Table Of ContentMICROWAVE
MOLECULAR
SPECTRA
WALTER GORDY
Duke University
Durham, North Carolina
ROBERT L. COOK
Mississippi State University
Mississippi State, Mississippi
A WILEY-INTERSCIENCE PUBLICATION
JOHN WILEY & SONS
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Copyright@ 1984 by John Wiley & Sons, Inc.
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10 9 8 7 6 5 4 3 2 1
TO THE DUKE MICROWAVERS
The more than one hundred graduate students
and research associates who have contributed much
to the development of microwave spectroscopy.
INTRODUCTION TO THE SERIES
Techniques of Chemistry is the successor to the Technique of Organic Chemistry
Series and its companion- Technique of Inorganic Chemistry. Because many
of the methods are employed in all branches of chemical science, the division
into techniques for organic and inorganic chemistry has become increasingly
artificial. Accordingly, the new series reflects the wider application of
techniques, and the component volumes for the most part provide complete
treatments of the methods covered. Volumes in which limited areas of
application are discussed can be easily recognized by their titles.
Like its predecessors, the series is devoted to a comprehensive presentation
of the respective techniques. The authors give the theoretical background for
an understanding of the various methods and operations and describe the
techniques and tools, their modifications, their merits and limitations, and
their handling. It is hoped that the series will contribute to a better under-
standing and a more rational and effective application of the respective
techniques.
Authors and editors hope that readers will find the volumes in this series
useful and will communicate to them any criticisms and suggestions for
improvements.
ARNOLD WEISSBERGER
Research Laboratories
Eastman Koahk Company
Rochester, New York
vii
PREFACE
Many exciting new developments in microwave spectroscopy have occurred
since the earlier edition of this book was published in 1970. The frequency
coverage of coherent microwave spectroscopy is still expanding. Although
not comparable to the fourfold expansion that occurred in the 17 years pre-
ceding the 1970 edition, the millimeter wave range has been extended from 800
GHz to above 1000 GHz since 1970. Subtle new techniques continue to improve
the sensitivity and resolving power of microwave spectrometers as well as their
applicability to new types of spectra.
Detection of the microwave spectra of nonpolar, spherical-top molecules
such as CH4 and of “forbidden” AK transitions in symmetric-top molecules
such as PH3 has been achieved. Microwave “molecular ion” spectroscopy has
become a practical reality since 1970. The observation of rotational spectra of
weak, hydrogen-bonded complexes and rare gas atom-molecule complexes
(van der Waals molecules) has become widespread. New techniques for
observation of molecules in highly excited vibrational states have been devised.
Significant advances in the theory of complex microwave molecular spectra
have been made. In the last 15 years microwave spectroscopy has advanced
from observation of molecules in laboratory cells to observation of molecules
in interstellar space. An important new field, microwave molecular astronomy,
has been created. Microwave sources and techniques have been combined with
infrared and optical lasers to form the new and rapidly advancing field of
microwave-optical double resonance spectroscopy.
Although the spectra described in the earlier edition are in no sense out
of date, the new developments made the revision of Microwave Molecular
Spectra desirable if not necessary. The basic theory and measurements of
microwave spectroscopy have a remarkable durability which results from the
high resolution and accuracy of measurement that characterize all coherent
radiation spectroscopy of sharp line spectra. Because we could not justifiably
delete nor significantly reduce the basic material of the earlier edition,
a moderate expansion of the volume was necessary to achieve an adequate
coverage of microwave molecular spectra in the 1980s.
As was true for the earlier edition, we are indebted to many people
for assistance in the revision of this book. Again, Vida Miller Gordy graciously
assisted with every phase of the manuscript preparation. We have benefited by
discussions with Frank De Lucia, Eric Herbst, Paul Helminger, and K. V. L. N.
Sastry. The Winnewissers- Manfred, Brenda, and Gisbert-have helped to
ix
X PREFACE
keep us informed about the latest results in the field. M. C. L. Gerry read parts
of the manuscript and made helpful suggestions. We are also grateful to other
spectroscopists for sending us preprints and reprints describing results obtained
in their laboratories. Among them are Lisa Nygaard, E. Tiemann, H. Dreizler,
H. D. Rudolph, A. F. Krupnov, and J. L. Destombes.
Finally, we wish to express a tribute to the memory of Dr. William West,
editor of the earlier edition. He was a great person, a considerate and competent
editor, and a treasured friend.
WALTER GORDY
ROBERT L. COOK
Durham, North Carolina
July 1984
PREFACE TO THE
SECOND EDITION
In the 17 years since the first book on microwave spectroscopy was written, the
field has developed so extensively that it is not possible to give a comprehensive
coverage of all its aspects within a single volume of manageable size. Not only
have the applications been increased enormously and the instruments and
techniques diversfied, but the microwave region itself has also been greatly
expanded. The frequency range in which spectral measurements can be made
with microwave methods has increased more than fourfold since 1953. Many
measurements are now made at submillimeter wavelengths. With the molecular
beam maser the already ultrahigh resolution of microwave spectroscopy has
been increased by more than an order of magnitude. Rapidly recording, highly
sensitive microwave spectrometers have become commercially available. High-
speed computers have taken much of the labor out of the analysis and have made
the study of complex molecules more feasible. New theoretical developments
have increased the possibility of understanding complex spectra and have also
increased the usefulness of such spectra. Microwave spectral measurements on
short-lived gaseous free radicals and on substances with vaporization
temperatures of the order of a thousand degrees are commonly made. Spectral
frequencies are measured to accuracies of the order of one part in lo8.A ccurate
molecular structures and other properties have been found for molecules
numbering into the thousands.
In this volume we have sought to provide a basis for the understanding
of microwave spectra in the gas phase. In doing this we have developed the
theory from what we considered to be the simplest approach consistent with
essential correctness and applicability. Although we make no effort to include
all the useful information about molecules that has been derived from the
spectra-a hardly achievable goal-we have included a variety of types of
information about selected molecules. A reasonably complete listing of the
molecular structures derived up to 1969 is given in the appendix. Although
the book is a member of the Technique of Organic Chemistry series, we
have by no means limited the coverage to organic molecules. To do so would
have been too wasteful because the theory applicable to organic molecules
is generally applicable to inorganic molecules. The book is written for chemical
physicists and physical chemists as well as for organic chemists-if indeed such
separate classifications are bona $de in this age. We have not included a
discussion of the determination of nuclear moments and masses, subjects that
xi
xii PREFACE
are perhaps of more interest to physicists than to chemists. Most nuclear
moments and isotopic masses that can be measured to advantage with
microwave spectra have already been measured. Rather we have treated nuclear
hyperfine structure and isotopic shifts of spectral lines with the aim of using
them to gain information about molecules. To achieve more thorough coverage
of gases we have omitted solid-state studies, which are made primarily with
microwave paramagnetic resonance (included in another volume of this series)
and liquid-state studies made chiefly through dielectric dispersion and
absorption. For the same reason we have omitted discussion of instruments
and techniques of measurement.
Nevertheless we have tried to serve the dual purpose of providing a convenient
source and reference book for much of the valuable information gained about
molecules through microwave spectroscopy and of providing a textbook that
explains essential theory for interpretation of the spectra and derivation of
information from spectra. Although not written specifically for the purpose, the
book can be used as a text for a course or seminar on microwave spectra. A
quantitative study of microwave spectroscopy provides numerous, rather
elegant examples of the application of quantum mechanics to problems of
molecular dynamics. Although the quantum mechanical treatment can in some
cases be somewhat complicated in its details, much of the information derivable
from microwave spectra of molecules is of such importance that it justifies more
than casual attention.
Several people have assisted considerably in the preparation of the volume.
Vida Miller Gordy has helped persistently and effectively in the preparation
and proofreading of the manuscript. Jean Luffman’s typing of the entire manu-
script presented us with a beautiful final copy from the many revisions given
her in the course of the writing. Janet Jackel drew most of the illustrations.
Several research associates and graduate students at Duke University-James
Cederberg, Frank De Lucia, Steve Guastafson, Paul Helminger, Sam McKnight,
William Oelfke, Edward Pearson, David Straub, Gisbert Winnewisser, Ray
Winton, and Fred Wyse-have read sections of the book and made helpful
suggestions. To each one we offer our thanks.
WALTER GORDY
ROBERT L. COOK
Durham, North Carolina
April 20, 1969
CONTENTS
CHAPTERS
I. Introduction 1
11. Theoretical Aspects of Molecular Rotation 11
111. Microwave Transitions-Line Intensities and Shapes 37
IV. Diatomic Molecules 71
V. Linear Polyatomic Molecules 125
VI. Symmetric-t op Molecules 175
VII. Asymmetric-top Molecules 227
VIII. The Distortable Rotor 297
IX. Nuclear Hyperfine Structure in Molecular Rotational Spectra 391
X. Effects of Applied Electric Fields 451
XI. Effects of Applied Magnetic Fields 505
XII. Internal Motions 569
XIII. Derivation of Molecular Structures 647
XIV. Quadrupole Couplings, Dipole Moments, and the Chemical Bond 725
xv.
Irreducible Tensor Methods for Calculation of Compiex Spectra 803
APPENDIXES
A. Notes on Matrix Mechanical Methods 841
B. Calculation of the Eigenvalues and Eigenvectors of a Hermitian
Tridiagonal Matrix by the Continued Fraction Method 849
C. The Van Vleck Transformation 853
D. Fundamental Constants and Conversion Factors 857
E. Isotopic Abundances, Masses, and Moments 859
xiii
xiv CONTENTS
F. Bond Radii 873
G. Electronegativities of the Elements 875
H. Computational Procedure for the Vibrational Eigenvalue Problem 879
I. Energies and Relative Intensities of Nuclear Quadrupole
Hyperfine Structure 881
J. Nuclear Quadrupole Second-Order Correction Energies for Linear
or Symmetric-top Molecules 895
Author Index 897
Subject Index 917
