Table Of ContentTheoretical Models of Chemical Bonding
Part 1
Atomic Hypothesis and
the Concept of Molecular
Structure
Editor: Z. B. Maksic
With contributions by
L. D. Barron, 1. E. Boggs, 1. P. Dahl,
Z. B. Maksic, A. Y Meyer, O. E. Polansky,
B. T. Sutcliffe, K.B. Wiberg
With 40 Figures and 51 Tables
Springer-Verlag Berlin Heidelberg New York
London Paris Tokyo Hong Kong
Professor Dr. Zvonimir B. Maksic
Theoretical Chemistry Group
The "Rudjer Boskovic" Institute
41001 Zagreb, Bijenicka 54/Croatia/Yugoslavia
and
Faculty of Natural Sciences and Mathematics
University of Zagreb
41000 Zagreb, Marnhiev trg 19, Croatia/Yugoslavia
Library of Congress Cataloging-in-Publication Data.
Atomic hypothesis and the concept of molecular structure / editor,
Z. B. Maksie ; with contributions by L. D. Barron ... fet al.l.
p. em. - (Theoretical models of chemical bonding; pt. 1)
ISBN-13: 978-3-642-64775-8 e-1SBN-13: 978-3-642-61279-4
001: 10.1007/978-3-642-61279-4
I. Molecular structure. 2. Atomic theory. I. Maksie, Z. B.
(Zvonimir B.) II. Barron, 1. D. III. Series.
QD461.A858 1990 541.2'2-dc20 90-9443 CIP
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© Springer-Verlag Berlin Heidelberg 1990
Softcover reprint of the hardcover 1s t edition 1990
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2152/3020-543210 - Printed on acid-free paper
To the memory ofm y parents
Olivera and Branko Maksic
Series Preface
"Imagination and shrewd guesswork
are powerful instruments for
acquiring scientific knowledge ... "
1. H. van't Hoff
The last decades have witnessed a rapid growth of quantum
chemistry and a tremendous increase in the number of very
accurate ab initio calculations of the electronic structure of
molecules yielding results of admirable accuracy. This dramatic
progress has opened a new stage in the quantum mechanical
description of matter at the molecular level. In the first place,
highly accurate results provide severe tests of the quantum mecha
nics. Secondly, modern quantitative computational ab initio
methods can be synergetically combined with various experimen
tal techniques thus enabling precise numerical characterization
of molecular properties better than ever anticipated earlier.
However, the role of theory is not exhausted in disclosing the
fundamental laws of Nature and production of ever increasing
sets of data of high accuracy. It has to provide additionally a
means of systematization, recognition of regularities, and ratio
nalization of the myriads of established facts avoiding in this
way complete chaos. Additional problems are represented by
molecular wavefunctions provided by the modern high-level
computational quantum chemistry methods. They involve, in
principle, all the information on molecular system, but they are
so immensely complex that can not be immediately understood
in simple and physically meaningful terms. Both of these aspects,
categorization and interpretation, call for conceptual models
which should be preferably pictorial, transparent, intuitively
appealing and well-founded, being sometimes useful for semi
quantitative purposes. They should reduce a posteriori the over
whelming information embodied in intricate wavefunctions to
manageable and memorable qualitative results and concepts.
Physically sound models have to provide an interpretation of
experimental and accurate ab initio results and serve as a tool
in unearthing common roots between seemingly unrelated data.
It is noteworthy that chemistry operating on the molecular level
uses its own scales provided by characteristic, standard or gauge
molecules. Hence, an adequate model should offer a rationale
VIII Series Preface
for the trends of changes of properties within families of related
compounds. Last but not least, qualitative models should try
to bridge a gap between rigorous quantum mechanics and the
empirical concepts of the phenomenological chemistry, or to
provide their reconciliation if possible.
It follows that models, both quantitative and qualitative, are
inevitable ingredients of the scientific method representing a
link in the cognitive chain between theory and experiment. A
harmonious development of molecular sciences requires a rather
uniform progress in experimental research and quantum, com
putational and interpretive, chemistry. For that purpose it is
of utmost importance to establish a common language - a sort
of scientific Esperanto - thus avoiding a scientific tower of Babel.
Important words in the scientific vocabulary are qualitative
concepts.
It is the aim of the present series of books "Theoretical Models
of Chemical Bonding" to provide a conceptual basis of modern
interpretive quantum chemistry. It will be shown that there are
qualitative models which meet all the attributes mentioned above.
A general theme of the series is the most important building block
of the macroworld - a molecule and its properties. The problems
addressed cover a wide spectrum of topics ranging from the basic
postulates of classical chemistry to a fine description of subtle
spectroscopic properties, electron correlation and relativistic
effects, intramolecular and intermolecular interactions, chemical
reactivity and biochemical activity etc. Chapters are produced
by a number of leading experts in the fields and they reflect much
of the current thinking. No attempt has been made to avoid an
overlap between the related articles, because some overlapping
is necessary if continuity and coherent presentation of the topics
considered is desired. A general level of theory is intermediate
and excessive mathematical formalism is avoided wherever per
mitted. In keeping with the general philosophy of the Series an
emphasis has been laid on chemical phenomena and experimental
facts and their interpretation in terms of qualitative models close
to chemical intution. The simplest possible description of mole
cular properties is striven for, carefully avoiding the Scylla of com
plexity and the Charybdis of oversimplification. It was impossible
to give a full account of quantitative models like the modern VB
approach and high-performance MO procedures because of
space limitations. Fortunately, they are well covered in other
books and review articles.
The introductory book of the Series is devoted to the notion
of atoms immersed in chemical environments and to the concept
of the molecular structure. A necessity for modelling in chemistry
and its striking features are expounded in the Prologue. In the
second book, which has been prepared in parallel, the third most
Series Preface IX
important postulate of classical chemistry is tackled: the pheno
menon of covalent bonding and a wide variety of its manifestations.
It is common wisdom today that molecular structure is the
central and most fruitful theme of modern chemistry, biology,
and to some extent of medicine. Knowledge of molecular geome
tric structural parameters gives important clues for understanding
electronic behaviour in molecules and it is a starting point for
more detailed studies. It is, therefore, rather disappointing that
it is extremely difficult, if not impossible, to derive the concept
of molecular structure from the first principles of quantum
mechanics (Chapter 1). It indicates at the same time that a deduc
tive method is not always the best way for acquiring scientific
information. Chapter 2 written by the late Professor O. E. Polansky
shows that some molecular properties are influenced by topo
logy alone. A brief discussion of the graph theoretical indices
is given in the Prologue too.
Two subsequent Chapters deal with molecular symmetry which,
revealing some of the most fundamental laws of Nature, gives
a penetrating insight into the structure and properties of matter.
Interestingly enough, there is a kinship between molecules and
elementary particles. Symmetry has a prominent role in chemical
and biochemical reactions to mention only chirality for example.
The following two chapters describe how good theory blended
with experiment can provide valuable information about mole
cular architecture. It illustrates rather nicely how the approxi
mate but shrewed guesswork of Born, Oppenheimer and Huang
yielded a model of molecular structure which proved enormously
useful in rationalizing spatial arrangements of atoms and chemical
bonds in nearly rigid molecules. It should be strongly pointed
out in this connection that clamped nuclei approximation actually
makes quantum mechanics a suitable theory for chemistry. Chapter
6 dwells on the simple ball-and-elastic spring model of molecules
which underlies the molecular mechanics methods. Various
applications to stereo-chemistry are thoroughly discussed.
The last two chapters elaborate on another pivotal topic:
a concept of atoms embedded in intramolecular potentials. It
appears, namely, that molecules have a "good memory" and
"remember" atoms which took part in their formation. In other
words, atoms are not scrambled by chemical bonding and retain
some individuality within molecular systems. Hence, the modified
atoms are natural constituents and basic units of molecules, which
is by no means obvious at first glance starting from the Schr6din
ger equation. Bader's elegant "zero-flux" theory of modified
atoms is discussed in Chapter 7. It turns out that a number of
empirical notions of classical chemistry can be translated into
quantum mechanical language by using the rigorously defined
concept of topological atoms. The concluding chapter describes
x Series Preface
modified atoms in molecules at the qualitative model level illustrat
ing a power and limitations of the conceptual approach. Naturally,
the last two chapters could have been placed at the very beginning
of this volume, for it is impossible to discuss molecular structure
without adopting the atomic hypothesis. Hoewever, they both
lean heavily on the use of the clamped nuclei approximation
and the molecular geometry concept. Therefore, the latter had
to be discussed first.
The present Series will hopefully strengthen interplay and in
crease creative interaction between the rigorous quantum theory,
conceptual modelling of the electronic structure of molecules,
and chemical phenomenology. Rapid concerted progress could
be expected by increasing the overlap between these areas, because
a fine balance between the very detailed results and development
of unifying ideas is its conditio sine qua non. If this goal is at
least partially fulfilled, our efforts will be greatly rewarded. It
is also hoped that the interested reader will share some of the
fascination and enthusiasm which played a great part in the pre
paration of these volumes.
Finally, I would like to express my sincere thanks to all the au
thors for their fine contributions and support which made this
endevour possible. Special thanks go to Professors E. Clementi,
T. Cvitas, R. Gleiter, W. Kutzelnigg, W. H. E. Schwarz, J. To
masi and M. C. Zerner for fruitful discussions and useful sugges
tions. A good deal of editing was done during my multiple stays
at the Organic Chemistry Institute of the University of Heidelberg
and financial support from the Alexander von Humboldt-Foun
dation is greatefully acknowledged.
Z. B. Maksic
Table of Contents
Prologue: Modelling - A Search for Simplicity
z. B. Maksic ..................... XIII
The Concept of Molecular Structure
B. T. Sutcliffe . . . . . . . . .
Topology and Properties of Molecules
O. E. Polansky . . . . . . . . . . 29
Symmetry in Molecules
J. P. Dahl ..... . 75
Chirality of Molecular Structures - Basic Principles
and Their Consequences
L. D. Barron. . . . . . . . . . . . . . . . . . 115
Interplay of Experiment and Theory in Determining Molecular
Geometries. A. The Experiments
J. E. Boggs. . . . . . . . . . . . . . . . . . . . . . 153
Interplay of Experiment and Theory in Determining Molecular
Geometries. B. Theoretical Methods
J. E. Boggs. . . . . . . . . . . . . . . . . . . .. 185
Molecular Mechanics alias Mass Points and Elastic Springs
Model of Molecules
A. Y. Meyer . . . . . . . . . . . . . . . . . . . . . 213
Atoms in Molecular Evironments
K. B. Wiberg. . . . . . . . . . . . . . . . . . . . . 255
The Modelling of Molecules as Collections of Modified Atoms
Z. B. Maksic. . . . . . . . . . . . . . . . . . . . . 283
Prologue
If you know a thing, it is simple,
If it is not simple, you don't know it.
Oriental proverb
Modelling - A Search for Simplicity
z.
B. Maksic
Ruder Boskovic Institute, POB 1016, 41001 Zagreb, Croatia, Yugoslavia
and Faculty of Natural Sciences and Mathematics, University of Zagreb,
Marulicev trg 19, 41000 Zagreb, Croatia, Yugoslavia
1 Introduction
Modelling is an important ingredient of the scientific method.
It is present in all sciences including humanities as an indispensable
tool for tackling otherwise intractable complex problems and
phenomena. We shall briefly comment here on modelling in
chemistry with particular emphasis on theoretical models. It
should be noted in passing that the present reflections are general
and that they might be of some relevance in other natural sciences
too.
There is no precise and unique definition of a model and con
sequently different people have different opinion about its notion,
meaning and relevance, which is sometimes a cause for serious
misconceptions and heated disussion. The reason is that models
vary considerably in their nature and serve quite different pur
poses. Another reason is that the art of modelling is not always
mastered leading to artificial results and consequently to a low
reputation of models in general. To put it succinetly, the defi
nition, classification and taxonomy of models is subjective and
perhaps they should be modelled themselves. Hence, what follows
is necessarily a personal view. The interested reader may also
consult several scholarly written reviews [1-6] and books [7-9]
or special subject issues of some journals [10-12]. Needless to
say, he is also encouraged to read the contributions collected
in this series of book written by experts in the field, who discuss
