Table Of Contents:
Physical Constants and Other Numerical Data xxxvii
Notation xxxix

Crystal Morphology and Crystal Symmetry 1(50)

Introduction 1(3)

The Crystalline State 4(13)

Reference Axes 4(5)

Crystallographic Axes 9(1)

Equation of a Plane 9(2)

Miller Indices 11(1)

Miller--Bravais Indices 12(2)

Axial Ratios 14(1)

Zones 14(1)

Interfacial Angles 15(2)

Stereographic Projection 17(6)

External Symmetry of Crystals 23(28)

Two-Dimensional Point Groups 24(1)

Rotation Symmetry 25(1)

Reflection Symmetry 26(2)

Three-Dimensional Point Groups 28(1)

Inversion Axes 29(2)

Crystal Classes 31(2)

Crystal Systems and Point-Group Scheme 33(5)

Subgroups and Laue Groups 38(2)

Noncrystallographic Point Groups 40(4)

Bibliography 44(1)

Problems 44(7)

Lattices and Space-Group Theory 51(66)

Introduction 51(1)

Lattices 51(11)

Two-Dimensional Lattices 52(1)

Choice of Unit Cell 53(1)

Three-Dimensional Lattices 54(2)

Triclinic Lattice 56(1)

Monoclinic Lattices 56(4)

Orthorhombic Lattices 60(1)

Tetragonal Lattices 60(1)

Cubic Lattices 61(1)

Hexagonal Lattice 61(1)

Lattices in the Trigonal System 61(1)

Families of Planes and Interplanar Spacings 62(2)

Reciprocal Lattice--Geometrical Treatment 64(2)

Unit-Cell Transformations 66(6)

Bravais Unit-Cell Vectors 67(1)

Zone Symbols and Directions 68(1)

Coordinates of Sites in the Unit Cell 69(1)

Miller Indices 69(1)

Reciprocal Unit-Cell Vectors 70(2)

Rotational Symmetries of Lattices 72(1)

Space Groups 73(30)

Two-Dimensional Space Groups 74(6)

Conditions Governing X-Ray Reflection 80(3)

Plane Groups Related to 2mm 83(1)

Three-Dimensional Space Groups 84(1)

Monoclinic Space Groups 84(4)

Screw Axes 88(1)

Limiting Conditions in C2 89(1)

Space Group P21 89(1)

Glide Planes 90(2)

Space Group P21/c 92(3)

Analysis of the Space-Group Symbol 95(2)

Orthorhombic Space Groups 97(1)

Relative Orientations of Symmetry Elements in Space Groups 98(1)

Half-Translation Rule 99(1)

General Equivalent Positions 100(1)

Tetragonal and Hexagonal Space Groups 101(1)

Tetragonal Space Group P4nc 101(1)

Hexagonal Space Group P63/m 102(1)

Matrix Representation of Symmetry Operations 103(5)

Matrices in Point-Group Symmetry 103(4)

Matrices in Space-Group Symmetry 107(1)

Diffraction Symbols 108(9)

Bibliography 111(1)

Problems 111(6)

X-rays, X-ray Diffraction, and Structure Factors 117(61)

Generation and Properties of X-rays 117(10)

X-rays and White Radiation 117(2)

Characteristic Radiation 119(1)

Absorption of X-rays 120(2)

Monochromatic (Filtered) Radiation 122(1)

Synchrotron Sources 123(4)

X-ray Scattering 127(11)

Scattering by a Single Electron 127(1)

Scattering by Two or More Electrons 128(2)

Representation of Waves and Wave Sums 130(3)

Coherent and Incoherent Scattering 133(2)

Scattering by an Atom 135(3)

Scattering by Regular Arrays of Atoms 138(6)

Laue Equations 138(4)

Bragg Equation 142(2)

Reciprocal Lattice--Analytical Treatment 144(9)

Unit-Cell Volumes in Real and Reciprocal Space 146(2)

Some Properties of the Reciprocal Lattice 148(1)

Interplanar Spacings 148(2)

Angle between Planes 150(1)

Weiss Zone Law 150(1)

Equation of a Plane 151(1)

Reciprocity of F and I Unit Cells 151(1)

Reciprocal Lattice and the Reflection Condition 152(1)

Scattering by a Crystal Structure 153(7)

Path Difference 154(3)

Argand Diagram 157(1)

Combination of n Waves 158(1)

Structure Factor Equation 159(1)

Using the Structure Factor Equation 160(2)

Friedel's Law 161(1)

Structure Factor for a Centrosymmetric Crystal 161(1)

Limiting Conditions and Systematic Absences 162(11)

Body-Centered Unit Cell 163(1)

Screw Axes and Glide Planes 164(1)

Space Group P21 164(1)

Limiting Conditions in P21 165(2)

Centric Zones 167(1)

Space Group Pc 168(1)

Space Group P2 1/c 168(1)

Space Group Pma2 169(3)

Space Group Pman 172(1)

Practical Determination of Space Groups from Diffraction Data 173(5)

Monoclinic Space Groups 173(2)

Orthorhombic Space Groups 175(3)

Intensities and Intensity Statistics 178(35)

Intensity Expressions and Factors Affecting Intensities 178(13)

Polarization and Lorentz Factors 179(2)

Extinction 181(2)

Absorption Measurement and Correction 183(1)

Empirical Absorption Correction with Diffractometer Data 183(1)

Transmission Profiles 184(1)

Absorption Correction with Area Detector Data 184(1)

Scaling 185(1)

Merging Equivalent Reflections 185(1)

Practical Intensity Expression and its Standard Deviation 186(1)

Scale Factor for |F0| 187(1)

Thermal Vibrations and the Temperature Factor 187(1)

Thermal Vibration in One Dimension 187(1)

Thermal Vibration in Three Dimensions 188(2)

Statistical Expectation Value of the Debye--Waller Factor 190(1)

Intensity Statistics 191(22)

Determining Scale and Temperature Factors 191(1)

Methodology 192(2)

Pathological Cases 194(1)

Statistics of Reciprocal Space 194(1)

Accidental Absences 194(1)

Laue Symmetry 195(1)

Systematic Absences 195(1)

Abnormal Averages 195(2)

Acentric and Centric Distributions 197(3)

Mean Values 200(2)

Normalized Structure Factors 202(2)

Cumulative Distributions 204(1)

Hypersymmetry 204(2)

Bibliography 206(1)

Problems 206(7)

Optical and X-ray Examination of Crystals 213(47)

Introduction 213(1)

Polarized Light 214(1)

Optical Classification of Crystals 215(8)

Uniaxial Crystals 215(3)

Birefringence 218(1)

Identification of the z Axis of a Uniaxial Crystal 219(1)

Biaxial Crystals 220(1)

Orthorhombic Crystals 220(1)

Monoclinic Crystals 221(1)

Triclinic Crystals 222(1)

Interference Figures 223(1)

Single-Crystal X-ray Techniques 223(34)

X-ray Photography 224(1)

Laue Method 225(2)

Laue Method and Synchrotron Radiation 227(5)

Oscillation Method 232(3)

Axial Spacings for Oscillation Photographs 235(2)

Crystal Setting 237(1)

Setting Technique 237(2)

Ewald's Construction 239(6)

Flat-Plate Oscillation Photography 245(3)

Weissenberg Method 248(2)

Unit-Cell Dimensions from a Weissenberg Photograph 250(2)

Precession Method 252(1)

Unit-Cell Dimensions from a Precession Photograph 252(2)

Setting a Crystal for Precession Photography 254(1)

Setting a Crystal Axis Parallel to the X-ray Beam 255(1)

The Vertical Correction ε0D' Defined by δD on the Film 255(1)

The Horizontal Correction ε0A' Defined by δA on the Film 256(1)

Setting a Reciprocal Lattice Row Horizontally 257(1)

Screen Setting 257(1)

Recognition of Crystal System 257(3)

Measurement of Intensity Data from Single Crystals 260(29)

Photographic Method 260(1)

Single Counter or Serial Diffractometers 261(1)

Area Detectors 261(1)

Intensity Measurements on Photographs 261(3)

Single-Crystal X-ray Diffractometry 264(5)

Instrument Geometry 265(1)

Rotation of the Crystal into a Diffracting Position 266(1)

Transformation from Miller Indices to Diffractometer Angles 267(1)

Data Collection 267(1)

Scanning Over a Peak: ω/θ versus ω Scans 268(1)

Area Detectors (Position-Sensitive Detectors) 269(8)

Multiwire Proportional Counter 270(1)

FAST Area Detector (Enraf--Nonius FAST) 271(1)

Image Plate 272(1)

Charge-Coupled Device Area Detectors 273(1)

Charge-Coupled Device versus Image Plate 274(3)

Monochromators 277(2)

Sealed or Rotating Anode Tube Radiation 277(1)

Single and Double Type Crystal Monochromators 278(1)

Monochromators for Synchrotron Radiation 278(1)

Focusing Mirrors 279(1)

Twinning 280(9)

Bibliography 282(1)

Problems 283(6)

Fourier Series and Fourier Transforms 289(46)

Image Formation and Focusing 289(2)

Fourier Series 291(6)

Analysis of the Square Wave 292(1)

Range of X 293(1)

Range of h 293(3)

Exponential Forms of Fourier Series 296(1)

Fourier Series in X-ray Crystallography 297(4)

One-Dimensional Function 297(2)

Two- and Three-Dimensional Functions 299(2)

Holes and Atoms 301(1)

Generalized Fourier Transform 302(3)

Fourier Transform of a Molecule 304(1)

Fourier Transform of a Unit Cell 305(1)

Practice with Transforms 305(15)

Optical Diffractometer 305(1)

Single Hole 306(1)

Two or More Holes 306(1)

Change of Origin 307(2)

Systematic Absences 309(1)

Reconstruction of the Image 309(1)

Representation of Fourier Transforms 310(2)

Transforms and Inverse Transforms 312(4)

Delta Function 316(2)

Weighted Reciprocal Lattice 318(2)

Some General Properties of Transforms 320(1)

Convolution 320(5)

Convolution and Diffraction 320(1)

Convolution Integral 321(2)

Crystal Structure and Convolution 323(2)

Structure Solution in Brief 325(10)

Use of Heavy Atoms 325(1)

Series Termination Effect 326(1)

General Phase-Free Transform 326(4)

Sign Relationships 330(1)

Bibliography 330(1)

Problems 331(4)

Fourier Techniques in X-ray Structure Determination 335(86)

Introduction 335(1)

Analysis of the Unit-Cell Contents 335(7)

Papaverine Hydrochloride, C20H21NO4·HCl 336(1)

Crystal Data 336(1)

Naphthalene, C10H8 336(1)

Crystal Data 336(1)

Molecular Symmetry 337(1)

Special Positions 338(2)

Nickel Tungstate, NiWO4 340(1)

Crystal Data 340(1)

Special Positions on 2-fold Axes 340(1)

Special Positions on Centers of Symmetry 341(1)

Interpretation of Electron Density Distributions 342(3)

Peak Heights and Weights 342(1)

Computation and Display of Electron Density Distributions 342(1)

Projections 343(2)

Methods of Solving the Phase Problem 345(47)

Number of Reflections in the Data Set 345(1)

The Patterson Function 346(1)

One-Dimensional Patterson Function 347(3)

Three-Dimensional Patterson Function 350(1)

Positions and Weights of Peaks in the Patterson Function 350(2)

Sharpened Patterson Function 352(1)

Symmetry of the Patterson Function for a Crystal of Space Group Pm 353(1)

Vector Interactions in Other Space Groups 354(1)

Examples of the Use of the Patterson Function in Solving the Phase Problem 355(1)

Bisdiphenylmethyldiselenide, (C6H5)2CHSe2CH(C6H5)2 355(7)

Minimum Function 362(1)

Determination of the Chlorine Atom Positions in Papaverine Hydrochloride 362(4)

Determination of the Mercury Atom Positions in KHg2 366(3)

Heavy-Atom Method and Partial Fourier Synthesis 369(3)

Reliability Factor 372(1)

Pseudosymmetry in Electron Density Maps 373(1)

Successive Fourier Refinement 373(1)

Difference-Fourier Synthesis 373(2)

Limitations of the Heavy-Atom Method 375(1)

Patterson Selection 375(2)

Isomorphous Replacement 377(3)

Centrosymmetric Projections 380(1)

Sign Determination for Centric Reflections in Protein Structures 381(1)

Location of Heavy-Atom Positions in Proteins 381(4)

Further Details of the Isomorphous Replacement Phasing Procedure 385(2)

Analytical Calculation of Phases in SIR and MIR 387(5)

Electron Density Maps Used in Large-Molecule Analysis 392(1)

Anomalous Scattering 392(13)

Hamilton's R Ratio and Flack's Parameter 394(2)

Effect of Anomalous Scattering on the Symmetry of Diffraction Patterns 396(1)

Diffraction Symmetry for a Crystal in Space Group P21 with No Anomalous Scattering 396(2)

Diffraction Symmetry for a Crystal in Space Group P21 for a Structure Containing Some Anomalous Scatterers 398(1)

Form of the Structure Factor for a Structure Composed of Heavy-Atom Anomalous Scatterers 399(2)

Phasing by Use of Anomalous Scattering 401(1)

Resolution of the Phase Problem for Proteins Using Anomalous Scattering Measurements (SIRAS Method) 402(1)

Protein Phasing Using the Multiple-Wavelength Anomalous Dispersion Technique (MAD) with Synchrotron Radiation (SR) 403(2)

Neutron Diffraction 405(16)

Complementary Nature of Neutron Diffraction 407(2)

Refinement of Hydrogen Atom Positions 409(1)

Bibliography 409(1)

Problems 410(11)

Direct Methods and Refinement 421(98)

Introduction 421(1)

Direct Methods of Phase Determination 421(40)

Normalized Structure Factors 421(1)

ε Factor 422(1)

|E| Statistics 423(1)

Structure Invariants and Origin-Fixing Reflections 423(2)

Sign Determination: Centrosymmetric Crystals 425(1)

Triple-Product Sign Relationship 426(2)

Σ2 Formula 428(2)

Amplitude Symmetry and Phase Symmetry 430(1)

Σ2 Listing 431(1)

Symbolic-Addition Procedure 431(1)

Crystal Data 431(1)

Sign Determination 431(2)

Calculation of E Maps 433(2)

Phase Determination: Noncentrosymmetric Crystals 435(5)

Σ1 Relationships 440(1)

Enantiomorph Selection 440(1)

Phase Determination in Space Group P21 441(4)

Advantages and Disadvantages of Symbolic Addition 445(1)

Multisolution Philosophy and Brief Description of the Program MULTAN 446(2)

Magic Integer Phase Assignment 448(3)

Figures of Merit 451(2)

Example of the Use of MULTAN: Methyl Warifteine (MEW) 453(1)

Some Experiences 453(1)

Some Prerequisites for Success in Using Direct Methods 454(1)

Figures of Merit: A Practical Guide 455(1)

Signs of Trouble, and Past Remedies when the Structure Failed to Solve 455(1)

Structure Invariants: Triplets, Quartets, and the SHELX Program Strategy 456(3)

Direct Methods in the Program SHELX-97 459(2)

Patterson Search Methods 461(25)

General Comments for Small Molecules and Macromolecules 461(1)

Intramolecular Interatomic Vectors and Molecular Orientation 462(1)

Rotation Stage of Patterson Search or Molecular Replacement 463(3)

Intermolecular Interatomic Vectors: Translation Stage of MR 466(1)

Crystal Packing and Refinement of the Structure 467(1)

Expansion and Refinement of the Structure 468(1)

Patterson Search Methods for Small Molecules 468(2)

The Program PATSEE 470(1)

Rotation Search Strategy used in PATSEE 471(1)

Translation Search Strategy Used in PATSEE 471(2)

Examples of Structure Solution using PATSEE 473(1)

Structure of 5,7-methoxy-8-(3-methyl-1-buten-3-ol)-coumarin 473(6)

Structure of Atropine: α-[Hydroxymethyl]benzeneacetic Acid 8-methyl-8-azabicyclo[3.2.1]oct-3-yl Ester 479(6)

Shake `n' Bake 485(1)

Least-Squares Refinement 486(8)

Unit-Cell Dimensions 486(1)

Least-Squares Parameters 487(1)

Temperature Factors 488(2)

Scale Factor 490(1)

Weights 490(1)

Precision 491(1)

Atoms in Special Positions 491(1)

Strategy in Least-Squares Refinement 492(1)

Model 492(1)

Data Errors 492(2)

Least-Squares Refinement Procedure 494(1)

Molecular Geometry 494(6)

Bond Lengths and Angles 494(2)

Torsion Angles 496(1)

Conformational Analysis 497(1)

Ring Conformations 497(1)

Asymmetry Parameters 498(2)

Mean Planes 500(1)

Precision 500(1)

Correctness of a Structure Analysis 501(3)

Data Bases 502(2)

Limitations of X-ray Structure Analysis 504(1)

Disorder in Single Crystals 505(6)

Computer Prediction of Crystal Structures 511(8)

Crystal Structure of 5-Azauracil 511(3)

Developments in Computer Crystal Structure Prediction 514(1)

Bibliography 515(1)

Problems 516(3)

Examples of Crystal Structure Determination 519(48)

Introduction 519(1)

Crystal Structure of 2-Bromobenzo[b]indeno[1,2-e]pyran 519(18)

Preliminary Physical and X-ray Measurements 520(3)

Intensity Measurement and Correction 523(2)

Structure Analysis in the xz Projection 525(3)

Three-Dimensional Structure Determination 528(3)

Refinement 531(1)

Molecular Geometry 532(5)

Crystal Structure of Potassium 2-Hydroxy-3,4-dioxocyclobut-1-ene-1-olate Monohydrate KHSO 537(11)

Preliminary X-ray and Physical Measurements 538(1)

Intensity Measurement and Correction 539(1)

Σ2 Listing 539(1)

Specifying the Origin 540(1)

Sign Determination 540(2)

Use of Sign Symbols 542(2)

The E-Map 544(1)

Completion and Refinement of the Structure 544(4)

Structure Analysis by X-ray and Neutron Diffraction 548(6)

Sample Preparation 549(1)

X-ray Diffraction Study 550(2)

Neutron Diffraction Study 552(1)

Some Structural Features 553(1)

Determination of an Intermediate Size Crystal Structure Using Direct Methods 554(7)

Introduction 554(1)

What We Expect to Learn from the X-ray Structure of Cyclosporin H 555(1)

Crystallization and Data Collection 556(1)

X-ray Analysis 556(1)

First Application of SHELXS-97 556(3)

Second Application of SHELXS-97 559(1)

Completion and Refinement of the Structure 559(1)

Results and Discussion 560(1)

Concluding Remarks 561(6)

Bibliography 561(1)

Problems 562(5)

X-ray Structure Determination with Powders 567(48)

Introduction 567(3)

Structure Determination Scheme 567(3)

Basis of the Powder Method 570(1)

Data Collection 571(7)

Guinier-type Cameras 571(2)

Image Plate Camera 573(2)

Powder Diffractometers 575(1)

Diffractometry at a Neutron Source 576(2)

Indexing Powder Patterns 578(9)

General Indexing 580(1)

Magnesium Tungstate 580(3)

Reduced and Conventional Unit Cells 583(1)

Computer Indexing of the Diffraction Pattern 584(1)

ITO Program System 584(1)

CRYSFIRE Program System 585(2)

Extracting Integrated Intensities from a Powder Pattern 587(2)

Rietveld Refinement 589(2)

Examples of Solved Structures 591(19)

Traditional Methods 592(1)

Calcium Uranate 592(1)

Manganese Phosphate Monohydrate 592(2)

Cimetidine 594(1)

SIR Program System 594(1)

Silver-Pyrazole Complex 595(1)

EXPO Program System 596(1)

Direct-Space Methods 597(1)

Zeolites and the FOCUS Algorithm 598(2)

Zincosilicate Complex VIP-9 600(3)

Monte Carlo Method 603(2)

p-Bromophenylethanoic Acid 605(1)

Simulated Annealing 606(1)

ESPOIR Program System 607(1)

α-Lanthanum Tungstate 608(2)

Powder Diffraction with Proteins 610(1)

T3R3 Zinc--insulin Complex 610(1)

Concluding Remarks 610(5)

Bibliography 612(1)

Problems 612(3)

Proteins and Macromolecular X-ray Analysis 615(66)

Introduction 615(3)

What is a Protein 616(2)

Crystallization of Proteins and Complexes for X-ray Analysis 618(8)

Introduction 618(1)

Crystallization Conditions for Macromolecules 619(1)

Properties of Protein Crystals 619(1)

Crystallization of Proteins 619(1)

Molecular Purity 620(1)

Practical Considerations 620(1)

Batch Crystallization 620(1)

Microbatch Screening 621(1)

Vapor Diffusion Techniques 622(1)

Hanging Drop 622(1)

Sitting Drop 622(1)

Vapor Diffusion Rate of Control 623(1)

Screening Crystallization Conditions 623(1)

Gel Crystallization using Silica Hydrogel 623(1)

Co-Crystallization 624(1)

How to Improve the Crystals 624(1)

Heavy-Atom Derivatives for MIR 625(1)

Protein Complex Crystals with Small Molecules 626(1)

Crystal Mounting for X-ray Data Collection 626(3)

Mounting at Room Temperature 626(1)

Cryo-Crystallography 627(2)

Macromolecular Crystallography 629(15)

Space Groups 629(1)

X-ray Diffraction from Macromolecular Crystals 629(1)

Crystal Selection 629(1)

Structure Factors and Temperature Factors 629(2)

Intensities and Phases 631(1)

Calculated Structure Factors and R-Factors 631(1)

Free R-Factor (Rfree) 632(1)

Recording X-ray Diffraction from Macromolecular Crystals 632(1)

Conventional X-ray Laboratory Sources 633(1)

Synchrotron X-ray Sources 633(1)

X-ray Cameras 633(1)

Diffractometers: Single Counter or Serial Diffractometers 633(1)

Diffractometers: Area Detectors 634(1)

Measurement of X-ray Diffraction from Macromolecular Crystals 634(1)

Area Detectors in Practice 634(1)

Image Plate Data Processing 635(1)

Partially Recorded Spots and Integration of Intensity Data 635(1)

Conversion to an Intensity Reading 635(1)

Post-Refinement 636(1)

Problems with Data Collection and Suggested Cures 637(2)

Preliminary Structure Determination 639(1)

Unit Cell, Laue Symmetry, and Systematically Absent Reflections 639(1)

Ricin Agglutinin 640(1)

Determination of the Space Group 640(1)

Resolution 641(1)

Number of Reflections in and Completeness of the Data Set 641(1)

Internal Consistency, Space Group Ambiguities, and Rmerge 642(1)

Number of Molecules per Unit-Cell 643(1)

Analysis of the Solvent Content in Ricin Agglutinin 644(1)

Types of Fourier Synthesis for Protein Analysis 644(2)

Reconstruction of the Molecular Structure 644(1)

Properties of the Electron Density 645(1)

Difference Electron Density 645(1)

The 2|Fo(hkl)|
|Fc(hkl)| Map 646(1)

Omit Maps 646(1)

Patterson Function 646(1)

Determination of the Phases for Protein Crystals 646(17)

Introduction 646(1)

Isomorphous Replacement (MIR) 647(1)

Heavy Atoms and Compounds for Isomorphous Replacement 647(1)

Preparation and Screening of Heavy-Atom Derivatives 648(1)

Soaking Method 648(1)

Co-Crystallization in the Presence of Heavy Atoms 648(1)

Screening Possible Derivatives 648(1)

How Many Derivatives are Required 649(1)

The Initial MIR Model 649(1)

Molecular Replacement 649(1)

Introduction 649(2)

Self-Rotation Function and Non-Crystallographic Symmetry 651(2)

Example of a Self-Rotation Function: Ricin Agglutinin 653(1)

Intermolecular Atomic Vectors and Translational Non-Crystallographic Symmetry 653(1)

Molecular Replacement in Practice 654(1)

The Search Model 654(1)

Data Base Searches 655(1)

The Target Patterson Function 655(1)

The Search Patterson Function 656(1)

Recognition of the Correct Rotation Solution 657(1)

The Rotation Function and Non-Crystallographic Symmetry 657(1)

The Translation Function 658(1)

Rigid Body Refinement 658(1)

Subunits and Non-Crystallographic Symmetry 659(1)

Phases Derived from Molecular Replacement 659(1)

Application of the AmoRe Algorithms to Ricin Agglutinin 659(2)

The Initial MR Model 661(2)

Siras and MAD Phasing 663(1)

Use of Phase Information and Density Modification 663(3)

Properties of ρ(xyz) for Proteins 664(1)

Programs for Density Modification 664(1)

Preparing to Refine the Structure 665(1)

Macromolecular Structure Refinement and Solvent and Ligand Fitting 666(7)

Refinement Techniques 666(1)

Further Details of Fourier Refinement 666(1)

Simulated Annealing 667(2)

Least-Squares Refinement: Constrained and Restrained Protocols 669(1)

Constrained or Rigid Body Refinement 669(1)

Restrained Refinement 670(1)

Solvent Molecules and Small Ligands: Fitting to the Electron Density 671(2)

Structure Validation: Final Checks 673(2)

R-Factors 673(2)

Evaluation of Errors 675(1)

Geometry Validation: Final Checks 675(6)

Bond Lengths, Bond Angles, Planarity, and Chirality 676(1)

Conformation 676(1)

Main-Chain Conformation 676(1)

Side-Chain Conformations 677(1)

Bibliography 678(1)

Problems 678(3)

Computer-Aided Crystallography 681(34)

Introduction 681(1)

Structure of Program CD Suite 682(1)

Derivation of Point Groups (EULR*) 682(2)

Point-Group Recognition (SYMM*) 684(2)

Structure Determination Simulation (XRAY*) 686(10)

Patterson Function 690(1)

Superposition Function 690(1)

Structure Factor Calculation 691(1)

Least-Squares Refinement 691(1)

Electron Density Maps 691(2)

Direct Methods: Calculation of |E| Values 693(1)

Calculation of |E| Maps 694(1)

Bond Lengths and Bond Angles 694(1)

Scale and Temperature Factors by Wilson's Method 695(1)

|E| Values Calculated from the Structure 695(1)

Crystal Structure Analysis Problems 696(5)

Ni o-Phenanthroline Complex (NIS2) 697(1)

2-Amino-4,6-dichloropyrimidine (CLIP) 698(1)

2-Amino-4-methyl-6-dichloropyrimidine (CL2P) 699(1)

m-Tolidine Dihydrochloride (MTOL) 699(1)

Nitroguanidine (NO2G) 700(1)

Bis(6-sulfanyloxy-1,3,5-triazin-2(1H)-one) (COSH) 700(1)

2-S-methylthiouracil (SMTU) 700(1)

General Crystal Structure and Other Programs 701(5)

One-Dimensional Fourier Summation (FOUR1D*) 701(1)

Two-Dimensional Fourier Summation (FOUR2D*) 701(1)

One-dimensional Fourier Transform (TRANS1*) 702(1)

Reciprocal Unit Cell (RECIP*) 702(1)

Molecular Geometry (MOLGOM*) 702(1)

Internal and Cartesian Coordinates (INTXYZ*) 703(1)

Linear Least Squares (LSLI*) 704(1)

Matrix Operations (MAT3*) 704(1)

Q-Values (Q-VALS*) 704(1)

Le Page---Unit-Cell Reduction (LEPAGE*) 704(2)

Automatic Powder Indexing (ITO12*) 706(1)

Automatic Powder Structure Solving (ESPOIR*) 707(8)

α-Alumina (Corundum) 707(3)

Aragonite 710(1)

2-S-Methylthiouracil 710(2)

1-Methylfluorene 712(3)

Appendices 715(26)

A1 Stereoviews and Crystal Models 715(2)

A1.1 Stereoviews 715(1)

A1.2 Model of a Tetragonal Crystal 716(1)

A2 Analytical Geometry of Direction Cosines 717(2)

A2.1 Direction Cosines of a Line 717(1)

A2.2 Angle between Two Lines 718(1)

A3 Schonflies' Symmetry Notation 719(1)

A3.1 Alternating Axis of Symmetry 719(1)

A3.2 Notation 720(1)

A4 Rotation Matrices 720(3)

A5 Spherical Trigonometry 723(2)

A5.1 Spherical Triangle 723(1)

A5.2 Polar Triangle 724(1)

A6 Trigonometrical Formulae 725(1)

A7 Cartesian Coordinates 725(3)

A7.1 Cartesian to Crystallographic Transformation and its Inverse 726(2)

A8 The integral ∫∞0[(sin x)/x]dx 728(1)

A9 Gamma Function 729(1)

A10 Crystallographic Software 730(11)

10.1 Single Crystal Suites 730(1)

Platon/System S for UNIX 731(1)

SIR97 for MS-Windows and UNIX 731(1)

WinGX for Windows 731(1)

A10.2 Single Crystal Structure Solution Programs 731(1)

CAOS (Crystal Analysis Operating System) for MS-Windows and UNIX 731(1)

CRYSTALS (11) for MS-Windows 731(1)

DIRDIF for PC/DOS and UNIX 731(1)

MULTAN Source Code 731(1)

PATSEE for PC/DOS and UNIX 732(1)

SHELXS86/SHELXS97/SHELXD 732(1)

SIR88/92/SIR97/SIR2001 732(1)

SnB (Shake ``n'' Bake) 732(1)

A10.3 Single Crystal Twinning Software 732(1)

TWIN 3.0 for Windows 732(1)

TwinRotMac 732(1)

A10.4 Freestanding Structure Visualization Software 733(1)

ORTEP-III 733(1)

A10.5 Powder Diffraction Data: Powder Indexing Suites (Dedicated and Other) 733(1)

Checkcell for Windows 733(1)

CRYSFIRE for DOS 733(1)

DICVOL91 733(1)

FJZN 733(1)

ITO13 source code and MS-Windows binary 733(1)

Kohl/TMO 733(1)

LOSH/LZON 734(1)

TAUP/Powder 734(1)

TREOR90 source code and MS-Windows binary 734(1)

A10.6 Powder Pattern Decomposition 734(1)

ALLHKL 734(1)

WPPF 734(1)

A10.7 Structure Solution from Powder Diffraction Data 734(1)

ESPOIR source code, DOS, Windows, and Linux binaries 734(1)

EXPO source code, Windows, and UNIX binaries 734(1)

EXTRA (Included in EXPO) 734(1)

FOCUS 734(1)

FullProf for DOS, Windows, and Linux 735(1)

GSAS for Windows, Linux, and SGI IRIX 735(1)

Powder Solve (Commercial) 735(1)

Profit for VMS, DOS and UNIX 735(1)

Rietan GPL'D Fortran source code, Mac, UNIX, and Linux binaries 735(1)

SIRPOW 735(1)

XRS-82/DLS source code 735(1)

A10.8 Software for Macromolecular Crystallography 736(1)

Data Processing 736(1)

Fourier and Structure Factor Calculations 736(1)

Molecular Replacement 737(1)

Single and Multiple Isomorphous Replacement 737(1)

Software for Packing and Molecular Geometry 737(1)

Software for Graphics and Model Building 738(1)

Software for Molecular Graphics and Display 738(1)

SETOR 738(1)

Software for Refinement 738(1)

Software for Molecular Dynamics and Energy Minimization 739(1)

Data Bases 739(1)

Synchrotrons Web Page 739(2)

Tutorial Solutions 741(56)

Solutions 1 741(2)

Solutions 2 743(10)

Solutions 3 753(5)

Solutions 4 758(3)

Solutions 5 761(6)

Solutions 6 767(12)

Solutions 7 779(3)

Solutions 8 782(4)

Solutions 9 786(5)

Solutions 10 791(6)
Index 797