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The molecular orbital theory of conjugated systems
Book Reviews physics are employed," as though they were separately more real than their fusion. There are some errors in fact. General relativity is not really required for the rotating disk problem (p. 237). Nor, of course, is the resultant of a time-like vector and an orthogonal space-like vector necessarily null (p. 263). Nor are the geodesics of the Minkowski continuum hyperbolae (p. 259). In addition, Arzelies shares the surprisingly common misbelief (p. 279) that the Lorentz transformation for v > c makes objects travelling faster than light return into the past and also undergo a spatial reflection. On the other hand his belief (p. 70) that 99 per cent of the galaxies possess velocities greater than c with respect to our own seems meaningless, strictly speaking. The masterful annotated bibliography Professor Arzelies has provided is especially valuable. All those concerned with teaching or learning special relativity will enjoy this book; especially the fine print. DAVID FINKELSTEIN Belfer Graduate School of Science Yeshiva University New York, N. Y.
THE
MOLECULAR ORBITAL THEORY OF
CONJUGATED SYSTEMS, by Lionel Salem. 576 pages, diagrams, 6 X 9 in. New York, W. A. Benjamin, Inc., 1966. Price, $19.75. Theoretical chemistry owes most of its present success to the development of the molecular orbital method. This has proved by far the most effective approximation for the interpretation of chemical problems in terms of quantum mechanics. The most striking achievements have been in three main areas: spectroscopy, tra1:sition metal chemistry, and the behavior of large organic molecules. It is therefore curious that so few accounts of this third area have appeared in bookform, the more so in view of the excellent texts that have appeared describing the two other fields. The few books on applications to organic chemistry have, moreover, been mostly of an elementary nature, designed to introduce organic chemists to the simple Htickel (HMO) treatment and paying little attention to recent developments.
74
Most of the work on organic molecules has made use of the so-called Htickel approximation; here electrons in a-bonds, or in isolated ~r-bonds, are assumed to be localized so that their contributions to the molecule can be represented as sums of additive contributions by individual bonds. In conjugated molecules, additivity breaks down; here the contributions of the ~r-electrons have to be calculated either by the HMO method or by some more sophisticated approach based on the self-consistent field approximation. Dr. Salem's book represents an attempt to describe the present status of such calculations, and their use in interpreting the physical and chemical properties of conjugated organic molecules. The simple HMO method and its application to a variety of problems concerned with the structures of conjugated molecules are discussed in the first chapter. This is followed by the corresponding SCF MO approach, including various pseudo-self-consistent treatments such as the Wheland-Mann approximation. Next, the author discusses a variety of ground state properties in more detail, including resonance energies, charge distributions, dipole moments, etc. Then he covers magnetic resonance spectroscopy, dealing first with the magnetic properties of closed shell molecules and the calculation of chemical shifts and coupling constants in nmr spectra, and secondly with the theoretical treatment of radicals and its application to esr spectroscopy. There is a discussion of chemical reactivity, followed by one on the excited states of molecules and their uv/visible spectra. And the final chapter covers a variety of problems concerned with distortions of molecules, in particular the Jahn-Teller effect and bond alternation. Unfortunately, this book suffers from two serious defects. First it places far too much emphasis on work published more than ten years ago and too little emphasis on recent developments. For example, in the chapter on light absorption, eighty-four pages are devoted to work published before 1956, while the coverage of the more recent literature is wholly inadequate, tIeilbronner's work is barely mentioned, and Ruedenberg's not at all. The chapter on chemical reactivity could have been written in 1954, while the coverage
Journal of The Franklin Institute
Book Reviews on radicals omits all reference to recent open shell calculations, using annihilation operators to remove contributions by higher spin states. Not only is the content unbalanced, but also its whole approach. One gets the impression that the book was first written a decade ago and recently updated by a hasty inclusion of references to later work. This would account for the cavalier treatment of SCF MO theory which the author seems to regard as too complicated and difficult for general use and for his apparent phobia of computers which are barely mentioned in the text. Ten years ago the SCF method certainly was too difficult to use since fast digital computers were not then generally available. A second weakness of this text lies in the very inadequate introduction given to the various theoretical treatments it describes. The introduction to SCF MO theory is particularly poor, and would be quite unintelligible to those without an extensive background in quantum theory. The discussion of the theory of diamagnetism and magnetic resonance spectroscopy is likewise very perfunctory, and would again provide very difficult reading for the uninitiated. However, in spite of its shortcomings, this is a very useful book in an area where at present there is no serious rival. I t contains a great deal of information, and the coverage of the literature, while by no means complete, is at least extensive enough to be useful. I t is also well written and well produced. Indeed if the price were more reasonable, it could be generally recommended, if only for lack of a better alternative. MICHAEL J. S. DEWAR
Department of Chemistry University of Texas Austin, Texas HIGH ENERGY BEAM OPTICS, by Klaus G. Steffen. 211 pages, diagrams, illustr. 6 X 9 in. New York, John Wiley & Sons, Inc., 1965. Price, $9.50. A comprehensive survey of both the basic concepts of high-energy beam optics and the tools and methods of practical beam and spectrometer design work is presented in this monograph. It begins with a derivation of the equations
Vol. 284,No. I, July 1967
of motion in a general magnetic field, and follows immediately with the standard analysis of the trajectory optics of a system consisting of one or more quadrupole magnets. The standard presentation up to this point gives way, in the latter 40 pages of Chap. 1, to a valuable discourse on theoretical and practical aspects of quadrupole system design, such as chromatic aberration, secondand third-order aberrations, end effects, effective quadrupole parameters, practical quadrupole cross sections, and finally a quadrupole design example. The author analyzes next the trajectory optics in deflecting magnets in much the same way that quadrupole magnets were analyzed in the first chapter. Here again, an important part of the material is devoted to higher-order effects such as dispersion, second-order aberrations, and end effects. Then some general properties of beam transport systems are investigated composed of quadrupoles and deflecting magnets. Nondispersive deflecting systems, isochronous deflecting systems and spectrometers (i.e., dispersive deflecting systems) are discussed in that order. The analyses are restricted, however, to the optical component in the plane of the deflection, while ignoring the component normal to this plane. This omission may have simplified the analysis to the point where the reader does not appreciate the problem of achieving a simultaneous solution for both components of the beam optics. The last chapter presents the tools for analyzing the effects of beam optical systems on regions of phase space, rather than on single particle trajectories. An elliptical region of phase space is defined, which can be used to represent either the acceptance of an optical system or the family of trajectories forming a "beam." Equations are given which describe how this ellipse transforms through any given optical system. This is an extremely powerful approach to the evaluation of optical systems, and the reviewer feels that the author should have placed more emphasis on it. Throughout the book, the author often presents more than one formulation of a given concept. When he does, his coverage of each formulation is somewhat superficial, yet sufficient to encourage the reader to consult the original papers on the subject. The references at the end of each chapter include
75
THE
MOLECULAR ORBITAL THEORY OF
CONJUGATED SYSTEMS, by Lionel Salem. 576 pages, diagrams, 6 X 9 in. New York, W. A. Benjamin, Inc., 1966. Price, $19.75. Theoretical chemistry owes most of its present success to the development of the molecular orbital method. This has proved by far the most effective approximation for the interpretation of chemical problems in terms of quantum mechanics. The most striking achievements have been in three main areas: spectroscopy, tra1:sition metal chemistry, and the behavior of large organic molecules. It is therefore curious that so few accounts of this third area have appeared in bookform, the more so in view of the excellent texts that have appeared describing the two other fields. The few books on applications to organic chemistry have, moreover, been mostly of an elementary nature, designed to introduce organic chemists to the simple Htickel (HMO) treatment and paying little attention to recent developments.
74
Most of the work on organic molecules has made use of the so-called Htickel approximation; here electrons in a-bonds, or in isolated ~r-bonds, are assumed to be localized so that their contributions to the molecule can be represented as sums of additive contributions by individual bonds. In conjugated molecules, additivity breaks down; here the contributions of the ~r-electrons have to be calculated either by the HMO method or by some more sophisticated approach based on the self-consistent field approximation. Dr. Salem's book represents an attempt to describe the present status of such calculations, and their use in interpreting the physical and chemical properties of conjugated organic molecules. The simple HMO method and its application to a variety of problems concerned with the structures of conjugated molecules are discussed in the first chapter. This is followed by the corresponding SCF MO approach, including various pseudo-self-consistent treatments such as the Wheland-Mann approximation. Next, the author discusses a variety of ground state properties in more detail, including resonance energies, charge distributions, dipole moments, etc. Then he covers magnetic resonance spectroscopy, dealing first with the magnetic properties of closed shell molecules and the calculation of chemical shifts and coupling constants in nmr spectra, and secondly with the theoretical treatment of radicals and its application to esr spectroscopy. There is a discussion of chemical reactivity, followed by one on the excited states of molecules and their uv/visible spectra. And the final chapter covers a variety of problems concerned with distortions of molecules, in particular the Jahn-Teller effect and bond alternation. Unfortunately, this book suffers from two serious defects. First it places far too much emphasis on work published more than ten years ago and too little emphasis on recent developments. For example, in the chapter on light absorption, eighty-four pages are devoted to work published before 1956, while the coverage of the more recent literature is wholly inadequate, tIeilbronner's work is barely mentioned, and Ruedenberg's not at all. The chapter on chemical reactivity could have been written in 1954, while the coverage
Journal of The Franklin Institute
Book Reviews on radicals omits all reference to recent open shell calculations, using annihilation operators to remove contributions by higher spin states. Not only is the content unbalanced, but also its whole approach. One gets the impression that the book was first written a decade ago and recently updated by a hasty inclusion of references to later work. This would account for the cavalier treatment of SCF MO theory which the author seems to regard as too complicated and difficult for general use and for his apparent phobia of computers which are barely mentioned in the text. Ten years ago the SCF method certainly was too difficult to use since fast digital computers were not then generally available. A second weakness of this text lies in the very inadequate introduction given to the various theoretical treatments it describes. The introduction to SCF MO theory is particularly poor, and would be quite unintelligible to those without an extensive background in quantum theory. The discussion of the theory of diamagnetism and magnetic resonance spectroscopy is likewise very perfunctory, and would again provide very difficult reading for the uninitiated. However, in spite of its shortcomings, this is a very useful book in an area where at present there is no serious rival. I t contains a great deal of information, and the coverage of the literature, while by no means complete, is at least extensive enough to be useful. I t is also well written and well produced. Indeed if the price were more reasonable, it could be generally recommended, if only for lack of a better alternative. MICHAEL J. S. DEWAR
Department of Chemistry University of Texas Austin, Texas HIGH ENERGY BEAM OPTICS, by Klaus G. Steffen. 211 pages, diagrams, illustr. 6 X 9 in. New York, John Wiley & Sons, Inc., 1965. Price, $9.50. A comprehensive survey of both the basic concepts of high-energy beam optics and the tools and methods of practical beam and spectrometer design work is presented in this monograph. It begins with a derivation of the equations
Vol. 284,No. I, July 1967
of motion in a general magnetic field, and follows immediately with the standard analysis of the trajectory optics of a system consisting of one or more quadrupole magnets. The standard presentation up to this point gives way, in the latter 40 pages of Chap. 1, to a valuable discourse on theoretical and practical aspects of quadrupole system design, such as chromatic aberration, secondand third-order aberrations, end effects, effective quadrupole parameters, practical quadrupole cross sections, and finally a quadrupole design example. The author analyzes next the trajectory optics in deflecting magnets in much the same way that quadrupole magnets were analyzed in the first chapter. Here again, an important part of the material is devoted to higher-order effects such as dispersion, second-order aberrations, and end effects. Then some general properties of beam transport systems are investigated composed of quadrupoles and deflecting magnets. Nondispersive deflecting systems, isochronous deflecting systems and spectrometers (i.e., dispersive deflecting systems) are discussed in that order. The analyses are restricted, however, to the optical component in the plane of the deflection, while ignoring the component normal to this plane. This omission may have simplified the analysis to the point where the reader does not appreciate the problem of achieving a simultaneous solution for both components of the beam optics. The last chapter presents the tools for analyzing the effects of beam optical systems on regions of phase space, rather than on single particle trajectories. An elliptical region of phase space is defined, which can be used to represent either the acceptance of an optical system or the family of trajectories forming a "beam." Equations are given which describe how this ellipse transforms through any given optical system. This is an extremely powerful approach to the evaluation of optical systems, and the reviewer feels that the author should have placed more emphasis on it. Throughout the book, the author often presents more than one formulation of a given concept. When he does, his coverage of each formulation is somewhat superficial, yet sufficient to encourage the reader to consult the original papers on the subject. The references at the end of each chapter include
75