Theory of Sum Frequency Generation Spectroscopy (eBook)

Akihiro Morita received his Ph. D. degree from Kyoto University in 1995. He worked at Kyoto University, University of Colorado, and Institute for Molecular Science before moving to Tohoku University. Currently he is a professor at the Department of Chemistry, Tohoku University, majoring computational molecular science. His research interests include electronic structure and molecular dynamics of liquids and interfaces. His recent works focus on theoretical aspects of liquid interfaces, often in collaboration with experiments, including the interfacial sum frequency generation spectroscopy and mass transfer kinetics at liquid interfaces. He was awarded the Chemical Society of Japan Award for Creative Work (2012) and 1st International Investigator Award of the Japan Society for Molecular Science (2016) for the development of the theories for exploring liquid interfaces.

Preface 7
Contents 9
1 Introduction 13
1.1 Sum Frequency Generation 13
1.2 Visible-Infrared SFG Vibrational Spectroscopy 16
1.3 Solutions to Problems 19
1.3.1 Inversion Symmetry of ?(2) 19
1.3.2 Time and Frequency Domains 19
1.3.3 Red Shift of O-H Frequency 21
Bibliography 22
2 Electrodynamics at Interface 24
2.1 Electromagnetic Fields at Interface 25
2.1.1 Maxwell Equations 25
2.1.2 Boundary Conditions at Interface 26
2.1.3 SFG Signal Emitted from Interface 29
2.1.4 Fresnel Factor 31
2.2 Response to Incident Lights 33
2.3 Summary of Factors in SFG Spectra 35
2.4 Solutions to Problems 36
2.4.1 Boundary Condition at Interface (1) 36
2.4.2 Boundary Condition at Interface (2) 38
2.4.3 Boundary Condition at Interface (3) 39
2.4.4 Electric Field and Interfacial Polarization 41
Appendix 45
A.1 Singularity of Source Polarization 45
A.2 Fresnel Factors for Two-Layer Model 47
A.3 Fresnel Factors for Three-Layer Model 50
A.3.1 Fields and Wavevectors 50
A.3.2 Boundary Conditions 52
(1) Medium i and Interface 52
(2) Interface and Medium j 53
(3) Media i and j 54
A.3.3 Solution of Boundary Equations 55
Bibliography 56
3 Microscopic Expressions of Nonlinear Polarization 58
3.1 Density Matrix 58
3.1.1 Definition 59
3.1.2 Features and Advantages 60
(i) Ensemble of States 60
(ii) Partial System in Bath 62
3.2 Perturbation Forms of Susceptibilities 64
3.2.1 Perturbation Expansion of Density Matrix 64
3.2.2 First-Order Susceptibility 65
3.2.3 Second-Order Susceptibility 67
3.3 Properties of ?(2) 69
3.3.1 Vibrational Resonance 69
3.3.2 Relation to Molecular Orientation 73
Two Factors: Density and Orientation 74
Rotational Matrix 74
3.3.3 Tensor Elements of ?(2) and Polarization 77
3.4 Solutions to Problems 79
3.4.1 Formulas for Mixed States 79
3.4.2 Pure and Mixed States 80
3.4.3 Derivation of ?(2) 82
3.4.4 Effective ?(2) Formula 83
Appendix 85
A.1 Off-Diagonal Elements of Density Matrix 85
A.2 Interaction Energy of Nonmagnetic Materials 87
A.3 Polarizability Approximation for Raman Tensor 88
Bibliography 90
4 Two Computational Schemes of ?(2) 91
4.1 Energy Representation 91
4.2 Examples of ?(2) Tensor and Orientation 94
4.2.1 O-H Stretching 95
4.2.2 C-H Stretching 97
4.3 Time-Dependent Representation 100
4.3.1 Time Correlation Function 100
4.3.2 Classical Analogue 102
4.4 Motional Effect on ?(2) 106
4.4.1 Relation of Two ?(2) Models 107
4.4.2 Slow Limit and Fast Limit 109
4.5 Solutions to Problems 110
4.5.1 Polarization Ratios 110
4.5.2 Canonical Time Correlation Function 112
Bibliography 112
5 Molecular Theory of Local Field 114
5.1 Local Field Correction Factor 115
5.2 Local Field Correction for ?(2) 121
5.3 Interfacial Dielectric Constant 124
5.4 Solutions to Problems 129
5.4.1 Interfacial Dielectric Constant 129
Bibliography 130
6 Charge Response Kernel for Electronic Polarization 132
6.1 Charge Response Kernel (CRK) 133
6.2 Electronic Structure Theory of CRK 134
6.3 Polarizable Model with CRK 140
6.4 ?(2) Formula with CRK Model 143
6.5 Solutions to Problems 145
6.5.1 ESP Charge 145
6.5.2 Charge Response Kernel 146
6.5.3 Energy and Force with Polarizable Model 148
6.5.4 Polarizability 149
Appendix 150
A.1 Derivation of CRK from CPHF Equation 150
A.1.1 Wavefunction Under External Field 150
A.1.2 Derivative of Wavefunction 152
A.1.3 Formula of CRK 155
A.2 Reorganization Energy of Electronic Polarization 155
A.2.1 Derivation of Reorganization Energy 156
A.2.2 Variational Principle of Polarization 157
Bibliography 158
7 Quadrupole Contributions from Interface and Bulk 160
7.1 Beyond the Three-Layer Model 161
7.2 Extended Nonlinear Susceptibility 166
7.2.1 Extended Source Polarization 166
7.2.2 Effective Polarization and Susceptibility 168
7.2.3 Interface Contribution 169
7.2.4 Bulk Contribution 171
7.2.5 Expression of Bulk Term ?B 175
7.2.6 Summary of Derivation 178
7.3 Microscopic Formulas of Quadrupolar Susceptibilities 181
7.3.1 Perturbation Expressions 181
7.3.2 Time-Dependent Expressions 187
7.4 Invariance to Molecular Origin 191
7.5 Summary 195
7.6 Solutions to Problems 195
7.6.1 Isotropic Tensor Components 195
7.6.2 Bulk Term ?B 198
7.6.3 Transformation of Quadrupolar Susceptibility 199
7.6.4 Levi-Civita Tensor 202
Appendix 203
A.1 Physical Meaning of ?IQB 203
A.2 Levi-Civita Antisymmetric Tensor 204
A.3 Definition of Bulk Polarization 207
Bibliography 208
8 Other Topics 210
8.1 ?(3) Effect at Charged Interfaces 211
8.1.1 Properties of ?(3) Tensor 211
8.1.2 Role of ?(3) in Electrolyte Solution 214
8.1.3 Calibrating ?(3) Effect in SFG Spectra 218
8.2 Chiral Elements of ?(2) 219
8.2.1 Symmetry 220
8.2.2 Intensity 222
8.2.3 Future Development 223
8.3 Solutions to Problems 224
8.3.1 Guoy-Chapman Theory 224
8.3.2 Chiral ?(2) Components 226
Bibliography 226
9 Applications: Aqueous Interfaces 228
9.1 Water Surface 229
9.2 Ice Surface 232
9.3 Electrolyte Solution Surfaces 234
9.3.1 Halide Ions: Surface Segregation 236
9.3.2 Buried Ions: F-, SO42- 239
9.3.3 Acid 241
9.3.4 Base 243
9.4 Oil/Water Interfaces 246
9.5 Water at Monolayers 248
Bibliography 250
10 Applications: Organic Interfaces 256
10.1 C–H Bands of Alkyl Groups 257
10.1.1 C–H Modes 257
10.1.2 Modeling of C–H 258
10.1.3 Methanol C–H Vibrations 259
10.1.4 Ethanol C–H Vibrations 261
10.2 Benzene: SFG from Centrosymmetric Molecules 262
10.3 Molecular Orientation and Polarization Analysis 263
10.3.1 Methanol 264
10.3.2 Acetonitrile 266
Bibliography 268
11 Summary 270
11.1 Outline of Theory 270
11.2 Future Directions 271
Bibliography 272