Nondirectional bonding and co-ordination numbers

This graph depicts the dependence of ionic crystal structure (empirically determined) on principle quantum number and electronegativity difference between ions.

Co-ordination number increases as n increases. Low co-ordination is preferred by crystals with covalent character. High co-ordination is preferred by crystals with metallic (non-directional) character. Non-directional bonding increases with n according to this quote:

The principal quantum number of an atom is a measure of the directional character of the bonds formed by this atom. As n increases, the atomic orbitals involved in the bond formation and hence the bonds themselves gradually lose their directional properties.

Non-directional character also increases with Δχ:

In compounds the directional character of the bonds does not depend only on n but also on the electronegativity difference, because the bonds become increasingly ionic and hence more nondirectional as Δχ increases.

Heavy group 14 compounds do not fit the pattern well in the above graph:

They are sometimes 6-coordinate when 4-coordinate is expected. This can be attributed to the inert pair effect. Lower group-14 elements are less likely to involve their two S electrons in bonding. This is the reason carbon and silicon tend to form a +4 oxidation state while lead and tin tend to form +2. Or the reason carbon dioxide is CO₂ while lead oxide is PbO.

Lack of involvement from the s orbital in bonding means the valance orbitals have p³ symmetry (two electrons resonating through three p orbitals), rather than sp³ symmetry.

p³

sp³

The p³ symmetry fits well into the octahedral coordination of the rock-salt structure.