Transform Techniques in Chemistry

Transform Techniques in Chemistry

MODERN ANALYTICAL CHEMISTRY Series Editor: David Hercules University of Pittsburgh ANALYTICAL ATOMIC SPECTROSCOPY By William G. Schrenk PHOTOELECTRON AND AUGER SPECTROSCOPY By Thomas A. Carlson MODERN FLUORESCENCE SPECTROSCOPY, VOLUME 1 Edited by E. L. Wehry MODERN FLUORESCENCE SPECTROSCOPY, VOLUME 2 Edited by E. L. Wehry APPUED ATOMIC SPECTROSCOPY, VOLUME 1 Edited by E. L. Grove APPLIED ATOMIC SPECTROSCOPY, VOLUME 2 Edited by E. L. Grove TRANSFORM TECHNIQUES IN CHEMISTRY Edited by Peter R. Griffiths ION-SELECTIVE ELECTRODES IN ANALYTICAL CHEMISTRY Edited by Henry Freiser

Transform Techniques in Chemistry Edited by Peter R. Griffiths Ohio University, Athens Plenum Press New York and London

Main entry under title: Library of Congress Cataloging in Publication Data Transform techniques in chemistry. ~Mode rn analytical chemistry) Includes bibliographical references and index. 1. Fourier transform spectroscopy. I. Griffiths, Peter A., 1942- QD96.F68T7 543'.085 ISBN 978-1-4684-2405-8 ISBN 978-1-4684-2403-4 (e9ook) 001 10.1007/978-1-4684-2403-4 77-29271 1978 Plenum Press, New York Softcover reprint of the hardcover 1st edition 1978 A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y. 10011 AU rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, me<:hanical, photocopying, microfilming, re<:ording, or otherwise, without written permission from the Publisher

Contributors Michael B. Comisarow, Chemistry Department, University of British Columbia, Vancouver, B.C., Canada V6T lw5 James W. Cooper, Department of Chemistry, Tufts University, Medford, Massachusetts 02155 Thomas C. Farrar, Chemistry Division, National Science Foundation, Washington, D.C., 20550 Charles T. Foskett, Digilab, Inc., Cambridge, Massachusetts 02139 Peter R. Griffiths, Department of Chemistry, Ohio University, Athens, Ohio 45701 Martin Harwit, Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853 Peter C. Jurs, Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802 Russell D. Larsen, Department of Chemistry, University of Nevada Reno, Reno, Nevada 89507. Present address: Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 John O. Lephardt, Phillip Morris U.S.A., Research Center, P. O. Box 26583, Richmond, Virginia 23261 Alan G. Marshall, Chemistry Department, University of British Columbia, Vancouver, B.C., Canada V6T 1 W5 Charles L. Wilkins, Department of Chemistry, University of Nebraska, Lincoln, Nebraska 68501 v

Preface The application of the Fourier transform is being seen to an increasing extent in all branches of chemistry, but it is in the area of chemical analysis that the greatest activity is taking place. Fourier transform infrared and nuclear magnetic resonance spectrometry are already routine methods for obtaining high-sensitivity IR and NMR spectra. Analogous methods are now being developed for mass spectrometry (Fourier transform ion cyclotron resonance spectrometry) and microwave spectroscopy, and Fourier transform techniques have been successfully applied in several areas of electrochemistry. In addition the fast Fourier transform algorithm has been used for smoothing, interpolation, and more efficient storage of data, and has been studied as a potential method for more efficient identification of samples using pattern recognition techniques. Linear transforms have also been shown to be useful in analytical chemistry. Probably the most important of these is the Hadamard transform, which has been applied in alternative methods for obtaining IR and NMR data at high sensitivity. Even though measurements involving this algorithm will probably not be applied as universally as their Fourier transform analogs, in the area of pattern recognition application of the Hadamard transform will in all probability prove more important than application of the Fourier transform. In this book, distinguished investigators in the various fields mentioned above have written on their area of expertise at a level that should be understandable to graduate analytical chemists and to the advanced undergraduate, as well as the professional maintaining and updating research skills. It is hoped that the similarities between the various spectroscopic and data manipulation techniques will become evident throughout the book. We have omitted treatment of crystallographic applications because they seem outside the mainstream of analytical interests. After a brieflook at the history of transform techniques in chemistry and an editorial forecast of their applications in the future (Chapter 1), the mathevii

viii Preface matical basis of the Fourier transform is introduced by Charles Foskett of Digilab, Inc., in Chapter 2. In Chapter 3, Alan Marshall and Melvin Comisarow of the University of British Columbia discuss the foundation of multiplex methods in spectroscopy, showing the origin of the advantages of instruments that do not measure a spectrum directly, but rather generate a signal that is related to the spectrum through the Fourier or Hadamard transform. In Chapter 4, James Cooper of Tufts University discusses the nature of the data-handling and computer capabilities required for on-line Fourier transform spectrometry. The next six chapters describe the theory, instrumentation, and applications of several different types of multiplex spectroscopy. In Chapters 5 and 6 the editor describes Fourier transform infrared spectrometry, and in Chapter 7 Martin Harwit of Cornell University describes Hadamard transform infrared spectrometry, including how this technique may be used to multiplex information both spectrally and spatially. In Chapter 8, Thomas Farrar of the National Science Foundation introduces Fourier transform-nmr spectrometry, and some of the more recent advances in this subject are described in the subsequent chapter (Chapter 9) by James Cooper. In Chapter 10, the nature of Fourier transform ion cyclotron resonance spectrometry is introduced by Melvin Comisarow. Several of the more important applications of the Fourier transform in data processing are discussed in Chapter 11 by John Lephardt of Philip Morris U.S.A., and in Chapter 12, the application of transform techniques in pattern recognition is described by Charles Wilkins of the University of Nebraska and Peter Jurs of Pennsylvania State University. Chapter 13, by Russell Larsen of the University of Nevada at Reno, describes potential applications of binary transforms for very rapid data processing; to a greater extent than the previous chapters, this represents a look into the future and is written to a slightly more advanced audience than the earlier chapters. We believe it represents an important new transform technique of the future and merits a more advanced treatment since there is little readily available reference material on this subject. Finally, the editor has summarized the applications of the Fourier transform in electrochemistry in a chapter that illustrates not only the sensitivity advantage obtained through acquiring data at several frequencies simultaneously but also shows how the information content of different types of electrochemical data may be enhanced by the application of the Fourier transform independently of the manner in which the data were acquired. That a volume such as this may be compiled is a tribute to the many pioneers in all the areas covered in this book. The fact that so many of the techniques that are described here are now available in the market place is similarly a tribute to the individuals and companies who had faith that transform techniques were of sufficient value to be developed commercially. On a more personal level, the editor and many of the authors would like

Preface ix to thank the various agencies that, in such timely fashion, supported their research and the many co-workers without whose cooperation and hard work many of the results described in this book would not have been found. Finally, the secretarial assistance so valuable in preparing the manuscripts of these chapters is gratefully acknowledged. Peter R. Griffiths

Contents Chapter 1 Transform Techniques in Chemistry: Past, Present, and Future Peter R. Griffiths 1.1. The Past................................................ 1 1.1.1. Optical Spectroscopy................................ 1 1.1.2. NMR Spectroscopy................................. 4 1.1.3. Data Processing.................................... 4 1.2.. The Present.............................................. 5 1.3. The Future.............................................. 6 References... 8 Chapter 2 The Fourier Transform and Related Concepts : A First Look Charles T. Foskett 2.1. Introduction: Guitar Tuning... 11 2.2. Differences in Space and Time: Phase... 14 2.3. Sums, Integrals, and Orthogonality............................ 15 2.4. Various Expressions of Fourier Transform Relationships........... 17 2.5. Concepts and Corollaries for Fourier Transforms... 19 2.6. More on Phase and Phase Correction.......................... 26 2.7. Apodization and Resolution Enhancement...................... 30 2.8. The Discrete Fourier Transform.............................. 33 2.9. Walsh and Hadamard Transforms....................... 35 2.1 O. Summary... 36 References... 37 xi

xii Contents Chapter 3 Multichannel Methods in Spectroscopy Alan G. Marshall and Melvin B. Comisarow 3.1. Introduction... 39 3.2. Spectrometer Sources and Detectors........................... 40 3.2.1. Terminology... 40 3.2.2. Single-Channel (Scanning-Type) Spectrometer............. 40 3.2.3. Multidetector Spectrometer... 41 3.3. Weights on a Balance: The Multichannel Advantage. Multiplex Methods................................................ 45 3.3.1. One-at-a-Time Weighing: The Scanning Spectrometer....... 45 3.3.2. Many Balances: The Multidetector Spectrometer........... 46 3.3.3. Half the Weights on the Balance at Once: Hadamard Multiplexing....................................... 47 3.3.4. All the Weights on the Balance at Once: The Fourier Advan tage... 48 3.4. Hadamard Multiplexing of Spatially Dispersed Spectra............ 49 3.5. Advantages of Coherent Radiation in Spectrometer Detection....... 53 3.6. Fourier Methods.......................................... 55 3.6.1. Fourier Multiplexing: The Multichannel Advantage... 55 3.6.2. Fourier Analysis of Detector Response: Spectral Line Shape.. 58 3.6.3. Pulsed Monochromatic Coherent Radiation as a Broad-Band Radiation Source................................... 60 3.7. Summary: Relations Between Different Spectrometers............. 61 3.8. Appendix. Noise Considerations for Multichannel Spectrometers... 63 3.8.1. NB oc (signal)l/2: "Source-Limited" Noise................ 65 3.8.2. NA = constant: "Detector-Limited" Noise... 65 3.8.3. NC oc signal: "Fluctuation" Noise...................... 65 References and Notes...................................... 66 Chapter 4 Data Handling in Fourier Transform Spectroscopy James W. Cooper 4.1. The Computer System... 69 4.1.1. Introduction to Computers... 69 4.1.2. Data Acquisition... 71 4.1.3. Timing in Data Acquisition........................... 71 4.1.4. The Sampling Theorem............................... 72 4.1.5. Digital Phase Correction.............................. 75 4.1.6. Signal Averaging.................................... 76 4.1.7. Signals Having High Dynamic Range.................... 79 4.1.8. Other Computer Requirements......................... 81 4.1.9. Disk-Based Data Acquisition.......................... 82 4.1.10. Comparison of Data System Requirements in NMR and IR.. 83 4.2. The Fourier Transform..................................... 84

Contents xiii 4.2.1. Introduction... 84 4.2.2. The Cooley-Tukey Algorithm... 84 4.2.3. The Signal Flow Graph... 86 4.2.4. In-Place Transforms................................. 88 4.3. Writing a Fourier Transform for a Minicomputer... 88 4.3.1. Introduction... 88 4.3.2. The Form of W..................................... 89 4.3.3. The Fundamental Operations.......................... 90 4.3.4. The Sine Look-Up Table... 90 4.3.5. Binary Fractions.................................... 91 4.3.6. The Sine Look-Up Routine............................ 92 4.3.7. Scaling during the Transform.......................... 94 4.3.8. Forward and Inverse Transforms....................... 95 4.3.9. Forward Transforms of Real Data...................... 95 4.3.10. Inverse Real Transforms.............................. 97 4.3.11. Baseline Correction.................................. 97 4.3.12. A Fourier Transform Routine... 99 4.3.13. Correlation........................................ 99 4.3.14. Disk-Based Fourier Transforms........................ 103 4.3.15. Hardware Fourier Processors.......................... 103 4.4. Noise in the Fourier Transform Process........................ 104 4.4.1. Round-Off Errors................................... 104 4.4.2. Block Averaging.................................... 106 4.4.3. Double-Precision Fourier Transforms... 106 4.5. Summary... 107 References... 108 Chapter 5 Fourier Transform Infrared Spectrometry: Theory and Instrumentation Peter R. Griffiths 5.1. Introduction... 109 5.2. The Michelson Interferometer... 109 5.3. Resolution and Apodization................................. 112 5.4. Effect of Beam Divergence.................................. 115 5.5. Mirror Drive Tolerance... 116 5.6. Dynamic Range...... 117 5.7. Scan Speed and Spectral Modulation.......................... 121 5.8. Data Acquisition.......................................... 123 5.9. Beamsplitters... 125 5.1 O. Lamellar Grating Interferometers............................. 128 5.11. Detectors for FT-IR....................................... 129 5.11.1. Far-Infrared Detectors.............................. 130 5.11.2. Mid- and Near-Infrared Detectors... 131 5.11.3. Ultraviolet-Visible Spectroscopy... 132 5.12. Auxiliary Optics... 133

xiv Contents 5.12.1. Source Optics................................ 133 5.12.2. Absorption Spectroscopy... 133 5.12.3. Reflection Spectroscopy............................ 134 5.13. Data Systems............................................ 135 5.13.1. Far-Infrared Spectroscopy........................... 135 5.13.2. Mid-Infrared Spectroscopy... ".... 136 5.13.3. Ultra-High-Resolution Spectroscopy................... 136 5.14. Dual-Beam Fourier Transform Spectroscopy.................... 137 References... 138 Chapter 6 Infrared Fourier Transform Spectrometry: Applications to Analytical Chemistry Peter R. Griffiths 6.1. FT -IR versus Grating Spectrophotometers... 141 6.1.1. Fellgett's Advantage................................. 141 6.1.2. Jacquinot's Advantage............................... 142 6.1.3. Effect of Detector Performance... 143 6.1.4. Other Differences... 144 6.1.5. Implications... 145 6.2. Spectra of Transient Species................................. 146 6.2.1.' GC-IR........................................... 147 6.2.2. LC-IR... 147 6.2.3. Reaction Kinetics................................... 149 6.3. Low-Energy Absorption Spectrometry... " 153 6.3.1. Far-Infrared Spectrometry............................ 153 6.3.2. Mid-Infrared Absorption Spectrometry... 154 6.4. Difference Spectroscopy.................................... 161 6.5. Reflection Spectrometry... " 163 6.6. Emission Spectrometry..................................... 166 6.7. Atomic Spectrometry... " 169 References... 171 Chapter 7 Hadamard Transform Analytical Systems Martin Harwit 7.1. Introduction... 173 7.2. Weighing Designs and Optical Multiplexing..................... 175 7.3. Historical Background of Multiplexing by Means of Masks... " 177 7.4. Mathematical Development................................. 179 7.5. Varieties of Encoded Spectrometers........................... 182 7.6. Limitations: HTS Instruments and Interferometers... 187 7.7. Imagers and Spectrometric Imagers... 189

Contents xv 7.8. Signal and Noise Limitations... 193 7.9. Special Optical Systems... 194 7.10. Some Future Applications... 195 References... 196 Chapter 8 Pulsed and Fourier Transform N M R Spectroscopy Thomas C. Farrar 8.1. Introduction... 199 8.2. Basic Concepts of FT-NMR... 200 8.3. Basic Instrumentation...................................... 207 8.3.1. The Spectrometer................................... 207 8.3.2. The Sample Probe................................... 212 8.4. Recent Instrumental Improvements........................... 213 8.4.1. Coherent Broad-Band Decoupling...................... 213 8.4.2. Gated Decoupling Methods and Quantitative Measurements.. 214 8.4.3. Microsample Techniques... 218 8.4.4. Selective Population Transfer.......................... 222 8.4.5. Studies of Chemical Dynamics......................... 222 8.4.6. High-Resolution 13C NMR in Solid Materials..., 223 8.4.7. FT-NMR at High Fields............................. 223 References... 225 Chapter 9 Advanced Techniques in Fourier Transform NMR James W. Cooper 9.1. Introduction... 227 9.2. Systematic Noise Reduction................................. 228 9.2.1. Noise Reduction Methods... 228 9.2.2. Relaxation Times and Spin Echoes...................... 230 9.3. Sideband Filters and Quadrature Detection NMR................ 231 9.3.1. The Crystal Sideband Filter... 231 9.3.2. Quadrature Detection Spectroscopy... " 231 9.3.3. Operational Details in Quadrature NMR................. 235 9.3.4. Comparison between Crystal Sideband Filter and Quadrature Detection................................ 236 9.4. Rapid-Scan (Correlation) NMR.............................. 237 9.4.1. General Description................................. 237 9.4.2. Data Processing Methods... " 238 9.5. Noise Excitation Methods... 241 9.5.1. Stochastic Resonance Spectroscopy..................... 241 9.5.2. Hadamard Transform NMR... 242 9.5.3. Tailored Excitation.................................. 242

xvi Contents 9.6. Measure of the Spin-Lattice Relaxation Time T j 243 9.6.1. General Description................................. 243 9.6.2. Reasons for Measuring T j 244 9.6.3. Methods of Measuring T j 245 9.6.4. Progressive Saturation... 248 9.6.5. Homospoil-Tj Methods.............................. 249 9.6.6. Experimental Techniques in the Measurement of T j 250 9.7. Techniques for the Suppression of Strong Solvent Peaks... 252 9.7.1. Introduction... 252 9.7.2. Block Averaging.................................... 254 References... 255 Chapter 10 Fourier Transform Ion Cyclotron Resonance Spectroscopy Melvin B. Comisarow 10.1. 10.2. 10.3. 10.4. 10.5. 10.6. Introduction.... Fundamental Equations for ICR Linewidth and Resolution.... Fourier Transform Ion Cyclotron Resonance (FT-ICR) Spectroscopy.... Analytical FT-ICR Linewidth and Mass Resolution.... FT-ICR Mass Range, Computer Data Size, and Sampling Rate.... Discussion.... References.... 257 261 262 264 268 274 284 Chapter 11 Fourier Domain Processing of General Data Arrays John O. Lephardt 11.1. 11.2. 1l.3. 11.4. 11.5. Introduction.... Fourier Transformation and a General Data Array.... Amplitude and Phase Arrays.... Transformation as a Reversible Operation.... Specific Manipulations of Data in the Fourier Domain.... 11.5.1. Fourier Domain Manipulations without Using Weighting Functions.... 11.5.1.1. Zero Filling.... 11.5.1.2. Contrast Enhancement.... 11.5.2. Fourier Domain Manipulations Using Weighting Functions. 11.5.2.1. Smoothing.... 11.5.2.2. Elimination of Low-Frequency Interferences.... 11.5.2.3. Differentiation and Integration.... 11.5.2.4. Resolution Enhancement and Functional 285 286 287 289 289 290 290 292 294 294 297 299 Isolation................................ 30 I

Contents xvii 11.6. Summary... 305 References.............................................. 305 Chapter 12 Fourier and Hadamard Transforms in Pattern Recognition Charles L. Wilkins and Peter C. Jurs 12.1. Introduction... 307 12.1.1. Basic Pattern Recognition System..................... 309 12.1.2. Preprocessor-Feature Extractor...................... 310 12.1.3. Classifier... 310 12.2. Binary Pattern Classifiers.................................. 312 12.2.1. Pattern Vectors................................... 312 12.2.2. Similarity and Clustering........................... 313 12.2.3. K-Nearest-Neighbor Classification.................... 314 12.2.4. Decision Surfaces...... 315 12.2.5. TLUs as Binary Pattern Classifiers..., 316 12.2.5.1. Training of TLUs Using Error Correction Feedback....................... 317 12.2.5.2. Properties oftlus........................ 319 12.2.6. Preprocessing and Transformations... 320 12.3. Fourier and Hadamard Transforms in Pattern Recognition..., 321 12.3.1. Feature Reduction..., 322 12.3.2. Pattern Recognition Analysis of NMR Data... " 324 12.3.2.1. Simulated Free-Induction Decay Analysis..... 325 12.3.2.2. Hadamard-Transformed Data Analysis........ 328 12.3.2.3. Autocorrelation Transforms................. 330 12.4. Conclusions... 331 References.............................................. 331 Chapter 13 Spectral Representations for Quantized Chemical Signals Russell D. Larsen 13.1. 13.2. 13.3. 13.4. 13.5. 13.6. 13.7. Introduction.... 13C FID Signals and Their Spectra.... Orthogonal Expansions and Spectral Representations.... Clipped Signals and Their Spectral Representations.... Random Real-Zero Signals.... Zero-Based Product Representations for Band-Limited Signals.... Spectra of Clipped FID Signals.... 333 334 335 342 344 344 347

xviii Cqntents 13.8. Summary, Implications, and Open Questions................... 348 Notation............................................... 350 Appendix. Intermodu1ation Distortion in the CFID.............. 351 References................................................ 352 Chapter 14 Applications of the FFT in Electrochemistry Peter R. Griffiths 14.1. 14.2. 14.3. 14.4. 14.5. 14.6. Introduction Faradaic Admittance Measurements-Basic Principles.... Instrumentation.... Kinetics of Electrode Processes.... Relevant Properties of the FFT for Electrochemical Relaxation Measurements.... Published and Future Applications of the FFT in Electrochemistry.... References.... 355 356 359 366 370 373 378 Index.... "....................................... 379