Numerical Methods and Applications/ Ward Cheney

BONDING AND MOLECULAR STRUCTURE:The Basics l
Molecular Graphic: Glycine, an organic molecule found :n space 1
1.1 Organic Chemistry and Life 2
1.2 The Structural Theory of Organic Chemistry 3
1.3 Isomers: The Importance of Structural Formulas 4
1.4 Chemical Bonds: The Octet Rule 5
1.5 Wr.ting Lewis Structures 7
1.6 Exceptions to the Octet Rule 9
1.7 Formal Charge 10
1.8 Resonance Theory 13
1.9 Quantum Mechanics and Atomic Structure 18
1.10 Atomic Orbitals and Electron Configuration 20
1.11 Molecular Orbitals 21
1.12 The Structure of Methane and Ethane:sp^ Hybridization 24
THE CHEMISTRY OF... Calculated Molecular Models: Electron Density Surfaces 28
1.13 The Structure ofEthene(Ethylene):sp^ Hybridization 28
1.14 The Structure of Ethyne(Acetylene):sp Hybridization 33
1.15 A Summary ofImportant Concepts that Come from Quantum Mechanics 35
1.16 Molecular Geometry: The Valence Shell Electron Pair Repulsion Model 36
1.17 Representation of Structural Formulas 39
1.18 Applications of Basic Principles 44
FUNCTIONAL GROUPS,INTERMOLECULAR FORCES,AND
INFRARED(IR)SPECTROSCOPY 51
Structure and Function: Organic Chemistry, Nanotechnology,and Bioengineering/
Molecular Graphic: A molecular template for bone growth 51
2.1 Carbon-Carbon Covalent Bonds 52
2.2 Hydrocarbons: Representative Alkanes, Alkenes, Alkynes,and Aromatic
Compounds 52
2.3 Polar Covalent Bonds55
THE CHEMISTRY OF...Calculated Molecular Models: Maps of Electrostatic Potential
2.4 Polar and Nonpolar Molecules 56
Functional Groups 59
AlkyI Halides or Haloalkanes 60
Alcohols 61
Ethers 63
Amines 63
Aldehydes and Ketones 65
Carboxylic Acids, Esters,and Amides 65
Nitriles 67
Summary ofImportant Families ofOrganic Compounds 68
Physical Properties and Molecular Structure 68
Summary ofAttractive Electric Forces 75
the CHEMISTRY OF...Organic Templates Engineered to Mimic Bone Growth 75
2.16 Infrared Spectroscopy:An Instrumental Method for Detecting Functional Groups
2.17 Applications ofBasic Principles 84
ACIDS AND BASES:An Introduction to
Organic Reactions and Their Mechanisms 91
Shuttling tfie Protons/Molecular Graphic: Diamox,a drug that prevents altitude
sickness 91
3.1 Reactions and Their Mechanisms 92
3.2 Acid-Base Reactions 94
THE CHEMISTRY OF...HOMOsand LUMOs in Reactions 97


3.3 Hcterolysis of Bondfi to
3.6 Predicting the Outcome of Acid-Base Reactions 103
3.7 The Relationsivp between Sinjcturo and Ac-d ry 105
3.8 Energy Changes 108
3.9 The Relationship between the ('quilibnum Constant ami tfu- Standard Free Energy
Change.SG" 110
3.10 The Acidity of Carboxylic Acids 111
3.11 The Effect of the Solvent on Aadity 115
3.12 Organic Compounds as Bases 116
3.13 A Mechanism for an Organic Reaction 117
THE CHEMISTRY OF . Carbonic Anhydrasc 118
3.14 Acids and Bases m Nonaqueous Solutions 119
3.15 Acid-Base Reactions and the Synthesis of Deuterium- and
Tritium-Labeled Compounds 120
3.16 Applications of Basic Principles 121
NOMENCLATURE AND CONFORMATIONS
OFALKANES 129
7b Be Flexible or Inflexible - Molecular Structure Makes the Difference/ Molecular
Graphic: A portion of the structure ofdiamond,an exceptionally rigid molecule 129
4.1 Introduction to Alkanes and Cycloalkanes 130
^ THE CHEMISTRY OF... Petroleum Refining 130
4.2 Shapes ofAlkanes 132
4.3 lUPAC Nomenclature ofAlkanes. AlkyI Hahdes. and Alcohols 134
4.4 Nomenclature ofCycloalkanes 141
4.5 Nomenclature of Alkenes and Cycloalkenes 143
4.6 Nomenclature ofAlkynes 145
4.7 Physical Properties ofAlkanes and Cycloalkanes 146
'THE CHEMISTRY OF... Pheromones:Communication by Means of Chemicals 148
4.8 Sigma Bonds and Bond Rotation 148
4.9 Conformational Analysis of Butane 151
4.10 The Relative Stabilities ofCycloalkanes: Ring Strain 153
4.11 The Origin ofRing Strain in Cyclopropane and Cyclobutane:
Angle Strain and Torsional Strain 155
4.12 Conformations ofCyclohexane 156
THE CHEMISTRY OF... Nanoscale Motors and Molecular Switches 159
4.13 Substituted Cyclohexanes:Axial and Equatorial Hydrogen Atoms 160
4.14 Disubstituted Cycloalkanes: Cis-Trans Isomerism 163
4.15 Bicyclic and Polycyclic Alkanes 166
THE CHEMISTRY OF...Elemental Carbon 167
4.16 Chemical Reactions ofAlkanes 168
4.17 Synthesis ofAlkanes and Cycloalkanes 168
4.18 Structural Information from Molecular Formulas and the Index of
Hydrogen Deficiency 169
4.19 NMR Spectroscopy-A Practical Introduction 171
4.20 Applications ofBasic Principles 175
STEREOCHEMISTRY:Enantiomers and Diastereomers 181
The Handedness ofLife/Molecular Graphic: The mirror-image stereoisomers
alanine,a chiral amino acid 181
5.1 The Biological Significance ofChirality 182
5.2 Isonnerism: Constitutional Isomers ana Stereoisomers 183
5.3 Enantiomers and Chiral Molecules 184
5.4 More about the Biological Importance ofChirality 187
5.5 Historical Origin ofStereochemistry 1885.6 Tests for Chirality: Planes of Symmetry 189
5.7 Nomenclature ofEnantiomers: The R.S-Syslcm 190
5.8 Properties ofEnantiomers: Optical Activity 194
5.9 The Origin of Optical Activity 198
5.10 The Synthesis of Chiral Molecules 200
5.11 Chiral Drugs 202
THE CHEMISTRY OF ... Selective Binding of Drug Enantiomers to Left- and
Rigfit-Handed Coiled DNA 203
5.12 Molecules With More than One Chirality Center 203
5.13 Fischer Projection Formulas 207
5.14 Stereoisomerism of Cyclic Compounds 209
5.15 Relating Configurations through Reactions in WIvch No Bonds to
the Chirality Center Are Broken 211
5.16 Separation of Enantiomers: Resolution 213
5.17 Compounds with Chirality Centers Other than Carbon 214
5.18 Chiral Molecules that Do Not Possess a Chirality Center 215
i:
REACTIONS OF ALKYL HALIDES:
Nucleophilic Substitution and Elimination 221
Breaking Bacterial Cell Walls with Organic Chemistry/ Molecular Graphic: Lysozyme 221
6.1 Organic Halides 222
6.2 Nucleophilic Substitution Reactions 224
6.3 Nucleophiles 224
6.4 Leaving Groups 225
6.5 Kinetics ofa Nucleophilic Substitution Reaction: An Sf^2 Reaction 226
6.6 A Mechanism for the Sn2 Reaction 227
6.7 Transition State Theory: Free-Energy Diagrams 228
6.8 The Stereochemistry of Si\i2 Reactions 231
THE CHEMISTRY OF...Lysozyme 234
6.9 The Reaction oftert-Butyl Chloride with Hydroxide Ion:An Si^l Reaction 235
6.10 A Mechanism for the S^l Reaction 236
6.11 Carbocations 237
6.12 The Stereochemistry ofSnI Reactions 239
6.13 Factors Affecting the Rates ofS^l and Sf^2 Reactions 241
. 6.14 Organic Synthesis: Functional Group Transformations Using Sn2 Reactions 250
^ THECHEMISTRY OF...Biological Methylation:A Biological NucleophilicSubstitution
Reaction 251
6.15 Elimination Reactions ofAlky!Halides 253
6.16 The E2Reaction 255
6.17 The El Reaction 256
6.18 Substitution versus Elimination 257
6.19 Overall Summary 260
ALKENES AND ALKYNES-Part I:
Elimination Reactions of AlkyI Halides 269
Cell Membrane Fluidity/Molecular Graphic: cis-9-Octadecenoic acid,an unsaturated
fatty acid incorporated into cell membrane phospholipids 269
7.1 Introduction 270
7.2 The(EHZ)System for Designating Alkene Diastereomers 270
7.3 Relative Stabilities ofAlkenes 272
7.4 Cycloalkenes 274
7.5 Synthesis ofAlkenes via Elimination Reactions 274
7.6 Dehydrohalogenation ofAlkyI Halides 275
7.7 Acid-Catalyzed Dehydration ofAlcohols 280
7.8 Carbocation Stability and the Occurrence ofMolecular Rearrangements 285
7.9 Synthesis ofAlkynes by Elimination Reactions 2887.10 The Acidity of Torm-nal Alkynrs 290
7.11 Replacement of the Acotylcnic Hydrogc-n Atom of Terminal Alkynos 290
7.12 Alkylation of Alkynide Anions Some Gcncrai Principles of Structuio and
Reactivity Illustrated 292
^ 7.13 Hydrogonation of Alkcnes 292
ft 'THE CHEMISTRY OF . Hydrogcnaiion in the Food Industry 293
7.14 Hydrogenation The FufKtion of the Catalyst 294
THE CHEMISTRY OF Homogonoous Asymn^ctric Catalytic Hydrogenation,
Examples Involving i-DOPA.(S)-Nar;roxen. and Aspartame 295
7.15 Hydrogenation of Alkynes 297
_ 7.16 An Introduction to Orcjanic Synthesis 298
!?' the CHEMISTRY or , From the Inorganic!o the Organic 302
ALKENES AND ALKYNES- Part II:
Addition Reactions and Synthesis 311
The Sea:A Treasury of G(o/og'ca//y Active Natural Products / Molecular Graphic:
Dactylyne. a halogcnated marine natural product 311
8.1 Introduction: Addition to Alkcnes 312
8.2 Electrophihc Addition of Hydrogen Hahdes to Alkenes Mechanism and
Mar/covnifcov's Rule 314
8.3 Stereochemistry o/the Ionic Addition to an A/kcnc 319
8.4 Addition of Suifunc Acid to Alkcnes 320
8.5 Addition of Water to Alkenes: Acid-Catalyzed Hydralion 321
8.6 Alcohols from Alkenes through Oxymcrcuration-Demorcuration:
Markovnikov Addition 323
8.7 Alcohols from Alkenes through Hydroboration-Oxidation:
Anti-Markovnikov Syn Hydration 326
8.8 Hydroboration: Syntiiesis ofAlkylboranes 326
8.9 Oxidation and Hydrolysis of Alkyboranes 329
8.10 Summary ofAlkene Hydration Methods 331
8.11 Protonolysis ofAlkyboranes 331
8.12 Electrophilic Addition of Bromine and Chlorine to Alkenes 332
8.13 Stereochemistry of the Addition of Halogens to Alkenes 334
8.14 Halohydrin Formation 337
8.15 Divalent Carbon Compounds:Carbenes 338
8.16 Oxidations ofAlkenes: Syn 1,2-Dihydroxyiation 340
THE CHEMISTRY OF ... Catalytic Asymmetric Dihydroxyiation 342
8.17 Oxidative Cleavage ofAlkenes 343
8.18 Electrophilic Addition of Bromine and Chlorine to Alkynes 345
8.19 Addition of Hydrogen Halides to Alkynes 346
8.20 Oxidative Cleavage of Alkynes 347
.,8.21 Synthetic Strategies Pevisited 347* ... n
THE CHEMISTRY OF ... Cholesterol Biosynthesis: Elegant and Familiar Reactions
in Nature 350
NUCLEAR MAGNETIC RESONANCE AND MASS SPECTROMETRY:
Instrumental Methods for Structure Determination 363
A Thermos at Liquid Helium/Molecular Graphic: 1-chloro-2-propanol 363
9.1 Introduction 364
9.2 Nuclear Magnetic Resonance(NMR)Spectroscopy 364
9.3 Interpreting Proton NMR Spectra 369
9.4 Nuclear Spin: The Origin ofthe Signal 371
9.5 Detecting the Signal: Fourier Transform NMR Spectrometers 373
9.6 Shielding and Deshielding ofProtons 374
9.7 The Chemical Shift 376
9.8 Chemical Shift Equivalent and Nonequivalent Protons 377
9.9 Signal Splitting: Spin-Spin Coupling 379
9.10 Proton NMR Spectra and Rate Processes 3889.11 Carbon-13 NMR Spectroscopy 390
9.12 Two-Dimensional(2D)NMR Techniques 396
i?" THE CHEMISTRY OF... Magnetic Resonance Imaging m Medicine 399
9.13 An Introduction to Mass Spectrometry 399
9.14 Formation ofIons: Electron Impact lonization 400
9.15 Depicting the Molecular Ion 400
9.16 Fragmentation 401
9.17 Determination of Molecular Formulas and Molecular Weights 407
9.18 Mass Specfrometer /nstrument Designs 412
9.19 GC/MS Analysis 415
9.20 Mass Spectrometry of Biomolecules 416
REACTIONS INVOLVING RADICALS 427
Radicals in Biology. Medicine,and Industry/Molecular Graphic:
Nitric oxide and Cia/i's® 427
10.1 Introduction 428
10.2 Homolytic Bond Dissociation Energies 429
10.3 The Reactions ofAlkanes with Halogens 433
10.4 Chlorination of Methane: Mechanism of Reaction 435
10.5 Chlorination of Methane:Energy Changes 437
10.6 Halogenation of Higher Alkanes 443
10.7 The Geometry ofAlkyI Radicals 446
10.8 Reactions that Generate Tetrahedral Chirality Centers 446
10.9 Radical Addition to Alkenes: The Anti-Markovnikov Addition ofHydrogen Bromide 449
10.10 Radical Polymerization ofAlkenes: Chain-Growth Polymers 451
10.11 Other Important Radical Reaaions 455
THE CHEMISTRY OF... Callcheamidn A]':A Radical Device for Slicing the Backbone
of DNA 456
THE CHEMISTRY OF...Antioxidants 458
THE CHEMISTRY OF... Ozone Depletion and Chlorofluorocarbons(CFCs) 459
SPECIAL TOPIC A: CHAIN-GROWTH(ADDITION)POLYMERS 464

ETHERS AND ALCOHOLS 469
Molecular Hosts/Molecular Graphic: Monens/n sodium salt, an antibiotic that
transports ions across cell membranes 469