Group Theory and Its Applications in Physics pp 183-219 | Cite as

# Electronic States of Molecules

## Abstract

We treat in this chapter the symmetry of electronic states of molecules as an application of the representation theory of point groups. Our first problem is to characterize the orbitals of a molecule as the basis functions for the irreducible representations of the molecular symmetry group and to construct such orbitals in the form of linear combinations of atomic orbitals (LCAO). This is equivalent to reducing a representation based on the atomic orbitals into its irreducible components. Its inverse problem is to derive directed hybridized orbitals from constituent atomic orbitals. As another application, we consider the splitting of atomic levels in ligand fields (subduction to subgroups). When we go over to many-electron problems in the theory of molecules, we have to set up many-electron wavefunctions having correct symmetry and satisfying the Pauli exclusion principle. This can be solved in the same way as in the case of atomic systems.

### Keywords

Methane Manifold Benzene Subduction Halogen## Preview

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### References

- 9.1M. Kotani: J. Phys. Soc. Jpn.
**19**, 2150–2156 (1964)MathSciNetADSMATHCrossRefGoogle Scholar - 9.2J. S. Griffith:
(Prentice-Hall, Englewood Cliffs, NJ 1962) pp. 4–31Google Scholar**Irreducible Tensorial Method for Molecular Symmetry Groups**