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Vibrational Optical Activity Vibrational Optical Activity Principles and Applications LAURENCE A. NAFIE Department of Chemistry, Syracuse University Syracuse, New York, 13244-4100, USA This edition first published 2011 Ó 2011 John Wiley & Sons Ltd. Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. 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No warranty may be created or extended by any promotional statemen ts for this work. Neit her the publish er nor the author shall be liable for any damages arising herefrom. Library of Congress Cataloging-in-Publication Data Nafie, Laurence A. Vibrational optical activity : principles and applications / Laurence A. Nafie. p. cm. Includes bibliographical references and index. ISBN 978-0-470-03248-0 (cloth) 1. Vibrational spectra. I. Title. QC454.V5N34 2011 539.6–dc22 2011012255 A catalogue record for this book is available from the British Library. Print ISBN: 9780470032480 ePDF ISBN: 9781119976509 oBook ISBN: 9781119976516 ePub ISBN: 9781119977537 Mobi: 9781119977544 Set in 9/11pt Times by Thomson Digital, Noida, India This book is dedicated to the loving, nurturing, and inspiring support of both my parents, Marvin Daniel and Edith Fletcher Nafie and my mother’s parents Frederic Stark and Edith Webster Fletcher, and to my loving wife Rina Dukor who, for the last 15 years, has been my business and scientific partner in helping me to bring vibrational optical activity to the world, and who recently became, as well, my life’s partner in marriage. Contents Preface xvii 1 Overview of Vibrational Optical Activity 1 1.1 Introduction to Vibrational Optical Activity 1 1.1.1 Field of Vibrational Optical Activity 1 1.1.2 Definition of Vibrational Circular Dichroism 3 1.1.3 Definition of Vibrational Raman Optical Activity 5 1.1.4 Unique Attributes of Vibrational Optical Activity 7 1.1.4.1 VOA is the Richest Structural Probe of Molecular Chirality 7 1.1.4.2 VOA is the Most Structurally Sensitive Form of Vibrational Spectroscopy 8 1.1.4.3 VOA Can be Used to Determine Unambiguously the Absolute Configuration of a Chiral Molecule 8 1.1.4.4 VOA Spectra Can be Used to Determine the Solution-State Conformer Populations 8 1.1.4.5 VOA Can be Used to Determine the ee of Multiple Chiral Species of Changing Absolute and Relative Concentration 8 1.2 Origin and Discovery of Vibrational Optical Activity 9 1.2.1 Early Attempts to Measure VOA 9 1.2.2 Theoretical Predictions of VCD 10 1.2.3 Theoretical Predictions of ROA 11 1.2.4 Discovery and Confirmation of ROA 11 1.2.5 Discovery and Confirmation of VCD 13 1.3 VCD Instrumentation Development 14 1.3.1 First VCD Measurements – Dispersive, Hydrogen-Stretching Region 14 1.3.2 Near-IR VCD Measurements 14 1.3.3 Mid-IR VCD Measurements 15 1.3.4 Fourier Transform VCD Instrumentation 15 1.3.5 Commercially Available VCD Instrumentation 15 1.4 ROA Instrumentation Development 16 1.4.1 First ROA Measurements – Single Channel ICP-ROA 16 1.4.2 Multi-Channel ROA Measurements 17 1.4.3 Backscattering ROA Measurements 17 1.4.4 SCP-ROA Measurements 17 1.4.5 DCP-ROA Measurements 18 1.4.6 Commercially Available ROA Instruments 18 1.5 Development of VCD Theory and Calculations 18 1.5.1 Models of VCD Spectra 19 1.5.1.1 Coupled Oscillator Model 19 1.5.1.2 Fixed Partial Charge Model 19 1.5.1.3 Localized Molecular Orbital Model 19 1.5.1.4 Charge Flow Model 19 1.5.1.5 Ring Current Model 20 1.5.2 Vibronic Coupling Theory of VCD 20 1.5.3 Magnetic Field Perturbation Formulation of VCD 20 1.5.4 Nuclear Velocity Perturbation Formulation of VCD 21 1.5.5 Ab Initio Calculations of VCD Spectra 21 1.5.6 Commercially Available Software for VCD Calculations 22 1.6 Development of ROA Theory and Calculations 22 1.6.1 Original Theory of ROA 22 1.6.2 Models of ROA Spectra 23 1.6.3 General Unrestricted Theory of Circular Polarization ROA 23 1.6.4 Linear Polarization ROA 23 1.6.5 Theory of Resonance ROA in the SES Limit 24 1.6.6 Near Resonance Theory of ROA 24 1.6.7 Ab Initio Calculations of ROA Spectra 24 1.6.8 Quantum Chemistry Programs for ROA Calculations 25 1.7 Applications of Vibrational Optical Activity 25 1.7.1 Biological Applications of VOA 25 1.7.2 Absolute Configuration Determination 26 1.7.3 Solution-State Conformation Determination 26 1.7.4 Enantiomeric Excess and Reaction Monitoring 27 1.7.5 Applications with Solid-Phase Sampling 27 1.8 Comparison of Infrared and Raman Vibrational Optical Activity 28 1.8.1 Frequency Ranges and Structural Sensitivities 28 1.8.2 Instrumental Advantages and Disadvantages 29 1.8.3 Sampling Methods and Solvents 29 1.8.4 Computational Advantages and Disadvantages 30 1.9 Conclusions 30 References 30 2 Vibrational Frequencies and Intensities 35 2.1 Separation of Electronic and Vibrational Motion 35 2.1.1 Born–Oppenheimer Approximation 35 2.1.2 Electronic Structure Problem 36 2.1.3 Nuclear Structure Problem 37 2.1.4 Nuclear Potential Energy Surface 38 2.1.5 Transitions Between Electronic States 38 2.1.6 Electronic Transition Current Density 40 2.2 Normal Modes of Vibrational Motion 41 2.2.1 Vibrational Degrees of Freedom 42 2.2.2 Normal Modes of Vibrational Motion 42 2.2.3 Visualization of Normal Modes 43 2.2.4 Vibrational Energy Levels and States 44 2.2.5 Transitions Between Vibrational States 45 2.2.6 Complete Adiabatic Approximation 45 2.2.7 Vibrational Probability Density and Vibrational Transition Current Density 47 viii Contents 2.3 Infrared Vibrational Absorption Intensities 48 2.3.1 Position and Velocity Dipole Strengths 49 2.3.2 Atomic Polar Tensors 52 2.3.3 Nuclear Dependence of the Electronic Wavefunction 53 2.3.4 Vibronic Coupling Formulation of VA Intensities 54 2.3.5 Equivalence Relationships 55 2.4 Vibrational Raman Scattering Intensities 56 2.4.1 General Unrestricted (GU) Theory of Raman Scattering 57 2.4.2 Vibronic Theory of Raman Intensities 58 2.4.3 Raman Scattering Tensors and Invariants 60 2.4.4 Polarization Experiments and Scattering Geometries 60 2.4.5 Depolarization and Reversal Ratios 62 2.4.6 Isolation of Raman Scattering Invariants 63 2.4.7 Far-From-Resonance Approximation 63 2.4.8 Near Resonance Theory of Raman Scattering 65 2.4.9 Resonance Raman Scattering 67 2.4.10 Single Electronic State Resonance Approximation 68 References 69 3 Molecular Chirality and Optical Activity 71 3.1 Definition of Molecular Chirality 71 3.1.1 Historical Origins 72 3.1.2 Molecular Symmetry Definition of Chirality 72 3.1.3 Absolute Configuration of Chiral Molecules 73 3.1.3.1 Chiral Center 73 3.1.3.2 Helix 74 3.1.3.3 Chiral Axis 74 3.1.3.4 Chiral Plane 75 3.1.4 True and False Chirality 75 3.1.5 Enantiomers, Diastereomers, and Racemic Mixtures 75 3.2 Fundamental Principles of Natural Optical Activity 76 3.2.1 Polarization States of Radiation 76 3.2.2 Mueller Matrices and Stokes Vectors 78 3.2.3 Definition of Optical Activity 79 3.2.4 Optical Activity Observables 79 3.2.4.1 Complex Index of Refraction 80 3.2.4.2 Absorption Observables 80 3.2.4.3 Circular Dichroism and Ellipticity Observables 81 3.2.4.4 Optical Rotation Angle and Optical Rotatory Dispersion Observables 82 3.3 Classical Forms of Optical Activity 83 3.3.1 Optical Rotation and Optical Rotatory Dispersion 83 3.3.2 Circular Dichroism 83 3.3.3 Kramers–Kronig Transform Between CD and ORD 84 3.3.4 Lorentzian Dispersion and Absorption Relationships 85 3.3.5 Dipole and Rotational Strengths 86 3.3.6 Magnetic Optical Activity 88 3.4 Newer Forms of Optical Activity 88 3.4.1 Infrared Optical Activity, VCD, and IR-ECD 89 3.4.1.1 VCD–ECD Overlap 89 Contents ix 3.4.2 Vacuum Ultraviolet and Synchrotron Circular Dichroism 89 3.4.3 Rayleigh and Raman Optical Activity, RayOA and ROA 90 3.4.3.1 ROA Overlaps 90 3.4.4 Magnetic Vibrational Optical Activity 90 3.4.5 Fluorescence Optical Activity, FDCD and CPL 91 3.4.5.1 FOA and ROA Overlap 91 3.4.6 Other Forms of Optical Activity 91 3.4.6.1 X-Ray Circular Dichroism 92 3.4.6.2 Neutron Optical Activity 92 3.4.6.3 Far-Infrared and Rotational CD 92 3.4.6.4 NMR Chiral Discrimination 92 References 92 4 Theory of Vibrational Circular Dichroism 95 4.1 General Theory of VCD 96 4.1.1 Definitions of VCD Intensity and Rotational Strength 97 4.1.2 Complete Adiabatic Correction to the Born–Oppenheimer Approximation 98 4.1.3 Derivation of the Complete Adiabatic Wavefunction 100 4.1.4 Vibronic Coupling Theory of VCD and IR Intensity 102 4.1.5 Origin Dependence of the Rotational Strength 105 4.1.5.1 General Description of Origin Dependence 105 4.1.5.2 Distributed Origin Gauge and Effective Origin Independence 106 4.2 Formulations of VCD Theory 108 4.2.1 Average Excited-State Energy Approximation 108 4.2.2 Magnetic Field Perturbation Theory 108 4.2.3 Sum-Over-States Vibronic Coupling Theory 110 4.2.4 Nuclear Velocity Perturbation Theory 110 4.2.5 Energy Second-Derivative Theory 111 4.2.6 Other Formulations of VCD Theory 113 4.3 Atomic Orbital Level Formulations of VCD Intensity 114 4.3.1 Atomic Orbital Basis Descriptions of Transition Moments 114 4.3.1.1 Position Form of the Electronic APT 114 4.3.1.2 Velocity Form of the Electronic APT 116 4.3.1.3 Electronic AAT 118 4.3.2 Velocity Dependent Atomic Orbitals 118 4.3.2.1 Field Adiabatic Velocity Gauge 119 4.3.2.2 Complete Adiabatic Nuclear Velocity Gauge 119 4.3.3 Field Adiabatic Velocity Gauge Transition Moments 120 4.3.4 Gauge Invariant Atomic Orbitals and AATs 120 4.3.5 Complete Adiabatic Nuclear Velocity Gauge Transition Moments 122 4.3.5.1 Velocity APT with Nuclear Velocity Gauge Atomic Orbitals 122 4.4 Transition Current Density and VCD Intensities 124 4.4.1 Relationship Between Vibrational TCD and VA Intensity 125 4.4.2 Relationship Between Vibrational TCD and VCD Intensity 128 References 130 x Contents 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 5.2.1 Right-Angle ROA Scattering 133 5.2.2 Backscattering ROA 135 5.2.3 Forward and Magic Angle Scattering ROA 136 5.3 General Unrestricted (GU) Theory of ROA 137 5.3.1 ROA Tensors 137 5.3.2 Forms of ROA 141 5.3.3 CP-ROA Invariants 141 5.3.4 CP-ROA Observables and Invariant Combinations 143 5.3.5 Backscattering CP-ROA Observables 145 5.3.6 LP-ROA Invariants 146 5.3.7 LP-ROA Observables and Invariant Combinations 148 5.4 Vibronic Theories of ROA 148 5.4.1 General Unrestricted Vibronic ROA Theory 149 5.4.2 Vibronic Levels of Approximation 150 5.4.3 Near Resonance Vibronic Raman Theory 150 5.4.4 Levels of the Near Resonance Raman Theory 153 5.4.5 Near Resonance Theory of ROA 157 5.4.6 Reduction of the Near Resonance Theory to the Far-From Resonance Theory of ROA 157 5.5 Resonance ROA Theory 159 5.5.1 Strong Resonance in the Single Electronic State (SES) Limit 159 5.5.2 Strong Resonance Involving Two Excited Electronic States 163 5.5.2.1 TES Theory With a Single B-Term Contributing State (TES-B) 163 5.5.2.2 TES Theory with two A-Term Contributing States (TES-A) 166 References 167 6 Instrumentation for Vibrational Circular Dichroism 169 6.1 Polarization Modulation Circular Dichroism 169 6.1.1 Instrumental Measurement of Circular Dichroism 170 6.1.2 Calibration of CD Intensities 173 6.1.3 Photoelastic Modulator Optimization 176 6.2 Stokes–Mueller Optical Analysis 177 6.2.1 Basic Stokes–Mueller Formalism 177 6.2.2 Stokes–Mueller Derivation of Circular Dichroism Measurement 183 6.2.3 Stokes–Mueller Derivation of the CD Calibration 184 6.2.4 Measurement of Circular Birefringence 185 6.3 Fourier Transform VCD Measurement 187 6.3.1 Double-Modulation Instrumental Setup and Block Diagram 188 6.3.2 DC Interferogram and Phase Correction 188 6.3.3 AC Interferogram and Phase Correction 190 6.3.4 Polarization Division FT-VCD Measurement 192 6.3.5 Step-Scan FT-VCD Measurement 192 6.4 Commercial Instrumentation for VCD Measurement 193 6.4.1 VCD Side-Bench Accessories 193 6.4.2 Dedicated VCD Spectrometers 194 6.5 Advanced VCD Instrumentation 194 6.5.1 Dual Source Intensity Enhancement and Detector Saturation Suppression 194 Contents xi 6.5.2 Dual-PEM Theory of Artifact Suppression 196 6.5.3 Rotating Achromatic Half-Wave Plate 199 6.5.4 Rotating Sample Cell 200 6.5.5 Direct All-Digital VCD Measurement and Noise Improvement 201 6.5.6 Femtosecond-IR Laser-Pulse VOA Measurements 202 References 203 7 Instrumentation for Raman Optical Activity 205 7.1 Incident Circular Polarization ROA 205 7.1.1 Optical Block Diagram for ICP-Raman and ROA Scattering 207 7.1.2 Intensity Expressions 208 7.1.3 Advantages of Backscattering 209 7.1.4 Artifact Suppression 210 7.2 Scattered Circular Polarization ROA 211 7.2.1 Measurement of SCP-ROA and Raman Scattering 212 7.2.2 Optical Block Diagram for SCP-Raman and ROA Measurement 213 7.2.3 Comparison of ICP- and SCP-ROA 214 7.2.4 Artifact Reduction in SCP-ROA Measurement 215 7.3 Dual Circular Polarization ROA 215 7.3.1 Optical Setups for DCP-ROA Measurement 217 7.3.2 Comparison of ICP-, SCP-, and DCP I -ROA 218 7.3.3 Isolation of ROA Invariants 219 7.3.4 DCP II -ROA and the Onset of Pre-resonance Raman Scattering 220 7.4 Commercial Instrumentation for ROA Measurement 222 7.4.1 High Spectral Throughput 222 7.4.2 Artifact Suppression and the Virtual Enantiomer 224 7.5 Advanced ROA Instrumentation 225 7.5.1 Resonance ROA (RROA) 226 7.5.2 Near-Infrared Excitation ROA 226 7.5.3 Ultraviolet Excitation ROA 227 7.5.4 Linear Polarization ROA 227 7.5.5 Non-Linear and Time-Resolved ROA 229 7.5.6 Surfaced-Enhanced ROA 230 7.5.7 Rayleigh Optical Activity 230 References 231 8 Measurement of Vibrational Optical Activity 233 8.1 VOA Spectral Measurement 233 8.2 Measurement of IR and VCD Spectra 234 8.2.1 Selection of Frequency Range, Detector and Optical Components 234 8.2.1.1 Mid-Infrared Spectral Region 234 8.2.1.2 Hydrogen-Stretching Region 235 8.2.1.3 First Overtone and Combination-Band Region 236 8.2.1.4 Second Overtone and Second Combination Band Region 236 8.2.1.5 Third Overtone and Combination Band Region and Beyond 236 8.2.2 Choice of IR Solvents 236 8.2.3 Optimization of Concentration, Pathlength, and Spectral Resolution 237 8.2.4 Measurement and Optimization of VCD Spectra 238 8.2.4.1 Fourier Phase Correction for the VCD Interferogram 239 8.2.4.2 Setting the Retardation Value of the First PEM 239 xii Contents [...]... and extend the frontiers of VCD and ROA Palm Beach Gardens, Florida, USA February, 2011 1 Overview of Vibrational Optical Activity 1.1 Introduction to Vibrational Optical Activity Vibrational optical activity (VOA) is a new form of natural optical activity whose early history dates back to the nineteenth century We now know that the original observations of optical activity, the rotation of the plane... by Vibrational Optical Activity: Principles and Applications, First Edition Laurence A Nafie Ó 2011 John Wiley & Sons, Ltd Published 2011 by John Wiley & Sons, Ltd 2 Vibrational Optical Activity overtone and combination band transitions ROA has been measured to as low as 50 cmÀ1, a distinct difference compared with VCD, but ROA is more difficult to measure beyond the range of fundamental transitions and. .. optical activity that depends on transition moments which arise in both VCD and ROA Another class of optical activity that has VOA content is vibronic optical activity Here the source of optical activity is a combination of electronic optical activity (EOA) and VOA when changes to both electronic and vibrational states occur in a transition This form of EOA–VOA arises in ECD whenever vibronic detail... overcome in the near future 1.2 Origin and Discovery of Vibrational Optical Activity The emergence of VOA in the early 1970s was preceded by many earlier efforts to uncover the effects of vibrational transitions in optical activity spectra, primarily optical rotation measurements in the near-infrared and infrared regions Tracing the origins and subsequent development of ROA and VCD can only be done at a relatively... absorption and Raman scattering The infrared form is known as vibrational circular dichroism, or VCD, while the Raman form is known as vibrational Raman optical activity, VROA, or usually just ROA (Raman optical activity) VCD and ROA were discovered experimentally in the early 1970s and have since blossomed independently into two important new fields of spectroscopy for probing the structure and conformation... of vibrational spectroscopy, chirality, and optical activity and the frontier of research and applications of VOA The book could serve both as a textbook for graduate courses in chemistry or biophysics as well as a reference for the experienced researcher or scientist A basic understanding of spectroscopy and quantum mechanics is assumed, but beyond that, nothing further is needed besides patience and. .. absorption bands occur The search for vibrational optical activity followed a path similar to that of electronic optical activity just discussed Early attempts to measure vibrational optical activity consisted of measurements of OR extending to longer wavelengths towards the infrared spectral region The earliest such measurements (Lowry, 1935) yielded no indications that new sources of CD might lie in the vibrational. .. Field of Vibrational Optical Activity Vibrational optical activity, as the name implies, is the area of spectroscopy that results from the introduction of optical activity into the field of vibrational spectroscopy VOA can be broadly defined as the difference in the interaction of left and right circularly polarized radiation with a molecule or molecular assembly undergoing a vibrational transition This... Adiabatic and Magnetic-Field Perturbation Formalism D.3 Vibronic Coupling B-Term Derivation D.4 MCD from Transition Metal Complexes with Low-Lying Electronic States References 363 363 364 365 367 368 Index 369 Preface During the years surrounding the new millennium, the field of vibrational optical activity (VOA), comprised principally of vibrational circular dichroism (VCD) and vibrational Raman optical activity. .. and differences between VCD and ROA can most easily be seen Both of these fields rest on the foundations of vibrational spectroscopy and the science of describing the vibrational motion of molecules, and both are forms of molecular optical activity sensitive to chirality in molecules After a basic and somewhat historical introduction to VOA in Chapter 1, the fundamentals of vibrational spectroscopy are . of Vibrational Optical Activity 1 1.1 Introduction to Vibrational Optical Activity 1 1.1.1 Field of Vibrational Optical Activity 1 1.1.2 Definition of Vibrational. Vibrational Optical Activity Vibrational Optical Activity Principles and Applications LAURENCE A. NAFIE Department