Modern Vibrational Spectroscopy andMicro-Spectroscopy

Modern Vibrational Spectroscopy andMicro-Spectroscopy

Theory, Instrumentation and Biomedical Applications

MAX DIEMNortheastern University, USA

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Library of Congress Cataloging-in-Publication Data

Diem, Max, 1947-Modern vibrational spectroscopy and micro-spectroscopy : theory, instrumentation, and biomedical applications / Max Diem.

pages cmIncludes bibliographical references and index.ISBN 978-1-118-82486-3 (pbk.)1. Spectrum analysis–Diagnostic use 2. Vibrational spectra. I. Title.RC78.7.S65D54 2015616.07′54–dc23

2015019354

A catalogue record for this book is available from the British Library.

Set in 10/12pt TimesLTStd by SPi Global, Chennai, India

1 2015

I would like to dedicate this book to my wife, Mary Jo, who put up with myhiding away in my home office for many an evening and my absentmindednessfor 16 months during which this book was written.I also would like to acknowledge the excellent and enthusiastic crew of post-

docs, graduate and undergraduate students inmy research laboratory at North-eastern University who was responsible for the majority of the work presentedhere (listed chronologically).Milos, Christian, Susie, Melissa, Brian, Tatjana, Jen (I), Ben, Ellen, Kostas,

Antonella, Evgenia, Erin, Jen (II), Christina, Kathleen, and Doug.

Max Diem

Contents

Preface xvPreface to ‘Introduction to Modern Vibrational Spectroscopy’ (1994) xix

I MODERN VIBRATIONAL SPECTROSCOPY AND MICRO-SPECTROSCOPY:THEORY, INSTRUMENTATION AND BIOMEDICAL APPLICATIONS 1I.1 Historical Perspective of Vibrational Spectroscopy 1I.2 Vibrational Spectroscopy within Molecular Spectroscopy 2

References 4

1 Molecular Vibrational Motion 51.1 The concept of normal modes of vibration 61.2 The separation of vibrational, translational, and rotational coordinates 61.3 Classical vibrations in mass-weighted Cartesian displacement coordinates 71.4 Quantum mechanical description of molecular vibrations 13

1.4.1 Transition from classical to quantum mechanical description 131.4.2 Diatomic molecules: harmonic oscillator 141.4.3 Diatomic molecules: anharmonicity 191.4.4 Polyatomic molecules 20

1.5 Time-dependent description and the transition moment 221.5.1 Time-dependent perturbation of stationary states by electromagnetic radiation 221.5.2 The vibrational transition moment for absorption: harmonic diatomic molecules 251.5.3 The vibrational transition moment for absorption: anharmonic diatomic molecules 271.5.4 The vibrational transition moment for absorption: polyatomic molecules 301.5.5 Isotopic effects: diatomic molecules 31

1.6 Basic infrared and Raman spectroscopies 321.6.1 Infrared absorption spectroscopy 321.6.2 Raman (scattering) spectroscopy 35

1.7 Concluding remarks 38References 38

2 Symmetry Properties of Molecular Vibrations 392.1 Symmetry operations and symmetry groups 402.2 Group representations 442.3 Symmetry representations of molecular vibrations 502.4 Symmetry-based selection rules for absorption processes 542.5 Selection rules for Raman scattering 562.6 Discussion of selected small molecules 57

2.6.1 Tetrahedral molecules: carbon tetrachloride, CCl4, and methane, CH4 57

viii Contents

2.6.2 Chloroform and methyl chloride 642.6.3 Dichloromethane (methylene chloride), CH2Cl2 672.6.4 Dichloromethane-d1 (methylene chloride-d1), CHDCl2 68References 69

3 Infrared Spectroscopy 713.1 General aspects of IR spectroscopy 713.2 Instrumentation 73

3.2.1 Sources of infrared radiation: black body sources 733.2.2 Sources of infrared radiation: quantum-cascade lasers,

nonlinear devices 753.2.3 Transfer optics 763.2.4 Color sorting devices: monochromators 763.2.5 Color encoding devices: interferometers 793.2.6 Detectors 823.2.7 Read-out devices 84

3.3 Methods in interferometric IR spectroscopy 843.3.1 General instrumentation 843.3.2 Optical resolution 863.3.3 Zero filling and fourier smoothing 863.3.4 Phase correction 883.3.5 Apodization 91

3.4 Sampling strategies 923.4.1 Transmission measurement 923.4.2 Specular reflection 943.4.3 Diffuse reflection 953.4.4 Attenuated total reflection 973.4.5 Infrared reflection absorption spectroscopy (IRRAS) 993.4.6 Fourier transform photoacoustic spectroscopy (FT-PAS) 1003.4.7 Planar array infrared spectroscopy (PA-IRS) 1013.4.8 Two-dimensional FTIR 1013.4.9 Infrared microspectroscopy 102References 102

4 Raman Spectroscopy 1034.1 General aspects of Raman spectroscopy 1044.2 Polarizability 1054.3 Polarization of Raman scattering 1074.4 Dependence of depolarization ratios on scattering geometry 1114.5 A comparison between Raman and fluorescence spectroscopy 1144.6 Instrumentation for Raman spectroscopy 116

4.6.1 Sources 1164.6.2 Dispersive Raman instrumentation and multichannel detectors 1164.6.3 Interferometric Raman instrumentation 1214.6.4 Raman microspectroscopy 122References 122

Contents ix

5 A Deeper Look at Details in Vibrational Spectroscopy 1235.1 Fermi resonance 1245.2 Transition dipole coupling (TDC) 1285.3 Group frequencies 1295.4 Rot-vibrational spectroscopy 130

5.4.1 Classical rotational energy 1305.4.2 Quantum mechanics of rotational spectroscopy 1325.4.3 Rot-vibrational transitions 137References 141

6 Special Raman Methods: Resonance, Surface-Enhanced, and NonlinearRaman Techniques 143

6.1 Resonance Raman spectroscopy 1446.2 Surface-enhanced Raman scattering (SERS) 1466.3 Nonlinear Raman effects 149

6.3.1 Spontaneous (incoherent) nonlinear Raman effects 1496.3.2 Coherent nonlinear effects 152

6.4 Continuous wave and pulsed lasers 1596.4.1 Einstein coefficients and population inversion 1606.4.2 Operation of a gas laser 1626.4.3 Principles of pulsed lasers 1636.4.4 Operation of pulsed lasers 163

6.5 Epilogue 164References 164

7 Time-Resolved Methods in Vibrational Spectroscopy 1677.1 General remarks 1677.2 Time-resolved FT infrared (TR-FTIR) spectroscopy 168

7.2.1 Experimental aspects 1687.2.2 Applications of TR-FTIR spectroscopy 169

7.3 Time-resolved Raman and resonance Raman (TRRR) spectroscopy 1717.3.1 Instrumental aspects 1717.3.2 Applications of TRRR 1737.3.3 Heme group dynamic studies 1737.3.4 Rhodopsin studies 174References 175

8 Vibrational Optical Activity 1778.1 Introduction to optical activity and chirality 1778.2 Infrared vibrational circular dichroism (VCD) 179

8.2.1 Basic theory 1798.2.2 Exciton theory of optical activity 180

8.3 Observation of VCD 1818.4 Applications of VCD 185

8.4.1 VCD of biological molecules 1858.4.2 Small molecule VCD 185

x Contents

8.5 Raman optical activity 1868.6 Observation of ROA 1888.7 Applications of ROA 189

8.7.1 ROA of biological molecules 1898.7.2 Small molecules ROA 190References 190

9 Computation of Vibrational Frequencies and Intensities 1939.1 Historical approaches to the computation of vibrational frequencies 1939.2 Vibrational energy calculations 194

9.2.1 Classical approaches: the Wilson GF matrix method 1949.2.2 Early computer-based vibrational analysis 197

9.3 Ab initio quantum-mechanical normal coordinate computations 1979.4 Vibrational intensity calculations 198

9.4.1 Fixed partial charge method for infrared intensities 1989.4.2 Quantum mechanical infrared and Raman intensities: localized molecular orbitals 2009.4.3 The finite perturbation method 200References 202

II BIOPHYSICAL AND MEDICAL APPLICATIONS OF VIBRATIONALSPECTROSCOPY AND MICROSPECTROSCOPY 203

10 Biophysical Applications of Vibrational Spectroscopy 20510.1 Introduction 20510.2 Vibrations of the peptide linkage and of peptide models 206

10.2.1 Amino acids and the peptide linkage 20610.2.2 The vibrational modes of the peptide linkage 206

10.3 Conformational studies of peptides and polyamino acids 21010.4 Protein spectroscopy: IR, VCD, Raman, resonance Raman, and ROA spectra of proteins 21510.5 Nucleic acids 219

10.5.1 Structure and function of nucleic acids 21910.5.2 Phosphodiester vibrations 22210.5.3 Ribose vibrations 22210.5.4 Base vibrations 222

10.6 Conformational studies on DNA and DNA models using IR, Raman, and VCD spectroscopies 22310.7 Lipids and phospholipids 22710.8 Epilogue 231

References 231

11 Vibrational Microspectroscopy (MSP) 23511.1 General remarks 23511.2 General aspects of microscopy 23611.3 Raman microspectroscopy (RA-MSP) 239

11.3.1 Dispersive (single point) systems 24011.3.2 Micro-Raman imaging systems 241

Contents xi

11.4 CARS and FSRS microscopy 24211.5 Tip-enhanced Raman spectroscopy (TERS) 24311.6 Infrared microspectroscopy (IR-MSP) 243

11.6.1 Fourier-transform infrared imaging systems 24411.6.2 QCL-based systems 246

11.7 Sampling strategies for infrared microspectroscopy 24711.7.1 Transmission measurement 24711.7.2 Transflection measurement 24711.7.3 Attenuated total reflection (ATR) 248

11.8 Infrared near-field microscopy 249References 249

12 Data Preprocessing and Data Processing in Microspectral Analysis 25112.1 General remarks 25112.2 Data preprocessing 252

12.2.1 Cosmic ray filtering (Raman data sets only) 25312.2.2 Linear wavenumber interpolation (Raman data sets only) 25312.2.3 Conversion from transmittance to absorbance units (some infrared data sets) 25312.2.4 Normalization 25312.2.5 Noise reduction 25412.2.6 Conversion of spectra to second derivatives 256

12.3 Reduction of confounding spectral effects 25712.3.1 Reduction of water vapor contributions in cellular pixel spectra 25812.3.2 Mie and resonance Mie scattering 25812.3.3 Correction of dispersive band shapes 26012.3.4 Standing wave effect 262

12.4 Unsupervised multivariate methods of data segmentation 26312.4.1 Factor methods 26412.4.2 Data segmentation by clustering methods 269

12.5 Supervised multivariate methods 27212.5.1 Discussion of sensitivity, specificity, and accuracy 27212.5.2 Soft independent modeling of class analogy (SIMCA) 27312.5.3 Artificial neural networks (ANNs) 27412.5.4 Support vector machines (SVMs) 27512.5.5 Random forests (RFs) 27612.5.6 Cross-validation 277

12.6 Summary of data processing for microspectral analysis 27812.7 Two-dimensional correlation methods in infrared spectroscopy (2D-IR) 278

References 280

13 Infrared Microspectroscopy of Cells and Tissue in Medical Diagnostics 28313.1 Introduction 28313.2 Spectral histopathology (SHP) 284

13.2.1 Review of classical histopathology 28413.2.2 Spectral methods in histopathology 28513.2.3 Infrared absorption spectroscopy of cells and tissue: introductory comments 285

xii Contents

13.3 Methodology for SHP 28713.3.1 General approach 28713.3.2 Sequence of steps in classical histopathology 28813.3.3 Sequence of steps for spectral histopathology 288

13.4 Applications of SHP for the classification of primary tumors 29413.4.1 Cervical tissue and cervical cancer 29413.4.2 Lung cancer 29813.4.3 Prostate cancer 30313.4.4 Breast cancer 304

13.5 Application of SHP toward the detection and classification of metastatic tumors 30413.5.1 Detection of colon cancer metastases in lymph nodes 30413.5.2 Detection of breast cancer metastases in lymph nodes 30613.5.3 Detection and classification of brain metastases 307

13.6 Future prospects of SHP 30913.7 Infrared spectral cytopathology (SCP) 310

13.7.1 Classical cytopathology 31113.7.2 Spectral cytopathology 31413.7.3 Methods for SCP 314

13.8 SCP results 31613.8.1 Early results of SCP 31613.8.2 Fixation studies 31713.8.3 Spectral cytopathology of cervical mucosa 32013.8.4 Spectral cytopathology of the oral mucosa 32313.8.5 Spectral cytopathology of esophageal cells 326

13.9 SCP of cultured cells 32813.9.1 Early SCP efforts and general results 32813.9.2 SCP of cultured cells to study the effects of the cell cycle and of drugs on cells 328

13.10 Infrared spectroscopy of cells in aqueous media 33113.11 Future potential of SCP 333

References 333

14 Raman Microspectroscopy of Cells and Tissue in Medical Diagnostics 33914.1 Introduction 33914.2 Experimental Consideration for Raman Microspectroscopy 34114.3 High-Resolution Raman Spectral Cytopathology 343

14.3.1 Subcellular organization 34314.3.2 Subcellular transport phenomena 345

14.4 Low-Resolution Raman SCP of Cultured Cells In Vitro 34914.5 Raman SCP in Solution 352

14.5.1 Optical tweezing of cells in aqueous media 35214.5.2 Cells trapped in microfluidic chips 35314.5.3 Resonance Raman spectroscopy of erythrocytes 353

14.6 Raman Spectral Histopathology (Ra SHP) 35414.7 In Vivo Raman SHP 35614.8 Deep Tissue Raman SHP 357

14.8.1 Hard tissue diagnostics 357

Contents xiii

14.8.2 Deep tissue imaging of breast tissue and lymph nodes 358References 359

15 Summary and Epilogue 363

APPENDIXA The Particle in a Box: A Demonstration of Quantum Mechanical Principles fora Simple, One-Dimensional, One-Electron Model System 365

A.1 Definition of the Model System 365A.2 Solution of the Particle-in-a-Box Differential Equation 367A.3 Orthonormality of the Particle-in-a-Box Wavefunctions 370A.4 Dipole-Allowed Transitions for the Particle in a Box 370A.5 Real-World PiBs 371

APPENDIXB A summary of the Solution of the Harmonic Oscillator (Hermite) DifferentialEquation 373

APPENDIXC Character Tables for Chemically Important Symmetry Groups 377C.1 The nonaxial groups 377C.2 The Cn groups 377C.3 The Dn groups 379C.4 The Cn𝑣 groups 379C.5 The Dnh groups 382C.6 The Dnd groups 384C.7 The Sn groups 385C.8 The cubic groups 386C.9 The groups C∞, and D∞h for linear molecules 387C.10 The icosahedral groups 388

APPENDIXD Introduction to Fourier Series, the Fourier Transform, and the Fast FourierTransform Algorithm 389

D.1 Data Domains 389D.2 Fourier Series 390D.3 Fourier Transform 392D.4 Discrete and Fast Fourier Transform Algorithms 393

References 395

APPENDIXE List of Common Vibrational Group Frequencies (cm−1) 397

APPENDIX F Infrared and Raman Spectra of Selected Cellular Components 399

Index 405

Preface

Although this book was conceived as a second edition of Introduction to Modern Vibrational Spectroscopypublished by the author in 1993, it really is not a second edition, but a completely rewritten monograph ona subject that has changed so much in 20 years that the old edition appears seriously antiquated. In fact, fewother areas of spectroscopy have undergone such radical changes in the past two decades as vibrational spec-troscopy has: subjects that then were cutting edge technology have become so common that they have beenpart of undergraduate physical chemistry core laboratories for quite some time, and areas that were not eventhought about 20 years ago are on the verge of commercialization. This enormous progress was spawned bya fortuitous co-incidence of many factors, such as instrumental advances that allow the collection of 10 000infrared spectra within a few minutes, or the collection of Raman spectra of samples in the picogram regimein a few hundred milliseconds. The ready availability of pico- and femtosecond tunable laser sources hasmade routine acquisition possible of several nonlinear spectroscopic effects, based on excitation of short-livedvibrational states. Last not least, the enormous increase in computational power over the past 20 years hasopened entirely new avenues for data processing and statistical analyses of the plethora of data collected inshort times. In fact, the increased computational power is certainly one major enabling factor of an area ofvibrational spectroscopic imaging, in which between 10 000 and 100 000 individual pixel spectra are collectedthrough specialized microscopes and converted to pseudo-color images based on the vibrational spectroscopicfeatures. This increase in computational power can easily be felt considering that in 1993, a top-end personalcomputer (PC) incorporated less than 1MB of RAM, and was still based on Intel 386/387 processors andmuch of the scientific programming was carried out using FORTRAN compilers. Twenty years later, work-stations with between 16 and 48GB of RAM and multicore Pentium type processors are routine and availablefor a similar dollar amount required for the purchase of top-end PCs in 1993. The accessibility of thousandsof routines for data processing and analysis, and being contained in the MATLAB environment, have offeredsophisticated statistical and analysis routines even to the non-expert. Finally, theoretical developments havesolved some puzzling aspects of vibrational spectroscopy; the prime example here is the understanding ofthe theoretical foundations of surface-enhanced Raman spectroscopy (SERS). In 1993, an overall agree-ment on the theoretical foundations of this effect had not been reached. Furthermore, the field seemed tobe plagued by low reproducibility, which disappeared once the theory of surface enhancement was properlydeveloped.The need for inclusion of new techniques in vibrational spectroscopy, as well as the shifting research

interests of the author, contributed to the very new format of this book, and the material contained herein.Furthermore, the strategies for teaching concepts of vibrational spectroscopy have changed both at the grad-uate and the undergraduate levels. Finally, the intended readership of this book has changed since the firstedition addressed an audience of first year graduate students in chemistry while the present edition addresses,in addition, a readership interested primarily in the medical imaging and diagnostics fields. For these readers,the theory sections have been streamlined, and imaging aspects have been added. The first edition still con-tained a detailed discussion on how to perform empirical calculation of molecular force fields and vibrationalfrequencies. This subject has gone the path of dinosaurs, since such calculations are now all performed at theab initio molecular orbital level. In addition, methods of data handling and analysis have been added that arenecessary for both students and researchers in modern vibrational spectroscopy.

xvi Preface

All these changes have forced a total rewriting of the book. Part I of the reworked monograph containsthe theory of vibrational spectroscopy, presented both from the view of classical mechanics as well as fromquantum mechanics. Although the later parts of the book deal mostly with large biological molecules, ashort review of the group theoretical foundations of vibrational spectra of small molecules is included, aswell as basic instrumental aspects. New techniques – surface and nanostructure-based spectroscopies, nonlin-ear effects, and time-resolved methods – are introduced as well. Thus, Part I represents a short course into“Modern Vibrational Spectroscopy” and is somewhat comparable to the first edition.Part II deals with biophysical, medical, and diagnostic applications of vibrational spectroscopy. It starts with

a review of the biophysical applications of macroscopic vibrational spectroscopy, a field that has producedten thousands of papers on biomolecular structure, dynamics, and interactions. Subsequently, vibrationalmicrospectroscopy (also referred to as vibrational microscopy) will be introduced. Although infrared andRaman microspectroscopy were certainly known and applied in 1993, their relevance was relatively low, andthey were not included in the first edition. In contrast, both techniques are so prevalent now that they con-tribute to about 30% of sales in Raman and infrared spectral instrumentation. Both these techniques presenttheir own challenges in instrumentation, data manipulation, and analysis, and are discussed in detail.Vibrational microspectroscopy allows the detection and analysis of individual bacterial cells. In 1993, a

few brave souls had embarked into this field and found that infrared spectra proved phenomenally sensitivein distinguishing different bacterial species [1]. The analysis of cells and tissue has undergone an explosiveexpansion during the past decade, and is now on the verge of becoming a major diagnostic and prognostictool. Specialized journals, such as Biospectroscopy (now part of Biopolymers) and the Journal of Biopho-tonics are devoted to the application of (mostly) vibrational spectroscopy toward biological sciences andmedicine. Many journals that used to concentrate on classical analytical chemistry have devoted entire issuesto the emerging field of spectral diagnostics (see, for example, Analyst, Volume 135 and J. Biophotonics,Volumes 3 and 6).Thus, the author hopes that this book will provide a detailed background, from the quantum mechanical

foundation to the specific applications, for researchers in, or entering, the exciting and re-emerging field ofvibrational spectroscopy.In the years since the first edition was published, several new books have appeared discussing in detail

several aspects of vibrational spectroscopy, such as D.A. Long’s book on Raman theory [2], L.A. Nafie’s bookon Vibrational Optical Activity [3], volumes on Quantum Mechanics or Group Theory [4], monographs onmicrospectroscopy, and many more. The present book can impossibly compete with these specialized bookson the details presented, since it still was conceived as an “Introduction” to modern vibrational spectroscopy.Therefore, the subjects discussed here are more appropriate for a researcher entering this field, or for advancedundergraduate students in Chemistry or the Life Sciences.Finally, the author herewith apologizes categorically for one aspect in this book that is presented inconsis-

tently throughout the chapters: the presentation of spectra from left to right and from right to left. Historically,Raman spectra have been presented mostly from “left to right,” that is, from low to high wavenumber. Infraredspectra were originally presented from high wavenumber to low wavenumber, or from “right to left.” Ofcourse, this was due to the fact that the wavelength increases from “left to right” in this presentation. Althoughthere are some recommendations by IUPAC on the representation of spectra –Raman spectra from “left toright” and infrared spectra from “right to left” – too many researchers have not abided by this rule; conse-quently, spectra are displayed in the literature both ways. Since many figures in this book are taken fromthe work of many researchers, these figures could not be reversed to a standard theme. Thus, the reader isreminded to pay particular attention to the direction of the wavenumber scale in the figures.

Boston, July 2014

Preface xvii

References

1. Naumann, D., Fijala, V., Labischinski, H. and Giesbrecht, P. (1988) The rapid differentiation of pathogenic bacteriausing Fourier transform infrared spectroscopic and multivariate statistical analysis. J. Mol. Struct., 174, 165–170.

2. Long, D.A. (2002) The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules, JohnWiley & Sons, Ltd, Chichester.

3. Nafie, L.A. (2011) Vibrational Optical Activity: Principles and Applications, John Wiley & Sons, Ltd, Chichester.4. Cotton, F.A. (1990) Chemical Applications of Group Theory, 3rd edn, John Wiley & Sons, Inc., New York.

Preface to Introduction to Modern VibrationalSpectroscopy (1994)

The aim of this book is to provide a text for a course in modern vibrational spectroscopy. The course isintended for advanced undergraduate students, who have had an introductory course in Quantum Chemistryand have been exposed to group theoretical concepts in an inorganic chemistry course, or for graduate studentswho have passed a graduate level course in Quantum Chemistry.There are probably a dozen or so recent books in vibrational spectroscopy, and a few classical texts over three

decades old. This large number seems to discourage any efforts to produce yet another book on the subject,unless one is willing to pursue a novel approach in presenting the material. This is, of course, exactly whatwas attempted with the present book, and the approach taken will be outlined in the following paragraphs.There are two classical and comprehensive texts on vibrational spectroscopy,Molecular Spectra andMolec-

ular Structure. II. Infrared and Raman Spectra of Polyatomic Molecules by Herzberg [1] and MolecularVibrations by Wilson et al. [2]. Both of these books are absolutely essential for an in-depth understand-ing of vibrational spectroscopy, and devote hundreds of pages to theoretical derivations. However, due tothe rapid progress in instrumental techniques and computational methods and due to the fact that thousandsof molecules have been studied since these two books were written, the practical aspects of these booksare certainly limited. However, the value of these classic books for the serious vibrational spectroscopist isimmeasurable, since they provide many of the fine points needed for a detailed understanding of the subject.Among the more recent books, the reader will find either very specialized works dealing with one or a few

specific topics of vibrational spectroscopy, or books that are more a compilation of data than a comprehensivetext. The more practically oriented books often emphasize correlations of observed spectra with molecularstructural features, and may contain large compilations of spectra and group frequencies, and only cursorytreatment of theoretical principles. These books are essential for researchers who wish to employ vibrationalspectroscopy as a qualitative structural tool.However, neither of these could be used as a text book in a course, nor could they be used by a researcher

who wants to gain insight into modern aspects of vibrational spectroscopy. Thus, the author was faced with thechallenging task of writing a text that incorporates some theoretical background material which is necessaryfor the understanding of the principles of vibrational spectroscopy, in addition to computational methods,instrumental aspects, novel developments in vibrational spectroscopy, and a number of relatively detailedexamples for the interpretations of vibrational spectra. Since the scope of this book is much broader than anyof the aforementioned specialized texts, some of the theoretical material needed to be adjusted accordingly.Thus, the quantum mechanics of molecular vibrations, time-dependent perturbations, transition moments,and many other topics are only summarized in this text, and detailed derivations are omitted. For details,the reader is referred to specialized books, such as any one of the many available text books on QuantumChemistry (see, for example, Levine,Quantum Chemistry, Volumes (I) and (II) [3]). For a detailed theoreticalbackground on symmetry aspects, the classical book (Cotton, Chemical Applications of Group Theory [4]) isrecommended, and the aforementioned books on vibrational spectroscopy for a more thorough treatment oftheoretical aspects of molecular vibrations.

xx Preface to Introduction to Modern Vibrational Spectroscopy (1994)

Thus, the present book does not supersede any of the classical texts, but is a further extension of them, andintends to bring the reader to a more practical and up-to-date level of understanding in the field of vibrationalspectroscopy. Subjects such as Raman spectroscopy, which has become a major area of research in vibrationalspectroscopy, is not treated as an afterthought, but experimental and theoretical aspects are discussed in detail.Items of historical significance, such as the Toronto arc for excitation of Raman spectra (which was actuallymentioned as a viable source for Raman spectroscopy in a recent text), or themanual solution of the vibrationalsecular equation, have been banished from this book. Instead, modern experimental aspects, such as multi-channel Raman instrumentation, time-resolved and resonance Raman techniques, nonlinear Raman effects,and Fourier transform infrared and Raman techniques are introduced. In addition, computational methods forthe calculation of normal modes of vibration are treated in detail in this book.One chapter is devoted to the biological applications of vibrational spectroscopy. This is a rapidly developing

field, and perhaps the most fascinating, for the molecules are often very large and difficult to study due tolow solubility and solvent interference. It is in this area that the enormous progress of modern vibrationalspectroscopy can best be gauged, since this field is not even discussed in the books of 30 or 40 years ago.The final chapter is devoted to a new branch of vibrational spectroscopy carried out with circularly polarizedlight. The new techniques introduced here combine principles of vibrational spectroscopywith those of opticalactivity measurements of chiral molecules. Applications of these techniques to biological molecules, and tosimple chiral systems, are presented.The author would like to thank his colleague, Prof. John Lombardi from the Department of Chemistry,

City University of New York, City College, for his encouragement about this book, and for correcting a largenumber of errors in the original manuscript. The Graduate Spectroscopy class (U761) at the City University ofNew York in Spring, 1992, also was instrumental in pointing out inconsistencies in the manuscript, when anearly version was used for the first time. The author is grateful for the input he received from these students.

New York, January 1993

References

1. Herzberg, G. (1945)Molecular Spectra and Molecular Structure, Van Nostrand Reinhold Company, New York.2. Wilson, E.B., Decius, J.C. and Cross, P.C. (1955)Molecular Vibrations, McGraw-Hill.3. Levine, I. (1970) Quantum Chemistry, vol. 1 and 2, Allyn & Bacon, Boston.4. Cotton, F.A. (1990) Chemical Applications of Group Theory, 3rd edn, John Wiley & Sons, Inc., New York.

Part IModern Vibrational Spectroscopy and

Micro-spectroscopy: Theory,Instrumentation and Biomedical

Applications

Introduction

I.1 Historical Perspective of Vibrational Spectroscopy

The subject of this monograph, vibrational spectroscopy, derives its name from the fact that atoms inmolecules undergo continuous vibrational motion about their equilibrium position, and that these vibrationalmotions can be probed via one of two major techniques: infrared (IR) absorption spectroscopy and Ramanscattering, and several variants of these two major categories. IR spectroscopy experienced a boon in theyears of World War II, when the US military was involved in an effort to produce and characterize syntheticrubber. Vibrational spectroscopy, for which industrial application guides were published as early as 1944 [1],turned out to be a fast and accurate way to identify different synthetic products. The rapid growth of the fieldof vibrational spectroscopy can be gauged by the fact that by the mid-1940s, the field was firmly establishedas a scientific endeavor, and the volume “Molecular Spectra and Molecular Structure” by Herzberg (onevolume of a trilogy of incredibly advanced treatises on molecular spectroscopy [2]) reported infrared andRaman results on hundreds of small molecules. Similarly, the earliest efforts to use infrared spectroscopy as ameans to distinguish normal and diseased tissue – the subject of Part II of this book –were reported by Bloutand Mellors [3] and by Woernley [4] by the late 1940s and early 1950s. In the 1960s, the petroleum industryadded another industrial use for these spectroscopic techniques when it was realized that hydrocarbons ofdifferent chain lengths and degrees of saturation produced distinct infrared spectral patterns, and for the firsttime, computational methods to understand, reproduce, and predict spectral patterns were introduced [5]. Bythen, commercial scanning infrared spectrometers were commercially available.The 1970 produced another boon when commercial Fourier transform (FT) infrared spectrometers became

commercially available, and gas lasers replaced the mercury arc lamp as excitation source for Ramanspectroscopy. Before lasers, Raman spectroscopy was a somewhat esoteric technique, since large samplevolumes and a lot of time were required to collect Raman data with the prevailing Hg arc excitation sources.Yet, after the introduction of laser sources, Raman spectra could be acquired rapidly and as easily as infraredspectra. After the introduction and wide acceptance of interferometry, infrared spectroscopy became the

2 Modern Vibrational Spectroscopy and Micro-Spectroscopy

method of choice for many routine and quality control applications. During the ensuing decade, the field ofvibrational spectroscopy blossomed at a phenomenal rate, and it is safe to state that no other spectroscopygrew at such a pace than vibrational spectroscopy, perhaps with the exception of nuclear magnetic resonancetechniques. Other spectroscopic methods, such as ultraviolet/visible (UV/vis), microwave, or electronparamagnetic resonance (EPR) spectroscopy certainly profited from theoretical and technical advances;however, in vibrational spectroscopy, the sensitivity of the measurements increased by orders of magnitudewhile the time requirements for data acquisition dropped similarly.After the introduction of tunable, high power, and pulsed lasers, not only were faster and more sensitive

techniques developed (for example, resonance Raman and time-resolved techniques), but also, entirely newspectroscopic methods were discovered, among them a number of “non-linear” Raman techniques (such asHyper-Raman and Coherent Anti-Stokes Raman Scattering, CARS) in which the effect depends non-linearlyon the laser field strength. Dramatic progress was also achieved in IR spectroscopy, due to the advent ofinfrared lasers and further refinements of interferometric methods.Aside from small molecule applications of vibrational spectroscopy, the past three decades have seen an

ever increasing use of vibrational spectroscopy in biophysical, biochemical, and biomedical studies. Thisfield has enormously enhanced the ability to determine solution conformations of biological molecules, theirinteraction and even reaction pathways. All major classes of biological molecules, proteins, nucleic acids, andlipids, exhibit vibrational spectra that are enormously sensitive to structure and structural changes, and thou-sands of research papers have been published demonstrating the value of these methods for the understandingof biochemical processes.With the advent of vibrational micro-spectroscopic instruments, that is, infrared or Raman spectrometers

coupled to optical microscopes, cell biological and medical application of vibrational spectroscopy was prac-tical since the spatial resolution in Raman and infrared absorption microscopy is sufficient to distinguish, byspectral features, parts of cells and tissue. These methods are poised to enter the medical diagnostic field asinherently reproducible and objective tools. This monograph will provide an introduction to many of thesefields mentioned above.

I.2 Vibrational Spectroscopy within Molecular Spectroscopy

Molecular spectroscopy is a branch of science in which the interactions of electromagnetic radiation andmatter are studied. While the theory of these interactions itself is the subject of ongoing research, the aimand goal of the discussions here is the elucidation of information on molecular structure and dynamics, theenvironment of the sample molecules and their state of association, interactions with solvent, and manyother topics.Molecular (or atomic) spectroscopy is usually classified by the wavelength ranges (or energies) of the elec-

tromagnetic radiation (e.g., microwave or infrared spectroscopies) interacting with the molecular systems.These spectral ranges are summarized in Table I.1.In Table I.1, NMR and EPR stand for nuclear magnetic and electron paramagnetic resonance spectroscopy,

respectively. In both these spectroscopic techniques, the transition energy of a proton or electron spin dependson the applied magnetic field strength. All techniques listed in Table I.1 can be described by absorptionprocesses (see below) although other descriptions, such as bulk magnetization in NMR, are possible as well.The interaction of the radiation with molecules or atoms that was referred to above as an “absorption

process” requires that the energy difference between two (molecular or atomic) “stationary states” exactlymatches the energy of the photon:

ΔEmolecule = (h𝜈)photon

Theory, Instrumentation and Biomedical Applications 3

Table I.1 Table of photon energies and spectroscopic ranges

𝜈photon 𝜆photon Ephoton (J) Ephoton (kJ mol−1) Ephoton (cm−1) Transition

Radio 750 MHz 0.4 m 5×10−25 3×10−4 0.025 NMRMicrowave 3 GHz 10 cm 2×10−24 0.001 0.1 EPRMicrowave 30 GHz 1 cm 2×10−23 0.012 1 RotationalInfrared 3× 1013 Hz 10 μm 2×10−20 12 1 000 VibrationalUV-visible 1015 300 nm 6×10−19 360 30 000 ElectronicX-ray 1018 0.3 nm 6×10−16 3.6×105 3× 107 X-ray absorption

where h denotes Planck’s constant (h= 6.6× 10−34Js) and 𝜈 the frequency of the photon, in s−1. As seen fromTable I.1, these photon energies are between 10−16 and 10−25 J/molecule or about 10−4 to 105 kJ/(mol pho-tons). In an absorption process, one photon interacts with one atom or molecule to promote it into a state ofhigher excitation, and the photon is annihilated. The reverse process also occurs where an atomic or molecularsystem undergoes a transition from a more highly excited to a less highly excited state; in this process, aphoton is created. However, this view of the interaction between light and matter is somewhat restrictive,since radiation interacts with matter even if its wavelength is far different than the specific wavelength atwhich a transition occurs. Thus, a classification of spectroscopy, which is more general than that given bythe wavelength range alone, would be a resonance/off-resonance distinction. Many of the effects describedand discussed in spectroscopy books are observed as resonance interactions where the incident light, indeed,possesses the exact energy of the molecular transition in question. IR and UV/vis absorption spectroscopy,microwave spectroscopy, or EPR are examples of such resonance interactions. However, interaction of lightand matter occurs, in a more subtle way, even if the wavelength of light is different from that of a molec-ular transition. These off-resonance interactions between electromagnetic radiation and matter give rise towell-known phenomena such as the refractive index of dielectric materials, and the anomalous dispersion ofthe refractive index with wavelength. The normal (non-resonant) Raman effect also is a phenomenon that isbest described in terms of off-resonance models. A discussion of non-resonance effects ties together manywell-known aspects of classical optics and spectroscopy.This interplay between classical optics and spectroscopy will be emphasized throughout the book, and the

study of vibrational or other fields of spectroscopy exposes students to a more unified picture of physicalphenomena than individual courses in chemistry or physics provide. As such, vibrational spectroscopy hasenormous pedagogical values, because it provides the link between different scientific fields: data can be col-lected easily by students in the laboratory, often on compounds synthesized or prepared by them. The spectralresults are tangible, qualitatively interpretable and can be used to identify compounds. A deeper exposure tothe material can be used to explain eigenvector/eigenvalue problems and demonstrate quantum mechanicalprinciples such as allowed and forbidden transitions, breakdown of first order approximations andmanymore.Symmetry and group theory can be introduced logically when discussing vibrational spectroscopy, since thesymmetry of atomic displacements during a normal mode of vibrations can be visualized easily and providean intuitive approach for teaching the concepts of symmetry. Furthermore, vibrational spectroscopy is a use-ful probe for the structure of small molecules, because vibrational spectra can be predicted from symmetryconsiderations (group theory) and group frequencies. In fact, microwave (rotational) and vibrational spec-troscopies were instrumental in determining the structure and symmetries of many small molecules. Rulesfor predicting the structures and shapes of small molecules, such as the VSEPR (Valence Shell Electron PairRepulsion) model taught routinely in introductory chemistry classes are partially based on vibrational spec-troscopic results of the 1950s and 1960s. This aspect of the importance of vibrational spectroscopy becomes

4 Modern Vibrational Spectroscopy and Micro-Spectroscopy

apparent when one reads the chapter on “Individual Molecules” in Molecular Spectra and Molecular Struc-ture [2] because in the 1940s, many structures were not known for certain. In fact, for many molecules thatare now known to exhibit tetrahedral shapes, alternative structures were offered then, and the implications ofother structures on the observed vibrational spectra were discussed.Thus, vibrational spectroscopy cannot be regarded as a static field which has outlived its usefulness. Quite

contrary, it is a very dynamic and innovative field, and there is no reason to believe that the progress inthis field is slowing down. Thus, this book emphasizes many of these new developments. As mentioned inthe foreword, this volume is not intended to replace the previous books on vibrational spectroscopy, but tocombine in one volume the necessary background to understand vibrational spectroscopy, and to introducethe reader to the many new and fascinating techniques and results.

References

1. Barnes, R.B., Gore, R.C., Liddel, U., et al. (1944) Infrared Spectroscopy. Industrial Applications and Biography,Reinhold Publishing Co, New York.

2. Herzberg, G. (1945)Molecular Spectra and Molecular Structure, Van Nostrand Reinhold Co, New York.3. Blout, E.R. and Mellors, R.C. (1949) Infrared spectra of tissues. Science, 110, 137–138.4. Woernley, D.L. (1952) Infrared absorption curves for normal and neoplastic tissues and related biological substances.

Cancer Res., 12, 516–523.5. Schachtschneider, J.H. (1965) Vibrational Analysis of Polyatomic Molecules: FORTRAN IV Programs for solving

the vibrational secular equation and least-square refinement of force constants, The Shell Development Company,Emeryville, USA.

1Molecular Vibrational Motion

The atoms in matter – be it in gaseous, liquid, or condensed phases – are in constant motion. The amplitudeof this motion increases with increasing temperature; however, even at absolute zero temperature, it neverapproaches zero or perfect stillness. Furthermore, the amplitude of the atomic motion is a measure of thethermodynamic heat content as measured by the product of the specific heat times the absolute temperature.If one could observe the motion in real time – which is not possible because the motions occur at a timescaleof about 1013 Hz – one would find that it is completely random and that the atoms are most likely to be foundin ellipsoidal regions in space, such as the ones depicted in X-ray crystallographic structures. Yet, the randommotion can be decomposed into distinct “normal modes of vibration.” These normal modes can be derivedfrom classical physical principles (see Section 1.2) and are defined as follows: in a normal mode, all atomsvibrate, or oscillate, at the same frequency and phase, but with different amplitudes, to produce motions thatare referred as symmetric and antisymmetric stretching, deformation, twisting modes, and so on. In general,a molecule with N atoms will have 3N− 6 normal modes of vibrational normal modes.At this point, a discrepancy arises between the classical (Newtonian) description of the motion of atoms

in a molecule and the quantum mechanical description. While in the classical description the amplitude ofthe motion, and thereby the kinetic energy of the moving atoms, can increase in arbitrarily small increments,the quantum mechanical description predicts that the increase in energy is quantized, and that infrared (IR)photons can be absorbed by a vibrating molecular system to increase the energy along one of the normalmodes of vibration.In the discussion to follow, the concepts of normal modes of vibration will be introduced for a system of

spring-coupled masses, as shown in Figure 1.1, a typical mechanical model for a molecular system. Througha series of mathematical steps, the principle of normal modes will be derived from Newtonian laws of motion.Once this set of “normal modes” is defined, it is relatively trivial to extend these coordinates to a quantummechanical description that results in the basic formalism for stationary vibrational states in molecules, andthe transitions between these stationary states that are observed in IR and Raman spectroscopies.Sections 1.1–1.7 are aimed at presenting a summary of the physical principles required for understanding the

principles of vibrational spectroscopy. They do not present the subject with the mathematical rigor presentedin earlier treatments, for example, in Wilson et al. [1] for the classical description of normal modes nor thequantum mechanical detail found in typical texts such as those by Kauzman [2] or Levine [3]. However,sufficient detail is provided to expose the reader to the necessary physical principles such as normal modes

Modern Vibrational Spectroscopy and Micro-Spectroscopy: Theory, Instrumentation and Biomedical Applications, First Edition.Max Diem.© 2015 John Wiley & Sons, Ltd. Published 2015 by John Wiley & Sons, Ltd.

6 Modern Vibrational Spectroscopy and Micro-Spectroscopy

1

2 3

x

x x

y

y y

z

z z

Figure 1.1 “Mass-and-spring” model of Cartesian displacement vectors for a triatomic molecule. The gray cylin-ders represent springs obeying Hook’s law

of vibration and normal coordinates, the basic quantum mechanics of vibrating systems, and the transitionmoment, but in addition to the aforementioned texts, it will introduce the reader to many practical aspects ofvibrational spectroscopy, as well as branches of vibrational spectroscopy that were not included in the earliertreatments.For the remainder of this book, a standard convention for expressing vibrational energies in wavenumber

units will be followed. Although energies should be expressed in units of Joule (1 J= kgm2 s−2), these num-bers are unyielding, and wavenumber units are used throughout. The following energy unit conversions apply:

E = h𝜈 = hc𝜆

= h c��

Here, h has the value of 6.6× 10−34 J s. Using h𝜈 = hc��, one finds that 1 cm−1 ≈ 30GHz= 2× 10−23 J (seealso the table in the introduction and comments after Eqs. 1.31 and 1.63). Herewith, the author categoricallyapologizes for referring to transitions, expressed in wavenumber units, as “energies.”

1.1 The concept of normal modes of vibration

Consider a set of masses connected by springs that obey Hook’s law, as shown in Figure 1.1. Two of thesesprings act as restoring force when the “bonds” between atoms 1 and 2 and between atoms 1 and 3 are elon-gated or compressed, whereas one spring acts to restore the bond angle between atoms 2–1–3. Furthermore,we assume that the force required to move one atom along a coordinate depends on the momentary position ofall other atoms: the force required to extend bond 1–2 may decrease if bond 1–3 is elongated. In a mechanicalsystem, this situation is referred to as a coupled spring ensemble, where the stiffness of a spring depends onall coordinates. In a molecular system, this corresponds to electron rearrangement when the molecular shapechanges, with a concomitant change in bond strength. In order to describe the atomic motions in a vibratingsystem, one attaches a system of Cartesian displacement coordinates to every atom, as shown in Figure 1.1.A normal mode of vibration then can be described as a combination of properly scaled displacement vectorcomponents.

1.2 The separation of vibrational, translational, and rotational coordinates

Based on Figure 1.1, one may expect a system of N atoms to exhibit 3N degrees of vibrational freedom: adegree of freedom for all three Cartesian displacement coordinates of each atom, or any linear combinations

Molecular Vibrational Motion 7

of them. However, vibrational spectroscopy depends on a restoring force to bring the atoms of a molecule backto their equilibrium position. If, for example, all atoms in a molecule move simultaneously in the x-direction,by the same amount, no bonds are being compressed or elongated. Thus, this motion is not that of an internalvibrational coordinate but that of a translation. There are three translational degrees of freedom, correspondingto amotion of all atoms along the x, y, or z axes by the same amount. Another view of the same fact is that thesemodes have zero frequencies as there is no restoring force acting during the atomic displacements. This viewwill be favored in the derivation of the concepts of normal modes presented in Section 1.3, which is carried outin (mass-weighted) Cartesian displacement coordinates. Later on, a different and simpler coordinate systemwill be introduced as well.Similarly, one can argue that certain combinations of Cartesian displacements correspond to a rotation of the

entire molecule, where there is no change in the intermolecular potential of the atoms. There are three degreesof rotational freedom of a molecule, corresponding to rotations about the three axes of inertia. Subtractingthese from the remaining number of degrees of freedom, one arrives at 3N− 6 degrees of vibrational freedomfor a polyatomic, nonlinearmolecule. Linearmolecules have onemore (3N− 5) degree of vibrational freedom,because they have only two moments of inertia. This is because one assumes a zero moment of inertia for arotation about the longitudinal axis.Mathematically, the separation of rotation and translation from the vibration of a molecule proceeds as fol-

lows: in order for the translational energy of the molecule to be zero at all times, one defines a coordinatesystem that translates with the molecule. In this coordinate system, the translational energy is zero by defini-tion. The translating coordinate system is defined such that the center of mass of the molecule is at the originof the coordinate system at all times. This leads to the condition∑N

𝛼=1m𝛼

𝜉

𝛼

= 0 (1.1)

where 𝜉 denotes the X, Y, and Z coordinates of the 𝛼’th atom of a molecule with N atoms. Similarly, therotational energy can be reduced to zero by defining a coordinate system that rotates with the molecule. Thisrequires that the angular moments of the molecule in the rotating coordinate frame are zero, which leads tothree more equations of zero frequencies. These six equations are needed to define a coordinate system inwhich both translational and rotational energies are zero. Details of this derivation can be found in Wilsonet al. [1, Chapters 2 and 11].

1.3 Classical vibrations in mass-weighted Cartesian displacement coordinates

The concept of normal modes of vibration, necessary for understanding the quantum mechanical descriptionof vibrational spectroscopy and obtaining a pictorial description of the atomic motions, can be introduced bythe previously described classical model of a molecule consisting of a number of point masses, held in theirequilibrium positions by springs. This kind of discussion is treated in complete detail in the classic books onvibrational spectroscopy, for example, in Chapter 2 of Wilson et al. [1].The treatment starts with Lagrange’s equation of motion:

ddt𝜕T𝜕xi

+ 𝜕V𝜕xi

= 0 (1.2)

where T and V are the kinetic and potential energies, respectively, the xi are the Cartesian displacement coor-dinates, and the dot denotes the derivative with respect to time. Equation 1.2 is another statement of Newton’sequation of motion (Eq. 1.3) expressed in terms of the kinetic and potential energies, rather than terms offorce and acceleration:

Fi = mid2xidt2

(1.3)

8 Modern Vibrational Spectroscopy and Micro-Spectroscopy

In Eq. 1.3, F represents the force, which is related to the potential energy by

Fi = −dVdxi

= kxi (1.4)

Equation 1.4 is Hook’s law, which states that the force F needed to elongate or compress a spring dependson the spring’s stiffness, expressed by the force constant k, multiplied by the elongation of the spring, x. Theacceleration (d2xi/dt

2) in Eq. 1.3 can be related to the kinetic energy as follows:

T = 12

(∑imix

2i

)(1.5)

Thus,dTdxi

= mixi (1.6)

Substituting Eqs. 1.4 and 1.6 into Eq. 1.3 yields Lagrange’s equation of motion in which the expressions forkinetic and potential energies appear separately. This formulation is advantageous for writing the quantummechanical Hamiltonian, cf. the following section.Next, one rewrites Eq. 1.2 in terms of mass-weighted displacement coordinates, qi. The reason for this

is that the amplitude of a particle’s oscillation depends on its mass. When mass-weighted coordinates areused, all amplitudes are properly adjusted for the different masses of the particles. In addition, the use ofmass-weighted coordinates simplifies the formalism quite a bit. Let

qi =√mixi (1.7)

Then, the kinetic energy can be written as

2T =∑3N

i(qi)2 (1.8)

Note that Eq. 1.8 contains only “diagonal terms”; that is, no cross terms qij appear in the summation. (Theterm “diagonal” here refers to a matrix notation to be introduced shortly.) Next, the potential energy of theparticles needs to be defined. For masses connected by springs obeying Hook’s law, one may assume thatthe potential energy along each Cartesian displacement coordinate is given by

V = 12

∑3N

i=1

∑3N

j=1

(𝜕

2V𝜕qi𝜕qj

)dqidqj (1.9)

orV = 1

2

∑3N

i=1

∑3N

j=1fijdqidqj (1.10)

with

fij =(

𝜕

2V𝜕qi𝜕qj

)(1.11)

The fij are known as mass-weighted Cartesian force constants and differ from the force constant k defined inEq. 1.4 by the fact that latter does not explicitly contain the masses of the atoms. The constants fij express thechange in potential energy as an atom or group is moved along the directions given by qi and qj. For smalldisplacements about the equilibrium positions, Eq. 1.10 can be written as

2V =∑3N

i=1

∑3N

j=1fij qiqj (1.12)

In contrast to the kinetic energy expression in mass-weighted Cartesian coordinates (Eq. 1.8), the potentialenergy depends on diagonal (fiiqi

2) and off-diagonal (fijqiqj) terms as pointed out earlier. Taking the required