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Spins in Chemistry
Spins in Chemistry
Spins in Chemistry
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Spins in Chemistry

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Originally delivered as a series of lectures, this volume systematically traces the evolution of the "spin" concept from its role in quantum mechanics to its assimilation into the field of chemistry. Author Roy McWeeny presents an in-depth illustration of the deductive methods of quantum theory and their application to spins in chemistry, following the path from the earliest concepts to the sophisticated physical methods employed in the investigation of molecular structure and properties.
Starting with the origin and development of the spin concept, the text advances to an examination of spin and valence; reviews a simple example of the origin of spin Hamiltonians; and explores spin density, spin populations, and spin correlation. Additional topics include nuclear hyperfine effects and electron spin-spin coupling, the g tensor, and chemical shifts and nuclear spin-spin coupling.
LanguageEnglish
Release dateJan 18, 2013
ISBN9780486150192
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    Spins in Chemistry - Roy McWeeny

    DOVER BOOKS ON CHEMISTRY

    ELEMENTARY CHEMICAL REA CTOR ANALYSIS, Rutherford Aris. (40928-7)

    GROUP THEORY AND CHEMISTRY, David M. Bishop. (67355-3)

    CHEMICAL AND CATALYTIC REACTION ENGINEERING, James J. Carberry. (41736-0)

    MOLECULAR QUANTUM ELECTRODYNAMICS, D. P. Craig and T. Thirunamachandran. (40214-2)

    RADIOACTIVE SUBSTANCES, Marie Curie. (42550-9)

    THE CHEMICAL PHILOSOPHY, Allen G. Debus. (42175-9)

    CHEMICAL MAGIC, Leonard A. Ford. (Second Edition, revised by E. Winston Grundmeier.) (67628-5)

    SYMMETRY AND SPECTROSCOPY: AN INTRODUCTION TO VIBRATIONAL AND ELECTRONIC SPECTROSCOPY, Daniel C. Harris and Michael D. Bertolucci. (66144-X)

    ION EXCHANGE, Friedrich Helfferich. (68784-8)

    ADVENTURES WITH A MICROSCOPE, Richard Headstrom. (23471-1)

    CRYSTAL GROWTH IN GELS, Heinz K. Henisch. (68915-8)

    ATOMIC SPECTRA AND ATOMIC STRUCTURE, Gerhard Herzberg. (60115-3)

    ALCHEMY, E. J. Holmyard. (26298-7)

    THE DEVELOPMENT OF MODERN CHEMISTRY, Aaron J. Ihde. (64235-6)

    CRUCIBLES: THE STORY OF CHEMISTRY FROM ANCIENT ALCHEMY TO NUCLEAR FISSION, Bernard Jaffe. (23342-1)

    SYMMETRY IN CHEMISTRY, Hans H. Jaffé and Milton Orchin. (42181-3)

    CRYSTAL CHEMISTRY AND REFRACTIVITY, Howard W. Jaffe. (69173-X)

    CATALYSIS IN CHEMISTRY AND ENZYMOLOGY, William P. Jencks. (65460-5)

    THE DEVELOPMENT OF CHEMICAL PRINCIPLES, Cooper H. Langford and Ralph A. Beebe. (68359-1)

    ELEMENTS OF CHEMISTRY, Antoine Lavoisier. (64624-6)

    RATES AND EQUILIBRIA OF ORGANIC REACTIONS: AS TREATED BY STATISTICAL, THERMODYNAMIC AND EXTRATHERMODYNAMIC METHODS, John E. Leffler and Ernest Grunwald. (66068-0)

    THE HISTORICAL BACKGROUND OF CHEMISTRY, Henry M. Leicester. (61053-5)

    QUANTUM MECHANICS OF MOLECULAR RATE PROCESSES, Raphael D. Levine. (40692-X)

    QUANTUM MECHANICS, Albert Messiah. (40924-4)

    A SHORT HISTORY OF CHEMISTRY (3RD EDITION), J. R. Partington. (65977-1)

    GENERAL CHEMISTRY, Linus Pauling. (65622-5)

    ELEMENTARY QUANTUM CHEMISTRY, SECOND EDITION, Frank L. Pilar. (41464-7)

    FROM ALCHEMY TO CHEMISTRY, John Read. (28690-8)

    ELECTROLYTE SOLUTIONS: SECOND REVISED EDITION, R. A. Robinson and R. H. Stokes. (42225-9)

    FIRE: SERVANT, SCOURGE, AND ENIGMA, Hazel Rossotti. (42261-5)

    INTRODUCTION TO CRYSTALLOGRAPHY, Donald E. Sands. (67839-3)

    QUANTUM MECHANICS IN CHEMISTRY, George C. Schatz and Mark A. Ratner. (42003-5)

    MODERN QUANTUM CHEMISTRY: INTRODUCTION TO ADVANCED ELECTRONIC STRUCTURE THEORY, Attila Szabo and Neil S. Ostlund. (69186-1)

    THEORY OF THE STABILITY OF LYOPHOBIC COLLOIDS, E. J. W. Verwey and J. Th. G. Overbeek. (40929-5)

    MAGNETIC ATOMS AND MOLECULES, William Weltner, Jr. (66140-7)

    MATERIAL CONCEPTS IN SURFACE REACTIVITY AND CATALYSIS, Henry Wise and Jacques Oudar. (41978-9)

    Paperbound unless otherwise indicated. Available at your book dealer, online at www.doverpublications.com, or by writing to Dept. 23, Dover Publications, Inc., 31 East 2nd Street, Mineola, NY 11501. For current price information or for free catalogs (please indicate field of interest), write to Dover Publications or log on to www.doverpublications.com and see every Dover book in print. Each year Dover publishes over 500 books on fine art, music, crafts and needlework, antiques, languages, literature, children’s books, chess, cookery, nature, anthropology, science, mathematics, and other areas.

    Manufactured in the U.S.A.

    Copyright

    Copyright © 1970, 1998 by R. McWeeny All rights reserved.

    Bibliographical Note

    This Dover edition, first published in 2004, is a republication of the work originally published by Academic Press, Inc., New York, in 1970, when it appeared as part of the Current Chemical Concepts series of monographs produced by the Polytechnic Press of the Polytechnic Institute of Brooklyn. A Foreword regarding that series has been omitted.

    9780486150192

    Manufactured in the United States of America

    Dover Publications, Inc., 31 East 2nd Street, Mineola, N.Y. 11501

    PREFACE

    In preparing these notes for publication I have not attempted to produce a textbook: Neither the material, nor its mode of presentation—as a series of Science Development Lectures—seemed appropriate for that purpose. The aim of the lectures, as I understood it, was to select some theme or concept of current importance in chemistry and to trace its evolution fairly systematically, from its early beginnings to its present stage of development. The first lecture should interest and entertain a large audience consisting of professors and students alike, from chemistry and from related disciplines, while the last would certainly have reached the present frontiers of research and would consequently have more appeal to the specialist. These are not the aims of a textbook. Now that I have to go into print, I feel more than ever that it would be a mistake to replace the spontaneity and informality of the lecture room by the formalities of a textbook style; the lectures are therefore published more or less exactly as they were given, with only the addition of an appendix and literature references.

    The choice of topic needs some explanation. As a theoretician, I wanted to find a theme that would illustrate at some depth the deductive methods of quantum theory and their impact on many areas of chemistry. Spin seemed to offer the right opportunities: The idea in itself is abstruse enough to present a conceptual challenge, its assimilation into quantum mechanics beautifully illustrates the mathematical machinery of the subject, and spin has so many implications in chemistry—particularly with the rapid advance of spin resonance techniques—that no chemist can afford to be wholly ignorant of recent developments in the field. The description of spin couplings by means of a spin Hamiltonian goes back forty years; but even today the spin-Hamiltonian concept is widely misunderstood and frequently misused. For all these reasons, it seemed well worthwhile to go back and try to find the path leading from the principles of quantum mechanics, through what some would call the mathematical wilderness, to an understanding and interpretation of the sophisticated physical methods now employed in the investigation of molecular structure and properties.

    The lectures were given during March 1969. It is a great pleasure to record my thanks to my hosts in the chemistry department, particularly to Professors Loebl, Banks, and Beringer, for their hospitality, and to all who helped make my visit such a pleasant one.

    My thanks are due also to Mrs. S. P. Rogers for producing an excellent typescript from my barely legible notes, and to Academic Press and the editor of this series for their speed and efficiency in publishing this monograph.

    R. McWEENY

    January, 1970

    Table of Contents

    DOVER BOOKS ON CHEMISTRY

    Title Page

    Copyright Page

    PREFACE

    1 - THE ORIGIN AND DEVELOPMENT OF THE SPIN CONCEPT

    2 - SPIN AND VALENCE

    3 - THE ORIGIN OF SPIN HAMILTONIANS:

    4 - SPIN DENSITY, SPIN POPULATIONS, AND SPIN CORRELATION

    5 - NUCLEAR HYPERFINE EFFECTS AND ELECTRON SPIN-SPIN COUPLING

    6 - THE g TENSOR, CHEMICAL SHIFTS, NUCLEAR SPIN-SPIN COUPLING

    APPENDIX - THE INTERACTION OF TWO ELECTRONIC SYSTEMS

    AUTHOR INDEX

    SUBJECT INDEX

    A CATALOG OF SELECTED DOVER BOOKS IN SCIENCE AND MATHEMATICS

    1

    THE ORIGIN AND DEVELOPMENT OF THE SPIN CONCEPT

    In this first lecture we shall discuss the historical origins of the spin concept, show how it was successfully assimilated into Schrödinger’s wave mechanics, and give a preview of its implications in optical, electron spin resonance (ESR), and nuclear magnetic resonance (NMR) spectroscopy. In succeeding lectures we shall build up gradually the theory of the spin Hamiltonian, which provides the essential link between theory and experiment.

    In 1921 Stern and Gerlach set out to measure the magnetic moments of atoms by deflecting an atomic beam in an inhomogeneous magnetic field. Their experiment, in retrospect, was a milestone in physics and chemistry. First, it provided an experimental basis for the concept of spin, later introduced by Goudsmit and Uhlenbeck in their efforts to resuscitate the old quantum theory and reconcile it with the spectroscopic facts; second, it exemplified the ideal measurement in the sense of modern quantum mechanics. Indeed, it is possible to squeeze out of this one experiment a profound insight into the methods and interpretation of quantum mechanics.

    THE STERN—GERLACH EXPERIMENT

    Let us recall the Stern–Gerlach experiment (Fig. 1.1a): Particles emerge from a furnace and a narrow beam passes between the poles of an electromagnet (shaped to produce a strongly inhomogeneous field). A magnetic dipole is deflected slightly by such a field, up or down according to the component of its moment along the field direction. When there is no field, the beam makes a spot on a photographic plate; but when the field is switched on, we find two spots, three spots, or more, depending on the atoms used (e.g., two for sodium, three for zinc). We consider the simplest case of two spots. The implication is that the component of magnetic moment can take only two values, corresponding to a magnet pointing parallel or antiparallel to the field. It is conventional to adopt the field direction as a z axis. Corresponding to the component of magnetic moment μz , we define an intrinsic angular momentuma component Sz , referred to as the "z component of spin." If the particle were actually a spinning distribution of negative charge, classical physics would predict a proportionality μz = −βSz , where the numerical constant β is the Bohr magneton but to allow more flexibility we write μz = −gβSz , where the numerical factor g may depend on the type of particle (e.g., for electrons it turns out that g = 2). This is just a hunch so far; but later it is found that Sz does possess all the properties of angular momentum, behaving just like Lz , the angular momentum due to orbital motion of a particle.

    What does this experiment tell us. It indicates that Sz can be found with two possible values (λ1, or λ2, say, where λ2 = −λ1 since the beam is displaced equally in the up and down directions); we have made an observation that determines the value of the quantity we are trying to observe; and we find half the particles in the up-spin beam, half in the down-spin beam. If we repeat the experiment on either one of these beams (Fig. 1.1b), we verify that Sz has a value λ1 (up-spin beam) or λ2 (down-spin beam), with no further splitting occurring. In this case the second observation does not disturb the value already recorded, and this is the criterion for an ideal observation in quantum mechanics. But if we twist the first analyzer around, so that the up-spins are definitely pointing toward us (Fig. 1.1c) while the down-spin beam is cut off by means of a stop, the second analyzer again splits the beam. In other words, a particle with a definite x component (λ1) is found after observation to have z component λ1 or λ2 , with a fifty-fifty chance of either. The incoming particle could be described as either

    i. In a state with Sx = λ1 definitely

    or

    ii. In a state with Sz = λ)

    = λ)

    FIG. 1.1. The Stern–Gerlach experiment. (a) Spinning particles proceed from furnace (left), split by inhomogeous magnetic field. (b) Effect of a second magnet (analyzer). (c) Effect of analyzer on beam after rotation of Stern–Gerlach experiment through 90°.

    Each is an equally valid description of the state of the incoming particle. If we agree to have the field in the z direction while making observations, any state of the incoming particle can be indicated statistically by giving the two fractions p1, and p2 into which the beam is resolved. Observation, then, consists in sorting results into categories. The result is in general indefinite and the state of a system (e.g., one particle) is described by stating the probabilities, p1 and p2 , with which various possible results are

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