2.2 Covalent Bonds
25
(a)
-2 -1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
3
-2 -1
0
1
2
-2
-1
0
1
2
(b)
-2 -1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
3
-2 -1
0
1
2
-2
-1
0
1
2
(c)
-2 -1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
3
-2 -1
0
1
2
-2
-1
0
1
2
(d)
-2 -1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
3
-2 -1
0
1
2
-2
-1
0
1
2
Fig. 2.7 Schematic representation of a, c bonding and b, d antibinding symmetric a, b and nonsymmetric c, d sp 3
orbitals
(a)
(b)
(c)
Fig. 2.8 Schematic representation of the a σ and b π bonds in benzene, c schematic symbol for benzene
2.2.3 sp 2 Bonds
Organic semiconductors (see Chap. 18) are made up from carbon compounds. While for inorganic
semiconductors the covalent (or mixed, cf. Sect. 2.4) bond with sp
3 hybridization is important, the
organic compounds are based on the sp
2 hybridization. This bonding mechanism, which is present
in graphite, is stronger than the sp
3 -bond present in diamond. The prototype organic molecule is the
benzene ring
3 (C 6 H 6 ), shown in Fig. 2.8. The benzene ring is the building block for small organic
molecules and polymers.
In the benzene molecule neighboring carbon atoms are bonded within the ring plane via the binding
σ states of the sp
2 orbitals (Fig. 2.8a). The wavefunctions (Fig. 2.9) are given by (2.2ac).
1 = (s +
√
2 p x )/
√
3
(2.2a)
2 = (s −
1/2 p x +
3/2 p y )/
√
3
(2.2b)
3 = (s −
1/2 p x −
3/2 p y )/
√
3 .
(2.2c)
The ‘remaining’ p z orbitals do not directly take part in the binding (Fig. 2.8b) and form bonding (π ,
filled) and antibinding (π *, empty) orbitals (see Fig. 2.10). The π and π * states are delocalized over
the ring. A more in-depth view considers the alternating ’staggered’ spin configuration around the ring
[177]. Between the highest populated molecular orbital (HOMO) and the lowest unoccupied molecular
orbital (LUMO) is typically an energy gap (Fig. 2.11). The antibinding σ
∗ orbitals are energetically
above the π * states.
3 Supposedly, the chemist Friedrich August Kekulé von Stadonitz had a dream about dancing carbon molecules and thus
came up with the ring-like molecule structure [176].
25
(a)
-2 -1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
3
-2 -1
0
1
2
-2
-1
0
1
2
(b)
-2 -1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
3
-2 -1
0
1
2
-2
-1
0
1
2
(c)
-2 -1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
3
-2 -1
0
1
2
-2
-1
0
1
2
(d)
-2 -1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
3
-2 -1
0
1
2
-2
-1
0
1
2
Fig. 2.7 Schematic representation of a, c bonding and b, d antibinding symmetric a, b and nonsymmetric c, d sp 3
orbitals
(a)
(b)
(c)
Fig. 2.8 Schematic representation of the a σ and b π bonds in benzene, c schematic symbol for benzene
2.2.3 sp 2 Bonds
Organic semiconductors (see Chap. 18) are made up from carbon compounds. While for inorganic
semiconductors the covalent (or mixed, cf. Sect. 2.4) bond with sp
3 hybridization is important, the
organic compounds are based on the sp
2 hybridization. This bonding mechanism, which is present
in graphite, is stronger than the sp
3 -bond present in diamond. The prototype organic molecule is the
benzene ring
3 (C 6 H 6 ), shown in Fig. 2.8. The benzene ring is the building block for small organic
molecules and polymers.
In the benzene molecule neighboring carbon atoms are bonded within the ring plane via the binding
σ states of the sp
2 orbitals (Fig. 2.8a). The wavefunctions (Fig. 2.9) are given by (2.2ac).
1 = (s +
√
2 p x )/
√
3
(2.2a)
2 = (s −
1/2 p x +
3/2 p y )/
√
3
(2.2b)
3 = (s −
1/2 p x −
3/2 p y )/
√
3 .
(2.2c)
The ‘remaining’ p z orbitals do not directly take part in the binding (Fig. 2.8b) and form bonding (π ,
filled) and antibinding (π *, empty) orbitals (see Fig. 2.10). The π and π * states are delocalized over
the ring. A more in-depth view considers the alternating ’staggered’ spin configuration around the ring
[177]. Between the highest populated molecular orbital (HOMO) and the lowest unoccupied molecular
orbital (LUMO) is typically an energy gap (Fig. 2.11). The antibinding σ
∗ orbitals are energetically
above the π * states.
3 Supposedly, the chemist Friedrich August Kekulé von Stadonitz had a dream about dancing carbon molecules and thus
came up with the ring-like molecule structure [176].