Computational Chemistry

and so forE(stab) (¼EDorER) we get

E(stap, cyclobutadiene)¼EpðcyclobutadieneÞ"EpðreferenceÞ

¼ð 4 aþ 4 bÞ"ð 4 aþ 4 bÞ¼ 0

Cyclobutadiene is predicted by this calculation to have no resonance energy,
although we can readily draw two “resonance structures” exactly analogous to the
Kekule ́structures of benzene. The SHM predicts a resonance energy of 2bfor
benzene. Equating 2|b| with the commonly-quoted resonance energy of 150 kJ mol"^1
(36 kcal mol"^1 ) for benzene gives a value of 75 kJ mol"^1 for |b|, but this should be
taken with more than a grain of salt, for outside a closely related series of
molecules,bhas little or no quantitative meaning [ 44 ]. However, in contrast to
the failure of simple resonance theory in predicting aromatic stabilization (and
other chemical phenomena) [ 45 ], the SHM is quite successful.
The cyclobutadiene dication(cf. Fig.4.17). The totalpelectronic energy is

EpðdicationÞ¼ 2 ðaþ 2 bÞ¼ 2 aþ 4 b

Using one ethene molecule as the reference:

EpðreferenceÞ¼ 2 aþ 2 b

and so

E(stab, dication)¼EpðdicationÞ"EpðreferenceÞ

¼ð 2 aþ 4 bÞ"ð 2 aþ 2 bÞ¼ 2 b

Thus the stabilization energy calculation agrees with the deduction from the
disposition of filled MOs (i.e. with the 4nþ2 rule) that the cyclobutadiene dication
should be stabilized by electron delocalization, which is in some agreement with
experiment [ 46 ].
More sophisticated calculations indicate that cyclic 4nsystems like cyclobuta-
diene (where planar; cyclooctatetraene, for example, is buckled by steric factors
and is simply an ordinary polyene) are actuallydestabilizedbypelectronic effects:
their resonance energy is not just zero, as predicted by the SHM, but less than zero.
Such systems areantiaromatic[ 17 , 46 ].

4.3.5.4 Bond Orders

The meaning of this term is easy to grasp in a qualitative, intuitive way: an ideal
single bond has a bond order of one, and ideal double and triple bonds have bond
orders of two and three, respectively. Invoking Lewis electron-dot structures, one
might say that the order of a bond is the number of electron pairs being shared
between the two bonded atoms. Calculated quantum mechanical bond orders should

4.3 The Application of the Schr€odinger Equation to Chemistry by H€uckel 141