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Optical properties and MOs in aromatics

Dear Reader,

Without aromatic compounds the world would be a less colourful place, many important dyes contain aromatic groups. Also many flourescent substances such as laser dyes and markers used for forensic purposes contain aromatic groups. Before we get going we need to consider the granddaddy of all aromatic things: Benzene. This is a colourless substance which I first came face to face with as a first year undergraduate when I did some chemistry which is severely banned in Swedish undergraduate chemistry.

I placed a large amount of magnesium turnings in a flask with some anhydrous benzene, I then added a solution of mercury chloride in acetone and watched the exotherm bring the mixture to reflux. After the exotherm died down, I added some more acetone and then boiled the mixture before allowing it to cool. After quenching with water and doing some more things I was rewarded with a large beaker packed with pinacol hydrate. This was my first experience of organic synthesis where I had to face down an exothermic reaction which had the potential to go into a thermal runaway, and the experience reinforced my resolve to become a synthetic chemist. I felt that it was possible to master atoms and molecules and make them do my bidding. Well sometimes I can get the atoms / molecules to do as I want them to.

But unless you can see into the ultraviolet, benzene is colourless according to extended Huckel calculations the pi orbitals of benzene are widely spaced. We have a energy gap of about 15 eV between the HOMO and the LUMO.

When we move to naphthalene then the ten pi orbitals. Now the energy gap is predicted to be 2.4 eV. This is clearly a smaller energy gap. I have used the software to calculate the pi orbital energies for anthracene and tetracene. These are hydrocarbons with more benzene rings.

I think that while the software has got some things wrong, it has got one important thing right, that is the fact that the energy difference between the pi orbitals in the larger hydrocarbons are smaller than in benzene. Below is a graph of the pi orbital energies as predicted by the extended Huckel software.

Pi orbital energies of aromatic hydrocarbons

Now if we calculate the average energy gap between the pi orbitals we get the following values for the hydrocarbons.

Benzene, 6.55 eV

Napthelene, 4.24 eV

Anthracene, 3.09 eV

Tetracene, 2.42 eV

What this means is that as the hydrocarbons become larger, because their pi systems are getting larger their absorption and emission of light will be shifted to longer and longer wavelengths. What happens when a photon of light is absorbed by one of these hydrocarbons is that an electron will be moved from the HOMO or some other filled orbital into an unfilled orbital. In the diagram below you can see a molecule being excited from the ground (S0, singlet 0) state into the first excited state (S1).

Light being absorbed thus making a vibrationally excited form of the first electronic excited state (S1)

Because of something called the Frank Condon effect the excited state will have vibrational energy. This is because the electrons move very quickly compared to the atoms. When the electrons are moved from one orbital to another the bonding changes instantly, as a result the atoms start to vibrate. This vibrational energy is typically lost before the electrons move orbital again. The reason I named the two states S0 and S1 is that they are singlet states where overall all the electrons are paired. They have no overall electron spin.

Next the vibrational energy is lost as the molecule goes down the vibrational states, this energy is lost as heat. Below we have the loss of vibrational energy.

Loss of vibrational energy

Then the excited molecule has a series of choices, it can then undergo an internal conversion where it changes from the vibrational ground state of the electronically excited state into a vibrationally excited state of the electronic ground state. This means in simple english that it changes all the energy associated with having the electron in the higher orbital into vibrational energy which makes it shake. Below I have drawn an enegy level diagram for this.

Internal conversion, all the energy from the electronic excitation is turned into heat

One of the alternatives to this is for the molecule to emit a photon of light and drop into the S0 state, because of the Frank Condon effect it has to drop into a vibrationally excited state of the electronic ground state (S0). Below we have a diagram which shows the change from the ground state of the S1 state to a vibrationally excited form of So. This process allows the emission of light with a longer wavelength than the original light.

Emission of light by moving from S1 to S0

As a result the florescence from a molecule will always have a longer wavelength than the light which excited the molecule in the first place. Now some of the smarter readers will know that a sodium doped bunsen flame is able to emit and absorb light of exactly the same wavelength, this is quite reasonable. The isolated gas phase atoms of sodium are single atoms, as a result they are exempt from the Frank Condon effects. A second way in which molecules can shift the light to longer wavelengths is to absorb photons which put the molecule into an excited state such as S2. The S2 state then decays into S1 which then can emit light. Below is a diagram which shows a system with two excited singlet states which can emit light from both the S2 to S1 and the S1 to S0 transitions.

A system with three singlet states

The take home message from today is that the bigger a pi system the closer the orbitials will be in energy, thus the difference between the energies of different states (S0, S1, S2 etc etc) will be smaller and as a result the longer the wavelengths of light which are absorbed and emitted by the pi system.

Florescence and pi system appear in funny places, those readers who are the same age as me might recall that in the 1980s a great storm of attention erupted when in 1983 someone claimed to have found Adolf Hitler’s personal diary for 1932 to 1945. It was found that the paper used for the diary contained chemicals such as optical brightness which were only brought onto the market after the end of world war two. Also the dyes used to stop fuel cheats use pi systems.

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