Miquel Solà, PhD, is Full Professor in the Department of Chemistry and researcher of the Institute of Computational Chemistry and Catalysis at the University of Girona. Alexander I. Boldyrev, PhD, is Full Professor in the Department of Chemistry and Biochemistry at Utah State University in the United States. Michał K. Cyrański, PhD, is Full Professor in the Faculty of Chemistry at the University of Warsaw in Poland. Tadeusz M. Krygowski, PhD, is Emeritus Professor in the Faculty of Chemistry at the University of Warsaw in Poland. Gabriel Merino, PhD, is Full Professor at the Centro de Investigación y de Estudios Avanzados in Mérida, Mexico.

• Foreword xiPreface xiiiList of Abbreviations xvii1 Historical Overview 1References 72 Simple Electron Counting Rules 112.1 Introduction 112.2 Hückel’s 4n +2 Rule 122.3 Baird’s 4n π-Electron Rule for the Lowest-Lying Triplet Excited State 132.4 Soncini and Fowler’s Rule 162.5 Möbius’ 4n π-Electron Rule 162.6 The Linking Number Rule 182.7 Platt’s Ring Perimeter Model 192.8 Clar’s π-Sextet Rule 202.8.1 Glidewell and Lloyd’s Rule 232.8.2 The Y-Rule 232.9 Hirsch’s 2(n +1)2 Rule 242.10 The 2n2 +2n+ 1 (S = n+ 1/2) Rule 262.11 Wade–Mingos’ 2n+ 2 Rule 262.11.1 Jemmis’ mno Rule 272.11.2 Equivalence between Hückel’s andWade–Mingos’ Rules 282.12 Other Rules 29References 303 Aromaticity from Organic to Inorganic Compounds 353.1 Introduction 353.2 π-Aromatic Inorganic Species 363.3 Aromaticity in Main Group Metal Compounds 423.4 Aromaticity in Transition Metal Compounds 443.5 Conclusions 49References 494 Stability and Reactivity in Aromatic Compounds 554.1 Introduction 554.2 Aromaticity and Thermodynamic Stability 564.3 Aromaticity and Kinetic Stability 614.3.1 Acenes 614.3.2 Pericyclic Reactions 644.3.2.1 Diels–Alder Cycloadditions 654.3.2.2 [2+2+2] Cycloadditions 674.3.2.3 [1,7]-Sigmatropic Migrations 684.3.2.4 Fullerene Additions 68References 725 Descriptors of Aromaticity: Geometric Criteria 775.1 Introduction 775.2 Geometry-Based Estimation of the Molecular Energy 785.3 Bond Length Alternation as a Basis for Defining Aromaticity Indices 805.3.1 The Julg Aromaticity Index AJ 815.3.2 The Harmonic Oscillator Model of Aromaticity, HOMA (1972 and 1993) 825.4 Separation of HOMA into Two Components EN and GEO (1996) 855.5 Harmonic Oscillator Model of Electron Delocalization, HOMED (2007) 865.6 Harmonic Oscillator Model for Heterocycles with π Electron and/or n-Electron Delocalization: The HOMHED Index (2012) 875.7 Applications of the Bond Orders for Estimating Aromaticity 885.8 Bird’s Aromaticity Indices I5 and I6 (1985) 905.9 Pozharskii Criterion of Aromaticity, ΔN (1985) and Bond Alternation Coefficient, BAC (1995) 905.10 Applications 915.11 Impact of the Electric Field on Aromaticity 945.12 Stacking Interactions versus H-Bonding in Nucleobases 955.13 Showing the Interaction Path for Substituent Effects 965.14 Applications in the Field of Quasiaromatic Systems 1005.15 Extension of HOMA to Noncyclic and Non-π-electron Systems 1015.16 Conclusions 103References 1046 Descriptors of Aromaticity: Energetic Criteria 1116.1 Introduction 1116.2 Thermochemical Approaches 1146.3 Energetic Approaches Based on Molecular Geometry 1156.4 Theoretical Approaches 117References 1267 Descriptors of Aromaticity: Magnetic Criteria 1317.1 Introduction 1317.2 NMR Chemical Shifts 1347.3 Nucleus Independent Chemical Shifts 1357.4 Magnetically Induced Current Densities 1387.5 Anisotropy of the Induced Current Density Tensor 140References 1418 Descriptors of Aromaticity: Electronic Criteria 1458.1 Introduction 1458.2 Density Functions 1468.3 Measures of Electron Delocalization 1508.3.1 The Electron Sharing Indices (ESI) 1508.3.2 The Electron Localization Function (ELF) 1528.4 Electronic Descriptors of Aromaticity 155References 1609 Heteroaromaticity 1659.1 Introduction 1659.2 Six-Membered Organic and Inorganic Heterocycles 1689.3 Polycyclic Heteroaromatic Hydrocarbons 1789.4 Five-Membered Organic Heterocycles 1799.5 Aromaticity of Nucleic Bases 183References 18710 Möbius Aromaticity 19310.1 Introduction 19310.2 Metallacyclic Möbius Aromatic Species 19710.3 Macrocyclic Möbius Aromaticity 199References 20411 𝛔-, 𝛑-, 𝛅-, and 𝛗-Aromaticity 20711.1 Introduction 20711.2 σ-Aromatic and σ-Antiaromatic Species 20911.2.1 σ-Aromatic Species 20911.2.2 σ-Antiaromatic Species 21011.3 σ-, π-Doubly Aromatic, and σ-, π-Doubly Antiaromatic Species and Species with σ-, π-Conflicting Aromaticity 21111.3.1 σ-, π-Doubly Aromatic Species 21111.3.2 σ-, π-Doubly Antiaromatic Species 21211.3.3 Species with σ-Antiaromaticity and π-Aromaticity 21311.3.4 Species with σ-Aromaticity and π-Antiaromaticity 21411.4 δ-Aromaticity 21511.5 ϕ-Aromaticity 21811.6 Conclusions 219References 22012 The Distortivity of 𝛑-Electrons 22312.1 Introduction 22312.2 The Kekulean Distortion 22412.3 Frequencies of the Kekulé Vibrational Mode in Benzene 22512.4 Changes in Aromaticity in the Kekulean Distortion 22712.5 The Maximum Hardness and Minimum Polarizability Principles 22812.6 The Distortive Nature of π-Electrons 22912.7 Conclusions 236References 23613 Three-Dimensional Aromaticity 24113.1 Introduction 24113.2 Spherical Aromaticity 24213.2.1 Aromaticity on the Surface of the Sphere 24213.2.2 Aromaticity Inside the Sphere 24713.2.2.1 Closo Boranes 24813.2.2.2 Jellium Cluster Model 25013.3 Octahedral Aromaticity 25113.4 Cubic Aromaticity 25313.5 Tetrahedral Aromaticity 25513.6 Cylindrical Aromaticity 256References 25914 Excited State Aromaticity 26514.1 Introduction 26514.2 Theoretical and Experimental Studies of Excited State Aromaticity 26614.2.1 Theoretical and Computational Studies 26714.2.2 Experimental Studies 26914.3 Influence of Aromaticity in the Excited State Properties 27114.3.1 Molecular Dipole Moments 27114.3.2 Singlet-Triplet Energy Gaps 27214.3.3 Photoacidity 27314.4 Influence of Aromaticity in the Excited State Reactivity 27414.4.1 Photoisomerizations 27514.4.2 Excited State Intramolecular Proton Transfer 27614.4.3 Photochemical Formation of Ortho-Xylylenes 27814.4.4 Photochemical Pericyclic Reactions 279References 281Index 285

Miquel Solà, PhD, is Full Professor in the Department of Chemistry and researcher of the Institute of Computational Chemistry and Catalysis at the University of Girona. Alexander I. Boldyrev, PhD, is Full Professor in the Department of Chemistry and Biochemistry at Utah State University in the United States. Michał K. Cyrański, PhD, is Full Professor in the Faculty of Chemistry at the University of Warsaw in Poland. Tadeusz M. Krygowski, PhD, is Emeritus Professor in the Faculty of Chemistry at the University of Warsaw in Poland. Gabriel Merino, PhD, is Full Professor at the Centro de Investigación y de Estudios Avanzados in Mérida, Mexico.

• Foreword xiPreface xiiiList of Abbreviations xvii1 Historical Overview 1References 72 Simple Electron Counting Rules 112.1 Introduction 112.2 Hückel’s 4n +2 Rule 122.3 Baird’s 4n π-Electron Rule for the Lowest-Lying Triplet Excited State 132.4 Soncini and Fowler’s Rule 162.5 Möbius’ 4n π-Electron Rule 162.6 The Linking Number Rule 182.7 Platt’s Ring Perimeter Model 192.8 Clar’s π-Sextet Rule 202.8.1 Glidewell and Lloyd’s Rule 232.8.2 The Y-Rule 232.9 Hirsch’s 2(n +1)2 Rule 242.10 The 2n2 +2n+ 1 (S = n+ 1/2) Rule 262.11 Wade–Mingos’ 2n+ 2 Rule 262.11.1 Jemmis’ mno Rule 272.11.2 Equivalence between Hückel’s andWade–Mingos’ Rules 282.12 Other Rules 29References 303 Aromaticity from Organic to Inorganic Compounds 353.1 Introduction 353.2 π-Aromatic Inorganic Species 363.3 Aromaticity in Main Group Metal Compounds 423.4 Aromaticity in Transition Metal Compounds 443.5 Conclusions 49References 494 Stability and Reactivity in Aromatic Compounds 554.1 Introduction 554.2 Aromaticity and Thermodynamic Stability 564.3 Aromaticity and Kinetic Stability 614.3.1 Acenes 614.3.2 Pericyclic Reactions 644.3.2.1 Diels–Alder Cycloadditions 654.3.2.2 [2+2+2] Cycloadditions 674.3.2.3 [1,7]-Sigmatropic Migrations 684.3.2.4 Fullerene Additions 68References 725 Descriptors of Aromaticity: Geometric Criteria 775.1 Introduction 775.2 Geometry-Based Estimation of the Molecular Energy 785.3 Bond Length Alternation as a Basis for Defining Aromaticity Indices 805.3.1 The Julg Aromaticity Index AJ 815.3.2 The Harmonic Oscillator Model of Aromaticity, HOMA (1972 and 1993) 825.4 Separation of HOMA into Two Components EN and GEO (1996) 855.5 Harmonic Oscillator Model of Electron Delocalization, HOMED (2007) 865.6 Harmonic Oscillator Model for Heterocycles with π Electron and/or n-Electron Delocalization: The HOMHED Index (2012) 875.7 Applications of the Bond Orders for Estimating Aromaticity 885.8 Bird’s Aromaticity Indices I5 and I6 (1985) 905.9 Pozharskii Criterion of Aromaticity, ΔN (1985) and Bond Alternation Coefficient, BAC (1995) 905.10 Applications 915.11 Impact of the Electric Field on Aromaticity 945.12 Stacking Interactions versus H-Bonding in Nucleobases 955.13 Showing the Interaction Path for Substituent Effects 965.14 Applications in the Field of Quasiaromatic Systems 1005.15 Extension of HOMA to Noncyclic and Non-π-electron Systems 1015.16 Conclusions 103References 1046 Descriptors of Aromaticity: Energetic Criteria 1116.1 Introduction 1116.2 Thermochemical Approaches 1146.3 Energetic Approaches Based on Molecular Geometry 1156.4 Theoretical Approaches 117References 1267 Descriptors of Aromaticity: Magnetic Criteria 1317.1 Introduction 1317.2 NMR Chemical Shifts 1347.3 Nucleus Independent Chemical Shifts 1357.4 Magnetically Induced Current Densities 1387.5 Anisotropy of the Induced Current Density Tensor 140References 1418 Descriptors of Aromaticity: Electronic Criteria 1458.1 Introduction 1458.2 Density Functions 1468.3 Measures of Electron Delocalization 1508.3.1 The Electron Sharing Indices (ESI) 1508.3.2 The Electron Localization Function (ELF) 1528.4 Electronic Descriptors of Aromaticity 155References 1609 Heteroaromaticity 1659.1 Introduction 1659.2 Six-Membered Organic and Inorganic Heterocycles 1689.3 Polycyclic Heteroaromatic Hydrocarbons 1789.4 Five-Membered Organic Heterocycles 1799.5 Aromaticity of Nucleic Bases 183References 18710 Möbius Aromaticity 19310.1 Introduction 19310.2 Metallacyclic Möbius Aromatic Species 19710.3 Macrocyclic Möbius Aromaticity 199References 20411 𝛔-, 𝛑-, 𝛅-, and 𝛗-Aromaticity 20711.1 Introduction 20711.2 σ-Aromatic and σ-Antiaromatic Species 20911.2.1 σ-Aromatic Species 20911.2.2 σ-Antiaromatic Species 21011.3 σ-, π-Doubly Aromatic, and σ-, π-Doubly Antiaromatic Species and Species with σ-, π-Conflicting Aromaticity 21111.3.1 σ-, π-Doubly Aromatic Species 21111.3.2 σ-, π-Doubly Antiaromatic Species 21211.3.3 Species with σ-Antiaromaticity and π-Aromaticity 21311.3.4 Species with σ-Aromaticity and π-Antiaromaticity 21411.4 δ-Aromaticity 21511.5 ϕ-Aromaticity 21811.6 Conclusions 219References 22012 The Distortivity of 𝛑-Electrons 22312.1 Introduction 22312.2 The Kekulean Distortion 22412.3 Frequencies of the Kekulé Vibrational Mode in Benzene 22512.4 Changes in Aromaticity in the Kekulean Distortion 22712.5 The Maximum Hardness and Minimum Polarizability Principles 22812.6 The Distortive Nature of π-Electrons 22912.7 Conclusions 236References 23613 Three-Dimensional Aromaticity 24113.1 Introduction 24113.2 Spherical Aromaticity 24213.2.1 Aromaticity on the Surface of the Sphere 24213.2.2 Aromaticity Inside the Sphere 24713.2.2.1 Closo Boranes 24813.2.2.2 Jellium Cluster Model 25013.3 Octahedral Aromaticity 25113.4 Cubic Aromaticity 25313.5 Tetrahedral Aromaticity 25513.6 Cylindrical Aromaticity 256References 25914 Excited State Aromaticity 26514.1 Introduction 26514.2 Theoretical and Experimental Studies of Excited State Aromaticity 26614.2.1 Theoretical and Computational Studies 26714.2.2 Experimental Studies 26914.3 Influence of Aromaticity in the Excited State Properties 27114.3.1 Molecular Dipole Moments 27114.3.2 Singlet-Triplet Energy Gaps 27214.3.3 Photoacidity 27314.4 Influence of Aromaticity in the Excited State Reactivity 27414.4.1 Photoisomerizations 27514.4.2 Excited State Intramolecular Proton Transfer 27614.4.3 Photochemical Formation of Ortho-Xylylenes 27814.4.4 Photochemical Pericyclic Reactions 279References 281Index 285

Miquel Solà, PhD, is Full Professor in the Department of Chemistry and researcher of the Institute of Computational Chemistry and Catalysis at the University of Girona. Alexander I. Boldyrev, PhD, is Full Professor in the Department of Chemistry and Biochemistry at Utah State University in the United States. Michał K. Cyrański, PhD, is Full Professor in the Faculty of Chemistry at the University of Warsaw in Poland. Tadeusz M. Krygowski, PhD, is Emeritus Professor in the Faculty of Chemistry at the University of Warsaw in Poland. Gabriel Merino, PhD, is Full Professor at the Centro de Investigación y de Estudios Avanzados in Mérida, Mexico.

• Foreword xiPreface xiiiList of Abbreviations xvii1 Historical Overview 1References 72 Simple Electron Counting Rules 112.1 Introduction 112.2 Hückel’s 4n +2 Rule 122.3 Baird’s 4n π-Electron Rule for the Lowest-Lying Triplet Excited State 132.4 Soncini and Fowler’s Rule 162.5 Möbius’ 4n π-Electron Rule 162.6 The Linking Number Rule 182.7 Platt’s Ring Perimeter Model 192.8 Clar’s π-Sextet Rule 202.8.1 Glidewell and Lloyd’s Rule 232.8.2 The Y-Rule 232.9 Hirsch’s 2(n +1)2 Rule 242.10 The 2n2 +2n+ 1 (S = n+ 1/2) Rule 262.11 Wade–Mingos’ 2n+ 2 Rule 262.11.1 Jemmis’ mno Rule 272.11.2 Equivalence between Hückel’s andWade–Mingos’ Rules 282.12 Other Rules 29References 303 Aromaticity from Organic to Inorganic Compounds 353.1 Introduction 353.2 π-Aromatic Inorganic Species 363.3 Aromaticity in Main Group Metal Compounds 423.4 Aromaticity in Transition Metal Compounds 443.5 Conclusions 49References 494 Stability and Reactivity in Aromatic Compounds 554.1 Introduction 554.2 Aromaticity and Thermodynamic Stability 564.3 Aromaticity and Kinetic Stability 614.3.1 Acenes 614.3.2 Pericyclic Reactions 644.3.2.1 Diels–Alder Cycloadditions 654.3.2.2 [2+2+2] Cycloadditions 674.3.2.3 [1,7]-Sigmatropic Migrations 684.3.2.4 Fullerene Additions 68References 725 Descriptors of Aromaticity: Geometric Criteria 775.1 Introduction 775.2 Geometry-Based Estimation of the Molecular Energy 785.3 Bond Length Alternation as a Basis for Defining Aromaticity Indices 805.3.1 The Julg Aromaticity Index AJ 815.3.2 The Harmonic Oscillator Model of Aromaticity, HOMA (1972 and 1993) 825.4 Separation of HOMA into Two Components EN and GEO (1996) 855.5 Harmonic Oscillator Model of Electron Delocalization, HOMED (2007) 865.6 Harmonic Oscillator Model for Heterocycles with π Electron and/or n-Electron Delocalization: The HOMHED Index (2012) 875.7 Applications of the Bond Orders for Estimating Aromaticity 885.8 Bird’s Aromaticity Indices I5 and I6 (1985) 905.9 Pozharskii Criterion of Aromaticity, ΔN (1985) and Bond Alternation Coefficient, BAC (1995) 905.10 Applications 915.11 Impact of the Electric Field on Aromaticity 945.12 Stacking Interactions versus H-Bonding in Nucleobases 955.13 Showing the Interaction Path for Substituent Effects 965.14 Applications in the Field of Quasiaromatic Systems 1005.15 Extension of HOMA to Noncyclic and Non-π-electron Systems 1015.16 Conclusions 103References 1046 Descriptors of Aromaticity: Energetic Criteria 1116.1 Introduction 1116.2 Thermochemical Approaches 1146.3 Energetic Approaches Based on Molecular Geometry 1156.4 Theoretical Approaches 117References 1267 Descriptors of Aromaticity: Magnetic Criteria 1317.1 Introduction 1317.2 NMR Chemical Shifts 1347.3 Nucleus Independent Chemical Shifts 1357.4 Magnetically Induced Current Densities 1387.5 Anisotropy of the Induced Current Density Tensor 140References 1418 Descriptors of Aromaticity: Electronic Criteria 1458.1 Introduction 1458.2 Density Functions 1468.3 Measures of Electron Delocalization 1508.3.1 The Electron Sharing Indices (ESI) 1508.3.2 The Electron Localization Function (ELF) 1528.4 Electronic Descriptors of Aromaticity 155References 1609 Heteroaromaticity 1659.1 Introduction 1659.2 Six-Membered Organic and Inorganic Heterocycles 1689.3 Polycyclic Heteroaromatic Hydrocarbons 1789.4 Five-Membered Organic Heterocycles 1799.5 Aromaticity of Nucleic Bases 183References 18710 Möbius Aromaticity 19310.1 Introduction 19310.2 Metallacyclic Möbius Aromatic Species 19710.3 Macrocyclic Möbius Aromaticity 199References 20411 𝛔-, 𝛑-, 𝛅-, and 𝛗-Aromaticity 20711.1 Introduction 20711.2 σ-Aromatic and σ-Antiaromatic Species 20911.2.1 σ-Aromatic Species 20911.2.2 σ-Antiaromatic Species 21011.3 σ-, π-Doubly Aromatic, and σ-, π-Doubly Antiaromatic Species and Species with σ-, π-Conflicting Aromaticity 21111.3.1 σ-, π-Doubly Aromatic Species 21111.3.2 σ-, π-Doubly Antiaromatic Species 21211.3.3 Species with σ-Antiaromaticity and π-Aromaticity 21311.3.4 Species with σ-Aromaticity and π-Antiaromaticity 21411.4 δ-Aromaticity 21511.5 ϕ-Aromaticity 21811.6 Conclusions 219References 22012 The Distortivity of 𝛑-Electrons 22312.1 Introduction 22312.2 The Kekulean Distortion 22412.3 Frequencies of the Kekulé Vibrational Mode in Benzene 22512.4 Changes in Aromaticity in the Kekulean Distortion 22712.5 The Maximum Hardness and Minimum Polarizability Principles 22812.6 The Distortive Nature of π-Electrons 22912.7 Conclusions 236References 23613 Three-Dimensional Aromaticity 24113.1 Introduction 24113.2 Spherical Aromaticity 24213.2.1 Aromaticity on the Surface of the Sphere 24213.2.2 Aromaticity Inside the Sphere 24713.2.2.1 Closo Boranes 24813.2.2.2 Jellium Cluster Model 25013.3 Octahedral Aromaticity 25113.4 Cubic Aromaticity 25313.5 Tetrahedral Aromaticity 25513.6 Cylindrical Aromaticity 256References 25914 Excited State Aromaticity 26514.1 Introduction 26514.2 Theoretical and Experimental Studies of Excited State Aromaticity 26614.2.1 Theoretical and Computational Studies 26714.2.2 Experimental Studies 26914.3 Influence of Aromaticity in the Excited State Properties 27114.3.1 Molecular Dipole Moments 27114.3.2 Singlet-Triplet Energy Gaps 27214.3.3 Photoacidity 27314.4 Influence of Aromaticity in the Excited State Reactivity 27414.4.1 Photoisomerizations 27514.4.2 Excited State Intramolecular Proton Transfer 27614.4.3 Photochemical Formation of Ortho-Xylylenes 27814.4.4 Photochemical Pericyclic Reactions 279References 281Index 285