Computational Chemistry

and Liebman [ 169 ]. Schleyer and Puhlhofer discuss various isodesmic schemes and
recommend for calculating resonance energies (which we take here as being
aromatic stabilization energies) isomerization methyl/methylene reactions like
[ 170 ]:

CH 3 CH 2

They consider the resonance energy of benzene from reasonable isodesmic reac-
tions to be ca. 125 kJ mol#^1. Mo has reviewed the various ways of assigning resonance
energy to benzene and studied the problem with the valence bond method [ 171 ].
Now we turn from benzene to another cyclically delocalized molecule, oxirene
or oxacyclopropene [ 172 ]. Is oxirene stabilized or destabilized by itsp-electron
system? We can answer this question using an isodesmic equation, with B3LYP/
6–31G* energies/geometries as usual. Here we try to cancel out the strain in oxirene
by having on each side of the equation about the same amount of ring strain (on
each side two sp^2 C–O bonds, etc):

O.. O.

+ +

–152.46609 –194.03545 –116.61905 –229.93969

ASE ¼#½Š# 116 : 61905 # 229 : 93969 ½Š 152 : 46609 # 194 : 03545

¼# 346 : 55874 þ 346 : 50154 ¼# 0 : 05720 ¼#150 kJ mol#^1

We calculated the ASE as product energies minus reactant energies, as we did
for benzene, and it came out negative, which means that the aromatic “stabiliza-
tion” energy here is really destabilizing: oxirene is antiaromatic [ 173 ].
One has to be careful with balancing bonds in isodesmic reactions. Consider this
equation:

+ 2 3

–232.24958 –235.87949 –234.64832

Here ASE ¼½½# 3 ðŠ## 234 : 64832 232 : 24958 þ 2 ðފ# 235 : 87949

¼# 703 : 94496 þ 704 : 00856 ¼ 0 : 06360 ¼167 kJ mol#^1

308 5 Ab initio Calculations