Polygon rule

[bluemonster]

Today, BM introduce you about the polygon rule. It is a method to determine the relative energies of molecular orbitals of conjugated cyclopolyenes. And you will predict aromaticity, antiaromaticity, or nonaromaticity in term of molecular orbital energy levels.
The regular polygon inscribed in a circle with one vertex at the bottom of the circle. The vertices represent the relative the MO’s energies which increasing from the the bottom to the top of the circle. The verticles below the horizontal diameter are bonding pi’s, those above are antibonding pi*’s, and those on the diameter are nonbonding pi's .
Aromaticity is observed when all bonding MO’s are filled and nonbonding MO’s, if present, are empty or completely filled.
A species is antiaromatic if it has e in MO*’s or if it has half-filled MO’s or MO nonbonding’s, provided it is planar.
Nonaromatic when cyclopolyenes is not coplanar.
For examples:
Apply the polygon rule to 3-, 4-, 5-, 7-, and 8-carbon systems and indicate the character of the molecular orbitals:

For polyene ring systems, each C atom of ring contribute an electron pi, for example, benzene, six p AO’s, one from each C, yield six pi molecular orbitals. Cyclopropene, three electron pi , yield three pi molecular orbitals… total of number electrons will be arranged in the molecular orbitals with Hun rule. From there, we predict character of system, aromatic, nonaromatic, or antiaromatic.
For example:
+Cyclobutadiene is an antiaromatic system, because has half-filled MO nonbonding and it is planar.
+Cyclopentadiene is an nonaromatic system, because has one C is sp3 hybridized.
+Cyclooctatetrene, since the pi nonbonding are half-filled, so would be predicted to be antiaromatic. But cyclooctatetrene is not planar, it is actually tub-shaped, the p orbitals of one C=C ar not coplanar with those of a neighboring C=C, and ther can be no effective overlap for delocalization.This noncoplanarity avoids the antiaromaticity which requires coplanarity.

[kokoro]

Qui tắc này nói chung khó mà áp dụng cho các hệ thống polyene lớn, nếu ta không nắm chắc cấu trúc không gian của nó, ví dụ như vòng [8]-Annulene nếu theo qui tắc Huckel xác định vòng thơm thì nó phản thơm, nhưng nếu không chú ý đến cấu trúc không gian của nó thì không sao biết được nó là hợp chất không thơm chứ không phải phản thơm.
Thanks BM!