book reviews problems into the hands of students. It may exceed the needs of students in introductory courses, but i t may be an excellent review source for advanced students. GEORGE L. HARDGROVE JR. St. Olaf College North,field, Minnesota 56057
Quantum Mechanics of Molecular Rate Processes
R. D. Iminr, Ohio State University. Oxford University Press, London, 1969. xi 335 pp. Fig. 13 X 23.3 cm. $14.40.
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The significance of quantum mechanics for chemixtry is that in principle it gives the solution to almost every chemical problem. However, in practice, the situation is, as 1)irac sbsted in 1929, "The underlying physical laws necessary for the mnthematici~l theory of s. large part of physic? and the whole of chemistry we thus completely known, and the difficulty is only tbe exact application of these laws leads to equations much too complicated to be solvable." Due to the mathematical diffimlty, the quantum-mechanical theory of rate processes has only recently been suffioiently developed and fundamenial qnxntnm mechanical treatments have been carried out for only certain simple reactions. Neverthelesz, the importance of qnant,um mechanical treatrnentz for chemical reaction rates is well known by now. In dealing with chemical rate processes, t,he very simple hard-sphere collision theory of react,ions was widely used a t one time, but. was soon found to he unsabisfactory. In the 1930's t,he development of nbsolute reaction r8t.e theory represented s very important achievement. However, crossed molecular beam and infrared chemiluminescenee experiments have recently been developed to such an extent that i t is now possible t,o obtsin det,aiIed information shout reaction mechanisms, e.g., one csn measure t,he energy and angular distributions of the prodricts. Such results cannot be intepreted by t,he absolute reaction rate theory. These experiments have led to t,he formulation of alt,ernat,ivet,heories which are more nseful and treat rnoleculm collisions in a much more realistic way than had previowly been possible. This book is written to survey these alternative theories whieh have been developed in the last few years. In the first part of the book, the neces sclry quantum mechanical concepts are introduced in terms of a discussion of physical "at,tributes2' and their a v e r q e values as measured in an ensemble of identical, noninteracting systems. The concepts of a state and its representation by s n amplitude and the spectral representation of operators are discussed as tools designed for the evaluation of average values of attributes. The equations of motion for the average values and Green's operator for
A724 / Journal o f Chemical Education
the Schr6dinger equation are also briefly described. The second part of the book is devoted to the quanta1 collision theory. The Lippmen-Schwinger equation in stationary collision theory is inbaduced. This equstion for structureless particles (potential scattering theory) is discussed and solved for the case of separable intersctions. Concepts of scattering amplitude and cross-section are introduced and evaluated exactly for separable inter&* tions and, in general, to the lowest order in the interaction (the Born tapproximatian). The method of partial-wave analysis is described and applied to scattering by a central potential. The equations for relative motion during a collision of molecules with internal structure m e derived. Application to rotational excitation and the Born approximation are also discussed. After the introductory discussion of collision theory, the author presents the operator formulation of collision theory and introduces the concept of the S matrix and the techniques nsed in the bheory of seattering by two and by several potentials. The discussion is extended to cover react,ive collisions. The author also treats the formulation of collision theory from a time-dependent point of view. The technique of t,ime ordering is used to reintruduee the wtwe operator that transforms the wavefunction for the svstem., -in the absence of interaction, to the actual wavefunction. The m e of symmetry in collisions, in particular, time-revernal invariance and its consequences in the form of t,he reciprocit,y and the microscopic reversibility theorem is also discussed. The applicabion and extension of the collision theory are considered in Part 3. After introducing the partitioning technique, the author uses i t in various aspects of molecular encounters. This technique is also applied to the operator formulation of callision theory. Various models in collision theory, whieh are designed to replace an exact solution for the dynamics of the collision, are described. The theory of unimolecular reactions i q discussed. The author concludes the book with a formal disoussion of time-correlation funetions and their application in the study of the linear response of s. system to an external pertmbrttion. The Liouville operator, which enables one to employ the ~artitioninetechniaue in the solution of
treatment is elegant. However, for a book of this type one should expect a more critical and analytical discussion on varinus theories and methods, not just a, restatement or reformulation. Besides, some topics are treated in quite a. terse style. They may not be intelligible to the reader with only a. conventional introductory undergraduate quantum mechanics course, as the author assumed for this book (see the preface). Ilespite these minor shortoomings, I still highly recommend this book to readers with strong quantum mechanical background and rwearch workers in the fields of theoretical chemistry and chemical kinetics because the present book does give a. logical and rigorous description of the quantum me-
last few years.
Ynn KANGPAN Boston College Chestnut Hill, Mess. 02167
Enzymic Calalyrir
John Westley, University of Chicago. Harper and Row, Publishers, New York, 1969. xiii 206 pp. Figs. and tables. 15.5 X 23.5 em. Softbound. $5.95.
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According t o its author, this book is directed as an aid t o "graduate students in biochemistry and dlied fields who combine a curiosity about enzyme mechanisms with some background in organic chemistry and biochemistry, and a t least an introduction t o physical chemistry." In reality, its audience would seem t o be restricted t o those well versed in physical organic chemistry. Anyone who would pick up this book with the idea of casually reading i t for general information on enzyme eat& ysis and mechanisms would be in for s. rude awakening. But for those who are oriented toward the interface of physical organic chemistry and biochemistry, the book does a thorounh and commendable iob. I t is broken-down into four parts. Part I, Fundamental8 of Enzymology, goes into both the chemiiitsy of proteins and the behavior of catalysed reactions in general. Part 11, The Farms of Enzyme Mechanisms, deals primarily with the kinetic analysis of two-substrate reactions. Past 111, The Particulars of Ensyme Mechanisms, is devoted to methods of determining rate constants for individual reactions and for identifying the particular enzymic groups involved in catalysis. I n the latter vein, Chapter 14 is devoted t o Identification of Specific Groups: Use of pH Variation and "Group-Specific" Reagents. I t appears t o this reviewer that the author must have decided a t the last minute t o throw in the sections on groupspecific reagents because it was the "in" thing to do, and that he should have either left them out entirely or devoted more time t o them. Part IV, Metabolic Control a t the Enzyme Level, deals primarily with "allosteric" enzyme svstems. The author's coverage of this very interesting and emerging area is minimal, and this reviewer believes that more time might also have beenspent on this topic. Although the scope of this book was intended t o reach a general audience, its usefulness would seem t o be as a reference work for someone actively involved in the area. Each of the chapters is well documented with both general references and numerous specific references. Thus, the book could be used t.o advantage in a graduate course devoted t o enzyme catalysis and mechanisms.
C. L. Bonoms, JR. College of Wooster Woostw, Ohio (Continued a page A726)
