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?
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4$\begingroup$ 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. $\endgroup$– Nicolau Saker NetoCommented Aug 17, 2016 at 3:49
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1$\begingroup$ @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. $\endgroup$– CoffeeIsLifeCommented Aug 17, 2016 at 8:08
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1$\begingroup$ @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. $\endgroup$– Ghosal_CCommented Aug 20, 2016 at 5:24
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1$\begingroup$ @ubuntu_noob I agree. It is quite interesting. I will try to look into it. From what journal did you get the results? $\endgroup$– CoffeeIsLifeCommented Aug 26, 2016 at 2:48
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1$\begingroup$ 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. $\endgroup$– Raphael J.F. BergerCommented Jul 29, 2017 at 10:26
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1 Answer
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One of the explanation for answering this question can be provided as, moving from lower to higher Fullerenes the number of atoms in the structure increase, increasing the number of atoms in the system results in reduction of the discreteness of energy states, which results in decrease of the gap between HOMO and LUMO, thus the band gap is reduced. You can also check for the particle in box model of the Quantum Physics for better understanding.
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$\begingroup$ Fullerenes are not fully aromatic, there are certain junctions which prevent the delocalization of the gas and hence the box boundary is not necessarily extended up to he physical dimensions defined by the number of atoms...so $\endgroup$– Ghosal_CCommented Sep 10, 2017 at 9:06