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Lecture 14 APPLICATIONS OF GROUP THEORY 1) Symmetry of atomic orbitals

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 THEORY 1) Symmetry of atomic orbitals

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  1. 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:

  2. 2) Examples of atomic orbitals symmetry analysis

  3. 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. 4) Symmetry adapted linear combinations of AO’s for s-bonding

  5. 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. 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.

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