Same potential users will question the author's use of 25'C as standard temperature in gas law problems, his continued use of proportion and formulas to teach stoichiometry and the other quantitative aspects of the course, and his use of Kg,% in some equilibrium calculations. The careful painstaking revision, the inclusion of many interesting, unusual analogies and illustrations chosen and included especially for the student, the attractive new format and the calculated pitch to the current level of general chemistry students will commend this new edition to many students and their instructors. Monnrs M. OLDHAM U.S. Naval A e a d a y Annapolis, Ma~yland
The Liquid State
J. A. Pryde, Sir John Cass College, London. Hutchinson University Lib brary, London, 1966. viii 179 pp. Figs. and tables. 13 X 21 cm. Paperbound, $2.10; clothbound, $4.90.
+
According to the author's preface, the purpose of this book is '(to provide for undergraduate and postgraduate students a simplified treatment of some recent molecular theories of the liquid state of matter." The author further sets as an objective "the attempt to relate the necessary mathematics to the physical ideas expressed, omitting lengthy justifications of particular steps when these would seem to add little to the physical development." The result is a particularly effective introduction to the modem liquid state in a form and at a price that should make the monograph attractive as a supplementary source for undergraduate or firstyear graduate courses in physical chemistry, chemical physics, statistical mechanics, or molecular theory of matter. There is the usual comparison between the properties and the molecular behavior of solids, liquids, and gases. Thii is followed by description of sttempts to treat liquids as modified dense gases on one hand, or as disordered solids on the other. There is a. rrseful neneral chanter on the nature of the pair-wise intemolecular fume, with enough physm and quantitatiw dtxcriplion to make cmdible the usually assumed inverse sixth power for the attractive contribution and the more sharply rising repulsive term. After a brief review of necessary macroscopic thermodynamics and some principles of elementary statistical mechanim, the author discusses various attempts to describe the liquid state hy creating a model from which the partition function can he explicitly calculated. This includes brief mention of the Mayer cluster expansion method for dense eases. - . enough descri~tion of the law of eorrespundin~stntew astablish its molecular basla, and fairly extenswe disrussiun of vsrioua wll theortes ~
~
of liquids. This latter includes a quantitative description of the Lennard-Jones and Devanshire theory, including a penetrating discussion of the communal fne energy and entropy problem. The modem tone of the hook is reflected in a very interesting chapter on molecular dynamics and Monte Carlo methods for estimating the equations of motion for agroup of particles large enough in number to be a reasonable replica of the ~.ealsystem. The author presents same of the digital computer techniques and approximations that are used along with estimates of computing time, total number of particles that are feasible to handle, etc. Typical mults sre shown for the computation of the potential energy and the compressibility factor, with indications of phsse transitions. These computations are compared with estimates from the cell model, Lennard-Jones and Dewnshire theory, solutions of several integral equations, and a few experimental points. In addition, the dust jacket contains a photograph of the classic Alder and Wainwright computation showing the time dependence of the position of the collection of particles, as traeed out an the oscilloscope screen. In spite of all this, in this chapter the author perhaps misleads the unwary reader by conveying the impression that these Monte Carlo and molecular dynamics experiments are essentially one means of solving the liquid state problem. Such is not the case. I t h i i it is quite well agreed at the present time that the objective of these computations is not necessarily to attempt to predict the red behavior of matter, but rather to provide a nomerical experimental result in order to compare with the estimates from various integral equations or other theories of the liquid stste, the cmpa7iron being made on the basasis of the aame assumed intennoleculur potential function. There is a very good chapter on the radial distribution function, including formulas relating the macroscopic pressure and internal energy to integrals over the potential function and the radial distribution function. There is a derivation of the Kirkwood-Bogoluhov-Yvon-Born & Green integral equation in a fonn that should be easy to follow by those uninitiated in notation and concepts of distribution functions. The superposition appmximation is also discussed. The reviewer suffered one disappointment in this chapter: he first was very pleased to find a readable and plausible description of the basis for the PercwYevick equation and some description of the methods that have been used to solve the PY equation; however, the author fails to state in print the Percus-Yevick equation. The derivation is admittedly complex and of course might best be omitted in a monograph of this type; however, the final result is probably less complex than the KBYBG equation. Should the author undertake a revision, one would also hope that he would mention the direct correlation function, and particularly the simple assumed interrelationships between the radial distribution function, the direct correlation function, and the intermolecular potential function which serve as a basis of the Percus-Yevick and other integral equations.
The two concluding chapters are concerned with transport properties and molecular-level problems of the irreversibility, still a very difficult area of current m a r c h . The author chooses to typify the problem of transport pwpertiea with x discussion of visuosity, and this is largely restricted to the anal\.& bv H. S. G w n , which expresses the transhrt properties in t e r n of perturbations to the equilibrium radial distribution function. This is a formally elegant method, hut one that holds not much promise a t the present time since there is no known way to reach any firm conclusion about the perturbations. Here again, the discussion could have been strengthened by a t least brief mention of another technique, namely the formal representation of the transport coefficients in terms of correlation functions. The book invites comparison to the recently published book, "Kinetic Theory of Gases." bv W. Kauamann (W. Benjamin,~nc:,19i6). The two books are at a wmparable level and could serve as complementary t a t s for outside reading in a physical chemistry course. The Kauzmann book seems to have one obvious advantaEe, namely alame number of workedout e ~ & ~ l eatid s supplementary prublern~ We have referred several tin~estu poa.lble u e of "The Liauid Statc" for allvnlementary reading i n undergradua&- or postgraduate courses. For that purpose it is firmly recommended. In addition, it may well be of considerable use to anybody with research interests in the structure. of matter. As an experimentdit concerned with liquid state physics, the reviewer has long felt the need for a monograph-length discussion of liquids which would on one hand he quantitative and up-to-date, but on the other hand not overwhelm the reader with overly sophisticated mathematical manlpulstions. I shall heartily recommend the volume to my beginning research students. C. 3. PINGS California Institute of Technology Pasadena
Introduction to Molecular Orbital Theory
A m Lskles, Fsirleigh Dickimon University, Temeck, New Jersey. Holt, Rinehart, and Winston, Inc., New York, 198 pp. Figs. and tables. 1966. ix 16 X 23.5 cm. $5.95.
+
This text is intended for an introductory course in molecular orbital theory or individual study. Knuwledge of modern physics, wave mechanics, and higher mathematim is not required. The first two chapters develop the Bohr theory of the hydrogen atom, the b i n d e p e n d e n t Schfidinger equation, and the solution of Sch16dinger's equation for systems that can be solved exactly, e.g., the particle in a box. The following two chapters develop the simple Hiickel
Volume 44, Number 2, February 1967
/ 117
linear ccombinrttion of stomic orbitals (LCAO>molecular orbital thwry and energy calculations. The Hiickel theory is then applied to a number of organic moleculsr and ionic system3. The H t h chapter defines and illustrates the calcul* tions of electron and charge densities, bond order and free valence. The last two chapters extend the Huckel theory to heterocyclic molecules (taking pyrrole as an example) and consider the concept of 2 rule, and aromaticity, Hiickel's 4n the valence bond treatment of benzene. Each chapter is followed by a number of well-chosen problems. A number of chapters include references to the literature. A list of b o o k recommended for additional reading is appended. Although it treats only the simple Hiickel MO theory, the book serves as a useful introduction to the techniques and jargon of the trade. The author states in the preface that juniors and seniors had no difficulty assimilating the material. I n the reviewer's experience the detailed calculations presented for a number of systems, e.g., the ally1 carbanion, illustrate the computational techniques so well that students have little trouble working through the problems a t the end of each chapter or extra problem which are assigned by the instructor. The book stimulates the reader to study the more advanced treatments of the MO thwry of organic systems such as the text by Streitwieser. The book is highly recommended as an introduction to the topic and as supplementary material for courses in valence theory and advanced organic chemistry.
+
JOHN R. WASSON Illimis Institute of Technology Chicago
An lntrodurtion to Electron Parmmagnetic Resonance Malcolm Bwsohn, University of Toronto, and James C. Baird, Brown University, Providence, Rhode Island. W. A. Bmjamin, Inc., New York, 1966. Frontiers in Chemistry Series. 274 pp. Figs. and tables. 16 xi X 23.5 em. 513.75.
+
The stated purpme of this book is to present an introduction to the fundamentals of electron paramagnetic resonance (EPR) for chemists and biochemists. As such, it is the first book we have with this orientation, and for this reason it could be considered a welcome volume. However, there are a number of faults one can find with it. The book is elementary enough that students and researchers without any quantum mechanical background can read it largely because of its qualitative treatment of the subject matter. But the significant lack of quantitative development results in a, superficial treatment of much of the material. One glaring example is the fact that two chapters are devoted to relaxation phenomena and line shapes and to intensity of spectra, yet the classic Bloch Equa-
1 18
/
Journal of Chemical Edvcofion
tions, from which so mueh useful information on magnetic resonance Speb troscopy may be obtained, are not even mentioned, nor is there any reference to them in the whole bwk! Largely as a result of their absence, these two chapters lack an adequate base of fundamental principles which would serve to clarify the discussion of the aforementioned topics, and (as is true of mueh of the book) tend to be made up of rather loosely coupled sections. I t also becomes difficult to determine the applicability of certain ideas and definitions to different cases, such as the significance of T? in liquids versus solids, and its relationship to whether the resonance is homogeneously broadened or not. The definition of T2as a spin-spin relaxation time as well as essentially an inverse linewidth is certainly insufficient. In fact it may be said that the treatment of relaxation phenomena for free radicals in the liquids (probably the case of most interest to chemists), is quite inadequate and in many ways contrary to much of what is presently known on the subject. Unfortunately, the reader will not find adequate references on this topic nor on numerous other topics treated in this book. One also gets the impression that this book was put together without sufficient care. For example on p. 3 the reader may be surprised to learn that.: "the g-factor is a dimensionless constant which is a physical property of the electron.. The g-factor is a proportionality constant between the magnetic moment and the angular momentum." Can magnetic moments and angular momentum actually have the same dimensions? On p. 257 one learns that the two apparently different radicals the tetramethyl-1,4dinitrobenzene anion and the 1,4dinitro-2,3,5,6 tetramethyl benzene anion have different splittings. Indeed they do, but only when they are prepared in different solvents! Despite the de-emphasis of a quantitative treatment the authors nevertheless included a short chapter summarizing quantum mechanics. I t is difficult to see how any "beginner" in ESR, who would be interested to learn that "for an electron, there are only two possible values for [the orientation], i.e., approximately 35'15' and 144-45',. . . " (p. 5) could possibly profit from such a br~efsummary of quantum meohanicd formalism or of the incomplete, but quantitative, appendices. The book is perhaps s t its best treating such topics as the appearance of the hyperfine structure in various liquid state free radical spectra. There are also some useful tables on hyperfine splittings and g-values. However, very little is said about the electronic or valence mechan i s m that give rise to hyperfine splittings, and g-shifts. The later chapters on the triplet state, inorganic applications, double resonance, applications of EPR to chemistry and to biology all suffer from the defects already noted. Nevertheless, they do includes. number of interesting topics. On the whole, the book does indicate the great variety of ideas, techniques, and applications currently associated with E P R even though the treatment given is often too sketchy to obtain a usefulunderstanding. This book could probablv have
.
been improved had i t been written with more care and planning and with s. greater respect for the knowledge of the reader. Cornell University I t h a , New York
Valence Theory
J. N. Murrell, University of Sussex, England, S. F. A. Kettle, University of Sheffield, England, and J . M. Tedda, University of St. Andrews, Scotland. John Wiley and Sons, Inc., New York, 1965. xiii + 401 pp. Figs. and tables. 16 X 23.5 cm. $7.75. In the preface, the authors state their intention of writing a book "to bridge the gap between the semiqualitative picture given in Coulson's "Valence" and the formal mathematicd account given in Eyring, Walter, and Kimbdl's "Quantum Chemistry!' The aut,hors have achieved their goal. The first five chapters (pp. 1 4 0 ) are introductory. The chapters include (1) The Foundations of Atomic Theory, which leads up to and introduces the Schrodinger equation, (2) The Electron in a Constant Potential, which in a very cursory manner illustrates the quantization of energy, quantum numbers, and zero-point energy, (3) The Hydrogen Atom, which develop the concept of atomic orbitals from sohtiom of the Schrodinger equation,, Many-electron Atoms and the Penod~o Table, which desoribes the n, 1, m, and s quantum numbers and their use for understanding the periodicity of elements, and (5) Basic Principles of the Theory of Valence, which is essentially a qualitative discussion of covalent bonding in terms of molecular-orhital and valence bond theory. The level of material presented in these five chapters is erratic. For example, bonding in simple hydrocarbons is discussed a t a level found in the average general chemistry book, whereas the mathematical justificetion of atomic orbitals is discussed a t an advanced level. In C h a p t,er 5, the concept of symmetry is used to develop the idea of hybridization, even though symmetry is not discussed until Chapter 8. In the next four chapters (pp. 61-1311, the more formal mathematical aspects of quantum theory are described. This materiel includes normalization! Hamiltonian Operstors, eigenvalues, e~genfunctions, Hermetians, variation and perturbation theory, antisymmetry rule, BornOppenbeimer approximations, symmetry groups, group theory, angular momentum operators, Russell-Saunders coupling, flnd parity. I n this part of the book, a n l n e page rigorous treatment of the helium atom is resented to illustrate the techniques for obtaining approximate solutions of the Schriidinger equation. The discussion of symmetry groups could have been greatly aided by more illustrations and lmproved art work. However, the discussion of Hermetian operators is very good. I n Chaptels 10, 11 and 12 (pp. 132-2011
(4)
(Continued on page Al58)
