Computational Chemistry

A

B B

A

B B

A

B B

A

B B

(1) and

(2)

two different molecules if

we distinguish (somehow label)

the Bs

a resonance hybrid

Since A–B1 and A–B2 have the same force constant, a structure with unequal
bond lengths represents only vibrational extremes arising from a symmetric A–B
stretch: the molecule must vibrate around an equilibrium structure with equal A–B
lengths. If you doubt this, imagine constructing a ball and springs model of AB 2
with identical A–B springs but different equilibrium A–B lengths; this is clearly
impossible.
The case of cyclobutadiene may at first seem to contradict the above assertion
that if a “central” atom A is connected to two atoms B the force constants must be
the same, giving rise to equal bond lengths. Cyclobutadiene is rectangular rather
than square and so one bond from a carbon is single, and one is double, say the
bonds designated here C1–C2 and C1–C3; 1 and 2 are distinct molecules separated
by a barrier [1]:

C1 C2

C3 C

H

H

H

H C1 C2

C3 C

H

H

H

H

1 2

1 and 2 are not canonical forms of a resonance hybrid, but rather

distinct molecules:

chemical reaction

NOT resonance

Here we can call C1 our central atom, and it seems to be connected to B/C2 by a
single bond and to B/C3 by a double bond. However, C2 and C3 are not equivalent
for our analysis: moving away from C1, C2 is followed by a double bond, and C3 is
followed by a single bond. Whether a molecule will exhibit valence isomerism, as
shown by cyclobutadiene, or resonance, as shown by benzene, is not always easy
to predict.

Reference

1. Santo-Garcı ́a JC, Pe ́rez-Jime ́nez AJ, Moscardo ́F (2000) Chem Phys Lett 317:245, and refer-
   ences therein

Answers 597