Vibrational Optical Activity

1 Overview of Vibrational Optical Activity 1

1.1 Introduction to Vibrational Optical Activity 1

1.2 Origin and Discovery of Vibrational Optical Activity 9

1.3 VCD Instrumentation Development 14

1.4 ROA Instrumentation Development 16

1.5 Development of VCD Theory and Calculations 18

1.6 Development of ROA Theory and Calculations 22

1.7 Applications of Vibrational Optical Activity 25

1.8 Comparison of Infrared and Raman Vibrational Optical Activity 28

1.9 Conclusions 30

2 Vibrational Frequencies and Intensities 35

2.1 Separation of Electronic and Vibrational Motion 35

2.2 Normal Modes of Vibrational Motion 41

2.3 Infrared Vibrational Absorption Intensities 48

2.4 Vibrational Raman Scattering Intensities 56

3 Molecular Chirality and Optical Activity 71

3.1 Definition of Molecular Chirality 71

3.2 Fundamental Principles of Natural Optical Activity 76

3.3 Classical Forms of Optical Activity 83

3.4 Newer Forms of Optical Activity 88

4 Theory of Vibrational Circular Dichroism 95

4.1 General Theory of VCD 96

4.2 Formulations of VCD Theory 108

4.3 Atomic Orbital Level Formulations of VCD Intensity 114

4.4 Transition Current Density and VCD Intensities 124

5 Theory of Raman Optical Activity 131

5.1 Comparison of ROA to VCD Theory 131

5.2 Far-From Resonance Theory (FFR) of ROA 133

5.3 General Unrestricted (GU) Theory of ROA 137

5.4 Vibronic Theories of ROA 148

5.5 Resonance ROA Theory 159

6 Instrumentation for Vibrational Circular Dichroism 169

6.1 Polarization Modulation Circular Dichroism 169

6.2 Stokes-Mueller Optical Analysis 177

6.3 Fourier Transform VCD Measurement 187

6.4 Commercial Instrumentation for VCD Measurement 193

6.5 Advanced VCD Instrumentation 194

7 Instrumentation for Raman Optical Activity 205

7.1 Incident Circular Polarization ROA 205

7.2 Scattered Circular Polarization ROA 211

7.3 Dual Circular Polarization ROA 215

7.4 Commercial Instrumentation for ROA Measurement 222

7.5 Advanced ROA Instrumentation 225

8 Measurement of Vibrational Optical Activity 233

8.1 VOA Spectral Measurement 233

8.2 Measurement of IR and VCD Spectra 234

8.3 Measurement of Raman and ROA Spectra 251

9 Calculation of Vibrational Optical Activity 261

9.1 Quantum Chemistry Formulations of VOA 261

9.2 Fundamental Steps of VOA Calculations 274

9.3 Methods and Visualization of VOA Calculations 282

9.4 Calculation of Electronic Optical Activity 289

10 Applications of Vibrational Optical Activity 293

10.1 Classes of Chiral Molecules 293

10.2 Determination of Absolute Configuration 296

10.3 Determination of Enantiomeric Excess and Reaction Monitoring 302

10.4 Biological Applications of VOA 307

10.5 Future Applications of VOA 329

Appendices.

A Models of VOA Intensity 335

A.1 Estimate of CD Intensity Relative to Absorption Intensity 335

A.2 Degenerate Coupled Oscillator Model of Circular Dichroism 336

A.3 Fixed Partial Charge Model of VCD 338

A.4 Localized Molecular Orbital Model of VCD 340

A.5 Ring Current Model and Other Vibrational Electronic Current Models 341

A.6 Two-Group and Related Models of ROA 342

B Derivation of Probability and Current Densities from Multi-Electron Wavefunctions for Electronic and Vibrational Transitions 345

B.1 Transition Probability Density 345

B.2 Transition Current Density 347

B.3 Conservation of Transition Probability and Current Density 348

B.4 Conservation Equation for Vibrational Transitions 349

C Theory of VCD for Molecules with Low-Lying Excited Electronic States 353

C.1 Background Theoretical Expressions 353

C.2 Lowest-Order Vibronic Theory Including Low-Lying Electronic States 355

C.3 Vibronic Energy Approximation 356

C.4 Low-Lying Magnetic-Dipole-Allowed Excited Electronic States 360

D Magnetic VCD in Molecules with Non-Degenerate States 363

D.1 General Theory 363

D.2 Combined Complete Adiabatic and Magnetic-Field Perturbation Formalism 364

D.3 Vibronic Coupling B-Term Derivation 365

D.4 MCD from Transition Metal Complexes with Low-Lying Electronic States 367

References 368

Index 369