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Raman Spectroscopy: Theory and Practice PDF

225 Pages·1970·16.73 MB·English
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Volume 2 RAMAN SPECTROSCOPY Theory and Practice Volume 2 RAMAN SPECTROSCOPY Theory and Practice Edited by Herman A. Szymanski Dean of the College Alliance College Cambridge Springs, Pennsylvania ~ PLENUM PRESS· NEW YORK-LONDON· 1970 Library of Congress Catalog Card Number 64-23241 ISBN-13: 978-1-4684-3029-5 e-ISBN-13: 978-1-4684-3027-1 001: 10.1007/978-1-4684-3027-1 © 1970 Plenum Press, New York Softcover reprint of the hardcover 1s t edition 1970 A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y. 10011 United Kingdom edition published by Plenum Press, London A Division of Plenum Publishing Company, Ltd. Donington House, 30 Norfolk Street, London W.C.2, England All rights reserved No part of this publication may be reproduced in any form without written permission from the publisher Preface Raman Spectroscopy, Volume 1, was conceived to provide integrated and comprehensive coverage of all aspects of the field by a group of specialists. However, in the three years since the first volume was published much important work has been done. Since Volume 1 was very well received, this second volume has been prepared in the belief that an extension of the coverage it offers will satisfy a real need in this rapidly changing and extremely interesting field. Any pretension to comprehensive coverage, however, had to be abandoned. In order to keep the material in a work of this nature up to date, a cutoff date has to be set. Inevitably one or two of the planned articles fail to materialize by this deadline, and other interesting topics may come into focus too late to permit the preparation of a worthwhile discussion by the target date. Still, in fairness to those authors who kept to the schedule, the cutoff date has to be enforced, even though this means sacrificing breadth of coverage to timeliness. I wish to thank all the contributors to this volume for their effort, their cooperation, and their punctuality, and it is my hope that the policy I have followed will result in the presentation of current thought on a series of interesting aspects of the subject of Raman spectroscopy. May 1970 H.A.S. Contents Chapter 1 Vibrational Rules of Selection and Polarization: Their Practical Uses and Limitations .................... . L. A. Woodward Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Vibrational Selection Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Polarization Rule for Raman Scattering . . . . . . . . . . . . . . . . . 3 Predictions from the Rules .............. '. . . . . . . . . . . . . . . 4 Rough Estimates of Fundamental Frequencies. . . . . . . . . . . . 5 Simple Examples of Structure Determination. . . . . . . . . . . . . 7 Complications and Limitations. . . . . . . . . . . . . . . . . . . . . . . . . 15 Further Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Concluding Comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 References .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Chapter 2 Developments in the Theories of Vibrational Raman Intensities 33 J. Tang and A. C. Albrecht Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Vibronic Expansion Approach . . . . . . . . . . . . . . . . . . . . . . . . . 35 Ground-State Approach .............................. 45 Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Appendix C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Chapter 3 Raman Spectroscopy with Laser Excitation . . . . . . . . . . . . . . . . . 69 H. W. Schrotter Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Experimental Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Methods and Results for Amorphous Media . . . . . . . . . . . . . 88 vii viii Contents Methods and Results for Crystals. . . . . . . . . . . . . . . . . . . . . . . 10 1 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Chapter 4 Low-Frequency Raman Spectra of Liquids .. .. .. . .. . . .. . .. . . 121 L. A. Blatz Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Experimental Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Future. . . . . . .. . . . . . . . . . . . .. . . . . . . .. . . . . . . .. . . .. .. . . . 139 References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Chapter 5 High- and Low-Temperature Raman Spectroscopy. . . . . . . . . . . 141 Ronald E. Hester Introduction. . .. . . . . . . . . . . . . . . .. . . . .. . . . .. . . . . . . . . . . . 141 High-Temperature Techniques. . . . . . . . . . . . . . . . . . . . . . . . . 142 Low-Temperature Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . 148 Molten Salts and Other High-Temperature Systems. . . . . . . 156 Results from Low-Temperature Studies. . . . . . . . . . . . . . . . . . 161 Assessment of Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Chapter 6 Raman Spectroscopy with Poor Scatterers . . . . . . . . . . . . . . . . . . 17 5 E. Steger Definition of Poorly Scattering Sample. . . . . . . . . . . . . . . . . . 175 Instrumentation Considerations. . . . . . . . . . . . . . . . . . . . . . . . 180 Sample Improvement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 Appendix Comments on the Derivation of the Dispersion Equation for Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Gene P. Barnett and A. C. Albrecht Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Contents ix The Zeroth-Order Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Quantum Description of the Radiation Field. . . . . . . . . . . . . 208 The Interaction Term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 The Dispersion Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 The Molecular Polarizability . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Index.. . . . . . . . .. . . . . .. . . .. . . . . . . . . . .. . . . . .. . . . . . . . .. . . 219 Chapter 1 Vibrational Rules of Selection and Polarization: Their Practical Uses and Limitations L. A. Woodward University of Oxford Oxford, England INTRODUCTION The vibrational selection rules for the Raman effect and for infrared absorption and the rule of polarization for vibrational Raman lines are based solely on symmetry considerations. For a molecule whose structure (and hence whose symmetry point group) is known, applica- tion of the rules gives information as to the number of fundamental vibrational frequencies permitted in either type of spectrum and the number whose Raman lines will be polarized. If we are concerned with a molecule of unknown structure for which two (or more) models with different symmetries can be reason- ably proposed, we can make predictions of the above kinds for each. In general, the predictions for the rival models will be different, so that by experimental observation of the actual spectra it will be possible, in principle, to discriminate between the proposed types of structure and to decide which is the right one for the molecule in question. It is important to note that this method, being based solely on general symmetry theory, is quite independent of the special nature of the molecular force field. For this reason it is, in principle, a method of great power; for a complete description of the force field is generally inaccessible. Indeed, the method has often been used with notable success. Nevertheless, it is true that in certain cases circumstances may arise which limit its usefulness. It is the object of this chapter to discuss the method in general, and to illustrate both its power and its limitations by examples from the literature. 2 L. A. Woodward VIBRATIONAL SELECTION RULES Before discussing applications, it will be convenient to give a brief resume of the derivation of the selection rules. We shall concern our- selves throughout only with fundamentals, because generally speaking they are most easily observable. Corresponding selection rules can be derived for overtones and combination tones, but these usually appear with relatively low intensity, especially in Raman spectra. The intensity of a transition is proportional to the square of the relevant transition moment, and so the condition that a transition be allowed is that the transition moment shall not vanish. Infrared Absorption For a fundamental transition (vibrational quantum number change from 0 to 1) the transition moment for infrared absorption is given by , where t/Jo, t/Jl are, respectively, the wave functions of the initial and final states, 11 is the electric dipole moment of the molecule as a function of Q, and Q is the normal coordinate of the vibrational mode. The integral is to be extended over the whole coordinate range. We must bear in mind that the dipole moment, being a vector, has three components (l1x, l1y, I1z in a Cartesian system), and that, in greater detail, an integral of the above kind applies separately to each. The condition that the integral for the component l1i (where i denotes either x, y, or z) shall not vanish is that the integrand t/JOl1it/Jl shall be totally symmetric, i.e., shall be transformed into itself by all the symmetry operations of the molecular point group. Since t/Jo (ground vibrational state) is known always to be totally symmetric, it follows that the product l1it/J 1 must be totally symmetric. This is only the case if both factors belong to the same symmetry species. For the transition to be permitted, it will suffice if this is so for at least one of the compon- ents of 11. Now it is also known that t/J 1 always belongs to the same symmetry species as does the vibration itself. We can therefore state the infrared-absorption selection rule for fundamentals as follows: A fundamental is permitted in infrared absorption only if its species is the same as that of at least one of the components of the electric dipole moment. Vibrational Rules of Selection and Polarization 3 The species of the dipole-moment components are the same as those of the corresponding translations, and these are customarily given in the point-group character tables. It is therefore a simple matter to read off from these tables the selection rules for vibrations of any species. Raman Effect In considering Raman scattering we are not concerned at all with the intrinsic dipole moment J1 of the molecule, but only with the dipole moment P which is induced in the molecule by the electric field E of the incident light. This is given by P = (XE where (X is the molecular polarizability. For a fundamental Raman transition the transition moment is, accordingly, Here we must remember that (X is a tensor quantity representable by an array of nine components «(Xxx, (Xxy, etc.). However, because the tensor is a symmetric one (which means that (X,) = (X},), only six of the nine components are distinct. In greater detail, a transition-moment integral of the above form applies separately to each component. Just as in the case of infrared absorption (see above), we can state the selection rule for Raman scattering as follows: Afundamental is permitted in Raman scattering only ifits species is the same as that of at least one of the components of the polarizability. A component (X,) transforms in the same way as does the product of the translations 1', and ~,and the species of the components of (X (or in certain cases suitable linear combinations of them) are customarily given in the point-group character tables. It is therefore an easy matter to read off the selection rules for vibrations of any species. POLARIZATION RULE FOR RAMAN SCATTERING For a fluid sample, when the incident light is natural (ie., un- polarized) and the scattering is observed at right angles to the incident direction, the degree of depolarization Pn of a Raman fundamental is

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