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Book Review Ab Initio Calculation of the Structures and Properties of Molecules. By C. E. Dykstra

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feeling that we are living at a unique moment in the history
of science. The world appears to us at the same time as more
strange, but also more connected and more harmonious,
than to any of the generations which have preceded us. I can
only hope that Cramer’s book will inspire many readers and
will receive the international acclaim it fully deserves.
Zlya Prigogine [NB 985 I E ]
Faculte des Sciences
Universite Libre de Bruxelles
Brussels (Belgium)
and Department of Statistical Mechanics
and Thermodynamics
University of Texas
Austin, TX (USA)
Ab Initio Calculation of the Structures and Properties of
Molecules. By C. E. Dyksfra. Elsevier, Amsterdam 1988.
x, 275 pp., hard cover, HFI 210.00.-ISBN 0-444-43013-X
The development of useful approximate methods and the
enormous progress made in computer technology have enabled quantum chemical ab initio methods to become an
equal partner alongside experimental methods in determining structures and properties of molecules in the gas phase.
However, it is difficult for the non-specialist to assess the
credibility and reliability of results obtained from a particular calculation, despite the fact that the subtle factors which
determine the accuracy that can be achieved for a given
problem are generally well understood in quantum chemistry. The author of this book has set himself the commendable objectives of equipping the non-specialist with the
knowledge needed to make such a judgement, and providing
him with a survey of the capabilities of modern ab initio
methods. This has confronted him with the difficult task of
conveying in a condensed form the required knowledge of
the methods and the terminology used. Dykstra tackles this
in a descriptive manner with the authority of an experienced
quantum chemist (Chapter 3, 40 pp.). Whether or not this
presentation is informative even for the non-specialist will be
tested by the verdict of this reader.
In Chapter 1 (10 pp.) the nature of the task of theoretically
determining molecular structures is illustrated by five examples from astrophysics. After an explanation of the fundamental concept of the potential surface (and that of the property surface) as applied in the Born-Oppenheimer
approximation, Chapter 4 (21 pp.) gives a systematic ac-
count of ab initio structures. Chapters 6 to 8 deal in turn with
molecular vibrations (1 8 pp.), electrical properties (44 pp.)
and magnetic properties (22 pp.). The 390 literature references, which extend up to the beginning of 1988, are arranged alphabetically in the form of a bibliography, and it is
pleasing that they also include the titles of the papers cited.
An author index and a subject index are also included, although regrettably the latter does not include details of
which molecules are covered in the text.
The compilation and discussion of results is not cornprehensive. I t deals almost exclusively with molecules and
molecular complexes which contain two or three atoms of
elements of Period 2 together with some hydrogen atoms
(only two pages are devoted to heavy elements). The author,
who naturally draws mainly on results in his own field of
research, has consciously applied this restriction. Nevertheless, it is difficult to understand why there are no references
to earlier books on the same subject, such as those of Hehre,
Radom, Schleyer and Pople (1 986)[*’, Mulliken and Ermler
(1981), and Cursky and Urban (1980), nor to relevant review
articles. The author’s special area of interest also accounts
for the relatively large amount of space given to the rather
formal description of the role of analytical derivations in
quantum chemistry (Chapter 5, 26 pp.), and to the “Polymatrix Approach for SCF and Local Space SCF” (1 1 pages
in Chapter 9).
The book is well written, and its production and presentation are such that it is pleasing to read. The number of
printing errors is within acceptable limits, and they only alter
the meaning in a few cases, e.g. on page 118 where “quartic”
has become “quadratic”. All quantum chemists will welcome the compilation of important results which this volume
contains. On the other hand, the non-specialist will need to
supplement his reading with other monographs, review articles and original papers in order to get a full and balanced
view of the capabilities of ab initio methods and the results
that it has given up to now, especially as quantum chemists
themselves have still not reached agreement on the usefulness of some of the approximate methods (e.g. those for
taking account of electron correlation in structure determination).
Joachim Sauer [NB 968 IE]
Zentralinstitut fur Physikalische Chemie
der Akademie der Wissenschaften der DDR
Berlin (GDR)
[“I
See W. Kutzelnigg, Angew. Chem. 100 (1988) 312; AnKen. Chem. In!. Ed.
EngI. 27 (1988) 862.
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Angew. Chem. In[. Ed. Engl. 28 (1989) No. 10
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