Quantum Theory of Atoms in Molecules

Chérif 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.

"…a handsome text that serves to create a one-stop reference point exploring the quantum theory of atoms and molecules in complete detail." (Electric Review, May 2007)

• Foreword viiPreface xixList of Abbreviations Appearing in this Volume xxviiList of Contributors xxxiii1 An Introduction to the Quantum Theory of Atoms in Molecules 1Chérif F. Matta and Russell J. Boyd1.1 Introduction 11.2 The Topology of the Electron Density 11.3 The Topology of the Electron Density Dictates the Form of Atoms in Molecules 51.4 The Bond and Virial Paths, and the Molecular and Virial Graphs 81.5 The Atomic Partitioning of Molecular Properties 91.6 The Nodal Surface in the Laplacian as the Reactive Surface of a Molecule 101.7 Bond Properties 101.8 Atomic Properties 151.9 "Practical" Uses and Utility of QTAIM Bond and Atomic Properties 251.10 Steps of a Typical QTAIM Calculation 27Part I Advances in Theory 352 The Lagrangian Approach to Chemistry 37Richard F. W. Bader2.1 Introduction 372.2 The Lagrangian Approach 382.3 The Action Principle in Quantum Mechanics 422.4 From Schrödinger to Schwinger 482.5 Molecular Structure and Structural Stability 522.6 Reflections and the Future 533 Atomic Response Properties 61Todd A. Keith3.1 Introduction 613.2 Apparent Origin-dependence of Some Atomic Response Properties 623.3 Bond Contributions to "Null" Molecular Properties 643.4 Bond Contributions to Atomic Charges in Neutral Molecules 703.5 Atomic Contributions to Electric Dipole Moments of Neutral Molecules 713.6 Atomic Contributions to Electric Polarizabilities 733.7 Atomic Contributions to Vibrational Infrared Absorption Intensities 783.8 Atomic Nuclear Virial Energies 823.9 Atomic Contributions to Induced Electronic Magnetic Dipole Moments 883.10 Atomic Contributions to Magnetizabilities of Closed-Shell Molecules 904 QTAIM Analysis of Raman Scattering Intensities: Insights into the Relationship Between Molecular Structure and Electronic Charge Flow 95Kathleen M. Gough, Richard Dawes, Jason R. Dwyer, and Tammy L. Welshman4.1 Introduction 954.2 Background to the Problem 964.3 Methodology 1004.4 Specific Examples of the Use of AIM2000 Software to Analyze Raman Intensities 1034.5 Patterns in α That Are Discovered Through QTAIM 1094.6 Patterns in ∂α/∂rCH That Apply Across Different Structures, Conformations, Molecular Types: What is Transferable? 1114.7 What Can We Deduce From Simple Inspection of ∂α/∂rCH and ∂α/∂rCC From Gaussian? 1144.8 Conclusion 1185 Topological Atom–Atom Partitioning of Molecular Exchange Energy and its Multipolar Convergence 121Michel Rafat and Paul L. A. Popelier5.1 Introduction 1215.2 Theoretical Background 1235.3 Details of Calculations 1285.4 Results and Discussion 1305.5 Conclusion 1396 The ELF Topological Analysis Contribution to Conceptual Chemistry and Phenomenological Models 141Bernard Silvi and Ronald J. Gillespie6.1 Introduction 1416.2 Why ELF and What is ELF? 1426.3 Concepts from the ELF Topology 1446.4 VSEPR Electron Domains and the Volume of ELF Basins 1496.5 Examples of the Correspondence Between ELF Basins and the Domains of the VSEPR Model 1536.6 Conclusions 158Part II Solid State and Surfaces 1637 Solid State Applications of QTAIM and the Source Function – Molecular Crystals, Surfaces, Host–Guest Systems and Molecular Complexes 165Carlo Gatti7.1 Introduction 1657.2 QTAIM Applied to Solids – the TOPOND Package 1667.3 QTAIM Applied to Molecular Crystals 1707.4 QTAIM Applied to Surfaces 1797.5 QTAIM Applied to Host–Guest Systems 1867.6 The Source Function: Theory 1928 Topology and Properties of the Electron Density in Solids 207Víctor Luaña, Miguel A. Blanco, Aurora Costales, Paula Mori-Sánchez, and Angel Martín Penda´s8.1 Introduction 2078.2 The Electron Density Topology and the Atomic Basin Shape 2098.3 Crystalline Isostructural Families and Topological Polymorphism 2138.4 Topological Classification of Crystals 2158.5 Bond Properties – Continuity from the Molecular to the Crystalline Regime 2178.6 Basin Partition of the Thermodynamic Properties 2198.7 Obtaining the Electron Density of Crystals 2229 Atoms in Molecules Theory for Exploring the Nature of the Active Sites on Surfaces 231Yosslen Aray, Jesus Rodríguez, and David Vega9.1 Introduction 2319.2 Implementing the Determination of the Topological Properties of p(r) from a Three-dimensional Grid 2319.3 An Application to Nanocatalyts – Exploring the Structure of the Hydrodesulfurization MoS2 Catalysts 236Part III Experimental Electron Densities and Biological Molecules 25710 Interpretation of Experimental Electron Densities by Combination of the QTAMC and DFT 259Vladimir G. Tsirelson10.1 Introduction 25910.2 Specificity of the Experimental Electron Density 26110.3 Approximate Electronic Energy Densities 26210.4 The Integrated Energy Quantities 27510.5 Concluding Remarks 27611 Topological Analysis of Proteins as Derived from Medium and Highresolution Electron Density: Applications to Electrostatic Properties 285Laurence Leherte, Benoȋt Guillot, Daniel P. Vercauteren, Virginie Pichon-Pesme, Christian Jelsch, Angélique Lagoutte, and Claude Lecomte11.1 Introduction 28511.2 Methodology and Technical Details 28711.3 Topological Properties of Multipolar Electron Density Database 29411.4 Analysis of Local Maxima in Experimental and Promolecular Mediumresolution Electron Density Distributions 29811.5 Calculation of Electrostatic Properties from Atomic and Fragment Representations of Human Aldose Reductase 30511.6 Conclusions and Perspectives 31212 Fragment Transferability Studied Theoretically and Experimentally with QTAIM – Implications for Electron Density and Invariom Modeling 317Peter Luger and Birger Dittrich12.1 Introduction 31712.2 Experimental Electron-density Studies 31812.3 Studying Transferability with QTAIM – Atomic and Bond Topological Properties of Amino Acids and Oligopeptides 32312.4 Invariom Modeling 32812.5 Applications of Aspherical Invariom Scattering Factors 33412.6 Conclusion 338Part IV Chemical Bonding and Reactivity 34313 Interactions Involving Metals – From ‘‘Chemical Categories’’ to QTAIM, and Backwards 345Piero Macchi and Angelo Sironi13.1 Introduction 34513.2 The Electron Density in Isolated Metal Atoms – Hints of Anomalies 34513.3 Two-center Bonding 34913.4 Three-center Bonding 35613.5 Concluding Remarks 37114 Applications of the Quantum Theory of Atoms in Molecules in Organic Chemistry – Charge Distribution, Conformational Analysis and Molecular Interactions 375Jesús Hernández-Trujillo, Fernando Cortés-Guzmn, and Gabriel Cuevas14.1 Introduction 37514.2 Electron Delocalization 37514.3 Conformational Equilibria 38014.4 Aromatic Molecules 39114.5 Conclusions 39515 Aromaticity Analysis by Means of the Quantum Theory of Atoms in Molecules 399Eduard Matito, Jordi Poater, and Miquel Solà15.1 Introduction 39915.2 The Fermi Hole and the Delocalization Index 40115.3 Electron Delocalization in Aromatic Systems 40315.4 Aromaticity Electronic Criteria Based on QTAIM 40415.5 Applications of QTAIM to Aromaticity Analysis 40915.6 Conclusions 41916 Topological Properties of the Electron Distribution in Hydrogen-bonded Systems 425Ignasi Mata, Ibon Alkorta, Enrique Espinosa, Elies Molins, and José Elguero16.1 Introduction 42516.2 Topological Properties of the Hydrogen Bond 42616.3 Energy Properties at the Bond Critical Point (BCP) 43116.4 Topological Properties and Interaction Energy 43516.5 Electron Localization Function, n(r) 43816.6 Complete Interaction Range 44016.7 Concluding Remarks 45017 Relationships between QTAIM and the Decomposition of the Interaction Energy – Comparison of Different Kinds of Hydrogen Bond 453S³awomir J. Grabowski17.1 Introduction 45317.2 Diversity of Hydrogen-bonding Interactions 45617.3 The Decomposition of the Interaction Energy 45917.4 Relationships between the Topological and Energy Properties of Hydrogen Bonds 46017.5 Various Other Interactions Related to Hydrogen Bonds 46417.6 Summary 467Part V Application to Biological Sciences and Drug Design 47118 QTAIM in Drug Discovery and Protein Modeling 473Nagamani Sukumar and Curt M. Breneman18.1 QSAR and Drug Discovery 47318.2 Electron Density as the Basic Variable 47418.3 Atom Typing Scheme and Generation of the Transferable Atom Equivalent (TAE) Library 47618.4 TAE Reconstruction and Descriptor Generation 47818.5 QTAIM-based Descriptors 48018.6 Sample Applications 48918.7 Conclusions 49219 Fleshing-out Pharmacophores with Volume Rendering of the Laplacian of the Charge Density and Hyperwall Visualization Technology 499Preston J. MacDougall and Christopher E. Henze19.1 Introduction 49919.2 Computational and Visualization Methods 50119.3 Subatomic Pharmacophore Insights 50719.4 Conclusion 513References 514Index 515