Aromaticity
The remarkable stability and inertness of benzene is partly derived from the “circulation”
of π-electrons around the perimeter. This circulation leads to a number of measurable properties
- e.g. the C-C bond lengths in benzene are all 1.39Å.
In drawing M.O. diagrams for benzene, the first, most obvious factor is that while it is
possible to draw a diagram where there are no nodes:
However, you will note that it is not possible to draw a diagram where there is only ONE
node! This restriction against having an odd number of nodes is due to the cyclic nature of
benzene, and the high degree of symmetry involved. To make up for this, there are two
representatives of the 2-node system:
Although it is possible to draw an M.O. level for benzene with 3 nodes, we cannot use it
due to symmetry considerations. We thus jump to looking at levels with 4 nodes, of which again
there are two:
And finally, there is but one level with 6 nodes:
What does this all mean when we’re drawing the energy levels? The energy level
diagram is shown below. Note that the HOMO is comprised of two orbitals of equal energy –
these are called degenerate orbitals. There are also two degenerate (but unfilled) orbitals in the
LUMO.
Anti-Bonding Orbitals
Lowest Unccupied M.O. (LUMO)
Highest Occupied M.O. (HOMO)
Bonding Orbitals
There is a simple trick to quickly writing the orbital level diagrams:
1) For conjugated cycles with an EVEN number of atoms, there will be a single high
energy level, and a single low energy level. For conjugated cycles with an ODD number
of
atoms, there will be a single low energy level, and a degenerate (i.e. double) high energy
level.
2) There are as many levels as there are atoms, and the rest come as degenerate pairs!
3) The “nonbonding” energy level runs through the middle of the diagram.
So, as an example, the levels for cyclooctatetraene and cyclopentadienyl radical are
shown below:
Anti-Bonding Orbitals
Lowest Unccupied M.O. (LUMO)
Nonbonding level
Highest Occupied M.O. (HOMO)
Bonding Orbitals
1) Odd # of carbons -> a single low-energy level, a degenerate high-energy level: !
2) 5 carbons, minus the two high-energy levels and the one low energy levels leaved TWO, which must
come as a degenerate pair. !
3) The nonbonding level runs through the middle of the diagram. !
4) Add the electrons - five electrons leave the HOMO only 3/4 full - a bad situation.
Anti-Bonding Orbitals
Lowest Unccupied M.O. (LUMO)
Nonbonding Level
Highest Occupied M.O. (HOMO)
Bonding Orbitals
1) Even # of carbons -> a single lowest energy level, a single highest energy level: !
2) That leaves 6 more orbitals - arranged as degenrate pairs.!
3) The nonbonding level runs through the middle - through the HOMO!!
4) Fill it from the bottom up with the 8 electrons - leaving the HOMO half filled! :-(
We know that aromaticity provides the benefits of high stability, etc. . . But what is
required for a molecule to be aromatic? There are some simple rules (one of which you should
be able to derive from the previous diagrams...)
1) The molecule must be cyclic
2) This cycle must be fully conjugated
3) The cycle must be planar
4) The electrons must be able to “circulate”
5) The conjugated cycle must contain 4n+2 electrons, n = 0,1,2,3,4,.....
If the conjugated cycle has only 4n electrons, it is anti-aromatic, and will either be highly
reactive, or will distort in order to violate one of the other rules (1-4). Some examples:
Cyclobutadiene (4 π-electrons), on attempted preparation, rapidly dimerizes to give a
nonconjugated molecule:
(what sort of reaction is this...?)
When some sharp chemist made a cyclobutadiene derivative that was too sterically
hindered to react, it was discovered that the cycle had distorted – in this instance, by strongly
localizing the bonds, and violating rule 4.
Distorted, bond-localized
What does this distortion do to help out with the half-filled shell? If we look at the orbital
energy levels, we see that the distortion removes some of the orbital degeneracy (by lowering the
molecule’s symmetry). Both electrons populate the lower energy level:
Please notice that this leaves a HOMO and LUMO that are VERY close in energy –
highly conjugated antiaromatic cycles which distort in this way are often highly colored, because
of the closeness of these two energy levels (See Ch. 14, UV-Vis spectroscopy).
Cyclooctatetraene:
This molecule contains 8 (4n where n=2) electrons, and is antiaromatic. In order to avoid
this nasty situation, it distorts by bending (or folding) into a tub-shape:
We’re now violating rule #3 (and 4), and thus avoiding the aromaticity question altogether.
Is there a way to make anti-aromatic molecules aromatic? Of course - simply by adding
or removing electrons! For example, if cyclooctatetraene is reduced (electrochemically, or with
a metal like K), it easily picks up two electrons. The resulting dianion is planar, and aromatic
(10 π-electrons). Similarly, cyclopentadiene (non-aromatic) is very easily deprotonated to form
cyclopentadienyl anion (6 π-electrons).
Polycyclic aromatic hydrocarbons – which result from “fusing” benzene rings together –
are also aromatic. Below are a few examples:
Naphthalene
Anthracene
Pyrene
It is also possible to fuse rings of different sizes together – you should think about
whether these would be aromatic or not!
Annulenes:
Aromatic systems that are not comprised of benzene rings (often called non-benzenoid
aromatics) are a fascinating area of chemistry. These large-ring compounds are called
annulenes. One of the most significant members of this family is [18]annulene (the number in
brackets denotes the number of carbons in the ring and, usually, the number of π-electrons):
H H
H
H
H H
[18]annulene
hexadehydro[18]annulene
[18]annulene is a planar, fully aromatic compound. The ring is just large enough that the
hydrogens sticking into the middle of the ring do not interact to twist the molecule out of
planarity. In order to avoid these types of interactions, we also study dehydro annulenes (like
hexadehydro[18]annulene, above). These molecules have all internal hydrogens removed, and in
this case, also form aromatic systems. Anti-aromatic annulenes also exist, such as the
dehydro[12]annulene shown below. These compounds are usually easily reduced by two
electrons to form aromatic ions.
dehydro[12]annulene