MICROWAVE 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 New York Chichester Brisbane Toronto Singapore Copyright@ 1984 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. Library of Congress Catalogue Card Number: 84-40367 ISBN 0-471-08681-9 Printed in the United States of America 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