For a trigonal prismatic complex, [TiL], Table 8.6 indicates that the d_z^2 orbi

Question

For a trigonal prismatic complex, [TiL], Table 8.6 indicates that the d_z^2 orbital is at an energy level of 0.096 Delta_0 x^2 - y^2 and d_x^2 - y^2 and d_xy are at an energy level of - 0.584 Delta_0, and d_x; and d_y fall at an energy level of +0.536 Delta_0. Which of these d orbitals will be classified in irreducible representations beginning with the capital letter A ? Which beginning with capital letter E? which beginning with capital letter T? Energy Levels of d Orbitals in Complexes of Various Geometries Units of Delta_0, the octahedral crystal held splitting assuming the same overall charge density and distance. [Adapted from J. K Huheey. K A Keiter. and R L Reiter Inorganic Chemistry, Principles of Structure and Reactivity, 4th ed., Harper-Collins, New York. 1993, p. 405.) Coordination number = CN. Ligands lie along z axis. Ligands lie in xy plane. Pyramid base in xy plane.

Explanation / Answer

Before going for the solution, let’s get to the basic things –

Symmetry in a given molecule is studied by performing Symmetry Operation, which again is carried out by use of points/lines/planes, called as Symmetry Elements. Each molecule has set of Symmetry operations, giving a proper symmetry to the molecule. These set   of symmetry operations collectively, are called as Point Group of the molecule and the study of the groups is called as Group Theory. Each point group has a Character Table, supplemented with two additional columns   showing the transformation properties of the basis vectors,   their rotations and their quadratic combinations, from which Irreducible representation are identified. Irreducible representation is the one which can’t be further reduced from higher dimension to lower dimension.

So, moving ahead with the question,

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