Computational Chemistry

aromatic ring is opened isodesmically [ 165 ]. This gives consistent results in an
incrementally varying series of compounds [ 166 ]. Let’s apply this approach to
benzene using the same kind of equation as we did for cyclopropane and for
norbornane, above, continuing with B3LYP/6–31G* energies/geometries. We
should think in terms of the numbers of sp^2 –sp^2 C–C bonds and sp^2 C–H bonds,
rather than view benzene as having three double and three single C–C bonds,
although we will use the useful Kekule ́structure:

H 2 C CH 2

–232.24958

+ 2

–78.58745 –233.39857

+

–155.99213

Loss of aromaticity must correspond to an endothermic process and we take the
ASE as being positive for an aromatic compound, so this quantity is the energy of
the products minus that of the reactants. If the molecule being opened were strained,
that would have to be taken into account, for example by an extrapolation method
[ 167 ] or by balancing the strain on both sides of the equation, as in the oxirene
calculation below. The ASE is calculated here thus:

ASE¼#½Š## 233 : 39857 # 155 : 99213 ½Š 232 : 24958 # 78 : 58745

¼# 398 : 39070 þ 389 : 42448 ¼ 0 : 03378 ¼ 89 kJ mol#^1

There is no single correct isodesmic reaction for studying a phenomenon;
another reasonable, although conceptually less straightforward, reaction for obtain-
ing an ASE for benzene is:

CH 2

–78.58745 –155.99213

+ H 2 C

–232.24958

3 3

This too satisfies our isodesmic criterion, because on both sides of the equation
we have nine sp^2 –sp^2 C–C bonds and 18 sp^2 C–H bonds. This equation gives:

ASE ¼½Š## 3 ðÞ# 155 : 99213 ½Š 232 : 24958 þ 3 ðÞ# 78 : 58745

¼# 467 : 97639 þ 468 : 01193 ¼ 0 : 03554 ¼ 93 kJ mol#^1

Reactions of this kind have been applied to heteroatom analogues of benzene
[ 166 , 168 ]. Like our strain energy calculations, these energy changes are approx-
imations to 0 K enthalpy changes (we ignored ZPE and thermal energy increases on
going above 0 K). Isodesmic reactions and other aspects of the energetics of
benzene, cyclobutadiene and related compounds have been reviewed by Slayden

5.5 Applications of the Ab initio Method 307