# Band gap of fullerenes

From what I have read about fullerenes, the lower fullerenes like $\ce{C60}$ or $\ce{C70}$ have higher bandgaps around 3.5 eV or such, while the higher fullerenes have much smaller bandgaps of the order of 0.5 eV. Initially I thought that this could be explained using electron delocalization on the surface area of the sphere, but later I read that the fullerenes were not necessarily super-aromatic. What could be the reason behind such a dip of the HOMO-LUMO gap?

• Well, sufficiently large fullerenes can be thought of as multiple graphene sheets stitched into a 3D shape, and since graphene sheets have zero bandgap, you know what the limit of the system must tend to. – Nicolau Saker Neto Aug 17 '16 at 3:49
• @NicolauSakerNeto An interesting thing is that usually band gaps increase when layers are thinner. Monolayers of most semiconductors and insulators have a larger band gap than their bulk. So I am not sure how valid is that logic. – CoffeeIsLife Aug 17 '16 at 8:08
• @QuantumMOCHACCINO A decrement from 3.5eV to around 0.5eV is quite a huge jump considering that I'm just going from 60 atoms to 80. Even if we talk about the most common $CdSe$ QDs, the bandgap goes from 1.7eV to 2.3eV while it transitions from the bulk(theoretically infinite) atoms to the 4~5nm strong confinement regime. A jump from 3.5eV to 0.5eV, I'm almost dead convinced that something else is going on here, also the lack of super-aromaticity means that the change in the area of the wave localization is just a fraction of the area of the supposed sphere, doesn't seem that convincing. – ubuntu_noob Aug 20 '16 at 5:24
• @ubuntu_noob I agree. It is quite interesting. I will try to look into it. From what journal did you get the results? – CoffeeIsLife Aug 26 '16 at 2:48
• Its maybe a bit misleading to talk about band gaps in this context. The electronic structure of fullerenes is still better understood thinking of molecules (for which "jumps" are notorious). Hence HOMO-LUMO gap is more appropriate. Now look at benzene and cyclobutadiene, the former has a substantial gap the latter not (approaching even "zero" depending on the degree of geom. distortion). C$_{60}$ is non-aromatic while C$_{60}^{10+}$ is. The gap size really depends on the peculiarity of the electronic structure. (Multiple) Spherical Aromaticiy is maybe the simplest concept explaining it. – Rudi_Birnbaum Jul 29 '17 at 10:26