Symmetry of Crystals and Molecules / Mark Ladd, Formerly Head of Chemical Physics, University of Surrey.

Includes bibliographical references and index.

1. Symmetry everywhere -- 1.1. Introduction -- 1.2. Looking at symmetry -- 1.3. Some symmetrical objects -- 1.4. Denning symmetry -- 1.5. Symmetry in science -- 1.6. Symmetry in music -- 1.7. Symmetry in architecture -- 1.8. Summary and notation -- 1.8.1. Introducing symmetry notation -- References 1 -- Problems 1 -- 2. Geometry of crystals and molecules -- 2.1. Introduction -- 2.2. Reference axes -- 2.2.1. Crystallographic axes -- 2.3. Equation of a plane -- 2.4. Miller indices -- 2.4.1. Miller -- Bravais indices -- 2.5. Zones -- 2.5.1. Weiss zone equation -- 2.5.2. Addition rule for crystal planes -- 2.6. Projection of three-dimensional features -- 2.6.1. Stereographic projection -- 2.6.2. Calculations in stereographic projections -- 2.6.3. Axial ratios and interaxial angles -- 2.7. Molecular geometry: VSEPR theory -- 2.8. Molecular geometry: experimental determination -- 2.8.1. Interatomic distances and angles -- 2.8.2. Conformational parameters

2.8.3. Internal coordinates -- 2.8.4. Errors and precision -- 2.9. Molecular geometry: theoretical determination -- 2.9.1. The Schrodinger equation -- 2.9.2. Atomic orbitals -- 2.9.3. Normalization -- 2.9.4. Probability distributions -- 2.9.5. Atomic's and p orbitals -- 2.9.6. Chemical species and molecular orbitals -- 2.10. Crystal packing -- References 2 -- Problems 2 -- 3. Point group symmetry -- 3.1. Introduction -- 3.2. Symmetry elements, symmetry operations and symmetry operators -- 3.3. Point groups -- 3.4. Symmetry in two dimensions -- 3.4.1. Rotation symmetry -- 3.4.2. Reflection symmetry -- 3.4.3. Combinations of symmetry operations in two dimensions -- 3.4.4. Two-dimensional systems and point group notation -- 3.4.5. Subgroups -- 3.5. Three-dimensional point groups -- 3.5.1. Rotation symmetry in three dimensions -- 3.5.2. Reflection symmetry in three dimensions -- 3.5.3. Roto-inversion symmetry -- 3.5.4. Stereogram representations of three-dimensional point groups -- 3.5.5. Crystallographic point groups -- 3.5.6. Crystal classes

3.5.7. Crystal systems -- 3.6. Derivation of point groups -- 3.6.1. Ten simple point groups -- 3.6.2. Combinations of symmetry operations in three dimensions -- 3.6.3. Euler's construction -- 3.6.4. Centrosymmetric point groups (Laue groups) and Laue classes -- 3.6.5. Projected symmetry -- 3.7. Point groups and physical properties of crystals and molecules -- 3.7.1. Enantiomorphism and chirality -- 3.7.2. Optical properties -- 3.7.3. Pyroelectricity and piezoelectricity -- 3.7.4. Dipole moments -- 3.7.5. Infrared and Raman activity -- 3.8. Point groups and chemical species -- 3.8.1. Point groups R -- 3.8.2. Point groups R -- 3.8.3. Point groups R1 -- 3.8.4. Point groups R2 -- 3.8.5. Point groups Rm -- 3.8.6. Point groups Rm -- 3.8.7. Point groups R2 and 1 -- 3.9. Non-crystallographic point groups -- 3.10. Hermann -- Mauguin and Schonflies point group symmetry notations -- 3.10.1. Roto-reflection (alternating) axis of symmetry -- 3.10.2. The two symmetry notations compared -- 3.11. Point group recognition -- 3.12. Matrix representation of point group symmetry operations

3.12.1. Rotation matrices -- 3.13. Non-periodic crystals -- 3.13.1. Quasicrystals -- 3.13.2. Buckyballs -- 3.13.3. Icosahedral symmetry -- References 3 -- Problems 3 -- 4. Lattices -- 4.1. Introduction -- 4.2. One-dimensional lattice -- 4.3. Two-dimensional lattices -- 4.3.1. Choice of unit cell -- 4.3.2. Nets in the oblique system -- 4.3.3. Nets in the rectangular system -- 4.3.4. Square and hexagonal nets -- 4.3.5. Unit cell centring -- 4.4. Three-dimensional lattices -- 4.4.1. Triclinic lattice -- 4.4.2. Monoclinic lattices -- 4.4.3. Orthorhombic lattices -- 4.4.4. Tetragonal lattices -- 4.4.5. Cubic lattices -- 4.4.6. Hexagonal lattice -- 4.4.7. Trigonal lattices -- 4.5. Lattice directions -- 4.6. Law of rational intercepts: reticular density -- 4.7. Reciprocal lattice -- 4.8. Rotational symmetry of lattices -- 4.9. Lattice transformations -- 4.9.1. Bravais lattice unit cell vectors -- 4.9.2. Zone symbols and lattice directions -- 4.9.3. Coordinates of points in the direct unit cell -- 4.9.4. Miller indices -- 4.9.5. Reciprocal unit cell vectors

4.9.6. Volume relationships -- 4.9.7. Reciprocity of F and I unit cells -- 4.9.8. Wigner-Seitz cells -- References 4 -- Problems 4 -- 5. Space groups -- 5.1. Introduction -- 5.2. One-dimensional space groups -- 5.3. Two-dimensional space groups -- 5.3.1. Plane groups in the oblique system -- 5.3.2. Plane groups in the rectangular system -- 5.3.3. Limiting conditions on X-ray reflections -- 5.3.4. Plane groups in the square and hexagonal systems -- 5.3.5. The seventeen plane groups summarized -- 5.3.6. Comments on notation -- 5.4. Three-dimensional space groups -- 5.4.1. Triclinic space groups -- 5.4.2. Monoclinic space groups -- 5.4.3. Space groups related to point group 2 -- 5.4.4. Screw axes -- 5.4.5. Space groups related to point group m: glide planes -- 5.4.6. Space groups related to point group 2/m -- 5.4.7. Summary of the monoclinic space groups -- 5.4.8. Half-shift rule -- 5.4.9. Orthorhombic space groups -- 5.4.10. Change of origin -- 5.4.11. Standard and alternative settings of space groups -- 5.4.12. Tetragonal space groups

5.4.13. Space groups in the trigonal and hexagonal systems -- 5.4.14. Cubic space groups -- 5.4.15. Space groups and crystal structures -- 5.5. Matrix representation of space group symmetry operations -- 5.6. Black-white and colour symmetry -- 5.6.1. Black-white symmetry: potassium chloride -- 5.6.2. Colour symmetry -- 5.7. The international tables and other crystallographic compilations -- 5.7.1. The international tables for crystallography, Vol. A -- References 5 -- Problems 5 -- 6. Symmetry and X-ray diffraction -- 6.1. Introduction -- 6.2. X-ray diffraction -- 6.3. Recording X-ray diffraction spectra -- 6.4. Reciprocal lattice and Ewald's construction -- 6.5. X-ray intensity data collection -- 6.5.1. Laue X-ray photography -- 6.5.2. Laue projection symmetry -- 6.5.3. X-ray precession photography -- 6.5.4. Diffractometric and image plate recording of X-ray intensities -- 6.6. X-ray scattering by a crystal: the structure factor -- 6.6.1. Limiting conditions and the structure factor -- 6.6.2. Geometrical structure factor for a centrosymmetric crystal

6.6.3. Geometrical structure factor for an I centred unit cell -- 6.6.4. Geometrical structure factor for space group P21/c -- 6.6.5. Geometrical structure factor for space group Pmd2 -- 6.6.6. Geometrical structure factor for space group P63/m -- 6.7. Using X-ray diffraction information -- References 6 -- Problems 6 -- 7. Elements of group theory -- 7.1. Introduction -- 7.2. Group requirements -- 7.3. Group definitions -- 7.4. Examples of groups -- 7.4.1. Group multiplication tables -- 7.4.2. Reference axes in group theory -- 7.4.3. Subgroups and cosets -- 7.4.4. Similarity transformations, conjugates and symmetry classes -- 7.5. Representations and character tables -- 7.5.1. Representations on position vectors -- 7.5.2. Representations on basis vectors -- 7.5.3. Representations on atom vectors -- 7.5.4. Representations on functions -- 7.6. A first look at character tables -- 7.6.1. Transformation of atomic orbitals -- 7.6.2. Orthonormality and orthogonality -- 7.6.3. Notation for irreducible representations -- 7.6.4. Complex characters

7.6.5. Linear groups -- 7.6.6. Some properties of character tables -- 7.7. The great orthogonality theorem -- 7.8. Reduction of reducible representations -- 7.9. Constructing a character table -- 7.9.1. Summary of the properties of character tables -- 7.9.2. Constructing the character table for point group D3h -- 7.9.3. Handling complex characters -- 7.10. Direct products -- 7.10.1. Representations on direct product functions -- 7.10.2. Formation of a character table by direct products -- 7.10.3. How the direct product has been used -- References 7 -- Problems 7 -- 8. Applications of group theory -- 8.1. Introduction -- 8.2. Structure and symmetry in molecules and ions -- 8.2.1. Application of models -- 8.2.2. Application of diffraction studies -- 8.2.3. Application of theoretical studies -- 8.2.4. Monte Carlo and molecular dynamics techniques -- 8.2.5. Symmetry adapted molecular orbitals -- 8.2.6. Transition metal compounds: crystal-field and ligand-field theories -- 8.2.7. The hexacyanoferrate(II) ion -- 8.3. Vibrational studies

8.3.1. Symmetry of normal modes -- 8.3.2. Boron trifluoride -- 8.3.3. Selection rules for infrared and Raman activity: dipole moment and polarizability -- 8.3.4. Harmonics and combination vibrations -- 8.4. Group theory and point groups -- 8.4.1. Cyclic point groups -- 8.4.2. Dihedral point groups -- 8.4.3. Cubic rotation point groups -- 8.4.4. Point groups from combinations of operators -- 8.5. Group theory and space groups -- 8.5.1. Triclinic and monoclinic space groups -- 8.5.2. Orthorhombic space groups -- 8.5.3. Tetragonal space groups -- 8.5.4. Cubic space groups -- 8.6. Factor groups -- 8.6.1. Factor group analysis of iron(II) sulphide -- 8.6.2. Symmetry ascent and correlation -- 8.6.3. Site group and factor group analyses -- References 8 -- Problems 8 -- 9. Computer-assisted studies -- 9.1. Introduction

9.2. Derivation of point groups -- 9.3. Recognition of point groups -- 9.4. Internal and Cartesian coordinates -- 9.5. Molecular geometry -- 9.6. Best-fit plane -- 9.7. Reduction of a representation in point group D6h -- 9.8. Unit cell reduction -- 9.9. Matrix operations -- 9.10. Zone symbol or Miller indices -- 9.11. Linear least squares -- Reference 9 -- A1. Stereoviews and crystal models -- A1.1. Stereoviews and stereoviewing -- A1.2. Crystal models -- References -- A2. Analytical geometry of direction cosines -- A2.1. Direction cosines of a line -- A2.2. Angle between two lines -- A3. Vectors and matrices -- A3.1. Introduction -- A3.2. Vectors -- A3.3. Volume of a parallelepiped -- A3.4. Matrices -- A3.5. Normal to a plane (hkl) -- A3.6. Solution of linear simultaneous equations -- A3.7. Useful matrices -- A4. Stereographic projection of a circle is a circle

This text provides a comprehensive study of the symmetry and geometry of crystals and molecules, starting from first principles. The pre-knowledge assumed is mathematics and physical science to about A-level; additional mathematical topics are discussed in appendices. It is copiously illustrated, including many stereoviews, with instructions both for stereoviewing and for constructing a stereoviewer. Problems for each chapter are provided, with fully worked tutorial solutions.--

Text in English.