Aromatic rings

The Hückel MO approach treats the π electrons of rings like benzene. We imagine a framework of σ bonds created by sp²  hybrids on each carbon atom.  The six remaining 2p π orbitals overlap to create six delocalized MOs. Diagram 1a depicts the pattern of orbital energies predicted. The lowest energy MO  is created by combining all 2p orbitals with positive overlap to give full bonding; higher energy MOs are increasingly less bonding and more antibonding. Diagram 1 depicts the assignment of six π electrons  like in the ground  state of benzene.  Aromatic stability arises since the electrons are collectively more stable in these MOs  than they would  be within the three separate double bonds.

Fig. 1. Energies of π MOs in (a) benzene, (b) a four-membered ring compound.

For benzene the arrangement of MO  energies is paralleled  with  other ring sizes: in every case there is a single orbital of lowest energy followed by pairs of equivalent energy. Figure 1b depicts the energies for a four-membered ring. four π electrons' assignment does not lead to a closed-shell ground  state where every MO  is either empty or filled, and certainly the four-π-electron molecule cyclobutadiene C₄H₄  is extremely unstable. This kind of argument leads to the Hückel 4n+2 rule: irrespective of the ring size, aromatic stability needs 4n+2 π electrons, in which n is a whole number.  Feasible values are the 2, 6, 10,...but not 4, 8,.... One consequence is that the cyclopentadienyl fragment C₅H₅  is stable like a 6-π- electron anion [C₅H₅]^-, an significant ligand for organometallic compounds.

There are instances of inorganic rings that conform  to the Hückel rule. Heteroatom molecule B₃N₃H₆ is isoelectronic with benzene even though much more reactive due to the polarity in the B-N  bonds. The S₂N₂ ring (2) is an instance of a six-π-electron system even though the ring is four-membered. Electrons can be counted by the assigning two each to four localized S-N σ bonds and two electrons to a lone-pair on every atom. From the 22 valence electrons, six remain for delocalized π system. Ions [S₄]²⁺ and [Se₄]²⁺ have similar valence electron count as S₂N₂ and are also square planar.