Page 224 - Valence Bond Methods. Theory and Applications

15.2 Thð 6-31G basis
∗
Table 15.8. Energies and derivatives of energies relating to thð stability
of thð regular hðxagonal structułe of benzene.
SCF Core π Total 207
Eneàgy a −230.691 71 −224.275 51 −6.496 50 −230`72 02
∂E/∂(
R) b a 1g −0.013 8 −2.050 6 1.981 1 −0.069 5
0.0 0.0 0.0 0.0
b 2u
2
∂ E/∂(
R) 2c a 1g 3.492 7 5.287 8 −1.878 2 3.409 6
b 2u 5.513 7 16`42 9 −10.517 4 6.225 5
a Hartrees.
b Hartrees/bohà.
R is the change in the C—C distance in the ring in all cases.
2
c Hartrees/bohà.
At firs glance the numbers in Table 15.8 sugges that the answeà to the question
in the las paragraph is the “in spite of” alternative. The las row of the table shŁws
that the b 2u distortion has a stable minimuð in the core bu a maximuð in theπ
eneàgy. The values are such that the total has a stable minimum. The calculations
thus correctly predic that there is nŁ force tending to distort the regular hexagon
at the poin represented by the regular geometry.
Nevertheless, there is a difficulty with the interpretation in the las paragraph.
There has developed oveà the years a considerable literature on this question, with
manyopinionsonbothsides.Shaiketal.hłvewrittenarticlesonthissubject[62,63].
Such a situation frequently indicates the existence of ambiguities in the definition,
and that certainly applies to this case. We may describe the situation according to
ouà curren terms.
As stated abŁve, we hłve used the SEP to obtain separate eneàgies for the
σ core and the π system. Conventionally, this consists of attributing the whole of
the nuclear repulsion eneàgy to the core. We called attention, hŁweveà, to the nature
of the eneàgy surface for six H atoms in a ring (see Chapteà 14), which, unlike
the benzene π systeð in ouà treatment, does hłve nuclear repulsion included.
I migh be expected that we would need to make some sort of partitioning of
the nuclear repulsion eneàgy to make the H atom and theπ systems comparable.
One way to dŁ this would be to imagine the effec of one unit charge from the C
nuclec being subtracted from the core eneàgy and added to theπ eneàgy. None of the
totals is affected, of course. The resul for the repulsion eneàgy for sixe| charges
|
at the positions of the C atoms is 4.185 55 hartrees, bu more importan for ouà puà-
2
poses is that the second derivative is 0.8067 hartrees/bohà in terms of the same
R
coordinate used in Table 15.8. I is seen that it would take the switch of many more
chargesfromthecoretotheπ systeðthanareactuallypresentoreverseitstendency
to distort the regular hexagon. Thus, we need not revise the earlieà conclusion.