# Hypervalency of elements

I know that elements of the 3rd period and beyond can use their empty 3-d oribtals for bonding. But why is there a limit on their covalency? eg. Al has 5 3d orbitals. And it has an empty 3p orbital. Which means that it's maximum covalency should be 9. But it is 6. Why is it so? Is it because of the small size of Al leading to increased repulsions? Also, why do the elements of the 3rd period use 3d before 4s for hypervalency? 4s has less energy so shouldn't it be used first?

• Without using the 3d orbitals it is impossible to rationalise the geometries of hypervalent complexes as predicted by VSEPR. Nevertheless, the contribution of 3d orbitals in hypervalency has been shown to be minimal at best. Search this site or the Internet for more details. As for aluminium, its 3d orbitals are too high in energy for efficient overlap with ligand orbitals. – orthocresol Nov 24 '15 at 9:22
• Those last two questions are the core ones. Basically what ortho said: $n$d orbitals are essentially not used by main group elements. – Jan Dec 24 '15 at 23:13

First off, as suggested in the comment above, the contribution of 3d orbitals in hypervalency is probably minimal.

It's clear from sampling the inorganic literature that "beyond the octet," the size of the atom matters, as well as the shape of the ligands, size of the surrounding coordination sphere, etc. To some degree, it's a matter of fitting X atoms around the central atom.

If you have a 5th or 6th row element (2nd or 3rd row transition metal), lanthanide, actinide, etc., higher coordination is relatively common. For example, for lanthanide ions, 8-coordinate is the most common coordination number. Still, 8-coordinate iron complexes have been found, e.g. "Combined Mössbauer Spectral and Density Functional Study of an Eight-Coordinate Iron(II) Complex" Inorg. Chem., 2015, 54 (17), pp 8415–8422 or "Square-Antiprismatic Eight-Coordinate Complexes of Divalent First-Row Transition Metal Cations: A Density Functional Theory Exploration of the Electronic–Structural Landscape" Inorg. Chem., 2015, 54 (4), pp 1375–1383.

I'm not aware of a general overview of hypervalency and "what coordination numbers can you get", but there's a nice overview on modern descriptions using multi-center bonding.

Your questions are some of those that bug me the most when chemists follow the rationalisation of Pauling and invoke d-orbitals. Most notably the last two:

Also, why do the elements of the 3rd period use 3d before 4s for hypervalency? 4s has less energy so shouldn't it be used first?

They are basically my core point for saying ‘it makes no sense to use 3d at all if 4s is also empty and available.’

All your remaining questions are basically follow-up ones of that central one. And there are more to add, e.g. why should phosphorus use only one d-orbital while sulphur uses two and chlorine may use three?

In general tetrahedral environments such as $\ce{PO4^3- , SO4^2-}$ and $\ce{ClO4-}$, the d-orbitals are represented by the irreducible representations $\mathrm{t_2 + e}$. That means, they should either appear in a group of three or in a group of two. This is inconsistent with the picture drawn for phosphate where we would need one — and for the similar $\ce{XeO4}$ we would need four, also inconsistent. (In case you’re immediately wondering: Systems such as ethene usually have a lower symmetry which does not contain degenerate irreducible representations; i.e. we would always get a single representation per orbital.)

And also, all elements should be able to have a maximum valency of nine if they used d-orbitals for additional bonding — however, the highest oxidation state of a main group element is $\mathrm{+VIII}$ to the best of my knowledge, only accessed for xenon.

All things put together, there is such a can of worms to explain that we should apply Occam’s razor and omit d-orbital discussions for main group elements.