IR spectra with pulse shaping......Page 212
9.5 Data collection and data workup......Page 213
9.5.2 Under-sampling......Page 214
9.5.4 Fourier transform: Zero-padding......Page 216
9.5.5 Spectral interferometry: Detection in the frequency domain......Page 218
9.5.6 Phasing of 2D IR spectra......Page 219
Post–processing: Projection slice theorem......Page 220
Presetting the phase......Page 221
9.5.7 Window functions......Page 223
9.5.8 Cross-peak intensity and extracting accurate anharmonicities......Page 225
9.6 Experimental issues common to all methods......Page 226
Exercises......Page 228
10.1 2D lineshapes: Spectral diffusion of water......Page 229
10.1.1 MD simulation......Page 230
10.1.2 Relating structure to a vibrational frequency......Page 231
10.1.3 Frequency fluctuation correlation function......Page 234
10.1.4 2D IR spectra......Page 235
10.1.5 Avoiding the cumulant expansion......Page 236
10.2 Molecular couplings by ab initio calculations......Page 238
10.3 2D spectra using an exciton approach......Page 241
Exercises......Page 244
11.1 Two-quantum pulse sequence......Page 245
11.2 Rephased 2Q pulse sequence: Fifth-order spectroscopy......Page 248
11.2.1 Cascaded signals......Page 249
11.3.1 Two-quantum 3D IR spectroscopy......Page 251
11.3.2 Purely absorptive 3D IR spectroscopy......Page 253
11.4 Transient 2D IR spectroscopy......Page 255
11.5 Enhancement of 2D IR spectra through coherent control......Page 257
11.6 Mixed IR–Vis spectroscopies......Page 259
11.7.1 Study of molecular interfaces......Page 261
11.7.2 Beyond pair potentials......Page 262
11.7.3 Molecular movies......Page 263
Exercises......Page 264
Appendix A: Fourier transformation......Page 266
A.1 Sampling theorem, aliasing and under-sampling......Page 268
A.2 Discrete Fourier transformation......Page 269
Appendix B: The ladder operator formalism......Page 272
C.2 Units of common physical quantities......Page 274
C.3 Emitted field E(3)sig......Page 275
Appendix D: Legendre polynomials and spherical harmonics......Page 277
Appendix E: Recommended reading......Page 279
References......Page 281
Index......Page 293