Assignment

1. For each of the following geometries:

A Perfect octahedron

B Tetragonally distorted octahedron - elongation along the one of the C₄ rotation axis.

C Trigonally distorted octahedron - elongation along the one of the C₃ rotation axis

Answer the followings:

i State the group subgroup relations between the three geometries.

ii Identify the point groups

iii Assign symmetry species for orbitals 3d, 4s, 4p in the first row transition metals.

2. [Ni(CN)₅]^3- has square pyramidal geometry (C_4v). Derive a reducible representation for the hybrid orbitals on Ni²⁺ ion and determine the sets of specific atomic orbitals that can be combined to form these ho's.

3. Determine symmetry species for the SALCs required for the formation of Br - F s bonds by the 5 F atoms in BrF₅ (C_4v).

4 Suppose a single transition metal ion (dⁿ configuration) was trapped inside a bucky ball to form an endohedrally doped fullerene, M@C₆₀.

i How would you expect the energies of the d orbitals to be affected by this environment?  Note: buckministerfullerene belongs to the I_h point group.

ii List the symmetry species for all the valence orbitals in this metal ion: s; p_x, p_y, p_z;  d_z2, d_x2-y2 , d_xy, d_xz, d_yz.