Acknowledgments vii Preface xiii 1What Can We Do With Frontier Orbitals?1 1.1The Advantages of the Perturbation Method1 1.2The Uses of Frontier Orbitals2 1.2.1 Five Standard Frontier Orbital Treatments of Reactivity 2 1.2.2 Three Standard Frontier Orbital Treatments of Structural Problems 3 2Atomic and Molecular Orbitals5 2.1Atomic Orbitals5 2.2Molecular Orbitals9 2.3The MOs of a Homonuclear Diatomic Molecule10 2.3.1 Calculations 10 2.3.2 A Physical Interpretation 12 2.4MOs of a Heteronuclear Diatomic Molecule15 2.4.1 Calculations 15 2.4.2 A Physical Interpretation 16 2.5 π MOs of Polyatomic Molecules16 2.5.1 The Hückel Method for Polyatomic Molecules 16 2.5.2 How to Calculate Hückel MOs 21 2.6To Dig Deeper24 Contents x 3The Perturbation Method25 3.1Perturbations and Hückel Methods25 3.2Study of Bimolecular Reactions Using Perturbation Methods26 3.2.1 Two-orbital Systems 26 3.2.2 Systems Having More than Two Orbitals 27 3.2.3 The Frontier Orbital Approximation 28 3.2.4 Unimolecular Systems 28 3.3Perturbation Theory: The Practical Aspects29 3.3.1 Numerical Calculations 29 3.3.2 Qualitative Applications 32 3.4The Dewar PMO Method35 3.4.1 Alternant Hydrocarbons 35 3.4.2 The Dewar PMO Method 38 3.4.3 Advantages and Disadvantages of the PMO Method 43 3.5To Dig Deeper44 4Absolute and Relative Reactivities47 4.1Absolute Reactivity48 4.1.1 Bimolecular Reactions 48 4.1.2 Unimolecular Reactions 52 4.2Relative Reactivity57 4.2.1 Electrophilic Reactions 57 4.2.2 Nucleophilic Reactions 60 4.2.3 Cycloadditions 66 4.3Limitations of Rules 1 and 272 4.3.1 Some Difficulties Encountered with Rule 1 72 4.3.2 Problems with Rule 2 75 5Regioselectivity87 5.1Cycloadditions87 5.2Electrophilic Reactions96 5.2.1 Markovnikov’s Rule 96 xi Contents 5.2.2 Regioselectivity Involving Enols and Enolates 96 5.2.3 FO Theory and Ionic Reactions 102 5.3Nucleophilic Reactions106 5.3.1 Additions to Conjugated Carbonyl Compounds 106 5.4Radical Reactions110 5.5Periselectivity112 5.6Limitations of Rule 3113 6Stereoselectivity129 6.1Pericyclic Reactions129 6.1.1 Electrocyclic Reactions 129 6.1.2 Sigmatropic Rearrangements 138 6.1.3 Cycloadditions and their orientations 139 6.2Addition Reactions144 6.2.1 Nucleophilic Additions 144 6.2.2 Electrophilic Additions 172 6.2.3 Application to the Aldol Addition 175 6.3Substitution Reactions178 6.3.1 Bimolecular Electrophilic Substitutions 178 6.3.2 Bimolecular Nucleophilic Substitutions 178 6.4The Limitations of Rule 4181 7Some Structural Problems187 7.1Principle of the Method187 7.2Stable Conformations188 7.2.1 Aldehydes, Alkenes and Enol Ethers 188 7.2.2 Conformations of Some Ions 195 7.2.3 The Anomeric Effect 200 7.2.4 The Geminal Effect 203 7.2.5 The Gauche Effect 204 7.3Reactive Conformations206 Contents xii 7.4How to Stabilize Inherently Unstable Species207 7.4.1 Cyclobutadiene 207 7.4.2 Trimethylenemethane 208 7.4.3 Stable Carbenes 209 7.5Bonds with Abnormal Lengths210 7.5.1 Structural Consequences of HOMO–LUMO Interactions 210 7.5.2 Applications to Nucleophilic Additions 211 7.5.3 Substituent Effects 212 7.6Abnormal Valence Angles228 8Going Further231 8.1The Limits of Frontier Orbital Theory232 8.1.1 The Simplifying Hypotheses of Frontier Orbital Theory 232 8.1.2 Consequences 232 8.2The Capabilities of Computational Chemistry235 8.2.1 Structural Problems 235 8.2.2 Reactivity Problems 235 8.2.3 Beyond Potential Surfaces 236 8.3The Methods of Quantum Chemistry237 8.3.1 The Approximations 237 8.3.2 The Principal Theoretical Models 238 8.3.3 A Few Technical Points 242 8.4To Dig Deeper244 Appendix: MO Catalog 245 A1 Organization of the Catalog 245 A2 Chapter 3 245 A3 Chapter 4 247 A4 Chapter 5 264 A5 Chapter 6 276 A6 Summary Table 277 Index281