Can Hückel's rule be applied to inorganic compounds?

Question

Hückel's rule helps us know which molecular orbital, bonding or antibonding contains more electrons, and it is derived from the same. And on the basis of this, we can find out the stability of the compounds.

But, this rule was specifically introduced for cyclic organic compounds to know if they are aromatic or not. But again, the reasoning remains the same across all compounds, that is, if more electrons are in BMO than in ABMO – stable; otherwise not.

So, I was wondering why we couldn't use the same rule for cyclic inorganic compounds? I don't know, but I might be missing out somewhere. Any help would be appreciated.

Also: This pdf here, agrees that Hückel's rule can be applied to inorganic cyclic compounds, but with a 'maybe'.

Whereas organic compounds need to be planar to be aromatic, no such limitation applies to inorganics. An inorganic compound may be expected to be aromatic if it satisfies a “counting rule”; the familiar Hückel rule applies to planar aromatics and the Hirsch rule works for spherical analogs.

Answer 1

Huckel's rule can be applied to "inorganic" cyclic molecules but only if they have a delocalised pi system. They also have to have flat (or close to flat) rings.

Recently some N5 rings which 6 pi electrons have been made, these are "inorganic" aromatic rings.

Also borazine has been the subject of considerable debate, it has been discussed on stack exchange before. It is the subject of a interesting paper: Islas, R.; Chamorro, E.; Robles, J.; Heine, T.; Santos, J. C.; Merino, G. Borazine: to be or not to be aromatic. Struct Chem 2007, 18 (6), 833–839. DOI: 10.1007/s11224-007-9229-z.

Answer 2

This rule can also be applied to all-metal compounds, which due to the electron deficiency can have both pi- and sigma-aromaticity. See, e.g.: Wikipedia article on Metal Aromaticity or the paper: Boldyrev, A. I.; Wang, L. All-Metal Aromaticity and Antiaromaticity. Chem. Rev. 2005, 105 (10), 3716–3757 DOI: 10.1021/cr030091t.

Answer 3

The tetrasulfur dication, $\ce{S_4^{2+}}$, has six pi electrons in its four-membered ring and shows the symmetry expected of an aromatic ring (reference: Elemental Sulfur and Sulfur-Rich Compounds II, edited by Ralf Steudel). It has even been obtained as a salt, $\ce{S4(SO3F)2}$, suggesting enhanced stability.