The Quantum Theory of Atoms in Molecules

This book distills the knowledge gained from research into atoms in molecules over the last 10 years into a unique, handy reference. Throughout, the authors address a wide audience, such that this volume may equally be used as a textbook without compromising its research-oriented character. Clearly structured, the text begins with advances in theory before moving on to theoretical studies of chemical bonding and reactivity. There follow separate sections on solid state and surfaces as well as experimental electron densities, before finishing with applications in biological sciences and drug-design.
The result is a must-have for physicochemists, chemists, physicists, spectroscopists and materials scientists.

Auteur
Cherif F. Matta is an assistant professor of chemistry at Mount Saint Vincent University and an adjunct professor of chemistry at Dalhousie University, both in Halifax, Canada. He obtained his BSc from Alexandria University, Egypt, in 1987 and gained his PhD in theoretical chemistry from McMaster University, Hamilton, Canada in 2002. He was then a postdoctoral fellow at the University of Toronto, Canada, before being awarded an I. W. Killam Fellowship at Dalhousie University. Professor Matta has held the J. C. Polanyi Prize in Chemistry, two BioVision Next Fellowships, and a Chemistry Teaching Award, and has more than 40 papers and book chapters and two software programs to his credit. His research is in theoretical and computational chemistry with a focus on QTAIM and its applications.

Russell Boyd graduated from the University of British Columbia in chemistry in 1967, receiving his PhD in theoretical chemistry from McGill University in 1971. He subsequently went to Oxford University, UK, as a postdoctoral fellow, before returning to British Columbia with a Killam Postdoctoral Fellowship at the Department of Chemistry from 1973 to 1975. He then joined Dalhousie University, Halifax, where he held the Chair of Chemistry from 1992 to 2005 and became McLeod Chair in 2001. Professor Boyd has published about 200 papers in computational and theoretical chemistry. His current interests include the effects of radiation on DNA and proteins, the mechanism by which a leading anti-tumor drug cleaves DNA, and the design of catalysts.

Contenu

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
*Chérif 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 (*p*b) 11

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

1.7.3 The Laplacian of the Electron Density at the BCP (2*p*b) 11

1.7.4 The Bond Ellipticity () 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()] and Charge [q()] 16

1.8.2 Atomic Volume [Vol.()] 16

1.8.3 Kinetic Energy [T()] 17

1.8.4 Laplacian [L()] 17

1.8.5 Total Atomic Energy [*E*e()] 18

1.8.6 Atomic Dipolar Polarization [()] 20

1.8.7 Atomic Quadrupolar Polarization [Q()] 24

1.9 ''Practical'' Uses and Utility of QTAIM Bond and Atomic Properties 25

1.9.1 The Use of QTAIM Bond Critical Point Properties 25

1.9.2 The Use of QTAIM Atomic Properties 26

1.10 Steps of a Typical QTAIM Calculation 27

References 30

Part I Advances in Theory 35

2 The Lagrangian Approach to Chemistry 37
*Richard F. W. Bader*

2.1 Introduction 37

2.1.1 From Observation, to Physics, to QTAIM 37

2.2 The Lagrangian Approach 38

2.2.1 What is The Lagrangian Approach and What Does it Do? 38

2.2.2 The Lagrangian and the Action Principle A Return to the Beginnings 39

2.2.3 Minimization of the Action 40

2.2.4 Steps in Minimizing the Action 41

2.3 The Action Principle in Quantum Mechanics 42

2.3.1 Schrödinger's Appeal to the Action 42

2.3.2 Schrödinger's Minimization 42

2.3.2.1 Two Ways of Expressing the Kinetic Energy 43

2.3.3 Obtaining an Atom from Schrödinger's Variation 44

2.3.3.1 The Role of Laplacian in the Definition of an Atom 45

2.3.4 Getting Chemistry from G(, ; ) 46

2.4 From Schrödinger to Schwinger 48

2.4.1 From Dirac to Feynman and Schwinger 48

2.4.2 From Schwinger to an Atom in a Molecule 49

2.5 Molecular Structure and Structural Stability 52

2.5.1 Definition of Molecular Structure 52

2.5.2 Prediction of Structural Stability 53

2.6 Reflections and the Future 53

2.6.1 Reflections 53

2.6.2 The Future 55

References 57

3 Atomic Response Properties 61
*Todd A. Keith*

3.1 Introduction 61

3.2 Apparent Origin-dependence of Some Atomic Response Properties 62

3.3 Bond Contributions to ''Null'' Molecular Properties 64

3.4 Bond Contributions to Atomic Charges in Neutral Molecules 70

3.5 Atomic Contributions to Electric Dipole Moments of Neutral Molecules 71

3.6 Atomic Contributions to Electric Polarizabilities 73

3.7 Atomic Contributions to Vibrational Infrared Absorption Intensities 78

3.8 Atomic Nuclear Virial Energies 82

3.9 Atomic Contributions to Induced Electronic Magnetic Dipole Moments 88 3.10 Atomic Contributions to Magnetizabilities of Closed-Shell M...