Two-Dimensional Optical Spectroscopy Book

Preface ix

About the Author xi

Acknowledgments xiii

Chapter 1 Introduction 1

References 6

Chapter 2 Quantum Dynamics 9

2.1 Time Evolution in Hilbert Space 9

2.2 Time-Dependent Perturbation Theory in Hilbert Space 12

2.3 Diagram Representation of the Time-Dependent Perturbation Theory in Hilbert Space 15

2.4 Transition Amplitude and Probability in Hilbert Space 17

2.5 Time Evolution in Liouville Space 20

2.6 Time-Dependent Perturbation Theory in Liouville Space 22

2.7 Transition Probability in Liouville Space and Pathways 26

2.7.1 Second-Order Transition between Two Populations 26

2.7.2 Second-Order Transition between Two Coherences 28

2.7.3 First-Order Transition between Population and Coherence 29

References 30

Chapter 3 Linear Response Spectroscopy 31

3.1 Linear Response Function 33

3.2 System-Bath Interaction and Line Broadening 36

3.3 Rotational Averaging of Tensors 45

3.4 Linear Absorption Spectroscopy 47

3.5 Raman Scattering 50

3.6 Hyper-Raman Scattering 54

3.7 IR-Raman Surface Vibrational Spectroscopy 56

3.8 Raman-IR Surface Vibrational Spectroscopy 59

Appendix: Nonlinear Polarization and Generated Signal Electric Field 61

References 62

Chapter 4 Second-Order Response Spectroscopy 63

4.1 Second-Order Response Function 64

4.2 Three-Level System and Line-Broadening Function 68

4.3 Sum Frequency Generation 75

4.4 Difference Frequency Generation 76

4.5 IR-IR-vis Four-Wave Mixing 78

References 80

Chapter 5 Third-Order Response Spectroscopy 83

5.1 Third-Order Response Function 83

5.2 Four-Level System and Line-Broadening Function 87

5.3 Short-Time Approximation to the Third-Order Response Function 93

5.4Third-Order Response Function of a Two-Level System 96

5.5 Pump-Probe Spectroscopy of a Two-Level System 100

5.6 Rephasing Photon Echo Spectroscopy of a Two-Level System 103

5.7 Nonrephasing Photon Echo Spectroscopy of a Two-Level System 107

5.8 Three-Pulse Photon Echo Peak Shift (PEPS) 108

References 112

Chapter 6 Two-Dimensional Pump-Probe Spectroscopy 115

6.1 Introduction to Two-Dimensional Pump-Probe Spectroscopy 115

6.2 Two-Dimensional Pump-Probe Spectrum of Two-Level System 117

6.3 Two-Dimensional Pump-Probe Spectrum of an Anharmonic Oscillator 123

References 129

Chapter 7 Two-Dimensional Photon Echo Spectroscopy 131

7.1 Phase and Amplitude Detection of the Two-Dimensional Photon Echo Signal Field 132

7.2 Two-Dimensional Photon Echo Spectrum of a Two-Level System 135

7.3 Two-Dimensional Nonrephasing Photon Echo Spectrum of a Two-Level System 139

7.4 Two-Dimensional Photon Echo Spectrum of an Anharmonic Oscillator 142

7.5 Simple Two-Dimensional Lorentzian Peak Shape 144

7.6 Simple Two-Dimensional Gaussian Peak Shape 146

References 148

Chapter 8 Coupled Multi-Chromophore System 151

8.1 Frenkel Hamiltonian in Site Representation 152

8.2 Delocalized Exciton Representation 154

8.3 Delocalized State Energy and Transition Dipole Matrix Element 155

8.4 Transition Frequency-Frequency Correlation Functions 157

8.5 Exchange-Narrowing Effect on Absorption Spectrum 158

8.6 Measurements of Auto- and Cross-Frequency-Frequency Correlation Functions 160

8.7 Exciton Population Transfer 163

References 166

Chapter 9 Two-Dimensional Spectroscopy of Coupled Dimers 169

9.1 Model Hamiltonian of a Coupled Two-Level System Dimer 169

9.2 Delocalized Excited-State Energy Fluctuations and Time Correlation Functions 172

9.3 Coupled Two-Level System Dimer: Quantum Beats at Short Time 174

9.4 Coupled Two-Level System Dimer: Intermediate Time Region 179

9.5 Coupled Two-Level System Dimer: Population Transfer Effects 181

9.6 Coupled Anharmonic Oscillators: Model Hamiltonian 188

9.7 Coupled Anharmonic Oscillators: Two-Dimensional Photon Echo Spectrum at Short Time 191

9.8 Coupled Anharmonic Oscillators: Degenerate Case 195

9.9 Coupled Anharmonic Oscillators: Population Transfer Effects 204

References 207

Chapter 10 Chemical Exchange and Two-Dimensional Spectroscopy 209

10.1 Model System 210

10.2 Chemical Exchange Diagrams: Two-Level System 212

10.3 Chemical Exchange Diagrams: Anharmonic Oscillator 216

References 221

Chapter 11 Polarization-Controlled Two-Dimensional Spectroscopy 223

11.1 Parallel Polarization ZZZZ-Echo: Two-Level System 223

11.2 Perpendicular Polarization ZYYZ-Echo: Two-Level System 228

11.3 Difference Two-Dimensional Photon Echo Spectrum: Coupled Two-Level System Dimer 230

11.4 Parallel Polarization ZZZZ-Echo: Anharmonic Oscillators 231

11.5 Perpendicular Polarization ZYYZ-Echo: Anharmonic Oscillators 233

11.6 Difference Two-Dimensional Echo Spectrum: Coupled Anharmonic Oscillators 235

11.7 Generalized Polarization-Controlled Two-Dimensional Spectroscopy 237

11.8 Determination of the Angle between Any Two Transition Dipole Vectors 240

References 243

Chapter 12 Applications of Two-Dimensional Vibrational Spectroscopy 245

12.1 Single Anharmonic Oscillator Systems 246

12.2 Coupled Two-Oscillator Systems 253

12.3 Polypeptide Secondary Structures 258

12.4 Globular Proteins and Membrane-Bound Proteins 265

12.5 Nucleic Acids 266

12.6 Hydrogen-Bonding Dynamics and Chemical Exchange 267

12.7 Solute-Solvent Complexation and Micro-Solvation 270

12.8 Internal Rotation 272

12.9 Transient Two-Dimensional IR Spectroscopy: Protein Folding and Unfolding 272

References 274

Chapter 13 Applications of Two-Dimensional Electronic Spectroscopy 283

13.1 Application to Fenna-Matthews-Olson Light-Harvesting Complex 283

13.2 Application to Semiconductors 289

References 291

Chapter 14 Two-Dimensional Second-Order Response Spectroscopy 293

14.1 Two-Dimensional Sum Frequency Generation 294

14.2 Two-Dimensional Sum Frequency Generation of Solution Sample 296

14.3 Two-Dimensional Sum Frequency Generation of Coupled Two-Level System Dimer 298

14.4 Two-Dimensional Sum Frequency Generation of Coupled Anharmonic Oscillators 301

14.5 Two-Dimensional Difference Frequency Generation 305

14.6 IR-IR-vis Sum Frequency Generation and Difference Frequency Generation 306

14.7 Other IR-IR-vis Four-Wave-Mixings 313

14.8 Fifth-Order Raman Scattering 316

References 320

Chapter 15 Linear Optical Activity Spectroscopy 323

15.1 Radiation-Matter Interaction Hamiltonian and Polarization 324

15.2 Circular Dichroism and Optical Rotatory Dispersion 326

15.3 Raman Optical Activity 334

15.4 IR-Raman Optical Activity Spectroscopy 341

15.5 Raman-IR Optical Activity Spectroscopy 346

References 350

Chapter 16 Nonlinear Optical Activity Spectroscopy 351

16.1 Nonlinear Optical Activity Measurement Methods 351

16.2 Rotational Averaging of Higher-Rank Tensors 353

16.3 Two-Dimensional Optical Activity Pump-Probe: Two-Level System 358

16.4 Two-Dimensional Optical Activity Photon Echo: Two-Level System 367

16.5 Two-Dimensional Optical Activity Photon Echo of Coupled Two-Level System Dimer 369

References 373

Index 375