Huckel-Heilbronner MO Solution

Stage 3: Loss of π resonance energy becomes insignificant for > 20 AOs.

Hückel-Heilbronner MO Solution, T=1
No. AOs	Hückel	Heilbronner	Δ,β
4	4α + 5.65β	4α + 4.0β^a	1.65
6	6α + 6.93β	6α + 6.0β^b	0.93
7^-	8α + 8.99β	6α + 8.10β	0.89
8	8α + 10.50β	8α + 9.65β	0.85
9⁺	8α + 11.52β	8α + 10.83β	0.69
10	10α + 12.31β	10α + 11.71β^c	0.60
12	12α + 15.45β	12α + 14.93β	0.52
16	16α + 20.50β	16α + 20.11β	0.39
20	20α + 25.57β	20α + 25.26β	0.31

^aUntwisted energy: 4α + 4.0β ^bUntwisted energy: 6α + 8.0β ^cUntwisted energy: 10α + 12.94β

E. Heilbronner, Hückel molecular orbitals of Möbius-type conformations of annulenes, Tetrahedron Lett, 1964, 1923-1928. DOI: 10.1016/S0040-4039(01)89474-0