42
ATOMIC STRUCTURE AND BONDING
Energy
antibonding
molecular orbitals
bonding molecular
orbitals
six p atomic orbitals with six
unpaired electrons
molecular orbitals in benzene
Figure 2.27 Energy diagram: molecular orbitals of benzene
2.9.2 Cyclooctatetraene
Let us consider the origins of benzene’s aromatic stabilization. Another cyclic hydrocarbon, cyclooctatetraene (pronounced cyclo-octa-tetra-ene), certainly
looks conjugated according to our criteria, but chemical evidence shows that it is very much more reactive
than benzene, and does not undergo the same types
of reaction. It does not possess the enhanced aromatic
stability characteristic of benzene.
cyclooctatetraene
benzene
H
H
H
H
H
H
H
H
Further, cyclooctatetraene has been shown to be
non-planar; it adopts a tub shape. This originates from
bond angles. A regular octagon has internal bond
angles of 135
◦ , quite far from the optimum angle of
120
◦ for sp
2 hybridization. In benzene’s hexagon, the
internal angle is 120
◦ , a perfect fit for sp
2 geometry.
Cyclooctatetraene thus distorts from the planar to
relieve this strain. A careful consideration of this
shape may then suggest the immediate consequences.
These are that none of the double bonds are in
the same plane; therefore, there is going to be no
overlap of p orbitals between the double bonds. We
cannot get any enhanced stability associated with
conjugation.
2.9.3 H¨ uckel’s rule
Cyclooctatetraene has eight π electrons and benzene
has six. The number of π electrons that confer
aromaticity is given by H ¨
uckel’s rule: a planar cyclic
conjugated system will be particularly stable if the
number of π electrons is 4n + 2, where n is an
integer (0, 1, 2, 3, etc). Although the significance
of this will not become apparent until later (see
below), we must stress that 4n + 2 refers to the
number of π electrons, and not the number of
atoms in the ring. Benzene, therefore, with six π
electrons (n = 1, 4n + 2 = 6), is aromatic; however,
cyclooctatetraene, with eight π electrons, is not
aromatic. Also aromatic would be a system with 10 π
electrons (n = 2), or 14 π electrons (n = 3). The first
of these would be the compound [10]annulene, and
the second [14]annulene. Annulene is a general term
for a carbon ring system with alternating single and
double bonds; the number in brackets is the number
of carbons in the ring. For example, we could call
benzene [6]annulene, though in practice, nobody ever
does.
Whereas [14]annulene shows aromatic properties,
[10]annulene, unfortunately, does not, but we know
this is a consequence of the molecule adopting a
non-planar shape. The interior angle for a planar
10-carbon system would have to be 144
◦ , and this
is too far removed from the sp
2 -hybridized angle
of 120
◦ to be feasible. As ring sizes get larger, it
becomes possible to have a cyclic system where all
bond angles can be the ideal 120
◦ . There is a way
of drawing a 10-carbon ring system with angles of
ATOMIC STRUCTURE AND BONDING
Energy
antibonding
molecular orbitals
bonding molecular
orbitals
six p atomic orbitals with six
unpaired electrons
molecular orbitals in benzene
Figure 2.27 Energy diagram: molecular orbitals of benzene
2.9.2 Cyclooctatetraene
Let us consider the origins of benzene’s aromatic stabilization. Another cyclic hydrocarbon, cyclooctatetraene (pronounced cyclo-octa-tetra-ene), certainly
looks conjugated according to our criteria, but chemical evidence shows that it is very much more reactive
than benzene, and does not undergo the same types
of reaction. It does not possess the enhanced aromatic
stability characteristic of benzene.
cyclooctatetraene
benzene
H
H
H
H
H
H
H
H
Further, cyclooctatetraene has been shown to be
non-planar; it adopts a tub shape. This originates from
bond angles. A regular octagon has internal bond
angles of 135
◦ , quite far from the optimum angle of
120
◦ for sp
2 hybridization. In benzene’s hexagon, the
internal angle is 120
◦ , a perfect fit for sp
2 geometry.
Cyclooctatetraene thus distorts from the planar to
relieve this strain. A careful consideration of this
shape may then suggest the immediate consequences.
These are that none of the double bonds are in
the same plane; therefore, there is going to be no
overlap of p orbitals between the double bonds. We
cannot get any enhanced stability associated with
conjugation.
2.9.3 H¨ uckel’s rule
Cyclooctatetraene has eight π electrons and benzene
has six. The number of π electrons that confer
aromaticity is given by H ¨
uckel’s rule: a planar cyclic
conjugated system will be particularly stable if the
number of π electrons is 4n + 2, where n is an
integer (0, 1, 2, 3, etc). Although the significance
of this will not become apparent until later (see
below), we must stress that 4n + 2 refers to the
number of π electrons, and not the number of
atoms in the ring. Benzene, therefore, with six π
electrons (n = 1, 4n + 2 = 6), is aromatic; however,
cyclooctatetraene, with eight π electrons, is not
aromatic. Also aromatic would be a system with 10 π
electrons (n = 2), or 14 π electrons (n = 3). The first
of these would be the compound [10]annulene, and
the second [14]annulene. Annulene is a general term
for a carbon ring system with alternating single and
double bonds; the number in brackets is the number
of carbons in the ring. For example, we could call
benzene [6]annulene, though in practice, nobody ever
does.
Whereas [14]annulene shows aromatic properties,
[10]annulene, unfortunately, does not, but we know
this is a consequence of the molecule adopting a
non-planar shape. The interior angle for a planar
10-carbon system would have to be 144
◦ , and this
is too far removed from the sp
2 -hybridized angle
of 120
◦ to be feasible. As ring sizes get larger, it
becomes possible to have a cyclic system where all
bond angles can be the ideal 120
◦ . There is a way
of drawing a 10-carbon ring system with angles of