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Book Review Symmetry and Structure. Readable Group Theory for Chemists. 2nd edition. By S. F. A. Kettle

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young f x u l t y as well as students”.
Walling admits, “I wasn’t as much interested in contact with students as I was in
understanding physical phenomena and
explaining them to other people”. He won
the 1970 James Flack Norris Award in
Physical Organic Chemistry.
Like many of the other authors in Seeman’s series. Walling summarizes his career in a few words: “To someone of my
temperament, being able to pursue my curiosity through research and reading with
freedom and adequate support and to receive some recognition for my work have
been all I could ask for. I can’t think of
anything I’d rather have done ... I’m also
conscious of the part that chance (or luck)
has played in my career.”
This entertaining, informative, and attractively priced volume will be of interest
to both present and future generations of
students and instructors of chemistry and
history of chemistry courses as well as to
practicing chemists interested in the humanistic aspects of their science.
George B. Kaujfman
California State University, Fresno
Fresno, CA (USA)
Symmetry and Structure. Readable
Group Theory for Chemists. 2nd edition. By S. E A . Kettle. Wiley,
Chichester, 1995. 416 pp., paperback
.E 18.99.-ISBN 0-471-95476-4
This book is intended mainly for chemistry students. The title is rather misleading, as the book is not basically about the
symmetry of crystal structures. Instead it
is an introductory text concerned with the
relationship between the geometrical and
electronic structures of molecules and
their symmetry. Using the chemical bond
as an example. the reader is introduced to
group theory in a way that is both unconventional and easy to understand. The
book consists of 13 chapters and six appendices. The changes that have been
made in this second edition are mainly
small, but two additional chapters have
been included, on space groups and on
spectroscopic studies of crystals.
A n g o . Chem. In,. Ed. Engl. 1996. 35. No. 16
Chapter 1 (9 pp.) describes different cusses the occurrence of optical activity.
models for the bonding in the ammonia Next, in Chapter 12 (46 pp.), we move
molecule. Chapter 2 (25 pp.) contains a from point groups to space groups. The
lucid elementary introduction to point chapter deals in turn with the crystal sysgroups, group tables, character tables, tems, the Brdvais lattices, the crystalloand irreducible representations, using the graphic point groups, symmorphic and
water molecule as an example. Chapter 3 asymmorphic space groups, Hermann(28 pp.) then deals with the orthonor- Mauguin symbols, and unit cells. The fimality properties of irreducible represen- nal chapter (15 pp.) is devoted to spectrotations, the separation of reducible re- scopic investigations of crystals. The
presentations into their irreducible com- author shows that because most of the
ponents, transformation properties of phenomena on which spectroscopic meaatomic orbitals, symmetry-adjusted com- surements depend are translationally invariant, one can in general limit the disbinations of orbitals, interactions between
bonds, and orbital energy levels; the ex- cussion to the factor groups of the space
amples used for illustration are the elec- groups with respect to their translation
tronic structure of water and the point subgroups, i.e. to point groups.
Appendices 1 and 2, covering 42 pages,
group C 2 “ .Chapter 4 (34 pp.) introduces
give a brief mathematical introduction to
the point group D,, as the direct product
of its normal subgroups C , and Ci, then group theory and to the matrix represendiscusses the symmetry of the atomic or- tations of groups. Appendix 3 contains
bitals in C,H, and B,H,, the bonding in the character tables of the “most importhese molecules, and the method of pro- tant” point groups, namely I , and Z, Oh,
jection operators. In Chapter 5 (26 p ~ . ) 0, TdrThand T , D,,, Do,,
D,. C,, and c,
(all with 2 5 n 2 6 ) , C,,, C,,, Ci, S,, C,
the author takes the symmetry group C,,
of BrF, as an example of a fairly complex and C,. Appendix 4 (15 pp.) contains a
derivation of the group orbitals with xgroup, and shows how the orthonormality relationships provide a way of system- symmetry for fluorine in SF,. Appendix 5
atically deriving a complete character ( 5 pp.) treats the point groups C,, and
table. Chapter 6 (12 pp.) discusses again Czh. Appendix 6 consists of two tables
symmetry and bonding in the ammonia listing the Schoenflies and Hermannmolecule. Chapter 7 (42 pp.) is concerned Mauguin symbols for point groups
with the symmetry of cubic molecules (ex- alongside each other.
With its lucid and unconventional mode
ample: SF,) and with octahedral transition metal complexes, and introduces the of presentation the book makes good readpoint groups 0, Oh, and
together with ing and is on the whole easily understandtheir character tables. Chapter 8 (1 1 pp.) able. The number of printing errors is not
is of a more general nature, dealing with excessive. Unfortunately, however, these
the relationships between groups and comments d o not apply to the last two
their subgroups and between the irre- chapters which have been added for this
ducible representations of a given group second edition, and they are especially unand those of its subgroups. Chapter 9 true in the case of Appendix 6, where there
(14 pp.) explains how the symmetry of a is a much higher incidence of errors and
molecule is related to its vibrational spec- the presentation is far from clear. Many of
trum and introduces the normal modes of the Hermann-Mauguin symbols are garvibration. Chapter 10 (22 pp.) deals with bled in such a way that it is difficult to
the important topics of the direct prod- identify the groups. These chapters canucts of irreducible representations, prod- not be recommended to anyone as an inucts of wave-functions, the symmetry of troduction to space groups. They should
different electronic configurations, and be either left out completely or thoroughly
spectroscopic selection rules. In Chapter rewritten at the earliest opportunity.
Elke Koch
11 (18 pp.) the author introduces complex
Institut fur Mineralogie, Petrologie
characters, illustrated by the relatively
und Kristallographie
simple example of the x-orbitals of cyder Universitlt Marburg (Germany)
clobutadiene with C, symmetry, and dis-
Q VCH Verlagsgesellsrhojt mbH, 0-6945I Wernheim, 1996
$ I5.00f.25’0
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