Preface.1: The relationship between group theory and chemistry. 1.1. Introduction. 1.2. Applications of group theory.
2: Symmetry. 2.1. A bridge from geometry to arithmetic. 2.2. Classifying symmetry operations. 2.
3. Full analysis of the symmetry of the water molecule: Introduction to notation. 2.4. Products of covering operations: multiplication tables. 2.5. What is a group?3: Group theory.
3.1. Definition of a group. 3.2. Subgroups. 3.3.
Examples of groups.4: Point groups - The symmetry of groups of small molecules. 4.1. Introduction. 4.2. Axes of rotation: Cn.
4.3. Mirror planes: sigma. 4.4. Stereographic projection diagrams. 4.5.
Inversion: i. 4.6. Rotary reflections, or improper rotations, Sn. 4.7. Catalogue raisonèe of the common point groups: symbols, molecular examples and macroscopic examples.5: Introduction to linear algebra.
5.1. Introduction. 5.2. Systems of coordinates. 5.3.
Vectors. 5.4. Norm or length of a vector. 5.5. Angles and inner products. 5.
6. Generalizations to n dimensions. 5.7. Orthogonality and normality. 5.8. Linear transformations and matrices.
5.9. Successive transformations: matrix multiplication. 5.10. The effect on a matrix of a change in coordinate system. 5.11.
Orthogonal transformations. 5.12. Traces and determinants. 5.13. Matrix representation of symmetry groups.6: Group representations and character tables.
6.1. Introduction. 6.2. Group representations. 6.3.
Character tables. 6.4. Properties of character tables. 6.5. Calculations with character tables.7: Molecular vibrations.
7.1. Introduction. 7.2. Classical description of molecular vibrations. 7.3.
Eigenvalue problems. 7.4. Determination of the symmetries of the normal modes. 7.5. Use of internal coordinates.8: Electronic structure of atoms and molecules.
8.1. The quantum-mechanical background. 8.2. Symmetry properties of wave functions. 8.3.
Molecular wave functions. 8.4. Expectation values and the variation theorem.9: Symmetry properties of molecular orbitals. 9.1. Diatomic molecules.
9.2. Triatomic molecule - Walsh diagrams. 9.3. Molecular orbitals for the bent AH2 molecule (C2v). 9.4.
Molecular orbitals for the linear AH2 molecule (D8h). 9.5. Correlation of thew orbitals between bent and linear geometries.10: Spectroscopy and selection rules. 10.1. Introduction.
10.2. The relationship between symmetry properties and the vanishing of matrix elements. 10.3. The direct-product representation. 10.4.
Selection rules in spectroscopy.11: Molecular orbital theory of planar conjugated molecules. 11.1. Introduction. 11.2. The LCAO-MO description of pyridine.
11.3. Distribution of molecular orbitals among symmetry species. 11.4. The Hückel approximation. 11.5.
Projection operators. 11.6. General properties of projection operators. Conclusion. Index.