Modern Physical Organic Chemistry Eric V Anslyn UNIVERSITY OF TEXAS , AUSTI N Dennis A Dougherty CALIFORNIA I NSTITUTE OF TECH NOLOGY University Science Books www u scibooks.com Uni versity Science Books www uscibooks.com Production Manager: Christine Taylor Manuscript Editor: John Murdzek Designer: Robert Ish i Illustrator: Lineworks Compositor: Wilsted & Taylor Publishing Services Printe r & Binder: Edwards Brothers, Inc This book is p rinted on acid-free paper Cop yright © 2006 by University Science Books Reprodu ction or transla tion of any part o f this work beyond tha t permitted by Section 107 or 108 of the 1976 Un ited Sta tes Copyright Act w ithout the permission of the copyrigh t owner is unlawful Requests for permission or furth er informatio n shou ld be addressed to the Permissions Department, University Science Books Library o f Congress Cataloging-in-Publica tion Data An slyn, Eric V., 1960Modern physical organic chemistry I Eric V Anslyn, Dennis A Dougherty p em In cludes bibliographi cal references and index ISBN 978-1-891389-31-3 (alk paper) C hem istry, Ph ysica l organic I Dou gher ty, Dennis A., 1952- II Title QD476.A57 2004 547' 13-d c22 2004049617 Printed in the United States of America 10 Abbreviated Contents PART I: Molecular Structure and Thermodynamics CHAPTER PART Introduction to Structure and Models of Bonding Strain and Stability 65 Solutions and Non-Covalent Binding Forces 145 Molecular Recognition and Supramolecular Chemistry 207 Acid-Base Chemistry 259 Stereochemistry 297 II: Reactivity, Kinetics, and Mechanisms CHAPTER PART III: CHAPTER 10 Energy Surfaces and Kinetic Analyses 355 Experiments Related to Thermodynamics and Kinetics 421 Catalysis 489 Organic Reaction Mechanisms, Part 1: Reactions Involving Additions and / or Eliminations 537 11 Organic Reaction Mechanisms, Part 2: Substitutions at Aliphatic Centers and Thermal Isomerizations / Rearrangements 627 12 Organotransition Metal Reaction Mechanisms and Catalysis 13 Organic Polymer and Materials Chemistry 753 705 Electronic Structure: Theory and Applications 14 15 16 17 APPENDIX Advanced Concepts in Electronic Structure Theory Thermal Pericyclic Reactions 877 Photochemistry 935 Electronic Organic Materials 1001 807 Conversion Factors and Other Useful Data 1047 Electrostatic Potential Surfaces for Representative Organic Molecules Group Orbitals of Common Functional Groups: Representative Examples Using Simple Molecules 1051 The Organic Structures of Biology 1057 Pushing Electrons 1061 Reaction Mechanism Nomenclature 1075 INDEX 1049 1079 v Contents 1.3.2 1.3.3 1.3.4 1.3.5 List of Highlights xix Preface xxiii Acknowledgments xxv A Note to the Instructor xxvii PART I MOLECULAR STRUCTURE AND THERMODYNAMICS 1.3.6 1.3.7 CHAPTER 1: Introduction to Structure and Models of Bonding 1.3.8 1.3.9 Intent and Purpose 1.1 A Review of Basic Bonding Concepts 1.1.1 Quantum Numbers and Atomic Orbitals 1.1.2 Electron Configurations and Electronic Diagrams 1.1.3 Lewis Structures 1.1.4 Formal Charge 1.1.5 VSEPR 1.1.6 Hybridization 1.1.7 A Hybrid Valence Bond / MolecularOrbital Model of Bonding 10 Creating Localized CJand n Bonds 11 1.1.8 Polar Covalent Bonding 12 Electronegativity 12 Electrostatic Potential Surfaces 14 Inductive Effects 15 Group Eiectronegativities 16 Hybridization Effects 17 1.1.9 Bond Dipoles, Molecular Dipoles, and Quadrupoles 17 Bond Dipoles 17 Molecular Dipole Moments 18 Molecular Quadrupole Moments 19 1.1.10 Resonance 20 1.1.11 Bond Lengths 22 1.1.12 Polarizability 24 1.1.13 Summary of Concepts Used for the Simplest Model of Bonding in Organic Structures 26 1.2 A More Modern Theory of Organic Bonding 26 1.2.1 Molecular Orbital Theory 27 1.2.2 A Method for QMOT 28 1.2.3 Methyl in Detail 29 Planar Methyl 29 The Walsh Diagram: Pyramidal Methyl 31 "Group Orbitals"for Pyramidal Methyl 32 Putting the Electrons In - The MH3 System 33 1.2.4 The CH2 Group in Detail 33 The Walsh Diagram and Group Orbitals 33 Putting the Electrons In- The MH System 33 1.3 Orbital Mixing-Building Larger Molecules 1.3.1 Using Group Orbitals to Make Ethane 36 35 Using Grou p Orbitals to Make Ethy lene 38 The Effects of Heteroatoms-Formaldehyde 40 Making More Complex Alkanes 43 Three More Examples of Building Larger Molecules from Group Orbitals 43 Propene 43 Methyl Chloride 45 Butadiene 46 Group Orbitals of Representative TI Systems: Benzene, Benzyl, and Allyl 46 Understanding Common Functional Groups as Perturbations of Allyl 49 The Three Center-Two Electron Bo nd 50 Summary of the Concepts Involved in Our Second Model of Bonding 51 1.4 Bonding and Structures of Reactive Intermediates 52 1.4.1 Carbocations 52 Carbenium Ions 53 Interplay with Carbonium Ions 54 Carbonium Ions 55 1.4.2 Carbanions 56 1.4.3 Radicals 57 1.4.4 Carbenes 58 1.5 A Very Quick Look at Organometallic and Inorganic Bonding 59 Summary and Outlook EXERCISES 61 62 FURTHER READING CHAPTER 2: 64 Strain and Stability Intent and Purpose 65 65 2.1 Thermochemistry of Stable Molecules 66 2.1.1 The Concepts of Internal Strain and Relative Stability 66 2.1.2 Types of Energy 68 Gibbs Free Energy 68 Enthalpy 69 Entropy 70 2.1.3 Bond Dissociation Energies 70 Using BDEs to Predict Exothermicity and Endothermicity 72 2.1.4 An Introduction to Potential Functions and Surfaces- Bond Stretches 73 Infrared Spectroscopy 77 2.1.5 Heats of Formation and Combustion 77 2.1.6 The Group Increment Method 79 2.1.7 Strain Energy 82 Vll Vlll CON TENTS 2.2 Thermoch emistry of Reactive Interm ediates 82 2.2.1 Stability vs Persistence 82 2.2.2 Radicals 83 BDEs as a Measure of Stability 83 Radical Persistence 84 Group Increments for Radicals 86 2.2.3 Carbocations 87 Hydride Ion Affinities as a Measure of Stability 87 Lifetimes ofCarbocations 90 2.2.4 Carbanions 91 2.2.5 Summary 91 Electrostatic Interactions 131 Hydrogen Bonding 131 The Parameterization 132 Heat of Formation and Strain Energy 132 2.6.2 General Commen ts on the Molecular Mechanics Method 133 2.6.3 Molecul ar Mech anics on Biomolecules and Unnatu ral Polymers-"Modeling" 135 2.6.4 Molecu lar Mech anics Studies of Reactions 136 2.3 Rela tionships Between Struc ture and Energe ticsBasic Conformationa l Analysis 92 2.3.1 Acyclic Systems-Torsiona l Poten tial Surfaces 92 Ethane 92 Butane- The Gauche Interaction 95 Barrier Height 97 Barrier Foldedness 97 Tetraalky!ethanes 98 The g+g- Pentane Interaction 99 Allylic(A 1•3) Strain 100 2.3.2 Basic Cyclic Systems 100 Cyclopropane 100 Cyc!obutane 100 Cyc!opentalle 101 Cyc!ohcxanc 102 Larger Rings- Transamwlar Effects 107 Group ln creme11t Corrections for Ring Systems 109 Ri11g Torsional Modes 109 Bicyc!ic Ring Systems 110 Cycloalkencs and Bredt's Rule 110 SuJmJtan; of Conformational Analysis and Its Connection to Strain 112 EXERCISES 2.4 Electronic Effects 112 2.4.1 Inte ractions Involving TI Systems Subs titution 011 Alkenes 112 112 Confor/1/atiolls of Substituted Alkenes 113 Conjugation 115 Aromaticity 116 Antiaromaticity, An Unu sual Des tabilizing Effect 117 NM R Chemical Shifts 118 Polycyclic Aromatic Hydrocarbons 119 Large Annulenes 119 2.4.2 Effects of Multiple Heteroatoms 120 Bond Le11gth Effects 120 Orbital Effects 120 2.5 Highly-Strai ned Molecul es 124 2.5 Long Bonds and Large Angles 124 2.5.2 Sma ll Rings 125 2.5.3 Very Large Rotation Barriers 127 2.6 Molecular Mechanics 128 2.6.1 The Molecular Mechanics Mod el 129 Bond Stretching 129 Angle Bending 130 Torsion 130 Nonbonded Interactions 130 Cross Terms 131 Summary and Outlook 137 138 FURT HER READI NG 143 CH A PT ER 3: Solu tions and Non-Covalent Binding Forces 145 Intent and Purpose 145 3.1 Solvent and Solution Properties 3.1.1 N ature Abh ors a Vacuum 146 3.1.2 Solvent Scales 146 Dielectric Constant 147 Other Solvent Scales 148 Heat of Vaporization 150 145 Surface Tension and Wetting 150 Water 151 1.3 Solubility 153 General Overview 153 Shape 154 Using the "Like-Dissolves-Like" Paradigm 3.1.4 Solute Mobility 155 Diffusion 155 Fick's Law of Diffusion 156 Correlation Times 156 3.1.5 The Thermodynamics of Solutions 157 Chemical Potential 158 The Thermodynamics of Reactions 160 Calculating t1H and flS o 162 154 3.2 Binding Forces 162 3.2.1 Ion Pairing Interacti ons 163 Salt Bridges 164 3.2.2 Electrosta tic In teractions In volving Dipoles 165 Ion-Dipole Interactions 165 A Simple Model of Tonic Solvation The Born Equation 166 Dipole-Dipole Interactions 168 3.2.3 Hydrogen Bon d ing 168 Geometries 169 Strengths of Normal Hydrogen Bonds 171 i Solvation Effects 171 ii Electronegativity Effects 172 iii Resonance Assisted Hydrogen Bonds 173 iv Polarization Enhanced Hydrogen Bonds 174 v Secondary Interactions in Hydrogen Bonding Systems 175 CONTE vi CoopemtivihJ in Hydrogen Bonds 175 Vibra tional Properties of Hydrogen Bonds 176 Short-Strong Hydrogen Bonds 177 3.2.4 '1T Effects 180 Cation-rc Interactions 181 Polar-rc Interactions 183 Aromatic-Aromatic Interactions (rc Stacking) 184 The Arene-Perfluoroarene Interaction 184 rr: Donor-Acceptor Interactions 186 3.2.5 Indu ced -D ipole Interactio ns 186 /on- Induced-Dipole Interactions 187 Dipole-Induced-Dipole Interactions 187 lndttced-Dipole-lnduced-Dipole Interactions 188 Sunnttarizing Monopole, Dipole, and Induced-Dipole Binding Forces 188 3.2.6 The Hyd ro phobic Effect 189 Aggregation of Orga nics 189 The Origin of the Hydro phobic Effect 192 3.3 Computational Mod eling of Solva tio n 3.3.1 Conti nuum Solva ti on Mod els 196 3.3.2 Expli cit Solva tionModel s 197 3.3.3 Monte Carlo (MC) Method s 198 3.3.4 Molecula r Dyn amics (MD) 199 3.3.5 Stati sti cal Perturbation Theory/ Free Energy Pe rturba tion 200 Sum mary and Outlook 194 Molecular Recognition via Hydrogen Bonding in Water 232 4.2.4 Molecular Recognition with a Large H ydrop hobic Component 234 Cyclodextrins 234 Cyclophanes 234 A Sum mary of the Hydrophobic Co mpoueut of Molecular Recognition in Water 238 4.2.5 Molecul ar Recognition with a La rge '1T Componen t 239 Ca tion-lf Interactions 239 Polar-lf and Related Effects 241 4.2.6 Summary 241 4.3 Supramolecul ar Chemistry 243 4.3 Supra molecular Assembl y of Complex Architectures 244 Self-Assembly via Coordination Compounds 244 Self-Assernbly via Hydrogen Bonding 245 4.3.2 Novel Supra molecul a r Architectu res-Cate nanes, Rotaxa nes, and Knots 246 Nano technology 248 4.3.3 Container Compo w1ds-Molecu les w ithin M olecules 249 Summary and Outlook EXERCISES 201 252 253 FU RT H ER READING EXERC IS ES TS 256 202 FURTH ER READING CHAPTER 4: 204 M olecular Recognition and Supramolecular Chemistry In tent and Purpose CHAPTERS: 207 Acid-Base Chemistry Intent a nd Purpose 259 259 207 5.1 Bro ns ted Acid-Base Chemistry 4.1 Th erm od ynamic Anal yses of Binding Phen omena 207 4.1.1 General Thermodynamics of Bind ing 5.2 Aqueous Solutions 261 5.2.1 pK 261 5.2.2 pH 262 5.2.3 The Leveli ng Effect 264 5.2.4 Acti vity vs Concentration 266 5.2.5 Acidi ty Fu nction s: Acidity Sca les fo r Hig hl y Con centrated Acidic Solutions 266 5.2.6 Super Acid s 270 208 The Relevance of the Standard State 210 The Influence of a Change in Hea t Capacity 212 Coopera tivity 213 En thalpy-En tropy Compensation 216 4.1.2 The Binding Isotherm 21 4.1.3 Ex perimental Methods 21 U V/Vis or Fluorescence Methods 220 NMRMethods 220 Isothermal Calorimetry 221 4.2 M ol ecular Recognition 222 4.2.1 Comple mentarity and Preorgan ization 5.3 Nonaqueous Sys tems 271 5.3.1 p K, Shi fts at Enzyme Acti ve Sites 273 5.3.2 Solu tion Phase vs C as Ph ase 273 224 Crowns, Cryptands, and Sphera nds -Molecular Recogn ition with a Large Ion-Dipole Component T·weezers and Clefts 228 4.2.2 Molecul ar Recognition w ith a La rge Ion Pairing Component 228 4.2.3 Mo lecul ar Recognition with a Large H ydrogen Bonding Componen t 230 Represen tative Structures 230 259 224 5.4 Predicting Acid Stre n gth in Solution 276 5.4 Me thods Used to Measure Wea k Acid Strength 5.4.2 Tw o Gu iding Princip les for Predi ctin g Rela ti ve Acidities 277 5.4.3 Electronega tivity and Inducti on 278 5.4.4 Reson an ce 278 5.4.5 Bo nd Stre ngth s 283 5.4.6 Electrostatic Effects 283 5.4.7 H ybridi za ti on 283 276 IX X CONTENTS 5.4.8 Aromaticity 284 5.4.9 Solvation 284 5.4.10 Cationic Organic Structu res 6.6.3 NonplanarGraphs 326 6.6.4 Achievements in Top ologica l and Supram olecular Stereochemistry 327 285 5.5 Acids and Bases of Biological Interest 285 6.7 Stereochemical Issues in Polymer Chemistry 331 5.6 Lewis Acids/Bases and Electrophiles/ Nucleophiles 288 5.6.1 The Concept of Hard and Soft Acids and Bases, Genera l Lessons for Lewis Acid-Base In teractions, and Relative Nucleophilicity and Electrophilicity 289 Summary and O utlook 292 EXERCISES 292 FURTHER READING 294 6.8 Stereochemical Issues in Chemical Biology 6.8.1 Th e Linkages of Proteins, N ucleic Acids, and Polysacch arides 333 Proteins 333 Nucleic Acids 334 Polysaccharides 334 6.8.2 Helicity 336 Syn thetic Helical Polymers 337 6.8.3 Th e Origin of Ch ira lity in Nature 339 6.9 Stereochemical Terminology CHAPTER 6: Stereochemistry 297 Summary and Outlook Intent and Pu rpose 297 EXER C ISES 6.1 Stereogenicity and Stereoisomerism 297 6.1.1 Basic Concepts and Term inology 298 Classic Terminology 299 More Modem Terminology 301 6.1.2 Stereochemical Descriptors 303 R,S System 304 E,Z System 304 o and L 304 Erythro and Tlneo 305 Helical Descriptors- M and P 305 Ent nnd Epi 306 FURT HER READI NG Using Descriptors to Compare Structures 340 344 344 350 PART II REACTIVITY, KINETICS, AND MECHANISMS 306 6.1.3 Di stin gu ishing Enan tiomers 306 Optical Activity nnd Chirality 309 Why is Plane Polarized Light Rotated by a Chirnl Medium? 309 Circular Dichroism 310 X-Ray Crystallography 310 6.2 Sym metry and Stereochemis try 311 6.2 Basic Symmetry Ope rations 311 6.2 Chirality and Symmetry 311 6.2.3 Symmetry Arguments 313 6.2 Focusing on Carbon 314 6.3 Top icity Relations h ips 315 6.3.1 Homotopic, Enantiotopic, and Diastereotopic 315 6.3.2 To pi city Descri ptors-Pro-R I Pro-S and Re I Si 316 6.3.3 Chirotopicity 317 6.4 Reac tion Stereochemis try: Stereoselectivity and Stereospecifi city 317 6.4.1 Simple Guidelines for Reaction Stereoch emis try 317 6.4.2 Stereospecific and Stereoselective Reactions 319 6.5 Symmetry and Time Scale 333 CHAPTER 7: Energy Surfaces and Kinetic Analyses 355 Intent and Purpose 355 7.1 Energy Surfaces and Related Concepts 7.1.1 Energy Surfaces 357 7.1.2 Reaction Coordinate Diagrams 359 7.1.3 What is the Nature of the Activa ted Complex/ Transition State? 362 7.1.4 Rates and Rate Constants 363 7.1.5 Reaction Order and Rate Laws 364 356 7.2 Transition State Theory (TST) and Related Topics 365 7.2.1 The Mathem ati cs of Transition State Theory 365 7.2.2 Relationship to the Arrhenius Rate Law 367 7.2.3 Boltzmann Distributions and Temp erature Dependence 368 7.2.4 Revisi ting "Wh at is the Na tu re of the Acti va ted Complex?" and Why Does TST Work? 369 7.2.5 Experimental Determinations of Activa tion Param eters and Arrhenius Parameters 370 7.2.6 Examples of Acti va tion Param eters and Their Interpretations 372 7.2.7 Is TST Com p letely Correct? The Dynamic Beh avior of Organic Reactive Intermedia tes 372 322 6.6 Topological and Supramolecular Stereochemistry 324 6.6.1 Loops and Kno ts 325 6.6.2 Topological Chirality 326 7.3 Postulates and Principles Related to Kinetic Analysis 374 7.3.1 The Hammond Postulate 374 7.3.2 The Reacti vity vs Selectivity Principle 377 CO 7.3.3 The Curtin-Hammett Principle 378 7.3.4 Microscopic Reversibility 379 7.3.5 Kinetic vs Thermodynamic Control 380 7.4 Kinetic Experiments 382 7.4.1 How Kinetic Experimen ts are Performed 382 7.4.2 Kinetic Analyses for Simple Mechan isms 384 First Order Kinetics 385 Second Order Kinetics 386 Pseudo-First Order Kinetics 387 Equilibriu111 Kinetics 388 Initial-Rate Kinetics 389 Tal111lating a Series ofConwton Kinetic Scenarios 7.5 Complex Reactions-Deciphering Mechanisms 7.5.1 Steady Sta te Kinetics 390 7.5.2 Using the SSA to Predict Changes in Kinetic Order 395 7.5.3 Saturation Kinetics 396 7.5.4 Prior Rap id Equilibria 397 8.1 8.1.4 389 390 7.6 Methods for Following Kinetics 397 7.6.1 Reactions w ith Half-Lives Greater than a Few Seconds 398 7.6.2 Fast Kinetics Techniques 398 Flow Techniques 399 Flash Photolysis 399 Pnlse Radio/ ysis 401 7.6.3 Re laxation Methods 401 7.6.4 Summary of Kinetic Analyses 402 7.7 Calculating Rate Constants 403 7.7.1 Marcus Theory 403 7.7.2 Marcus Theory Ap plied to Electron Transfer 405 7.8 Considering Multiple Reaction Coordinates 407 7.8.1 Variation in Tra nsition Sta te Stru ctures Across a Series of Re la ted Reactions-An Example Using Substitution Reactions 407 7.8.2 More O'Ferrall-Jencks Plots 409 7.8.3 Changes in Vibrational State Along the Reaction Coordinate-Relating the Third Coordinate to Entropy 412 Summary and Outlook EXERC ISES 413 413 FURTHER READING 417 CHAPTER 8: Experiments Related to Thermodynamics and Kinetics Intent and Purpose 8.1.5 8.1.6 421 421 8.1 Isotope Effects 421 8.1.1 The Experiment 422 8.1.2 The Origin of Primary Kinetic Isotope Effects 422 Reaction Coordinate Diagrams and Isotope Effects 424 8.1.7 8.1.8 TENTS Primary Kinetic Isotope Effects for Linear Transition States as a Function ofExothermicity and Endothermicity 425 Isotope Effects for Linear vs Non-Linear Transition States 428 The Origin of Secondary Kineti c Isotope Effects Hybridization Changes 429 Steric isotope Effects 430 Equilibrium Isotope Effects 432 Isotopic Perturbation of EqtlilibriumApplications to Carbocations 432 Tunne ling 435 Solve nt Isotope Effects 437 Fractionation Factors 437 Proton In ventories 438 Heavy Atom Isotope Effects 441 Summ ary 441 8.2 Substituent Effects 441 8.2.1 The Origin of Substituent Effects Field Effects 443 Indu ctive Effects 443 Resonance Effects 444 Polarizability Effects 444 Steric Effects 445 Solvation Effects 445 428 443 8.3 Hammett Plots-The Most Common LFER A General Method for Examining Changes in Charges During a Reaction 445 8.3.1 Sigma (cr) 445 8.3.2 Rho (p) 447 8.3.3 The Power of Hamme tt Plots for Deciphering Mechanisms 448 8.3.4 Dev iati on s from Linearity 449 8.3.5 Separa ting Resonance from Induction 451 8.4 Other Linear Free Energy Relationships 454 8.4.1 Steric and Polar Effects-Taft Parameters 454 8.4.2 Solvent Effects- Grun wa ld- Winstein Plots 455 8.4.3 Schleyer Ad aptation 457 8.4.4 Nucleophilicity and N ucleofuga ljty 458 Basicity/Acidity 459 Solvation 460 Polarizability, Basicity, and Solvationlnterplay 460 Shape 461 8.4.5 Swa in-Scott Parameters-Nucleophilicity Parameters 461 8.4.6 Ed wards and Ritchie Correlati ons 463 8.5 Acid-Base Related EffectsBnmsted Relationships 464 8.5.1 fJNu c 464 8.5.2 f3Lc 464 8.5.3 Acid-Base Ca talysis 466 8.6 Why Linear Free Energy Relationships Work? 466 8.6.1 Gene ral Mathematics ofLFERs 467 8.6.2 Conditions to Create an LFER 468 8.6.3 The Isokine tic or Isoequilibrium Temperature 469 Xl xii CONTE TS 8.6.4 Wh y does Enthalpy-Entropy Compensa tion Occur? 469 Steric Effects 470 Solvation 470 8.7 Summary of Linear Free Energy Relationships 8.8 Miscellaneous Experiments for Studying Mechanisms 471 8.8.1 Productldentifi cation 472 8.8.2 Changing the Reactant Stru cture to Divert or Trap a Proposed Intermediate 473 8.8.3 Trapping and Competition Experiments 474 8.8.4 Checking fo r a Common In termediate 475 8.8.5 Cross-Over Experiments 476 8.8.6 Stereochemical Analysis 476 8.8.7 Isotope Scrambling 477 8.8.8 Techniques to Stud y Radicals: Clocks and Traps 8.8.9 Direct Isolation and Characterization of an Intermediate 480 8.8.10 Transien t Spectroscopy 480 8.8.11 Stable Media 481 Summary and Outlook EXERCISES 9.4 Enzymatic Catalysis 523 9.4.1 Michaelis-MentenKinetics 523 9.4.2 The Meaning of KM, kcau and kcatf KM 524 9.4.3 Enzyme Active Sites 525 9.4.4 [S] vs KM-Reaction Coordina te Diagrams 9.4.5 Sup ramolecular Interactions 529 EXERCISES 489 530 535 CHAPTER 10: Organic Reaction Mechanisms, Part 1: Reactions Involving Additions and/or Eliminations 537 489 9.1 General Principles of Catalysis 490 9.1.1 Binding the Transition State Better th an the Gro und State 491 9.1.2 A Thermodynamic Cycle Ana lysis 493 9.1.3 A Spa tial Temporal Approach 494 9.2 Forms of Catalysis 495 9.2.1 "Binding" is Akin to So lvation 495 9.2.2 Proximity as a Binding Phenomenon 9.2.3 Electro philic Ca talysis 499 Electrostatic fnteractions 499 Me tal Jon Catalysis 500 9.2.4 Acid-Base Cata lysis 502 9.2.5 Nucleophili c Catalysis 502 9.2.6 Cova lent Catalysis 504 9.2.7 Strain and Distortion 505 9.2.8 Phase Transfer Catalysis 507 527 531 FURTHER READIN G 487 CHAPTER 9: Catalysis Intent and Purpose 478 Summary and Outlook 482 482 FURTHER READING 470 9.3.4 Concerted or Sequential General-AcidGeneral-Base Catalysis 515 9.3.5 The Bremsted Catalysis Law and Its Ramifications 516 A Linear Free Energy Relationship 516 The Meaning of a and /3 517 a+/3=1 518 Deviations from Linearity 519 9.3.6 Predicting General-Add or General-Base Catalysis 520 The Libido Rule 520 Potential Energy Surfaces Dictate General or Specific Catalysis 521 9.3.7 The Dynamics of Proton Transfers 522 Marcus Analysis 522 495 9.3 Brans ted Acid-Base Catalysis 507 9.3.1 SpecificCatal ysis 507 The Mathematics of Specific Catalysis 507 Kine tic Plots 510 9.3.2 General Catalysis 510 The Mathematics of General Catalysis 511 Kinetic Plots 512 9.3.3 A Kinetic Equi valency 514 Intent and Purpose 537 10.1 Predicting Organic Reactivity 538 10.1.1 A Useful Paradigm for Polar Reactions 539 Nucleophiles and Electrophiles 539 Lewis Acids and Lewis Bases 540 Donor-A cceptor Orbital Interactions 540 10.1.2 Predicting Radical Reactivity 541 10.1.3 In Preparation for the Follow ing Sections 541 -ADDITION REACTIONS- 542 10.2 Hydration of Carbonyl Structures 542 10.2.1 Acid-Base Catalysis 543 10.2.2 The Thermodynamics of the Formation of Geminal Diols and H emiacetals 544 10.3 Electrophilic Addition of Water to Alkenes and Alkynes: Hydration 545 10.3.1 Electron Pushing 546 10.3.2 Acid-Catalyzed Aqueous Hydration 546 10.3.3 Regiochemistry 546 10.3.4 Alkyne Hydrati on 547 10.4 Electrophilic Addition of Hydrogen Halides to Alkenes and Alkynes 548 10.4.1 Electron Pushing 548 58 CHAPTER 1: INTRODU CTION TO STRUCTURE AN D MODELS O F BOND ING nounced than we saw for propene (Figure 1.18) Therefore, the SOMO is even more delocalized onto the neighboring R group, as shown in the margin for the propene radical cation, where a bracket is used to denote one electron and a formal positive charge in the MO 1.4.4 Carbenes Radical cation of propene Carbene electron configurations Resonance in singlet carbenes Lastly, let's consider carbenes, neutral :CR2 species, the prototype of which is the molecule methylene, :CH2 For the reactive intermediates we have considered so far-cations, anions, and radicals-the Walsh diagram for CH3 provides the starting point for the discussion For carbenes, the relevant electronic structure questions can be considered by referring to the Walsh diagram for CH2 in Figure 1.9 We begin with the linear form on the left side of Figure 1.9 Methylene has six valence electrons, and we can place two electrons each in the A and B MOs, leaving two valence electrons to occupy the degenerate C / D pair This leads to a unique feature of carbenes vs the other reactive intermediates we have studied Each carbene is in fact two reactive intermediates, differentiated by the spin state of the system If the spins are aligned, then the spin state of the system isS = ~ + ~ = 1, and the multiplicity is m5 = 25 + = This is a triplet state If we have opposing spins, S = ~ + (-~) = and ms = This is a singlet state These two states are expected to have substantially different molecular and electronic structures and to show distinct reactivities The Walsh diagram of Figure 1.9 provides an excellent starting point for considering these issues Hund's rule predicts the high-spin, triplet state should be preferred at the linear geometry, and indeed it is As the H-C-H angle contracts, a gap opens up between C and D If we keep one electron in each MO, this distortion should be mildly stabilizing With small bending, there is no large benefit to pairing two electrons into C, and the triplet is sti ll preferred However, when the angle becomes small enough, the lower energy of orbital C will overcome the electron repulsion energy, and a singlet with both electrons in C w ill become the ground state It is impossible to unambiguously predict the absolute ground state of m ethylene wi th simple models such as Walsh diagrams As w e will see in Chapter 14, understanding and predicting spin preferences requires more advanced treatments of electronic structure than we are providing here However, some predictions are still possible For example, the triplet state should have a wider H-C-H angle than the singlet This is indeed the case; the angle is 136° for the triplet and 105° for the singlet Experimentally it turns out that the triplet is the global ground state in methylene, by approximately kcal/ mol All simple dialkyl carbenes have triplet ground states The Walsh diagram provides a satisfying analysis of the electronic structure of carbenes, and the essential features of the system can be summarized by the simple representations shown in the margin The triplet has two electrons in two very different orbitals, what we have called panda( out) We might expect its reactivity to be similar to that of radicals, and indeed this is the case The singlet state is quite different It contains a lone p air of electrons in an MO [a(out)] that is reminiscent of an sp hybrid It also contains an empty p orbital, just like a simple carbenium ion Its reactivity patterns should be quite different from radicals, and we will see that they are (Chapter 10) While simple carbenes have a triplet ground state, appropriate substituents can reverse this preference, such that some substituted carbenes show a large energetic preference for the singlet The bonding and structural model we have developed provides excellent guidance as to how we might create a carbene that has a singlet ground state The most effective way is to interact with the empty D orbital of the singlet, as shown in the margin Carbenes with lone-pair donating substituents such as N, 0, and halogens can have singlet ground states because of such an interaction (see the next Going Deeper highlight for an example) The effect can be quite large; indifluorocarbene the singlet lies below the tripl et by - 50 kcal I mol! Detailed theoretical studies reveal a linear correlation between the singlet-triplet gap and the electron pair donating ability of the attached substituent(s) As is typical, a resonance model also nicely rationalizes the stabilizing effect of donating substituents on carbenes 1.5 A V ERY QUIC K LOOK AT ORGANOME TAL LI C AND I NORGAN I C BONDING Going Deeper Stable Carbenes We generally think of carbenes as extremel y reacti ve species, and for the most part they are In recent years, how ever, clever appl ication of the concepts described here has led to some remarkable new carbenes The breakthrough occurred in 1991 when Ardu engo and co-workers at DuPont reported the synthesis and isolation of carbene i Two factors contribute to the stability of this type of carbene First is the steric bulk of the R group The first exampl e had R = adamantyl, a large, aliphatic rin g system Later examples included heavily substituted aromatics as the R group The second effect is electronic Two potent electron donors are attached to the carbenic center As just discussed, these should grea tl y stabili ze the singlet state, and ind eed these types of carbenes ve a singlet ground state Remarkably, these molecules can be crystallized, and an x-ray structure reveals an N-C-N angle of 102° at the carbene center, in excellent agreemen t with the expectation for a singlet carbene Samples of i are stable for years, as long as they are protected from air Many deriva - 1.5 tives have been made, and extensive physical characterization has provided detailed insights into carbene electronic structure These stable carbenes are not solely theoretical curiosities They h ave recentl y found use as ligands for an important class of ruthenium-based olefin m etathesis catalysts that h ave profoundly influenced synthetic organic ch emistry (see Chapter 12) Thus, research into basic reactive intermediates can lead to fundamental insights and useful new materials I R I N [}-H N0 R N base C:> N I I R R A stable carbene Ard uengo, A j., IlL "Looking for Stable Carbenes." A ce Chem Res., 32, 913- 921 (1999) A Very Quick Look at Organometallic and Inorganic Bonding One theme of this textbook is to consistently tie organic chemistry to organometallic chemistry, which is just one of the current chemical subdisciplines where the tools of physical organic chemistry are often applied In this regard, it is useful in this chapter to develop a simple bonding model for organometallic and inorganic complexes, and not just look at organic bonding Here we examine a model analogous to the first VBT /MOT model of organic bonding given in Section 1.1 We will leave an examination of structure in organometallic systems to Chapter 12, and we will examine more complex MOT ideas about bonding in metal-containing systems in Chapter 14 The same kind of loca lized and discrete a and 'TT bonds often associated with organic compounds can be assigned to the bonding in organometallic compounds One simple concept for visualizing bonding in m etal-containing systems is to make direct analogies to such bonding in organic systems For example, let's examine the shapes and nodal properties of the d orbitals shown in Figure 1.26 First, notice that the d2 z orbital is directional along the z axis, as is a hybrid orbital along an axis, and is therefore "sigma-like" In fact, w e refer to it as having sigma symmetry along the z axis Likewise, the dx'-y' orbital is aligned along the x andy axes, and is therefore considered to have sigma symmetry when viewed down these axes Hence, when forming discrete localized bonds to ligands, the dz' orbital and the dx'-y' orbital can make sigma bonds that are placed along the z or the x andy axes, respectively We essentially use these orbitals just as we use hybrid or a( out) orbitals on carbon Now let's examine the analogies that can be drawn between the rest of the d orbitals and p orbitals When citing down the x axis, the dxz and dxy orbitals look like two orthogonal p orbitals Likewise, citing d own they axis, both the dyz and dxy look like p orbitals Therefore, these orbitals are considered to have 'TT symmetry When creating double bonds to ligands, 59 60 C H A PT E R 1: INTRODUCTIO N TO STRUCTURE AND MODELS OF BOND ING A Analogous to a carbon hybrid along the z axis § B Analogous to a carbon hybrid along the x or y axes c Analogous to a p orbital along the z axis or the y axis Analogous to a p orbital along the x axis or the y axis Analogous to a p orbital along the x axis or the z axis : : Figure 1.27 Orbita l mixing di agra m for th e combination of a TI-symme try d orbital with a carbon p orbita l to create a metal-carbon 1T bond Figure 1.26 Schem atic representations of d orbi tals a nd their analogous carbon orbitals A Looking along the positive z axis (designated as an eyeball), the carbo n hybrid along th e z axis a ppears the sa me as a dzz orbital They are referred to as having rr symmetry, analogo us to rr(out) orbitals or th e standard hybrid orbitals for making a bonds to orga nic groups B Looking alo ng the positive x or y axes, the dxLyz orbita l looks like a carbon hyb rid C The d,w d ,y, and du orbitals appear asp orbitals, depending upon the line of sight They a re referred to as hav ing 1T symmetry The a and b descriptors on each orbital refer to the line of sight for the cor responding eyeballs these orbitals on the metals are used exactly as we use p orbitals on carbons This combination is very clear in Figure 1.27, where an orbital mixing diagram is given for a 1T bond between a m etal and a carbon, as would be present in an organometallic complex that has an M = CR functional group Lastly, there is even a h ybrid orbital app roach to modeling the bonding in organometalli c and inorganic complexes Using the sam e concepts presented in Section 1.1.6 for the linear combinations of sand p orbitals to create hybrids, we can mix d orbi tals with the s and p orbitals For example, if you start with an sp2 h ybridization state, and mix the remaining p, orbital with the d,, orbital, a hybridiza tion state know as dsp is obtained As shown in Figure 1.28, the bonds to the apical positions are pd hybrid orbitals, while the equatorial positions are sp hybrid orbitals Such h ybridization is appropriate for trigonal bipyramidal complexes 1.5 A VERY Q U I CK LOOK AT OR GANOME TALLIC AND INORGAN I C BOND I NG sl Hybrid orbitals -. _; pd Hybrids Remains a =Apical positions; pd hybrid orbitals e = Equatorial positions; sp hybrid orbitals Figure 1.28 Hybridiza tion for h·i go na l bipy ramidal geometries starts w ith the ce ntral a tom sp hybridized The orbita ls a ligned along the equa torial positions remain as sp hybr ids However, the orbitals a long ap ica l positions are pd h ybrid s The mixing of an s, three p's, and the d~, and dx'-y' orbitals leads to d2 sp h ybridization, which is appropriate for octahedral co mplexes For almost all bonding geometries in inorganic and organometallic chemistry, hybrid orbitals are useful, and this very brief introduction to bonding using m etals will be enough to take u s a long way in understanding stru cture and reactivity Summary and Outlook This chapter represents just a beginning It is only a first look into bonding, with hints at structure and reactivity We presented two models for bondin g, a classical one and a more modern approach, and showed that they can be used to understand stable organic structures and reactive intermediates Hopefully this chapter has refreshed your m emory, and has sparked an interest in you to learn how these notions of bonding can be put to use We exactly tha t in the next several chapters where the focus is more upon structure Furthermore, after analyzing struchue, we can take the bonding concepts and loo k at reactivity Structure and reactivity actually take up approximately two-thirds of this book, and not until we have to look at some very specialized reactions (pericyclic and photochemical) will we need to develop a more so phisticated theory of bonding With our current qualitative models we can go a long way in our analysis of topics in organic chemistry For many students and professors, this chapter may completely suffice as a review of bondin g, because it is sufficient for almost all organic transformations For other students and professors, however, it may be desirable to now go directly to Chapter 14, w here the concepts introduced herein are discu ssed more quantitatively and modern methods in computational electronic struch1re th eory are covered This is a decision to be made on an individ ual basis However, it should be apprecia ted that to the bes t of th e authors' abilities, we took the topics of this chapter only to a depth that is routinely used when thinking about organic s tructure and bonding by a non-ex pert in quantitati ve methods Our intention is for Chap ter 14 to stand alone, so it can be covered at any point during the course to learn more advanced concep ts and quantitative methods 61 62 CHAPTER 1: I NTRODUCTION TO STRUCTURE AND MODE L S OF BOND I NG Exercises State the hybridization of the no n-hydrogen a to ms in the following structures H H I I A A N ~N c B D er N E # Assuming that each atom in the foll owing stru ctures has an octet of electrons, identify which compounds ve an a tom that has a formal charge Ide nti fy w hat and whe re tha t charge is In the compound s w itho ut form al ch arges, identify any significant bond polari za tio ns by w riting 8+ and 8- nea r the a ppropriate atom s s 0 B A )lo~ c D /""'- Br E For the bond polarizati ons in Exercise 2, draw a dipole arrow for the polarized bond s Draw the u and u* molecul ar orbitals fo r discre te and loca lized bo nds formed betwee n h ybridized carbo ns a nd heteroatoms (a heteroatom is any a tom besides C and H ), as well as heteroa toms and hyd rogen, in the following structures Indi ca te any p olari zation these bonds may have in your di agra m b y drawing the sh a pes of the discrete bonding and antibonding orbitals in a manne r indi ca tive of this polari zati on A B c \_ CI Dra w the TI and TI* molecul ar o rbitals for the discre te and loca lized TI bonds in the foll owing structures Indi ca te an y pola riza tion these bonds may have in yo ur diagram th rough the shapes of the discrete bonding and antibonding orbi tals A A c B D Show a ny pl ausible reson an ce structures for the molecules give n in Exercises and lf there are no pl au sible resonance structures, indi cate this (n ote th a t the molecul e corresponding to le tter A is the sam e in each proble m) Di scuss the hybridiza ti on in the C- C and C- H bonds of cyclopro p an e, given th at the H-C- H bond an gle is 118° Carbon te trachloride h as ne ithe r a dipole mome nt nor a qu adrupole moment, but it d oes have an octo pole m oment Prov ide a simple descripti o n o f this moment Formaldehyde has a fairly large dipole mome nt of 2.33 D, but CO h as a small dipole m oment of0.11 D Use resonance and electronegati vity arguments to explain these results 10 Consider bond dipoles to predi ct whi ch confo rme r of fo rmi c aci d s hould have the hi gher dipole mom e nt, A or B 0 A }-o, H H }- a B H H 11 Pauling proposed the fo !J owing correlation be tween electro nega tivi ty difference and percent ioni c characte r in a bond : Ionic ch aracter = 100 X [1 - e-