Chirality at Solid Surfaces

Preface xiii

Acknowledgements xxiii

1 Fundamentals of Chirality 1

1.1 Point and Space Groups 2

1.2 Proper and Improper Symmetry 4

1.3 Chirality in Finitude and Infinity 5

1.3.1 Molecular Chirality 5

1.3.2 Crystalline Chirality 8

1.4 Routes to Surface Chirality 9

1.4.1 Surfaces of Intrinsically Chiral Crystals 9

1.4.2 Intrinsically Chiral Surfaces of Achiral Crystals 10

1.4.3 Chiral Modification of Achiral Surfaces 11

1.5 Diastereoisomerism Defined 14

1.6 Quantifying Chirality? 15

1.7 Enantiomeric Excess 17

1.8 Synthesis, Separation and Sensing 19

References 20

2 Surface Symmetry and Structure 21

2.1 Spherical Representation of Symmetry 21

2.2 Spherical Representation of Structure 24

2.3 Stereographic Projections: Flattening the Globe 27

2.4 Surfaces of the Face-Centred Cubic Structure 29

2.4.1 Reconciliation of Symmetry and Primary Structure 29

2.4.2 Secondary and Tertiary Structure 32

2.4.3 Commentary 34

2.5 Surfaces of the Body-Centred Cubic Structure 36

2.5.1 Reconciliation of Symmetry and Primary Structure 37

2.5.2 Secondary and Tertiary Structure 39

2.5.3 Commentary 40

2.6 Surfaces of the Hexagonal Close-Packed Structure 42

2.6.1 Symmetry 43

2.6.2 Primary Structure 48

2.6.3 Reconciliation of Symmetry and Primary Structure 52

2.6.4 Commentary 55

2.7 Surfaces of the Diamond Structure 56

2.7.1 Symmetry 56

2.7.2 Primary Structure 58

2.7.3 Reconciliation of Symmetry and Primary Structure 59

2.7.4 Commentary 62

References 63

3 Surface Energy and Surface Stress 65

3.1 Thermodynamic Definition of Surface Energy 65

3.2 The Tensor Nature of Surface Stress 70

3.3 Visualisations of Surface Stress: Iconic Conics 71

3.3.1 The Normal Stress Conic 72

3.3.2 The Shear Stress Quartic 73

3.3.3 The Stress Ellipse 74

3.4 Symmetry of the Surface Stress: Eccentricity and Orientation 75

3.4.1 Stereography and Surface Stress 77

3.4.2 Racemic Surface Stress 79

3.4.3 Adsorbate-Induced Asymmetry in Surface Stress 80

3.5 Measurement of Differential Surface Stress 81

3.5.1 Island Shape Measurement 81

3.5.2 Contact Angle Measurement 82

3.5.3 Cantilever Deformation 85

3.6 Facet Formation and theWulff Construction 86

3.6.1 Ridge-and-Furrow Facets 86

3.6.2 Pyramid-and-Pit Facets 88

3.6.3 Geometrical Construction 89

References 91

4 Asymmetric Adsorption on Achiral Substrates 93

4.1 Achiral Adsorbates: GlidingThrough Broken Mirrors 93

4.2 Prochiral Adsorbates: Chirality in Context 97

4.2.1 Guanine on Au{111} 98

4.2.2 Stilbene Derivatives on Cu{100} and Cu{110} 101

4.2.3 Glycine on Cu{110} and Cu{311} 102

4.2.4 Succinic and Fumaric Acids on Cu{110} 107

4.2.5 Meso-Tartaric Acid on Cu{110} 111

4.3 Chiral Adsorbates: Act Locally,Think Globally 112

4.3.1 Alanine on Cu{110} and Cu{311} 112

4.3.2 Proline on Cu{110} and Cu{311} 120

4.3.3 Serine and Lysine on Cu{110} 125

4.3.4 Cysteine on Cu{110} and Au{110} 128

4.3.5 Tartaric Acid on Cu{110} 135

4.3.6 Glutamic Acid on Ag{110} and Ag{100} 140

4.3.7 2-Butanol on Au{111} 145

4.3.8 Tartaric Acid on Ni{111} 146

4.3.9 Alanine on Pd{111} 147

4.4 Chiral Facetting: Remodelling the Surface 149

4.4.1 Glycine, Alanine and Lysine on Cu{100} 150

4.5 Chiral Metallorganic Frameworks: Into the Second Dimension 151

4.5.1 Glutamic Acid on Ni/Au{111} 152

4.5.2 Lysine on Ni/Au{111} 153

4.5.3 Proline on Ni/Au{111} 154

4.6 Executive Summary 156

References 159

5 Asymmetric Adsorption on Chiral Substrates 165

5.1 Achiral Adsorbates on Intrinsically Chiral Substrates: Fault-Lines and Facets 165

5.1.1 Oxygen on Cu{531} 165

5.1.2 Cyclohexanone on Cu{643} 167

5.1.3 NaCl on Cu{532} 168

5.2 Prochiral Adsorbates on Intrinsically Chiral Substrates: Familiar and Strange 168

5.2.1 Glycine on Cu{531} 169

5.3 Chiral Adsorbates on Intrinsically Chiral Substrates: Diastereomeric Effects I 171

5.3.1 Alanine on Cu{531} 171

5.3.2 Serine on Cu{531} 173

5.3.3 Cysteine on Cu{531} and Au{17 11 9} 174

5.3.4 Tartaric Acid on Cu{531} 176

5.3.5 Propylene Oxide and 3-Methylcyclohexanone on Cu{643} 176

5.3.6 3-Methylcyclohexanone on Cu{531}, Cu{651} and Cu{13 9 1} 180

5.3.7 Alanine, Serine, Lysine, Phenylalanine and Aspartic Acid on Cu{3 1 17} 182

5.4 Chiral Adsorbates on Chirally Modified Substrates: Diastereomeric Effects II 184

5.4.1 Propylene Oxide on 2-Butanol-Modified Pd{111} and Pt{111} 185

5.4.2 Propylene Oxide on 2-Methylbutanoic Acid-Modified Pd{111} and Pt{111} 188

5.4.3 Propylene Oxide on Amino Acid-Modified Pd{111} 189

5.4.4 Glycidol on Tartaric Acid-Modified Pd{111} 190

5.4.5 Propylene Oxide on Lysine-Modified Cu{100} 191

5.5 Executive Summary 191

References 193

6 Chiral Amplification 197

6.1 Kinetic Amplification: Surface Explosions 197

6.1.1 Tartaric and Malic Acids on Cu{110} 200

6.1.2 Tartaric Acid on Cu{643}, Cu{17 5 1}, Cu{531} and Cu{651} 202

6.2 Thermodynamic Amplification: Sergeants, Soldiers and Majority Rule 206

6.2.1 Tartaric, Succinic and Malic Acids on Cu{110} 206

6.2.2 Heptahelicene on Cu{111}, Ag{111} and Au{111} 210

6.2.3 Aspartic Acid on Cu{111} 215

6.2.4 Supramolecular Assemblies on Highly Ordered Pyrolytic Graphite 217

References 222

7 Asymmetric Heterogeneous Catalysis 225

7.1 Electro-Oxidation of Glucose on Pt{643} and Pt{321} 227

7.2 Electron-Stimulated Oxidation of Methyl Lactate on Cu{643} 235

7.3 Hydrogenation of ?-Ketoesters over Platinum: The Orito Reaction 236

7.3.1 Adsorption Geometry of Methyl and Ethyl Pyruvate 237

7.3.2 Adsorption Geometry of Cinchonidine and its Cousins 240

7.3.3 Binding and Reaction in the Chiral Complex 244

7.4 Hydrogenation of ?-Ketoesters over Nickel: The Izumi Reaction 247

7.4.1 Adsorption Geometry of Methyl Acetoacetate 247

7.4.2 Two-Dimensional Cocrystallisation: Tartaric/Glutamic Acid Modification 248

7.4.3 Defect-Localised Oligomerisation:Modification by Aspartic Acid 250

References 253

8 Optical Consequences of Surface Chirality 257

8.1 The Nature of Light 258

8.2 Planar and Twisted Light 258

8.2.1 Linear and Circular Polarisation 259

8.2.2 Polarisation on a Helix 261

8.3 Dichroic Photoemission 262

8.4 Non-linear Optics in Chiral Systems 267

8.4.1 Symmetry Constraints on Non-linear Optical Phenomena 267

8.4.2 Implications for Chiral Surfaces 272

8.4.3 Chiral SHG on Cu{111} and Au{110} 273

8.5 Near-Field Phenomena 276

References 277

9 Magnetic Consequences of Surface Chirality 279

9.1 Spin and Orbital Magnetism 279

9.1.1 Fermions and the Dirac Equation 280

9.1.2 Spin–Orbit Coupling 283

9.2 Bulk Magnetocrystalline Anisotropy 285

9.2.1 Laue Class Oh (Cubic Crystal System: Oh, Td and O) 287

9.2.2 Laue Class Th (Cubic Crystal system: Th and T) 287

9.2.3 Laue Class D6h (Hexagonal Crystal System: D6h, D3h, C6? and D6) 287

9.2.4 Laue Class C6h (Hexagonal Crystal System: C6h, C3h and C6) 288

9.2.5 Laue Class D3d (Trigonal Crystal System: D3d, C3? and D3) 288

9.2.6 Laue Class S6 (Trigonal Crystal System: S6 and C3) 289

9.2.7 Laue Class D4h (Tetragonal Crystal System: D4h, D2d, C4? and D4) 289

9.2.8 Laue Class C4h (Tetragonal Crystal System: C4h, S4, & C4) 290

9.2.9 Laue Class D2h (Orthorhombic Crystal System: D2h, C2?, and D2) 290

9.2.10 Laue Class C2h (Monoclinic Crystal System: C2h, C1h, and C2) 292

9.2.11 Laue Class S2 (Triclinic Crystal System: S2 and C1) 293

9.2.12 General Comments 294

9.3 Surface Magnetocrystalline Anisotropy 295

9.3.1 Surface MCA of Face-Centred and Body-Centred Cubic Ferromagnets 296

9.3.2 Role of Adsorbates and Reconstruction 298

9.4 An Aside: Vectors and Pseudovectors 299

9.5 SpinWaves in Centrosymmetric Media 301

9.5.1 Spin Helices 301

9.5.2 Spin Spirals 303

9.6 SpinWaves at a Featureless Surface 304

9.6.1 Spin Helices 304

9.6.2 Spin Spirals 305

9.7 SpinWaves at Structured Surfaces 306

9.7.1 Spin Helices at Achiral Surfaces 306

9.7.2 Spin Helices at Chiral Surfaces 307

9.7.3 Spin Spirals at Achiral Surfaces 307

9.7.4 Spin Spirals at Chiral Surfaces 307

9.8 Surface Spin Spirals Observed 308

9.9 Skyrmions, or How to Brush a Hedgehog 309

References 313

10 Chiral Electronic States in Two Dimensions 315

10.1 Dirac Cones in Graphene 316

10.2 Dirac Cones at Half-Metal Surfaces 321

10.3 Dirac Cones at the Surfaces of Topological Insulators 323

10.4 Prospects for Electronic Chirality in the Chemical Context 328

References 329

11 Postscript 331

A List of Abbreviations 335

B Rules for Overlayer Periodicity Assignment 337

B.1 Substrate Lattice 337

B.2 Overlayer Lattice 338

B.3 Illustrative Examples 339

References 343

C Further Reading 345

Index 347