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Lecture 14 APPLICATIONS OF GROUP THEORY 1) Symmetry of atomic orbitals. When bonds are formed, atomic orbitals combine according to their symmetry.
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Lecture 14 APPLICATIONS OF GROUP THEORY1) Symmetry of atomic orbitals • When bonds are formed, atomic orbitals combine according to their symmetry. • Symmetry properties and degeneracy of orbitals can be learned from corresponding character tables by their inspection. Hold in mind the following transformational properties:
3) Symmetry adapter linear combinations of atomic orbitals (SALC’s) • Hybrid orbitals can be considered as basis functions for a reducible representation Gr within a molecule point group. • Let us choose vectors originating from the central atom to represent the hybrid orbitals suitable for s-bonding as a basis function for Gr. • When constructing a reducible representation Gr, we have to consider the effect of each of the group symmetry operations on these vectors. • The character of a particular symmetry operation is equal to the number of vectors that are unshifted by the operation.
4) Symmetry adapted linear combinations of AO’s for s-bonding
5) SALC’s of atomic orbitals suitable for p-bonding • Let us choose a set of vectors originating from the peripheral atoms and representing directions of the hybrid orbitals suitable for p-bonding with the central atom as a basis function for Gr. All vectors xi are directed toward z axis and all vectors yi are parallel to xy plane. • Only vectors of unshifted atoms contribute to the character of particular symmetry operations.
6) Polarity • A species of high symmetry (several rotational axes) cannot be polar. • The polarity is a feature of molecules belonging to the following symmetry point groups only: C1, Cs, Cn, Cnv.