Raman Spectroscopy: Theory and Practice

225 Pages·1970·16.73 MB·English

by  Herman A. Szymanski (eds.), L. A. Woodward (auth.)

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