Re: Is it possible to hybridize 'f' orbitals? What would they look like?

Yes it is possible but ...

1. Hybrid orbitals are not something that exists in nature, but a 
construction that is used in the Valence Bond model of molecular structure.

2. In recent times, the Valence Bond model has been almost completely 
overshadowed by the Molecular Orbital model. This is not because there is 
anything wrong with the Valence Bond model, but because it is not so easily 
adaptable to large and general computer calculations of molecular structure.

3. Generally speaking, f orbitals play little part in bonding. This is why 
the f-orbital elements (rare earths) are like peas in a pod, and very 
difficult to separate on the basis of their chemical properties.

4. In a typical rare earth element, the 4f-orbital has a smaller average 
radius than the 5d and 6s orbitals that have nearly the same energy, and a 
very much smaller radial distribution. That is, a 4f electron is on average 
closer to the nucleus than a 5d or 6s electron. And also, a 4f electron 
spends nearly all its time near the average distance, in contrast to the 5d 
and particularly 6s electrons, which make frequent excursions very close to 
and very far from the nucleus. This is part of the reason why f orbitals get 
little involved in bonding, and why there is little to be gained by 
including f-orbitals in hybridization schemes.

If you want to get seriously into this stuff, I would recommend that you 
start with two of the classic textbooks of molecular structure.

1. 'The Nature of the Chemical Bond', by Linus Pauling

2. 'Valence', by Charles Coulson, or 'Coulson's Valence', by Roy McWeeny (in 
essence a posthumous update).