Coordination complexes exhibit different geometries like octahedral, tetrahedral, and square planar, depending on the metal orbitals participating in the coordinate covalent bonds.

Valence bond theory, or VBT, explains this based on the metal’s hybridization of s, p, and d orbitals. Hybridization provides vacant orbitals of equivalent energies that can coordinate to the filled ligand orbitals.

Consider an octahedral complex, hexafluorocobaltate(III). The Co³⁺ ion has  partially filled 3d⁶ orbitals and vacant 4s, 4p, and 4d orbitals. 

To form the complex, the metal's six empty orbitals, 4s, 4p, and two 4d, are hybridized to six sp³d² orbitals, which are pointing towards the corners of an octahedron. The hybrid orbitals accept lone pairs from the six fluoride groups to form the paramagnetic complex.

In the hexamminecobalt(III), the amino groups cause the 3d electrons of cobalt to rearrange, creating two vacant 3d orbitals. 

These combine with the 4s and 4p orbitals to generate six d²sp³ hybrid orbitals, which then coordinately bind to the six ammonia groups to form the diamagnetic complex. 

Now, consider a tetrahedral complex — tetrachloronickelate.  Nⁱ²+ ion has a 3d⁸ configuration. The empty 4s and 4p orbitals hybridize to give four sp³ orbitals that point towards the corners of a tetrahedron. 

Here, four pairs of electrons, one from each chloride group, occupy the hybrid orbitals to form the paramagnetic complex. 

Lastly, examine a square planar complex like tetrachloroplatinate. The Pt²⁺ ion has a d⁸ configuration.

The chloride groups force the metal’s 3d electrons to rearrange, creating a vacant orbital. The vacant orbital combines with the 4s and two 4p orbitals to give four dsp² hybrid orbitals directed towards the corners of a square.

Upon accepting the electron pairs from the chloride ligands, the diamagnetic complex is formed. 

Although the coordination complexes vary in their colors and magnetic behavior, VBT does not explain their electronic spectra and the variation in their magnetic behavior with temperature.