Book contents
- Frontmatter
- Contents
- Preface
- 1 Introductory example: Squarene
- 2 Molecular vibrations of isotopically substituted AB2 molecules
- 3 Spherical symmetry and the full rotation group
- 4 Crystal-field theory
- 5 Electron spin and angular momentum
- 6 Molecular electronic structure: The LCAO model
- 7 Electronic states of diatomic molecules
- 8 Transition-metal complexes
- 9 Space groups and crystalline solids
- 10 Application of space-group theory: Energy bands for the perovskite structure
- 11 Applications of space-group theory: Lattice vibration
- 12 Time reversal and magnetic groups
- 13 Graphene
- 14 Carbon nanotubes
- Appendix A Vectors and matrices
- Appendix B Basics of point-group theory
- Appendix C Character tables for point groups
- Appendix D Tensors, vectors, and equivalent electrons
- Appendix E The octahedral group, O and Oh
- Appendix F The tetrahedral group, Td
- Appendix G Identifying point groups
- Index
- References
6 - Molecular electronic structure: The LCAO model
Published online by Cambridge University Press: 18 December 2013
- Frontmatter
- Contents
- Preface
- 1 Introductory example: Squarene
- 2 Molecular vibrations of isotopically substituted AB2 molecules
- 3 Spherical symmetry and the full rotation group
- 4 Crystal-field theory
- 5 Electron spin and angular momentum
- 6 Molecular electronic structure: The LCAO model
- 7 Electronic states of diatomic molecules
- 8 Transition-metal complexes
- 9 Space groups and crystalline solids
- 10 Application of space-group theory: Energy bands for the perovskite structure
- 11 Applications of space-group theory: Lattice vibration
- 12 Time reversal and magnetic groups
- 13 Graphene
- 14 Carbon nanotubes
- Appendix A Vectors and matrices
- Appendix B Basics of point-group theory
- Appendix C Character tables for point groups
- Appendix D Tensors, vectors, and equivalent electrons
- Appendix E The octahedral group, O and Oh
- Appendix F The tetrahedral group, Td
- Appendix G Identifying point groups
- Index
- References
Summary
Much of what we understand about the chemistry and optical properties of molecules has come from theoretical studies of very simple, empirical models. In most cases the theoretical models employ such drastic approximations that one may wonder why the results have any relevance at all to actual molecular systems. The success of these models may be attributed almost entirely to their use of group-theoretical concepts. In many cases symmetry is the dominant factor determining the electronic structure of a molecule. While the models are crude approximations, the general structure imposed by symmetry is usually exact and often independent of the details of the model employed. As a result many of the features have a much deeper truth than the model from which they are derived.
In this chapter we discuss the use of the LCAO method (linear combinations of atomic orbitals) to analyze the electronic structure of molecules. The term “atomic orbitals” is used loosely to mean one-electron orbitals whose angular functions are the spherical harmonics. The precise specifications of the radial parts of the orbitals are not needed for our discussion.
N-electron systems
It is generally assumed that the electronic states of a molecule or solid can be calculated for fixed positions of the nuclei. The electron's velocity is very large compared with the speed of vibratory motion, so that in effect the electrons instantly readjust to any motion of the nuclei. This assumption is referred to as the Born–Oppenheimer approximation.
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- Information
- Applications of Group Theory to Atoms, Molecules, and Solids , pp. 158 - 192Publisher: Cambridge University PressPrint publication year: 2014