Computational Chemistry

nonplanar systems [ 22 ]. Because of the importance of the concept of hybridization
in the simple H€uckel method a brief discussion of this concept is warranted.

4.3.2 Hybridization

Hybridization is the mixing of orbitals on an atom to produce new, “hybridized” (in
the spirit of the biological use of the term), atomic orbitals. This is done mathemat-
ically but can be appreciated pictorially (Fig.4.5). One way to justify the procedure
theoretically is to recognize that atomic orbitals are vectors in the generalized

y

z

+–

an sp hybrid

y

z

2 s

2 py

2

1

2

2s –^12 p

y

2

1

2

(^12) p
i.e. 2s + (– ) y
2
1
2
(^12) p
2 s + y
z

an sp hybrid

y

Fig. 4.5 Hybridization is forming new atomic orbitals, on an atom, by mathematically mixing
(combining) “original” atomic orbitals on that atom. Mixing two orbitals gives two hybrid orbitals,
and in generalnAOs givenhybrid AOs. Orbitals are mathematical functions and so can be added
and subtracted as shown in the figure

i.e.

C 4 H 6

i.e.

C 4 H 6

C 6 H 6

..

i.e.

Fig. 4.4 The simple H€uckel
method is used mainly for
planar arrays ofpsystems

4.3 The Application of the Schr€odinger Equation to Chemistry by H€uckel 103