Theory of Sum Frequency Generation Spectroscopy

Abstract

This book describes fundamental theory and recent advances of sum frequency generation (SFG) spectroscopy. SFG spectroscopy is widely used as a powerful tool of surface characterization, although theoretical interpretation of the obtained spectra has been a major bottleneck for most users. Recent advances in SFG theory have brought about a breakthrough in the analysis methods beyond conventional empirical ones, and molecular dynamics (MD) simulation of SFG spectroscopy allows for simultaneous understanding of observed spectra and interface structure in unprecedented detail. This book explains these recently understood theoretical aspects of SFG spectroscopy by the major developer of the theory. The theoretical topics are treated at basic levels for undergraduate students and are described in relation to computational chemistry, such as molecular modeling and MD simulation, toward close collaboration of SFG spectroscopy and computational chemistry in the near future. 1. Introduction -- 2. Electrodynamics at Interface -- 3. Microscopic Expressions of Nonlinear Polarization -- 4. Two Computational Schemes of X(2) -- 5. Molecular Theory of Local Field -- 6. Charge Response Kernel for Electronic Polarization -- 7. Quadrupole Contributions from Interface and Bulk -- 8. Other Topics -- 9. Applications: Aqueous Interfaces -- 10. Applications: Organic Interfaces. -- Summary. 3.1.2 Features and Advantages(i) Ensemble of States; (ii) Partial System in Bath; 3.2 Perturbation Forms of Susceptibilities; 3.2.1 Perturbation Expansion of Density Matrix; 3.2.2 First-Order Susceptibility; 3.2.3 Second-Order Susceptibility; 3.3 Properties of χ(2); 3.3.1 Vibrational Resonance; 3.3.2 Relation to Molecular Orientation; Two Factors: Density and Orientation; Rotational Matrix; 3.3.3 Tensor Elements of χ(2) and Polarization; 3.4 Solutions to Problems; 3.4.1 Formulas for Mixed States; 3.4.2 Pure and Mixed States; 3.4.3 Derivation of χ(2); 3.4.4 Effective χ(2) Formula; Appendix. A.1 Off-Diagonal Elements of Density MatrixA. 2 Interaction Energy of Nonmagnetic Materials; A.3 Polarizability Approximation for Raman Tensor; Bibliography; 4 Two Computational Schemes of χ(2); 4.1 Energy Representation; 4.2 Examples of χ(2) Tensor and Orientation; 4.2.1 O-H Stretching; 4.2.2 C-H Stretching; 4.3 Time-Dependent Representation; 4.3.1 Time Correlation Function; 4.3.2 Classical Analogue; 4.4 Motional Effect on χ(2); 4.4.1 Relation of Two χ(2) Models; 4.4.2 Slow Limit and Fast Limit; 4.5 Solutions to Problems; 4.5.1 Polarization Ratios; 4.5.2 Canonical Time Correlation Function. Intro; Preface; Contents; 1 Introduction; 1.1 Sum Frequency Generation; 1.2 Visible-Infrared SFG Vibrational Spectroscopy; 1.3 Solutions to Problems; 1.3.1 Inversion Symmetry of χ(2); 1.3.2 Time and Frequency Domains; 1.3.3 Red Shift of O-H Frequency; Bibliography; 2 Electrodynamics at Interface; 2.1 Electromagnetic Fields at Interface; 2.1.1 Maxwell Equations; 2.1.2 Boundary Conditions at Interface; 2.1.3 SFG Signal Emitted from Interface; 2.1.4 Fresnel Factor; 2.2 Response to Incident Lights; 2.3 Summary of Factors in SFG Spectra; 2.4 Solutions to Problems. Bibliography5 Molecular Theory of Local Field; 5.1 Local Field Correction Factor; 5.2 Local Field Correction for χ(2); 5.3 Interfacial Dielectric Constant; 5.4 Solutions to Problems; 5.4.1 Interfacial Dielectric Constant; Bibliography; 6 Charge Response Kernel for Electronic Polarization; 6.1 Charge Response Kernel (CRK); 6.2 Electronic Structure Theory of CRK; 6.3 Polarizable Model with CRK; 6.4 χ(2) Formula with CRK Model; 6.5 Solutions to Problems; 6.5.1 ESP Charge; 6.5.2 Charge Response Kernel; 6.5.3 Energy and Force with Polarizable Model; 6.5.4 Polarizability; Appendix.