Introduction to Symmetry and Group Theory for Chemists

ISBN-13: 9781402021503 / Angielski / Twarda / 2004 / 122 str.

Arthur M. Lesk; A. M. Lesk

Opis

This book is based on a one-semester course for advanced undergraduates specializing in physical chemistry. I am aware that the mathematical training of most science majors is more heavily weighted towards analysis - typ- ally calculus and differential equations - than towards algebra. But it remains my conviction that the basic ideas and applications of group theory are not only vital, but not dif?cult to learn, even though a formal mathematical setting with emphasis on rigor and completeness is not the place where most chemists would feel most comfortable in learning them. The presentation here is short, and limited to those aspects of symmetry and group theory that are directly useful in interpreting molecular structure and spectroscopy. Nevertheless I hope that the reader will begin to sense some of the beauty of the subject. Symmetry is at the heart of our understanding of the physical laws of nature. If a reader is happy with what appears in this book, I must count this a success. But if the book motivates a reader to move deeper into the subject, I shall be grati?ed.

Spis treści

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 raisonée 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.