The quantum theory of atoms and molecules

568 Pages·2007·6.393 MB·English

by  Chérif F. Matta, Russell J. Boyd, Axel Becke

The Quantum Theory
of Atoms in Molecules
Edited by
Che´rif F. Matta and
Russell J. Boyd

The Quantum Theory
of Atoms in Molecules
From Solid State to DNA and Drug Design
Edited by
Che´rif F. Matta and Russell J. Boyd
The Editors 9 All books published by Wiley-VCH are
carefully produced. Nevertheless, authors,
Prof. Che´rif F. Matta editors, and publisher do not warrant the
Department of Chemistry & Physics information contained in these books,
Mount Saint Vincent University including this book, to be free of errors.
Halifax, Nova Scotia, B3M 2J6 Readers are advised to keep in mind that
Canada statements, data, illustrations, procedural
and details or other items may inadvertently be
Department of Chemistry inaccurate.
Dalhousie University
Halifax, Nova Scotia, B3H 4J3 Library of Congress Card No.: applied for
Canada
British Library Cataloguing-in-Publication
Prof. Russell J. Boyd Data
Department of Chemistry A catalogue record for this book is available
Dalhousie University from the British Library.
Halifax, Nova Scotia, B3H 4J3
Canada Bibliographic information published by the
Deutsche Nationalbibliothek
Die Deutsche Nationalbibliothek lists this
publication in the Deutsche Nationalbibliog-
rafie; detailed bibliographic data are available
in the Internet at hhttp://dnb.d-nb.dei.
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ISBN 978-3-527-30748-7
This book is dedicated to
Professor Richard F.W. Bader
on the occasion of his 75th birthday,
for his invaluable contributions to the
physical theory of chemistry.
‘‘. . . it is in virtue of the form that the matter is some one definite
thing, and this is the substance of the thing. What Aristotle
means seems to be plain common sense: a ‘thing’ must be
bounded, and the boundary constitutes its form. . . . We should not
naturally say that it is the form that confers substantiality, but
that is because the atomic hypothesis is ingrained in our imagina-
tion. Each atom, however, if it is a ‘thing’, is so in virtue of its
being delimited from other atoms, and so having, in some sense,
a ‘form’.’’
Bertrand Russell, A History of Western Philosophy;
Simon and Schuster, New York (1945).
VII
Foreword
As a graduate student at McMaster University in the years 1975–81 I had the
good fortune of knowing Richard Bader as a member of my supervisory commit-
tee. The departments of chemistry and physics shared facilities in the building
that was then called the Senior Sciences Building and is now called the A.N.
Bourns Building. I was a student in the department of physics, in the theoretical
physics group, with an office not far from the offices of the Bader group.
Richard was the first theoretical chemist I ever met. In addition to the annual
supervisory committee meetings, we chatted occasionally in his office. Looking
back on those years, I wonder how differently my own career might have turned
out had I not been inspired by those conversations. And inspired I was!
Anyone who knows Richard would agree that the single word describing him
best is passion. Richard Bader is passionate about science. His conviction and
enthusiasm for his own science, the theory of chemical bonding, are particularly
infectious. Every session with him left me exhilarated and, at the same time,
exhausted! His energy far outstripped mine.
What inspired me most was his passion for ideas and concepts. Our conversa-
tions were not about technical matters such as basis sets or levels of electron cor-
relation. We talked about densities and probabilities in chemical systems, what
makes a chemical bond, what is an atom in a molecule, why are atoms of a given
element similar in different molecular environments? Fundamental questions!
Fundamental ideas! My own efforts at the time were far off the beaten track –
basis-set-free computational schemes, Thomas Fermi-like molecular models, the
Hartree–Fock–Slater approximation. As a theoretical physics student with no ex-
pertise in theoretical chemistry, I relied heavily on Richard’s feedback. Any other
quantum chemist might have discouraged these unconventional projects, but not
Richard. He was encouraging. He called the work important. He gave me confi-
dence to pursue the unusual, ask the big questions, and, above all, seek out beau-
tiful ideas.
Science is inherently beautiful. The most powerful ideas are also the simplest
and the most beautiful. Early in the history of the density-functional theory of
electronic structure, long before DFT was fashionable, Richard Bader followed
his own path and developed some of the most beautiful ideas in chemistry. The
boundaries of atoms in molecules are uniquely and rigorously defined by the
VIII Foreword
electron-density distribution. The topology of the density distribution also maps
out all the bonds in a chemical system. Its Laplacian reveals the presence of local-
ized electron pairs. Atoms in molecules, bonds, localized electron pairs – these
are the most fundamental notions in chemistry. Richard Bader has taught us
that the total electronic density defines them all.
It is a pleasure and an honor to help celebrate such a uniquely creative career.
Thank you, Richard, for the inspiration and encouragement during my formative
McMaster years and throughout my career. And thank you for the beautiful con-
ceptual framework you gave to the theory of chemistry.
Dalhousie University, October 2006 Axel D. Becke
Killam Professor of
Computational Science, FRSC, FRS
IX
Contents
Foreword VII

Preface XIX

List of Abbreviations Appearing in this Volume XXVII
List of Contributors XXXIII
1 An Introduction to the Quantum Theory of Atoms in Molecules 1

Che´rif F. Matta and Russell J. Boyd
1.1 Introduction 1

1.2 The Topology of the Electron Density 1

1.3 The Topology of the Electron Density Dictates the Form of Atoms in

Molecules 5

1.4 The Bond and Virial Paths, and the Molecular and Virial Graphs 8

1.5 The Atomic Partitioning of Molecular Properties 9

1.6 The Nodal Surface in the Laplacian as the Reactive Surface of a

Molecule 10

1.7 Bond Properties 10

1.7.1 The Electron Density at the BCP (r ) 11

b
1.7.2 The Bonded Radius of an Atom (r ), and the Bond Path Length 11

b
1.7.3 The Laplacian of the Electron Density at the BCP (‘2 r ) 11

b
1.7.4 The Bond Ellipticity (e) 12

1.7.5 Energy Densities at the BCP 12

1.7.6 Electron Delocalization between Bonded Atoms: A Direct Measure of

Bond Order 13

1.8 Atomic Properties 15

1.8.1 Atomic Electron Population [N(W)] and Charge [q(W)] 16

1.8.2 Atomic Volume [Vol.(W)] 16

1.8.3 Kinetic Energy [T(W)] 17

1.8.4 Laplacian [L(W)] 17

1.8.5 Total Atomic Energy [E (W)] 18

e