Explain the octablral geometry of complexes using crystal field theory.

Explanation

(1) In an octahedral complex `[MX_(6)]^(n pm)`+, the metal atom or ion is placed at the centre of regular octaherdron at six vertices of the octahedron.

(2) Among five degenerate d-orbitals, two orbitals namely `d_(x^(2) - y^(2))` and `d_(z^(2))` are axial and have maximum electron density along the axes, while remaing three d-oritals namely `d_(xy) ,d_(yz) ` and `d_(zx)` are planar and have maximum electron density in the planes and in- bewteen the axes.
(3) Hence, when the ligands approach a metal ion, the orbitals `d_(x^(2)-y^(2))` and `d_(z^(2))` experience greater repulsion and the orbitals `d_(xy) ,d_(yz) and d_(zx)` experience less repulsion.
(4) Therefore the energy of `d_(x^(2) - y^(2))` and `d_(z^(3))` increase while the energy of `d_(xy), d_(yz) and d_(zx)` decrease and five d - orbital lose degeneracy and split into two point group . The orbitals `d_(xy), d_(xy) and d_(zx)` form `t_(2g)` group of lower energy while `d_(x^(2) - y^(2))` and `d_(z^(2))` form `e_(g)` group of higher energy .
Thus `t_(2g)` has three degenerate orbitals while `e_(g)` has two degenerate orbitals.

(5) Experimental calculations show that the energy of `t_(2g)` orbitals is lowered by `0.4Delta_(0)` or `4D_(q)` and energy of `e_(g)` orbital is increased by `0.6Delta` or `6D_(q)`. Thus energy difference between ty and eg orbitals is `Delta_(0)` or `10D_(q)` which is crystal field splitting energy.
(6) CFSE increases with the increasing strength of ligands and oxidation state of central metal ion.