Eusebio Juaristi, PhD, is Professor at Centro de Investigacion de Estudios Avanzados del Instituto Politecnico Nacional, Mexico City, Mexico.He has produced influential research in numerous areas of physical organic chemistry, particularly conformational analysis and stereochemistry, as well as computational chemistry, asymmetric organocatalysis, and sustainable chemistry. C. Gabriela Ávila-Ortiz, PhD, is a Research Assistant at Centro de Investigacion de Estudios Avanzados del Instituto Politecnico Nacional, Mexico City, Mexico. She works in Professor Juaristi’s research group studying the asymmetric synthesis of organic compounds, organocatalysis, and green chemistry. Alberto Vega-Peñaloza, PhD, is Serra Hunter Lecturer in the Section of Organic Chemistry at the University of Barcelona, Spain. He has worked as Senior Scientist I at Selvita S.A., Poland, as a postdoctoral fellow at the Faculty of Chemistry of the National Autonomous University of Mexico (UNAM), as a postdoctoral researcher at ICIQ in Spain, and at the University of Padova, Italy, where he was awarded the Seal of Excellence UniPD grant to work on the development of photocatalytic systems for sustainable synthetic methods.

• Preface ixChapter 1 Introduction and History of the Molecular Orbital Theory 1Introduction 1Nature of Electromagnetic Radiation 2The Wave Nature of Light 3Electromagnetic Spectrum 5The Distinction Between Energy and Matter 6The Particle Nature of Light 7Mass and Momentum Associated with a Light Quantum 11Wave-Particle Duality 13Application of Quantum Mechanics to Atomic Structure 14Schrödinger’s Equation 19Hydrogenic Orbitals 23Why Doesn’t the Electron Fall into the Nucleus? Bohr’s Legacy and the Quantum Mechanical Model 32Further Reading 33Exercises 34Chapter 2 Hybrid Orbitals 35Introduction 35Hybridisation Theory 37Wavefunctions Associated with Hybrid Orbitals 42Procedure to Build a Hybrid Orbital 43Orthogonality of Wave Functions (Orbitals) 44The Bent Bond or Tau Model 45Effects of Hybridisation 45Further Reading 51Exercises 51Chapter 3 Bond Formation from Atomic Orbitals 53Introduction 53Mixing of s Orbitals 53Mixing of p Orbitals 58Factors Affecting the Magnitude of Orbital Interactions 60Bonding in Homo-Diatomic Molecules 62Bonding in Hetero-Diatomic Molecules 68Bonding in Triatomic Molecules 72Conjugated Systems 84Further Reading 84Exercises 84Chapter 4 The Hückel Molecular Orbital Method (HMO) 85The Linear Combination of Atomic Orbitals (LCAO) Method 85The Hückel Molecular Orbital (HMO) Method 86Simplified Procedure for the Application of Hückel´s Method 91Application of Hückel´s Method: Several Examples 92Application to Larger Molecules 96Scope and Limitations of the Hückel Molecular Orbital Method 97Hückel Molecular Orbital Method in Cyclic ​π​-Systems 97Energy Diagrams for Acyclic Polyenes 101​π​-Systems Containing Heteroatoms 102Inclusion of Overlap Between Vicinal Atoms 106The Shape of the Molecular Orbitals 108Contribution of the AOs in a Molecular Orbital 108Symmetry Simplifications in Alternant Hydrocarbons 112Estimation of MO Energies and Coefficients 115Bond Orders ​(​P​ ij )​ 116Charge Distribution (​q​ I ) 118Index of Free Valence (​f​ I ) 119Further Reading 120Exercises 121Chapter 5 Interactions Between Molecular Orbitals: Chemical Reactions 123Introduction 123Molecular Orbital Theory of Selected Organic Reactions 127Summary 140Further Reading 141Exercises 141Chapter 6 Some Applications of Orbital Theory in OrganicChemistry 143Introduction 143Ultraviolet Spectroscopy 143Ionisation Potentials 146Photoelectron Spectroscopy (PES) 147Interactions Between ​π​ Orbitals 148Interactions Between n-Orbitals 151Electron Spectroscopy for Chemical Analysis (ESCA) Spectroscopy 155Charge Transfer Complexes (EDA Complexes) 155Further Reading 156Exercises 157Chapter 7 Conservation of Molecular OrbitalSymmetry: Introduction to PericyclicReactions – Cycloaddition Reactions 159Introduction 159Concerted Reactions 160Pericyclic Reactions 161Principles of the Conservation of Orbital Symmetry 164Symmetry Correlation Diagrams of Molecular Orbitals 164Analysis of the Symmetry of the HOMO/LUMO Frontier Orbitals (FMO) 168Analysis of the Nodal Properties at the Transition State of a Cyclisation Reaction 169Cycloaddition Reactions 1721,3-Butadiene + Ethylene ​⇌​ Cyclohexene 173Two Ethylene Molecules ​⇌​ Cyclobutane 175Supra- or Antarafacial Topicity in Cycloaddition Reactions 179Effect of Secondary Interactions Between Molecular Orbitals 180Further Reading 182Exercises 182Chapter 8 Cheletropic Reactions 185Introduction 185[2 + 2] Cheletropic Reactions 186[4 + 2] Cheletropic Reactions 190[6 + 2] Cheletropic Reactions 194Further Reading 196Exercises 196Chapter 9 Electrocyclic Reactions 199Introduction 1991,3-Butadiene ​⇋​ Cyclobutene 2011,3,5-Hexatriene ​⇋​ 1,3-Cyclohexadiene 204Photochemical Electrocyclic Reactions 207Further Reading 210Exercises 210Chapter 10 Sigmatropic Reactions 213Introduction 213[3,3] Sigmatropic Rearrangements 216[1,3] Sigmatropic Rearrangements of Alkyl Groups 218Analysis of Nodal Properties in the Transition State 221[1,5] Sigmatropic Rearrangements of Alkyl Groups 221[1,2] Sigmatropic Rearrangements of Alkyl Groups 225[1,3] Sigmatropic Rearrangements of Hydrogen 227[1,5] Sigmatropic Rearrangements of Hydrogen 228Further Reading 231Exercises 232Chapter 11 1,3-Dipolar Cycloadditions 235Introduction 235Classification of 1,3-Dipolar Reactants 235Frontier Molecular Orbital Analysis 236Analysis of Nodal Properties in the Transition State 238Types of 1,3-DPCA Reactions and Regioselectivity 2391,3-DPCA Reactions with Diazoalkanes 2421,3-DPCA Reactions with Nitrones 2431,3-DPCA Reactions with Azomethine Ylides as the1,3-Dipolar Reactant 2451,3-DPCA Reactions with Nitrile Oxides as 1,3-Dipolar Reactants 2471,3-DPCA Reactions with Azides, Osmium Tetroxide andOzone 248Further Reading 251Exercises 251Chapter 12 Stereoelectronic Interactions 255Introduction 255Interpretation of the anomeric effect 258Stereoelectronic interactions in S-C-P segments 261Further Reading 266Exercises 267Index 269

Eusebio Juaristi, PhD, is Professor at Centro de Investigacion de Estudios Avanzados del Instituto Politecnico Nacional, Mexico City, Mexico.He has produced influential research in numerous areas of physical organic chemistry, particularly conformational analysis and stereochemistry, as well as computational chemistry, asymmetric organocatalysis, and sustainable chemistry. C. Gabriela Ávila-Ortiz, PhD, is a Research Assistant at Centro de Investigacion de Estudios Avanzados del Instituto Politecnico Nacional, Mexico City, Mexico. She works in Professor Juaristi’s research group studying the asymmetric synthesis of organic compounds, organocatalysis, and green chemistry. Alberto Vega-Peñaloza, PhD, is Serra Hunter Lecturer in the Section of Organic Chemistry at the University of Barcelona, Spain. He has worked as Senior Scientist I at Selvita S.A., Poland, as a postdoctoral fellow at the Faculty of Chemistry of the National Autonomous University of Mexico (UNAM), as a postdoctoral researcher at ICIQ in Spain, and at the University of Padova, Italy, where he was awarded the Seal of Excellence UniPD grant to work on the development of photocatalytic systems for sustainable synthetic methods.

• Preface ixChapter 1 Introduction and History of the Molecular Orbital Theory 1Introduction 1Nature of Electromagnetic Radiation 2The Wave Nature of Light 3Electromagnetic Spectrum 5The Distinction Between Energy and Matter 6The Particle Nature of Light 7Mass and Momentum Associated with a Light Quantum 11Wave-Particle Duality 13Application of Quantum Mechanics to Atomic Structure 14Schrödinger’s Equation 19Hydrogenic Orbitals 23Why Doesn’t the Electron Fall into the Nucleus? Bohr’s Legacy and the Quantum Mechanical Model 32Further Reading 33Exercises 34Chapter 2 Hybrid Orbitals 35Introduction 35Hybridisation Theory 37Wavefunctions Associated with Hybrid Orbitals 42Procedure to Build a Hybrid Orbital 43Orthogonality of Wave Functions (Orbitals) 44The Bent Bond or Tau Model 45Effects of Hybridisation 45Further Reading 51Exercises 51Chapter 3 Bond Formation from Atomic Orbitals 53Introduction 53Mixing of s Orbitals 53Mixing of p Orbitals 58Factors Affecting the Magnitude of Orbital Interactions 60Bonding in Homo-Diatomic Molecules 62Bonding in Hetero-Diatomic Molecules 68Bonding in Triatomic Molecules 72Conjugated Systems 84Further Reading 84Exercises 84Chapter 4 The Hückel Molecular Orbital Method (HMO) 85The Linear Combination of Atomic Orbitals (LCAO) Method 85The Hückel Molecular Orbital (HMO) Method 86Simplified Procedure for the Application of Hückel´s Method 91Application of Hückel´s Method: Several Examples 92Application to Larger Molecules 96Scope and Limitations of the Hückel Molecular Orbital Method 97Hückel Molecular Orbital Method in Cyclic ​π​-Systems 97Energy Diagrams for Acyclic Polyenes 101​π​-Systems Containing Heteroatoms 102Inclusion of Overlap Between Vicinal Atoms 106The Shape of the Molecular Orbitals 108Contribution of the AOs in a Molecular Orbital 108Symmetry Simplifications in Alternant Hydrocarbons 112Estimation of MO Energies and Coefficients 115Bond Orders ​(​P​ ij )​ 116Charge Distribution (​q​ I ) 118Index of Free Valence (​f​ I ) 119Further Reading 120Exercises 121Chapter 5 Interactions Between Molecular Orbitals: Chemical Reactions 123Introduction 123Molecular Orbital Theory of Selected Organic Reactions 127Summary 140Further Reading 141Exercises 141Chapter 6 Some Applications of Orbital Theory in OrganicChemistry 143Introduction 143Ultraviolet Spectroscopy 143Ionisation Potentials 146Photoelectron Spectroscopy (PES) 147Interactions Between ​π​ Orbitals 148Interactions Between n-Orbitals 151Electron Spectroscopy for Chemical Analysis (ESCA) Spectroscopy 155Charge Transfer Complexes (EDA Complexes) 155Further Reading 156Exercises 157Chapter 7 Conservation of Molecular OrbitalSymmetry: Introduction to PericyclicReactions – Cycloaddition Reactions 159Introduction 159Concerted Reactions 160Pericyclic Reactions 161Principles of the Conservation of Orbital Symmetry 164Symmetry Correlation Diagrams of Molecular Orbitals 164Analysis of the Symmetry of the HOMO/LUMO Frontier Orbitals (FMO) 168Analysis of the Nodal Properties at the Transition State of a Cyclisation Reaction 169Cycloaddition Reactions 1721,3-Butadiene + Ethylene ​⇌​ Cyclohexene 173Two Ethylene Molecules ​⇌​ Cyclobutane 175Supra- or Antarafacial Topicity in Cycloaddition Reactions 179Effect of Secondary Interactions Between Molecular Orbitals 180Further Reading 182Exercises 182Chapter 8 Cheletropic Reactions 185Introduction 185[2 + 2] Cheletropic Reactions 186[4 + 2] Cheletropic Reactions 190[6 + 2] Cheletropic Reactions 194Further Reading 196Exercises 196Chapter 9 Electrocyclic Reactions 199Introduction 1991,3-Butadiene ​⇋​ Cyclobutene 2011,3,5-Hexatriene ​⇋​ 1,3-Cyclohexadiene 204Photochemical Electrocyclic Reactions 207Further Reading 210Exercises 210Chapter 10 Sigmatropic Reactions 213Introduction 213[3,3] Sigmatropic Rearrangements 216[1,3] Sigmatropic Rearrangements of Alkyl Groups 218Analysis of Nodal Properties in the Transition State 221[1,5] Sigmatropic Rearrangements of Alkyl Groups 221[1,2] Sigmatropic Rearrangements of Alkyl Groups 225[1,3] Sigmatropic Rearrangements of Hydrogen 227[1,5] Sigmatropic Rearrangements of Hydrogen 228Further Reading 231Exercises 232Chapter 11 1,3-Dipolar Cycloadditions 235Introduction 235Classification of 1,3-Dipolar Reactants 235Frontier Molecular Orbital Analysis 236Analysis of Nodal Properties in the Transition State 238Types of 1,3-DPCA Reactions and Regioselectivity 2391,3-DPCA Reactions with Diazoalkanes 2421,3-DPCA Reactions with Nitrones 2431,3-DPCA Reactions with Azomethine Ylides as the1,3-Dipolar Reactant 2451,3-DPCA Reactions with Nitrile Oxides as 1,3-Dipolar Reactants 2471,3-DPCA Reactions with Azides, Osmium Tetroxide andOzone 248Further Reading 251Exercises 251Chapter 12 Stereoelectronic Interactions 255Introduction 255Interpretation of the anomeric effect 258Stereoelectronic interactions in S-C-P segments 261Further Reading 266Exercises 267Index 269