Shubin Liu, PhD, is a Senior Computational Scientist at the Research Computing Center and Adjunct Professor of Chemistry at the University of North Carolina at Chapel Hill. A pioneer in density-based reactivity theory, he has co-authored over 300 peer-reviewed publications and is the recipient of the Wiley-IJQC Young Investigator Award. Dr. Liu has edited two Wiley-VCH books on conceptual density functional theory. He currently serves as Editor-in-Chief of the International Journal of Quantum Chemistry.

• Foreword xiiiAbout the Author xvPreface xviiPart I Frameworks 11 Introduction 31.1 Theoretical and Computational Chemistry 31.2 Multiscale Modeling 51.3 Orbital-based Theories 71.4 Density Functional Theory 131.5 Scope of This Book 182 Conceptual Density Functional Theory 232.1 Hypotheses and Brief History 232.2 Basic Formulation 252.3 Basic Concepts and Principles 332.4 Extensions 382.5 Concluding Remarks 463 Density-associated Quantities 533.1 Electron Density 543.2 Density Gradient and Laplacian 603.3 Topological Analysis 623.4 Quantum Theory of Atoms in Molecules 633.5 DAQ-based Indices 653.6 DAQs in Excited States 683.7 DAQ in Momentum Space 703.8 Concluding Remarks 714 Information-theoretic Approach 754.1 Overview 754.2 ITA Quantities 764.3 Four ITA Representations 804.4 Three ITA Principles 844.5 Two Identities Among ITA Quantities 874.6 Information Functional Theory 884.7 Applications for ITA Quantities 884.8 Conclusions and Outlook 895 Orbital-free Density Functional Theory 975.1 Overview 975.2 Theoretical Framework 100Contents vii5.3 Descriptors from OF-DFT 1105.4 Applications of OF-DFT 1145.5 Concluding Remarks 1146 Recent Advances in Density-based Frameworks 1196.1 Relationship Among Four Frameworks 1206.2 Topological Analysis of ITA Quantities 1246.3 Energetic Information 1266.4 ITA Extended to Pair Density 1306.5 Extension to Excited States 1326.6 Merging with Machine Learning 1336.7 Concluding Remarks and Outlook 134Part II Applications 1397 Covalent and Noncovalent Interactions 1417.1 Introduction 1417.2 Orbital-based Approaches 1437.3 Density-based Approaches 1457.4 Energetics of Bonding 1547.5 Recent Developments 1567.6 Concluding Remarks 1598 Cooperativity and Frustration 1638.1 Introduction 1638.2 Traditional Theory of Cooperativity 1648.3 Quantification of Cooperativity in Density Functional Theory 1668.4 Classical Theory of Frustration 1728.5 Quantification of Frustration in DFT 1748.6 Principle of Cooperativity and Frustrativity 1788.7 Recent Advances 1798.8 Outlook: From Cooperation and Frustration to Emergence 1809 Homochirality and Principle of Chirality Hierarchy 1839.1 What Is Chirality? 1839.2 Homochirality and Theories of Homochirality 1859.3 Types of Chirality and Chirality Hierarchy 1869.4 Chirality Transmission 1899.5 Chirality Hierarchy Case Study: Helices 1899.6 Chirality Hierarchy Case Study: Propellers 1929.7 Principle of Chirality Hierarchy 1959.8 Concluding Remarks 19610 Electrophilicity and Nucleophilicity 20110.1 Introduction 20110.2 Experimental Scales 20310.3 Quantification in Conceptual Density Functional Theory 20510.4 Quantification in ITA 21110.5 Regioselectivity 21410.6 Benchmark CDFT and ITA Quantifications 21510.7 Ortho/Para and Meta Group Directing Effect 21910.8 Concluding Remarks 22111 Steric Effect and Stereoselectivity 22511.1 Steric Effect 22511.2 Stereoselectivity 22811.3 Experimental Scales of Steric Effect 23211.4 Steric Effect: A Density-based Quantification 23411.5 Validation by Taft's Steric Parameters 23811.6 Stereoselectivity: A Density-based Description 23911.7 Quantification of Stereoselectivity 24111.8 Summary and Conclusions 24212 Acidity and Basicity 24712.1 Introduction 24712.2 Brønsted–Lowry Acidity and Basicity 24912.3 CDFT and Brønsted–Lowry Acidity and Basicity 25312.4 LA and LB 25612.5 HSAB Principle 26012.6 CDFT, ITA, and LA and LB 26112.7 Outlook: A Unified View of Acid–Base Chemistry 26513 Aromaticity and Antiaromaticity 27113.1 Introduction 27113.2 Aromaticity and Antiaromaticity in Ground State 27213.3 Other Types of Aromaticity and Antiaromaticity 27613.4 Descriptors of Aromaticity and Antiaromaticity 27813.5 QTAIM, DFT, CDFT, and Aromaticity 28313.6 ITA, Aromaticity, and Antiaromaticity 28513.7 Concluding Remarks: Toward a Unified Understanding 28814 Catalysis 29514.1 Introduction 29514.2 Theoretical Aspects of Catalysis 30014.3 Understanding Catalysis with Physicochemical Effects 30314.4 Catalytic Cycle and Mechanistic Aspects of Catalysis 30514.5 Emerging Areas and Main Challenges of Catalysis 31014.6 Toward the Ultimate Theory of Catalysis 31414.7 Conclusions 31815 Excited States 32315.1 Fundamentals of Excited States 32415.2 Theoretical Frameworks of Excited States 32515.3 Case Studies of Excited States 32815.4 Density-based Insights for Excited States 33115.5 Frontiers of Excited State Research 33615.6 Summary and Outlook 33816 Miscellaneous Applications 34316.1 Conformational Stability 34416.2 Anomeric and Related Effects 34516.3 SN2 Reactions 34716.4 Proton-coupled Electron Transfer 34816.5 Metal Specificity 34916.6 Oxidation States 35016.7 Impacts of EEFs 35116.8 Polarizability for Macromolecules 35316.9 Merging with ML 35416.10 Summary and Outlook 356Part III Perspectives 36117 From Chemical Concepts to Chemical Understanding 36317.1 Introduction 36317.2 Ontology, Chemical Ontology, and Relations with Physics and Biology 36417.3 Chemical Epistemology 368xii Contents17.4 Representations of Hypotheses 37017.5 Ontological Views of Hypotheses in MOT, VBT, and DFT 37217.6 Chemical Understanding 37417.7 Chemical Concepts as the Foundation 37617.8 Ontological and Epistemological Requirements for Future Theories 37918 Chemical Understanding with Machine Learning and Quantum Computers 38318.1 Introduction 38318.2 The Ultimate Challenge of In Silico Simulations in Chemistry 38518.3 Prior Paradigms: Orbital- and Density-based Frameworks 38718.4 Machine Learning as a New Paradigm 38918.5 The Coming Era of Quantum Computers 39218.6 How to Harvest Chemical Understanding from Theories 39418.7 From Multiscale Modeling to Hierarchical Modeling 39618.8 Concluding Synthesis: Toward a Unified View of Chemical Understanding 399References 399Index 403

Shubin Liu, PhD, is a Senior Computational Scientist at the Research Computing Center and Adjunct Professor of Chemistry at the University of North Carolina at Chapel Hill. A pioneer in density-based reactivity theory, he has co-authored over 300 peer-reviewed publications and is the recipient of the Wiley-IJQC Young Investigator Award. Dr. Liu has edited two Wiley-VCH books on conceptual density functional theory. He currently serves as Editor-in-Chief of the International Journal of Quantum Chemistry.

• Foreword xiiiAbout the Author xvPreface xviiPart I Frameworks 11 Introduction 31.1 Theoretical and Computational Chemistry 31.2 Multiscale Modeling 51.3 Orbital-based Theories 71.4 Density Functional Theory 131.5 Scope of This Book 182 Conceptual Density Functional Theory 232.1 Hypotheses and Brief History 232.2 Basic Formulation 252.3 Basic Concepts and Principles 332.4 Extensions 382.5 Concluding Remarks 463 Density-associated Quantities 533.1 Electron Density 543.2 Density Gradient and Laplacian 603.3 Topological Analysis 623.4 Quantum Theory of Atoms in Molecules 633.5 DAQ-based Indices 653.6 DAQs in Excited States 683.7 DAQ in Momentum Space 703.8 Concluding Remarks 714 Information-theoretic Approach 754.1 Overview 754.2 ITA Quantities 764.3 Four ITA Representations 804.4 Three ITA Principles 844.5 Two Identities Among ITA Quantities 874.6 Information Functional Theory 884.7 Applications for ITA Quantities 884.8 Conclusions and Outlook 895 Orbital-free Density Functional Theory 975.1 Overview 975.2 Theoretical Framework 100Contents vii5.3 Descriptors from OF-DFT 1105.4 Applications of OF-DFT 1145.5 Concluding Remarks 1146 Recent Advances in Density-based Frameworks 1196.1 Relationship Among Four Frameworks 1206.2 Topological Analysis of ITA Quantities 1246.3 Energetic Information 1266.4 ITA Extended to Pair Density 1306.5 Extension to Excited States 1326.6 Merging with Machine Learning 1336.7 Concluding Remarks and Outlook 134Part II Applications 1397 Covalent and Noncovalent Interactions 1417.1 Introduction 1417.2 Orbital-based Approaches 1437.3 Density-based Approaches 1457.4 Energetics of Bonding 1547.5 Recent Developments 1567.6 Concluding Remarks 1598 Cooperativity and Frustration 1638.1 Introduction 1638.2 Traditional Theory of Cooperativity 1648.3 Quantification of Cooperativity in Density Functional Theory 1668.4 Classical Theory of Frustration 1728.5 Quantification of Frustration in DFT 1748.6 Principle of Cooperativity and Frustrativity 1788.7 Recent Advances 1798.8 Outlook: From Cooperation and Frustration to Emergence 1809 Homochirality and Principle of Chirality Hierarchy 1839.1 What Is Chirality? 1839.2 Homochirality and Theories of Homochirality 1859.3 Types of Chirality and Chirality Hierarchy 1869.4 Chirality Transmission 1899.5 Chirality Hierarchy Case Study: Helices 1899.6 Chirality Hierarchy Case Study: Propellers 1929.7 Principle of Chirality Hierarchy 1959.8 Concluding Remarks 19610 Electrophilicity and Nucleophilicity 20110.1 Introduction 20110.2 Experimental Scales 20310.3 Quantification in Conceptual Density Functional Theory 20510.4 Quantification in ITA 21110.5 Regioselectivity 21410.6 Benchmark CDFT and ITA Quantifications 21510.7 Ortho/Para and Meta Group Directing Effect 21910.8 Concluding Remarks 22111 Steric Effect and Stereoselectivity 22511.1 Steric Effect 22511.2 Stereoselectivity 22811.3 Experimental Scales of Steric Effect 23211.4 Steric Effect: A Density-based Quantification 23411.5 Validation by Taft's Steric Parameters 23811.6 Stereoselectivity: A Density-based Description 23911.7 Quantification of Stereoselectivity 24111.8 Summary and Conclusions 24212 Acidity and Basicity 24712.1 Introduction 24712.2 Brønsted–Lowry Acidity and Basicity 24912.3 CDFT and Brønsted–Lowry Acidity and Basicity 25312.4 LA and LB 25612.5 HSAB Principle 26012.6 CDFT, ITA, and LA and LB 26112.7 Outlook: A Unified View of Acid–Base Chemistry 26513 Aromaticity and Antiaromaticity 27113.1 Introduction 27113.2 Aromaticity and Antiaromaticity in Ground State 27213.3 Other Types of Aromaticity and Antiaromaticity 27613.4 Descriptors of Aromaticity and Antiaromaticity 27813.5 QTAIM, DFT, CDFT, and Aromaticity 28313.6 ITA, Aromaticity, and Antiaromaticity 28513.7 Concluding Remarks: Toward a Unified Understanding 28814 Catalysis 29514.1 Introduction 29514.2 Theoretical Aspects of Catalysis 30014.3 Understanding Catalysis with Physicochemical Effects 30314.4 Catalytic Cycle and Mechanistic Aspects of Catalysis 30514.5 Emerging Areas and Main Challenges of Catalysis 31014.6 Toward the Ultimate Theory of Catalysis 31414.7 Conclusions 31815 Excited States 32315.1 Fundamentals of Excited States 32415.2 Theoretical Frameworks of Excited States 32515.3 Case Studies of Excited States 32815.4 Density-based Insights for Excited States 33115.5 Frontiers of Excited State Research 33615.6 Summary and Outlook 33816 Miscellaneous Applications 34316.1 Conformational Stability 34416.2 Anomeric and Related Effects 34516.3 SN2 Reactions 34716.4 Proton-coupled Electron Transfer 34816.5 Metal Specificity 34916.6 Oxidation States 35016.7 Impacts of EEFs 35116.8 Polarizability for Macromolecules 35316.9 Merging with ML 35416.10 Summary and Outlook 356Part III Perspectives 36117 From Chemical Concepts to Chemical Understanding 36317.1 Introduction 36317.2 Ontology, Chemical Ontology, and Relations with Physics and Biology 36417.3 Chemical Epistemology 368xii Contents17.4 Representations of Hypotheses 37017.5 Ontological Views of Hypotheses in MOT, VBT, and DFT 37217.6 Chemical Understanding 37417.7 Chemical Concepts as the Foundation 37617.8 Ontological and Epistemological Requirements for Future Theories 37918 Chemical Understanding with Machine Learning and Quantum Computers 38318.1 Introduction 38318.2 The Ultimate Challenge of In Silico Simulations in Chemistry 38518.3 Prior Paradigms: Orbital- and Density-based Frameworks 38718.4 Machine Learning as a New Paradigm 38918.5 The Coming Era of Quantum Computers 39218.6 How to Harvest Chemical Understanding from Theories 39418.7 From Multiscale Modeling to Hierarchical Modeling 39618.8 Concluding Synthesis: Toward a Unified View of Chemical Understanding 399References 399Index 403

Shubin Liu, PhD, is a Senior Computational Scientist at the Research Computing Center and Adjunct Professor of Chemistry at the University of North Carolina at Chapel Hill. A pioneer in density-based reactivity theory, he has co-authored over 300 peer-reviewed publications and is the recipient of the Wiley-IJQC Young Investigator Award. Dr. Liu has edited two Wiley-VCH books on conceptual density functional theory. He currently serves as Editor-in-Chief of the International Journal of Quantum Chemistry.

• Foreword xiiiAbout the Author xvPreface xviiPart I Frameworks 11 Introduction 31.1 Theoretical and Computational Chemistry 31.2 Multiscale Modeling 51.3 Orbital-based Theories 71.4 Density Functional Theory 131.5 Scope of This Book 182 Conceptual Density Functional Theory 232.1 Hypotheses and Brief History 232.2 Basic Formulation 252.3 Basic Concepts and Principles 332.4 Extensions 382.5 Concluding Remarks 463 Density-associated Quantities 533.1 Electron Density 543.2 Density Gradient and Laplacian 603.3 Topological Analysis 623.4 Quantum Theory of Atoms in Molecules 633.5 DAQ-based Indices 653.6 DAQs in Excited States 683.7 DAQ in Momentum Space 703.8 Concluding Remarks 714 Information-theoretic Approach 754.1 Overview 754.2 ITA Quantities 764.3 Four ITA Representations 804.4 Three ITA Principles 844.5 Two Identities Among ITA Quantities 874.6 Information Functional Theory 884.7 Applications for ITA Quantities 884.8 Conclusions and Outlook 895 Orbital-free Density Functional Theory 975.1 Overview 975.2 Theoretical Framework 100Contents vii5.3 Descriptors from OF-DFT 1105.4 Applications of OF-DFT 1145.5 Concluding Remarks 1146 Recent Advances in Density-based Frameworks 1196.1 Relationship Among Four Frameworks 1206.2 Topological Analysis of ITA Quantities 1246.3 Energetic Information 1266.4 ITA Extended to Pair Density 1306.5 Extension to Excited States 1326.6 Merging with Machine Learning 1336.7 Concluding Remarks and Outlook 134Part II Applications 1397 Covalent and Noncovalent Interactions 1417.1 Introduction 1417.2 Orbital-based Approaches 1437.3 Density-based Approaches 1457.4 Energetics of Bonding 1547.5 Recent Developments 1567.6 Concluding Remarks 1598 Cooperativity and Frustration 1638.1 Introduction 1638.2 Traditional Theory of Cooperativity 1648.3 Quantification of Cooperativity in Density Functional Theory 1668.4 Classical Theory of Frustration 1728.5 Quantification of Frustration in DFT 1748.6 Principle of Cooperativity and Frustrativity 1788.7 Recent Advances 1798.8 Outlook: From Cooperation and Frustration to Emergence 1809 Homochirality and Principle of Chirality Hierarchy 1839.1 What Is Chirality? 1839.2 Homochirality and Theories of Homochirality 1859.3 Types of Chirality and Chirality Hierarchy 1869.4 Chirality Transmission 1899.5 Chirality Hierarchy Case Study: Helices 1899.6 Chirality Hierarchy Case Study: Propellers 1929.7 Principle of Chirality Hierarchy 1959.8 Concluding Remarks 19610 Electrophilicity and Nucleophilicity 20110.1 Introduction 20110.2 Experimental Scales 20310.3 Quantification in Conceptual Density Functional Theory 20510.4 Quantification in ITA 21110.5 Regioselectivity 21410.6 Benchmark CDFT and ITA Quantifications 21510.7 Ortho/Para and Meta Group Directing Effect 21910.8 Concluding Remarks 22111 Steric Effect and Stereoselectivity 22511.1 Steric Effect 22511.2 Stereoselectivity 22811.3 Experimental Scales of Steric Effect 23211.4 Steric Effect: A Density-based Quantification 23411.5 Validation by Taft's Steric Parameters 23811.6 Stereoselectivity: A Density-based Description 23911.7 Quantification of Stereoselectivity 24111.8 Summary and Conclusions 24212 Acidity and Basicity 24712.1 Introduction 24712.2 Brønsted–Lowry Acidity and Basicity 24912.3 CDFT and Brønsted–Lowry Acidity and Basicity 25312.4 LA and LB 25612.5 HSAB Principle 26012.6 CDFT, ITA, and LA and LB 26112.7 Outlook: A Unified View of Acid–Base Chemistry 26513 Aromaticity and Antiaromaticity 27113.1 Introduction 27113.2 Aromaticity and Antiaromaticity in Ground State 27213.3 Other Types of Aromaticity and Antiaromaticity 27613.4 Descriptors of Aromaticity and Antiaromaticity 27813.5 QTAIM, DFT, CDFT, and Aromaticity 28313.6 ITA, Aromaticity, and Antiaromaticity 28513.7 Concluding Remarks: Toward a Unified Understanding 28814 Catalysis 29514.1 Introduction 29514.2 Theoretical Aspects of Catalysis 30014.3 Understanding Catalysis with Physicochemical Effects 30314.4 Catalytic Cycle and Mechanistic Aspects of Catalysis 30514.5 Emerging Areas and Main Challenges of Catalysis 31014.6 Toward the Ultimate Theory of Catalysis 31414.7 Conclusions 31815 Excited States 32315.1 Fundamentals of Excited States 32415.2 Theoretical Frameworks of Excited States 32515.3 Case Studies of Excited States 32815.4 Density-based Insights for Excited States 33115.5 Frontiers of Excited State Research 33615.6 Summary and Outlook 33816 Miscellaneous Applications 34316.1 Conformational Stability 34416.2 Anomeric and Related Effects 34516.3 SN2 Reactions 34716.4 Proton-coupled Electron Transfer 34816.5 Metal Specificity 34916.6 Oxidation States 35016.7 Impacts of EEFs 35116.8 Polarizability for Macromolecules 35316.9 Merging with ML 35416.10 Summary and Outlook 356Part III Perspectives 36117 From Chemical Concepts to Chemical Understanding 36317.1 Introduction 36317.2 Ontology, Chemical Ontology, and Relations with Physics and Biology 36417.3 Chemical Epistemology 368xii Contents17.4 Representations of Hypotheses 37017.5 Ontological Views of Hypotheses in MOT, VBT, and DFT 37217.6 Chemical Understanding 37417.7 Chemical Concepts as the Foundation 37617.8 Ontological and Epistemological Requirements for Future Theories 37918 Chemical Understanding with Machine Learning and Quantum Computers 38318.1 Introduction 38318.2 The Ultimate Challenge of In Silico Simulations in Chemistry 38518.3 Prior Paradigms: Orbital- and Density-based Frameworks 38718.4 Machine Learning as a New Paradigm 38918.5 The Coming Era of Quantum Computers 39218.6 How to Harvest Chemical Understanding from Theories 39418.7 From Multiscale Modeling to Hierarchical Modeling 39618.8 Concluding Synthesis: Toward a Unified View of Chemical Understanding 399References 399Index 403