Figure5.50shows three related molecules, the 7-methyl substituted (the visual
orbital progression explained here is not quite as smooth for the unsubstituted
molecules) derivatives of the 7-norbornyl cation (a), the neutral alkene norbornene
(b), and the 7-norbornenyl cation (c). For each species an orbital is shown as a 3D
region of space, rather than mapping it onto a surface as was done in Fig.5.49. In (a)
we see the LUMO, which is as expected essentially an empty p atomic orbital on C7,
and in (b) the HOMO, which is, as expected, largely thepmolecular orbital of the
double bond. The interesting conclusion from (c) is that in this ion the HOMO of the
double bond has donated electron density into the vacant orbital on C7 forming a
three-center, two-electron bond. Twopelectrons may be cyclically delocalized,
making the cation a bishomo (meaning expansion by two carbons) analogue of the
aromatic cyclopropenyl cation [ 326 ]. This delocalized bishomocyclopropenyl struc-
ture for 7-norbornenyl cations has been controversial, but is supported by NMR
studies [ 327 ].
5.5.6.4 Visualization – Closing Remarks
Other molecular properties and phenomena that can benefit from the aid of visuali-
zation are the distribution of unpaired electron spin in radicals and the changes in
orbitals and charge distribution as a reaction progresses. These and many other
Fig. 5.50 Visualization supports the view that the 7-methyl-7-norbornenyl cation is delocalized:
(a) In the 7-methyl-7-norbornyl cation (no double bond) the LUMO is largely an empty p atomic
orbital on C7; (b) In the neutral alkene norbornene the HOMO is largely the filled CCpmolecular
orbital; (c) In the 7-methyl-7-norbornenyl cation the HOMO is essentially the merged HOMO of
(b) and LUMO of (a), indicating donation of electron density from the CC double bond into the
“previously” empty orbital on C7
5.5 Applications of the Ab initio Method 371