Symmetry, Spectroscopy, and Crystallography: The Structural Nexus (Hardcover)

From the Author’s Desk XIII

1 Symmetry/Pseudosymmetry: Chirality in Molecules, in Nature, and in the Cosmos 1

1.1 Introduction 1

1.2 Rudimentary GroupTheory, Isometry, and Symmetry 4

1.3 Asymmetric versus Chiral: The I-Symmetry of Viral Capsids 7

1.4 The Birth of Chirality as a Chemical Concept 9

1.5 Apparent Symmetry (High-Fidelity Pseudosymmetry) and the Quantification of Distortion from the Ideal 11

1.6 Chirality in Form and Architecture: Symmetry versus Broken Symmetry 16

1.7 Chirality in Nature: Tropical Storms, Gastropods (Shells), and Fish 17

1.8 Extraterrestrial Macroscale Chirality: Spiral Galaxies, Martian Sand Devils, Jovian Great Red Spot, Neptune’s Great Dark Spot, and Venusian South-Pole Cloud Vortex 20

1.9 Analyses of Amino Acid Chirality in Extraterrestrial Samples with Gas–Liquid Chromatography Chiral Columns 23

2 Enantiospecificity of Pheromones, Sweeteners, Fragrances, and Drugs 25

2.1 Enantiospecificity of Pheromones, Sweeteners, and Fragrances 25

2.2 The Importance of Chirality in Drug Therapy 27

3 Bonding Parameters and the Effect of Local Environment on Molecular Structure 33

3.1 Symmetry Arguments and the Effect of the Environment on Molecular Structure 33

3.2 The Effect of Local Environment on Molecular Models and Molecular Structure 34

3.3 Torsion Angles and Molecular Conformation 35

3.4 Symmetry Considerations of Atomic Orbital Hybridization and Bonding Parameters 39

4 Historical Development of Structural Chemistry: From Alchemy to Modern Structural Theory 41

4.1 Hemihedralism in Quartz Crystals: Setting the Stage for the Birth of Stereochemistry 41

4.2 Tartaric Acid and Alchemy 45

4.3 Hemihedralism in Crystalline Tartaric Acid Salts: The Birth of Molecular Chirality 46

4.4 Gift for Prelog’s Retirement: A Matched Pair of u′,x′-Hemihedral Faced Right- and Left-Handed Quartz Crystals 54

4.5 Early Structural Representations of Organic Substances and the Development of Modern Structural Concepts 55

4.6 Fischer Projections to Determine α- and β-Anomeric Configurations 64

5 Chiroptical Properties 67

5.1 The Language of Symmetry, Isomerism, and the Characterization of Symmetry Relationships within and between Molecules 67

5.2 Chiroptical Properties: Circular Birefringence, Optical Rotatory Dispersion, and Circular Dichroism 68

5.3 Miller Indices and Fractional Coordinates in Crystallography 74

5.4 Scanning Tunneling Microscopy 78

5.5 Direct Visualization of an Enantiomer’s Absolute Configuration in the Gas Phase 82

6 Symmetry Comparison of Molecular Subunits: Symmetry in Nuclear Magnetic Resonance Spectroscopy and in Dynamic NMR 85

6.1 Symmetry in NMR Spectroscopy 85

6.2 Symmetry Comparison of Molecular Subunits, Topicity Relationships 87

6.3 Dynamic Stereochemistry, Dynamic Nuclear Magnetic Resonance Spectroscopy (DNMR) 90

6.4 Use of Permutations in DNMR for Topomerization-, Enantiomerization-, and Diastereomerization-Exchange Processes 92

7 Prochirality, Asymmetric Hydrogenation Reactions, and the Curtin–Hammett Principle 99

7.1 Prochirality of Enantiotopic Subunits 99

7.2 Homogeneous Hydrogenation by RhodiumI/Achiral Diphosphine Catalysts Differentiates the Diastereotopic Prochiral Faces of Olefins 101

7.3 Homogeneous Hydrogenation by RhodiumI/(Chiral Diphosphine) Catalysts Differentiates the Enantiotopic Prochiral Faces of Olefins: The Curtin–Hammett Principle 104

8 Stereogenic Elements, Chirotopicity, Permutational Isomers, and Gear-Like CorrelatedMotion of Molecular Subunits 113

8.1 Stereogenicity, Stereogenic Elements, Chirotopicity, and the Ambiguity of Some Stereochemical Terms 113

8.2 Triarylamine Propellers 115

8.3 Dynamic Stereochemistry of Permutational Isomers: Correlated Motion in Triarylamines 116

8.4 Relative Stereochemical Descriptors: Retro-Inverso Isomers 122

9 Symmetry in Extended Periodic Arrays of Molecular Crystals and the Relevance of Penrose Tiling Rules for Nonperiodic Quasicrystal Packing 127

9.1 Symmetry in Extended Arrays/Molecular Crystals 127

9.2 Achiral Periodic Arrays of Chiral Objects and Racemic Compound Crystal Lattices 132

9.3 Chiral Periodic Arrays 132

9.4 Occupancy of Special Positions in Periodic Arrays 136

9.5 The Bragg Law and X-Ray Diffraction 139

9.6 The Interferogram Phenomenon in Single-Crystal X-Ray Crystallography 140

9.7 X-Ray Fiber Diffraction 143

9.8 Penrose Tiling Matching Rules, Quasicrystal Packing, and Dodecahedrane 145

10 MultipleMolecules in the Asymmetric Unit, “Faking It”; Pseudosymmetry Emulation of Achiral Higher Order Space Filling in Kryptoracemate Chiral Crystals 149

10.1 Multiple Molecules within an Asymmetric Unit 149

10.2 “Faking It”: Pseudosymmetry Emulation of Achiral Higher-Order Space Filling in Kryptoracemate Chiral Crystals 151

10.3 Desymmetrization of Platonic-Solid Geometries Resulting from Crystallographic Symmetry Constraints 161

10.4 Mobility of Cubane and Dodecahedrane (CH)n Spherical Molecules within a Crystal Lattice 164

11 Platonic-Solid Geometry Molecules and Crystallographic Constraints upon Molecular Geometry, Symmetry Distortions from Ideality 169

11.1 Geometrical Considerations in High-Symmetry Molecules 169

11.2 Syntheses Strategies of High-Symmetry Chiral Molecules 171

11.3 Ethano-Bridge Enantiomerization of T-Symmetry Molecules 173

11.4 Self-Assembly of T-Symmetry Chiral Molecules 176

11.5 Enantiomerization of T-Symmetry Clusters 180

11.6 Tetradentate Edge-Linker Units Separated by a Spacer 183

11.7 Self-Assembly of O-Symmetry Chiral Molecules 184

11.8 O-Symmetry Ferritin Protein Octahedral Shell 185

11.9 Desymmetrization Resulting from Symmetry and Chemical Constraints 186

12 Solid-State NMR Spectroscopic/X-Ray Crystallographic Investigation of Conformational Polymorphism/Pseudopolymorphism in Crystalline Stable and Labile Hydrated Drugs 189

12.1 Divalent Anions Linking Conformationally Different Ammonium Cations 189

12.2 Cross Polarization/Magic Angle Spinning Solid-State NMR and X-Ray Crystallographic Studies on the Elusive “Trihydrate” Form of Scopolamine⋅Hydrobromide, an Anticholinergic Drug 191

13 NMR Spectroscopic Differentiation of Diastereomeric Isomers Having Special Positions of Molecular Symmetry 205

13.1 NMR Anisochronism of Nuclei at Special Positions of Molecular Symmetry 205

13.2 Pattern Recognition: A Graphical Approach to Deciphering Multiplet Patterns 207

14 Stereochemistry of Medium Ring Conformations 213

14.1 A Short Primer on Medium Ring Stereochemistry 213

14.2 Assignment of Equatorial-/Axial-Substituent Descriptors to Rings of Any Size 214

14.3 NMR Structure Determination of Medium-Ring Solution-State Conformations 216

14.4 Dynamic Disorder in Crystals 221

15 The PharmacophoreMethod for Computer Assisted Drug Design 229

15.1 The Pharmacophore, Neurotransmitters and Synapse 229

15.2 The Pharmacophore Method for Computer Assisted Drug Design 231

15.3 Determination of the Dopamine Reuptake Site Pharmacophore 233

15.4 Methylphenidate (Ritalin⋅HCl) and (−)-Cocaine⋅HCl 235

15.5 Ritalin Versus Cocaine: Binding Affinity and Inhibitory Concentration 238

15.6 Second Generation Pharmacophore:The Orientation of the NH Proton 242

15.7 Avoidance of Adjacent Gauche+Gauche− Interactions 244

15.8 Static Disorder in N-Methyl Ritalin Crystals 246

15.9 Development of Specific Dopamine Reuptake Inhibitors (SDRI) 250

16 The X-Ray Structure–Based Method of Rational Design 255

16.1 X-Ray Crystallographic Structure–Based Molecular Design 255

16.2 The Different Primary Ammonium and Quaternary Aminium Binding Modes 258

16.3 Search for Unused Binding Sites 263

16.4 Primary Ammonium and Quaternary Aminium Binding Modes in CB[7 and 8] Complexes of Diamantane-4,9-Substituted Guests 265

17 Helical Stereochemistry 269

17.1 Helical Stereochemistry 269

17.2 2nn-Symmetry Achiral Helical Pathways 273

17.3 “La Coupe du Roi”: Chiral Apple Halves Produced by a 42-Bisection 278

17.4 Intermeshing MolecularThreefold Helices: Symmetry, Chemical, and Phase Considerations 281

17.5 X-Ray Fiber versus Single-Crystal Diffraction Models 289

References 293

Index 301