Can MO Theory Explain the Electronic Structure of C60?

[Maria05]

Ok, i am investigating the electronic structure of fullerenes through Near edge x-ray absorption spectroscopy and I really need to know the connection between hybridization theory and LCAO. Everywhere I look it says the carbon atoms in C60 are sp2 hybridized ( sp3 due to angle strain), but as I am looking at the transition of a core electron into a pi antibonding molecular orbital this sortof forces me to combine the two theories. Can someone clarify this for me?

thank you

M

 

[chemisttree]

What about LCAO alone cannot help you? Hybridization theory is just rationalization and not very accurate I've heard.

 

[JPRitchie]

If you haven't already, read the Wiki articles on hybridization and LCAO.
Also, you should know about VSEPR theory, which extends Pauling's ideas.
Then, consider the following two examples.
Hybridization theory considers methane as being formed from four equivalent C-H bonds involving an sp^3 hybridized carbon. But, if one looks at the valence photoelectron spectrum one finds two peaks, not one. In contrast, molecular orbital theory predicts two peaks. There is a totally symmetric orbital that lies below the first absorption.
The second example is ethylene. Promotion of one of the pi electrons into the lowest unoccupied orbital (pi antibonding) obviously weakens the pi bond. But, whether this excited state can relax by pyramidalization or rotation or both can only be quantitatively predicted by numerical molecular orbital calculations.

So, only molecular orbital theory, which is quantum mechanics, can provide, a priori, a correct answer. If you have access to a computer, you might contemplate using it to interpret your results. Also, you might want to look at "Atoms in Molecules" by Richard Bader, which discusses at length the connection between VSEPR and molecular orbital theory.

Finally, I should mention that specialists in your area may have developed semi-empirical heuristics based on hybridization to interpret experimental results. But, I'm not a specialist in this area and cannot mention anything specific or say that they don't exist.
-Jim

 

[Maria05]

Thank you for your reply :)
From what I have read now there are three sigma bonds created by overlapping of the sp2 hybrid orbitals and one pi bond created by the 'promoted' electron in one of the p atomic orbitals. The connection I was looking for before was that of how the MO diagram looks for say overlap of two sp2 hybrid orbitals? So far all I've seen are MO diagrams for normal atomic orbitals.

M

 

[JPRitchie]

The mixing of two sp2 hybrid orbitals is easily described by an MO diagram. Start with two of the hybrids at infinite separation. They have the same energy. Now mix them by taking two combinations of them - one their sum, the other their difference to represent overlaping the hybrids. They should also be normalized. The lower energy one, the sum, lies below the separated orbitals and is strongly bonding. The other combination lies higher in energy than the separated orbitals, and is strongly antibonding. Look at my posts in the thread "Bonding-Antibonding Pair question" for more detail.
Finally, I would remark that the electronic energy given by quantum mechanics is invariant under a unitary transformation of the MO's. What this means is that the MO's have an inherent arbitrariness associated with them. So, it is possible, for example, to have MO's satisfying Schroedinger's equation that look like either normal AO's or as hybrids. But, they can both be for the identical electron density and electronic energy change.
-Jim