Dr. Shubin Liu, PhD, is a Senior Computational Scientist at the Research Computing Center and an Adjunct Professor in the Department of Chemistry, University of North Carolina at Chapel Hill. He has been an independent researcher since 2000, focusing on developing a chemical reactivity theory using density functional theory language. Dr. Liu has authored over 270 peer-reviewed publications and is recognized in the field by various scientific awards including the Wiley-IJQC Young Investigator Award. He edited the book Conceptual Density Functional Theory, published by Wiley-VCH in April 2022, and initiated and co/organized the series of international symposiums on Chemical Concepts from Theory and Computation (CCTC).

• Preface xvForeword xvii10 Questions About Exploring Chemical Concepts Through Theory and Computation xix1 Chemical Concepts from Molecular Orbital Theory 1Feng Long Gu, Jincheng Yu, and Weitao Yang1.1 Introduction 11.2 Molecular Orbital Theory 21.3 Canonical Molecular Orbitals 51.4 Frontier Molecular Orbital Theory 51.5 Localized Molecular Orbitals 61.6 Regularized Nonorthogonal Localized Molecular Orbitals 111.7 Molecular Orbitalets 152 Chemical Concepts from Ab Initio Valence Bond Theory 23Chen Zhou, Fuming Ying, and Wei Wu2.1 Introduction 232.2 Ab Initio Valence Bond Theory 242.3 Chemical Concepts in VB Theory 312.4 A Brief Guide to Perform VB Calculations 362.5 Concluding Remarks 383 Chemical Concepts from Conceptual Density Functional Theory 43Frank De Proft3.1 Introduction 433.2 The Fundamentals: Density Functional Theory (DFT) and Kohn-Sham DFT 463.3 The First Derivatives: The Electronic Chemical Potential and the Electron Density 483.4 The Second Derivatives: Chemical Hardness, Fukui Function, Linear Response Function, and Related Quantities 513.5 Perturbational Perspective of Chemical Reactivity 623.6 Conclusions 644 Chemical Concepts from Density-Based Approaches in Density Functional Theory 71Dongbo Zhao, Xin He, Chunying Rong, and Shubin Liu4.1 Introduction 714.2 Four Density-Based Frameworks 724.3 Applications of Density-Based Approaches 794.4 Concluding Remarks 945 Chemical Bonding 101Sudip Pan and Gernot Frenking5.1 Introduction 1015.2 The Physical Mechanism of the Chemical Bond 1035.3 Bonding Models 1085.4 Bond Length and Bond Strength 1115.5 Dative and Electron-Sharing Bonds 1205.6 Polar Bonds 1245.7 Atomic Partial Charges and Atomic Electronegativity 1305.8 Chemical Bonding in Main-Group Compounds: N2, CO, BF, LiF 1315.9 Chemical Bonding of the Heavier Main-Group Atoms 1355.10 Chemical Bonding in Transition Metal Complexes: M(CO)n (M = Ni, Fe, Cr, Ti, Ca; n = 4 - 8) 1435.11 Summary 1466 Partial Charges 161Tian Lu and Qinxue Chen6.1 Concept of Partial Charge 1616.2 Methods of Calculating Partial Charges 1666.3 Partial Charges of Typical Molecules 1766.4 Computer Codes for Evaluating Partial Charges 1796.5 Concluding Remarks 1807 Atoms in Molecules 189Ángel Martín Pendás, Evelio Francisco, Julen Munárriz, and Aurora Costales7.1 Introduction 1897.2 The Quantum Theory of Atoms in Molecules (QTAIM) 1907.3 QTAIM Atoms as Open Quantum Systems 1947.4 Interacting Quantum Atoms (IQA) 2008 Effective Oxidation States Analysis 207Pedro Salvador8.1 The Concept of Oxidation State 2078.2 Oxidation State is Not Related to the Partial Charge 2088.3 The Molecular Orbital Picture of the Ionic Approximation 2108.4 Spin-Resolved Effective Fragment Orbitals and Effective Oxidation States (EOS) Analysis 2138.5 EOS Analysis from Different AIM Schemes 2168.6 Summary 2209 Aromaticity and Antiaromaticity 223Yago García-Rodeja and Miquel Solà9.1 Definition of Aromaticity 2239.2 Physical Foundation 2249.3 Measures of Aromaticity 2269.4 Rules of Aromaticity 2339.5 Metallabenzenes and Related Compounds as an Example 23910 Acidity and Basicity 251Ranita Pal, Himangshu Mondal, and Pratim K. Chattaraj10.1 Introduction 25110.2 Definitions and Theories 25210.3 CDFT-Based Reactivity Descriptors 25710.4 CDFT-Based Electronic Structure Principles 25910.5 Systemics of Lewis Acid-Base Reactions: Drago-Wayland Equation 26110.6 Strengths of Acid and Bases 26210.7 Effect of External Perturbation 26710.8 CDFT and Acidity 27010.9 CDFT and ITA 27210.10 Are Strong Brønsted Acids Necessarily Strong Lewis Acids? 27610.11 Summary 27811 Sigma Hole Supported Interactions: Qualitative Features, Various Incarnations, and Disputations 285Kelling J. Donald11.1 Introduction 28511.2 Many Incarnations and Roles of a Single Phenomenon 28811.3 Related Interactions Elsewhere in the Main Group 30411.4 Contested Interpretations 30811.5 Conclusions 30812 On the Generalization of Marcus Theory for Two-State Photophysical Processes 317Chao-Ping Hsu and Chou-Hsun Yang12.1 Introduction 31712.2 The Golden Rule Rate Expression 31812.3 Application 32512.4 Conclusion 33013 Computational Modeling of CO2 Reduction and Conversion via Heterogeneous and Homogeneous Catalysis 335Yue Zhang, Lin Zhang, Denghui Ma, Xinrui Cao, and Zexing Cao13.1 Introduction 33513.2 Computational Methods 33613.3 Activation and Reduction of CO2 33813.4 Catalytic Coupling of CO2 with CH4 34513.5 Homogeneous Catalytic Conversion of CO2 34813.6 Conclusion and Outlook 35214 Excited States in Conceptual DFT 361Frédéric Guégan, Guillaume Hoffmann, Henry Chermette, and Christophe Morell14.1 Introduction 36114.2 Exploring Ground State Properties Thanks to Excited States 36114.3 Exploring the Reactivity of Excited States with Excited States 37114.4 Conclusion 37515 Modeling the Photophysical Processes of Organic Molecular Aggregates with Inclusion of Intermolecular Interactions and Vibronic Couplings 379WanZhen Liang, Yu-Chen Wang, Shishi Feng, and Yi Zhao15.1 Introduction 37915.2 Theoretical Approaches 38115.3 Concluding Remarks 39716 Duality of Conjugated Π Electrons 407Yirong Mo16.1 Introduction 40716.2 The New Concept of Intramolecular Multibond Strain 41216.3 Theoretical Method 41316.4 Computational Analysis of the Concept of Intramolecular Multibond Strain 41616.5 Experimental Evidence 42216.6 Summary 42617 Energy Decomposition Analysis and Its Applications 433Peifeng Su17.1 Introduction 43317.2 Methodology 43717.3 Applications of GKS-EDA 44217.4 Conclusion 45018 Chemical Concepts in Solids 455Peter C. Müller, David Schnieders, and Richard Dronskowski18.1 The Three Schisms of Solid-State Chemistry 45518.2 Bloch’s Theorem 45718.3 Basis Sets 46018.4 Interpretational Tools 46218.5 Applications 47018.6 Summary 47719 Toward Interpretable Machine Learning Models for Predicting Spectroscopy, Catalysis, and Reactions 481Jun Jiang and Shubin Liu19.1 Introduction 48119.2 ML in a Nutshell 48119.3 Chemistry-Based Descriptors as ML Features 48519.4 Selected ML Applications 49319.5 Concluding Remarks 50720 Learning Design Rules for Catalysts Through Computational Chemistry and Machine Learning 513Aditya Nandy and Heather J. Kulik20.1 Computational Catalysis 51320.2 Machine Learning (ML) in Catalysis 52920.3 Summary 545References 546Index 559

Dr. Shubin Liu, PhD, is a Senior Computational Scientist at the Research Computing Center and an Adjunct Professor in the Department of Chemistry, University of North Carolina at Chapel Hill. He has been an independent researcher since 2000, focusing on developing a chemical reactivity theory using density functional theory language. Dr. Liu has authored over 270 peer-reviewed publications and is recognized in the field by various scientific awards including the Wiley-IJQC Young Investigator Award. He edited the book Conceptual Density Functional Theory, published by Wiley-VCH in April 2022, and initiated and co/organized the series of international symposiums on Chemical Concepts from Theory and Computation (CCTC).

• Preface xvForeword xvii10 Questions About Exploring Chemical Concepts Through Theory and Computation xix1 Chemical Concepts from Molecular Orbital Theory 1Feng Long Gu, Jincheng Yu, and Weitao Yang1.1 Introduction 11.2 Molecular Orbital Theory 21.3 Canonical Molecular Orbitals 51.4 Frontier Molecular Orbital Theory 51.5 Localized Molecular Orbitals 61.6 Regularized Nonorthogonal Localized Molecular Orbitals 111.7 Molecular Orbitalets 152 Chemical Concepts from Ab Initio Valence Bond Theory 23Chen Zhou, Fuming Ying, and Wei Wu2.1 Introduction 232.2 Ab Initio Valence Bond Theory 242.3 Chemical Concepts in VB Theory 312.4 A Brief Guide to Perform VB Calculations 362.5 Concluding Remarks 383 Chemical Concepts from Conceptual Density Functional Theory 43Frank De Proft3.1 Introduction 433.2 The Fundamentals: Density Functional Theory (DFT) and Kohn-Sham DFT 463.3 The First Derivatives: The Electronic Chemical Potential and the Electron Density 483.4 The Second Derivatives: Chemical Hardness, Fukui Function, Linear Response Function, and Related Quantities 513.5 Perturbational Perspective of Chemical Reactivity 623.6 Conclusions 644 Chemical Concepts from Density-Based Approaches in Density Functional Theory 71Dongbo Zhao, Xin He, Chunying Rong, and Shubin Liu4.1 Introduction 714.2 Four Density-Based Frameworks 724.3 Applications of Density-Based Approaches 794.4 Concluding Remarks 945 Chemical Bonding 101Sudip Pan and Gernot Frenking5.1 Introduction 1015.2 The Physical Mechanism of the Chemical Bond 1035.3 Bonding Models 1085.4 Bond Length and Bond Strength 1115.5 Dative and Electron-Sharing Bonds 1205.6 Polar Bonds 1245.7 Atomic Partial Charges and Atomic Electronegativity 1305.8 Chemical Bonding in Main-Group Compounds: N2, CO, BF, LiF 1315.9 Chemical Bonding of the Heavier Main-Group Atoms 1355.10 Chemical Bonding in Transition Metal Complexes: M(CO)n (M = Ni, Fe, Cr, Ti, Ca; n = 4 - 8) 1435.11 Summary 1466 Partial Charges 161Tian Lu and Qinxue Chen6.1 Concept of Partial Charge 1616.2 Methods of Calculating Partial Charges 1666.3 Partial Charges of Typical Molecules 1766.4 Computer Codes for Evaluating Partial Charges 1796.5 Concluding Remarks 1807 Atoms in Molecules 189Ángel Martín Pendás, Evelio Francisco, Julen Munárriz, and Aurora Costales7.1 Introduction 1897.2 The Quantum Theory of Atoms in Molecules (QTAIM) 1907.3 QTAIM Atoms as Open Quantum Systems 1947.4 Interacting Quantum Atoms (IQA) 2008 Effective Oxidation States Analysis 207Pedro Salvador8.1 The Concept of Oxidation State 2078.2 Oxidation State is Not Related to the Partial Charge 2088.3 The Molecular Orbital Picture of the Ionic Approximation 2108.4 Spin-Resolved Effective Fragment Orbitals and Effective Oxidation States (EOS) Analysis 2138.5 EOS Analysis from Different AIM Schemes 2168.6 Summary 2209 Aromaticity and Antiaromaticity 223Yago García-Rodeja and Miquel Solà9.1 Definition of Aromaticity 2239.2 Physical Foundation 2249.3 Measures of Aromaticity 2269.4 Rules of Aromaticity 2339.5 Metallabenzenes and Related Compounds as an Example 23910 Acidity and Basicity 251Ranita Pal, Himangshu Mondal, and Pratim K. Chattaraj10.1 Introduction 25110.2 Definitions and Theories 25210.3 CDFT-Based Reactivity Descriptors 25710.4 CDFT-Based Electronic Structure Principles 25910.5 Systemics of Lewis Acid-Base Reactions: Drago-Wayland Equation 26110.6 Strengths of Acid and Bases 26210.7 Effect of External Perturbation 26710.8 CDFT and Acidity 27010.9 CDFT and ITA 27210.10 Are Strong Brønsted Acids Necessarily Strong Lewis Acids? 27610.11 Summary 27811 Sigma Hole Supported Interactions: Qualitative Features, Various Incarnations, and Disputations 285Kelling J. Donald11.1 Introduction 28511.2 Many Incarnations and Roles of a Single Phenomenon 28811.3 Related Interactions Elsewhere in the Main Group 30411.4 Contested Interpretations 30811.5 Conclusions 30812 On the Generalization of Marcus Theory for Two-State Photophysical Processes 317Chao-Ping Hsu and Chou-Hsun Yang12.1 Introduction 31712.2 The Golden Rule Rate Expression 31812.3 Application 32512.4 Conclusion 33013 Computational Modeling of CO2 Reduction and Conversion via Heterogeneous and Homogeneous Catalysis 335Yue Zhang, Lin Zhang, Denghui Ma, Xinrui Cao, and Zexing Cao13.1 Introduction 33513.2 Computational Methods 33613.3 Activation and Reduction of CO2 33813.4 Catalytic Coupling of CO2 with CH4 34513.5 Homogeneous Catalytic Conversion of CO2 34813.6 Conclusion and Outlook 35214 Excited States in Conceptual DFT 361Frédéric Guégan, Guillaume Hoffmann, Henry Chermette, and Christophe Morell14.1 Introduction 36114.2 Exploring Ground State Properties Thanks to Excited States 36114.3 Exploring the Reactivity of Excited States with Excited States 37114.4 Conclusion 37515 Modeling the Photophysical Processes of Organic Molecular Aggregates with Inclusion of Intermolecular Interactions and Vibronic Couplings 379WanZhen Liang, Yu-Chen Wang, Shishi Feng, and Yi Zhao15.1 Introduction 37915.2 Theoretical Approaches 38115.3 Concluding Remarks 39716 Duality of Conjugated Π Electrons 407Yirong Mo16.1 Introduction 40716.2 The New Concept of Intramolecular Multibond Strain 41216.3 Theoretical Method 41316.4 Computational Analysis of the Concept of Intramolecular Multibond Strain 41616.5 Experimental Evidence 42216.6 Summary 42617 Energy Decomposition Analysis and Its Applications 433Peifeng Su17.1 Introduction 43317.2 Methodology 43717.3 Applications of GKS-EDA 44217.4 Conclusion 45018 Chemical Concepts in Solids 455Peter C. Müller, David Schnieders, and Richard Dronskowski18.1 The Three Schisms of Solid-State Chemistry 45518.2 Bloch’s Theorem 45718.3 Basis Sets 46018.4 Interpretational Tools 46218.5 Applications 47018.6 Summary 47719 Toward Interpretable Machine Learning Models for Predicting Spectroscopy, Catalysis, and Reactions 481Jun Jiang and Shubin Liu19.1 Introduction 48119.2 ML in a Nutshell 48119.3 Chemistry-Based Descriptors as ML Features 48519.4 Selected ML Applications 49319.5 Concluding Remarks 50720 Learning Design Rules for Catalysts Through Computational Chemistry and Machine Learning 513Aditya Nandy and Heather J. Kulik20.1 Computational Catalysis 51320.2 Machine Learning (ML) in Catalysis 52920.3 Summary 545References 546Index 559

Dr. Shubin Liu, PhD, is a Senior Computational Scientist at the Research Computing Center and an Adjunct Professor in the Department of Chemistry, University of North Carolina at Chapel Hill. He has been an independent researcher since 2000, focusing on developing a chemical reactivity theory using density functional theory language. Dr. Liu has authored over 270 peer-reviewed publications and is recognized in the field by various scientific awards including the Wiley-IJQC Young Investigator Award. He edited the book Conceptual Density Functional Theory, published by Wiley-VCH in April 2022, and initiated and co/organized the series of international symposiums on Chemical Concepts from Theory and Computation (CCTC).

• Preface xvForeword xvii10 Questions About Exploring Chemical Concepts Through Theory and Computation xix1 Chemical Concepts from Molecular Orbital Theory 1Feng Long Gu, Jincheng Yu, and Weitao Yang1.1 Introduction 11.2 Molecular Orbital Theory 21.3 Canonical Molecular Orbitals 51.4 Frontier Molecular Orbital Theory 51.5 Localized Molecular Orbitals 61.6 Regularized Nonorthogonal Localized Molecular Orbitals 111.7 Molecular Orbitalets 152 Chemical Concepts from Ab Initio Valence Bond Theory 23Chen Zhou, Fuming Ying, and Wei Wu2.1 Introduction 232.2 Ab Initio Valence Bond Theory 242.3 Chemical Concepts in VB Theory 312.4 A Brief Guide to Perform VB Calculations 362.5 Concluding Remarks 383 Chemical Concepts from Conceptual Density Functional Theory 43Frank De Proft3.1 Introduction 433.2 The Fundamentals: Density Functional Theory (DFT) and Kohn-Sham DFT 463.3 The First Derivatives: The Electronic Chemical Potential and the Electron Density 483.4 The Second Derivatives: Chemical Hardness, Fukui Function, Linear Response Function, and Related Quantities 513.5 Perturbational Perspective of Chemical Reactivity 623.6 Conclusions 644 Chemical Concepts from Density-Based Approaches in Density Functional Theory 71Dongbo Zhao, Xin He, Chunying Rong, and Shubin Liu4.1 Introduction 714.2 Four Density-Based Frameworks 724.3 Applications of Density-Based Approaches 794.4 Concluding Remarks 945 Chemical Bonding 101Sudip Pan and Gernot Frenking5.1 Introduction 1015.2 The Physical Mechanism of the Chemical Bond 1035.3 Bonding Models 1085.4 Bond Length and Bond Strength 1115.5 Dative and Electron-Sharing Bonds 1205.6 Polar Bonds 1245.7 Atomic Partial Charges and Atomic Electronegativity 1305.8 Chemical Bonding in Main-Group Compounds: N2, CO, BF, LiF 1315.9 Chemical Bonding of the Heavier Main-Group Atoms 1355.10 Chemical Bonding in Transition Metal Complexes: M(CO)n (M = Ni, Fe, Cr, Ti, Ca; n = 4 - 8) 1435.11 Summary 1466 Partial Charges 161Tian Lu and Qinxue Chen6.1 Concept of Partial Charge 1616.2 Methods of Calculating Partial Charges 1666.3 Partial Charges of Typical Molecules 1766.4 Computer Codes for Evaluating Partial Charges 1796.5 Concluding Remarks 1807 Atoms in Molecules 189Ángel Martín Pendás, Evelio Francisco, Julen Munárriz, and Aurora Costales7.1 Introduction 1897.2 The Quantum Theory of Atoms in Molecules (QTAIM) 1907.3 QTAIM Atoms as Open Quantum Systems 1947.4 Interacting Quantum Atoms (IQA) 2008 Effective Oxidation States Analysis 207Pedro Salvador8.1 The Concept of Oxidation State 2078.2 Oxidation State is Not Related to the Partial Charge 2088.3 The Molecular Orbital Picture of the Ionic Approximation 2108.4 Spin-Resolved Effective Fragment Orbitals and Effective Oxidation States (EOS) Analysis 2138.5 EOS Analysis from Different AIM Schemes 2168.6 Summary 2209 Aromaticity and Antiaromaticity 223Yago García-Rodeja and Miquel Solà9.1 Definition of Aromaticity 2239.2 Physical Foundation 2249.3 Measures of Aromaticity 2269.4 Rules of Aromaticity 2339.5 Metallabenzenes and Related Compounds as an Example 23910 Acidity and Basicity 251Ranita Pal, Himangshu Mondal, and Pratim K. Chattaraj10.1 Introduction 25110.2 Definitions and Theories 25210.3 CDFT-Based Reactivity Descriptors 25710.4 CDFT-Based Electronic Structure Principles 25910.5 Systemics of Lewis Acid-Base Reactions: Drago-Wayland Equation 26110.6 Strengths of Acid and Bases 26210.7 Effect of External Perturbation 26710.8 CDFT and Acidity 27010.9 CDFT and ITA 27210.10 Are Strong Brønsted Acids Necessarily Strong Lewis Acids? 27610.11 Summary 27811 Sigma Hole Supported Interactions: Qualitative Features, Various Incarnations, and Disputations 285Kelling J. Donald11.1 Introduction 28511.2 Many Incarnations and Roles of a Single Phenomenon 28811.3 Related Interactions Elsewhere in the Main Group 30411.4 Contested Interpretations 30811.5 Conclusions 30812 On the Generalization of Marcus Theory for Two-State Photophysical Processes 317Chao-Ping Hsu and Chou-Hsun Yang12.1 Introduction 31712.2 The Golden Rule Rate Expression 31812.3 Application 32512.4 Conclusion 33013 Computational Modeling of CO2 Reduction and Conversion via Heterogeneous and Homogeneous Catalysis 335Yue Zhang, Lin Zhang, Denghui Ma, Xinrui Cao, and Zexing Cao13.1 Introduction 33513.2 Computational Methods 33613.3 Activation and Reduction of CO2 33813.4 Catalytic Coupling of CO2 with CH4 34513.5 Homogeneous Catalytic Conversion of CO2 34813.6 Conclusion and Outlook 35214 Excited States in Conceptual DFT 361Frédéric Guégan, Guillaume Hoffmann, Henry Chermette, and Christophe Morell14.1 Introduction 36114.2 Exploring Ground State Properties Thanks to Excited States 36114.3 Exploring the Reactivity of Excited States with Excited States 37114.4 Conclusion 37515 Modeling the Photophysical Processes of Organic Molecular Aggregates with Inclusion of Intermolecular Interactions and Vibronic Couplings 379WanZhen Liang, Yu-Chen Wang, Shishi Feng, and Yi Zhao15.1 Introduction 37915.2 Theoretical Approaches 38115.3 Concluding Remarks 39716 Duality of Conjugated Π Electrons 407Yirong Mo16.1 Introduction 40716.2 The New Concept of Intramolecular Multibond Strain 41216.3 Theoretical Method 41316.4 Computational Analysis of the Concept of Intramolecular Multibond Strain 41616.5 Experimental Evidence 42216.6 Summary 42617 Energy Decomposition Analysis and Its Applications 433Peifeng Su17.1 Introduction 43317.2 Methodology 43717.3 Applications of GKS-EDA 44217.4 Conclusion 45018 Chemical Concepts in Solids 455Peter C. Müller, David Schnieders, and Richard Dronskowski18.1 The Three Schisms of Solid-State Chemistry 45518.2 Bloch’s Theorem 45718.3 Basis Sets 46018.4 Interpretational Tools 46218.5 Applications 47018.6 Summary 47719 Toward Interpretable Machine Learning Models for Predicting Spectroscopy, Catalysis, and Reactions 481Jun Jiang and Shubin Liu19.1 Introduction 48119.2 ML in a Nutshell 48119.3 Chemistry-Based Descriptors as ML Features 48519.4 Selected ML Applications 49319.5 Concluding Remarks 50720 Learning Design Rules for Catalysts Through Computational Chemistry and Machine Learning 513Aditya Nandy and Heather J. Kulik20.1 Computational Catalysis 51320.2 Machine Learning (ML) in Catalysis 52920.3 Summary 545References 546Index 559