Computational Chemistry

rationalize acidities of hydrocarbons in terms of thescharacter of the carbon orbital
in a C–H bond [ 29 ] is an example of the usefulness of this idea. Most of the systems
studied by the simple H€uckel method are essentially flat, as expected forsp^2 arrays,
and many properties of these molecules can be at least qualitatively understood by
considering the in-planeselectrons of the overlappingsp^2 orbitals to simply
represent a framework that holds the perpendicularporbitals, in which we are
interested, in an orientation allowing neighboringporbitals to overlap.

C and

H

H

Csp^2 / H1s overlap

Csp^2 / H1s overlap

sp^5

sp^5

C

H

H

C

H

H

C

H

H

one sp^5 /sp^5 bond

another sp^5 /sp^5 bond

two banana bonds

1

(^66)
f (sp^5 ) =^5 p
f (sp^2 ) =
s+
1
3
2
3
s + p
Fig. 4.9 The C/C double bond can be built from twosp^5 orbitals. The result is the same as using
asbond and apbond (Fig.4.7): see Fig. 4.10
x
z

C C CC

C than like this: C

The C 2p electron

density (the square of

the wavefunction) looks

more like this:

The wavefunction

itself looks like

Hence p / p overlap looks like this: rather than like this:

Fig. 4.8 The electron density is represented by thesquareof the mathematical function we call
the orbital. A carbon 2porbital is actually more buxom than its conventional representation, and
two 2porbitals overlap better than the usual picture, e.g. Fig.4.7, suggests

4.3 The Application of the Schr€odinger Equation to Chemistry by H€uckel 107