Smooth Scaling of Valence Electronic Properties in Fullerenes: From One Carbon Atom, to C60, to Graphene

Abstract

Scaling of quantum capacitances and valence electron detachment energies is studied for icosahedral and nonicosahedral fullerenes. Scaling trends are considered from zero to infinite average radius, where a fullerene's local surface properties are similar to those of graphene. Detailed density functional theory calculations are performed to determine the geometries and detachment energies of icosahedral fullerenes, while values of these quantities are obtained for nonicosahedral species from previously published experimental results. Strongly linear, quasiclassical scaling versus average radii rn is seen for the quantum capacitances, but on two di↵erent scaling lines for icosahedral and nonicosahedral species, respectively. By contrast, nonclassical, nonlinear scaling versus 1/rn is seen for the electron detachment energies-i.e., the valence ionization potentials and electron a nities. This nonlinearity is not accounted for by classical theories that are used to explain trends in electronic properties of fullerenes and usually give accurate quantitative estimates. Instead, simple quantum equations are derived to account for nonlinearities in the metal-particle-like electron detachment energy scaling and to show that these are responsible for nonclassical, nonzero intercepts in the capacitance scaling lines of the fullerenes. Lastly, it is found that points representing the carbon atom and the graphene limit lie on scaling lines for icosahedral fullerenes, so their quantum capacitances and their detachment energies scale smoothly from one C atom, through C 60, to graphene.

Germanium Fluoride Nanocages as Optically Transparent n-Type Materials and Their Endohedral Metallofullerene Derivatives

“…The capacitance (0.158−0.242 eV −1 ) increases with molecular size from 1 to 13, in good correlation with the literature for molecular wires and large polyatomic bucky-like cages. 73,82 Although not explored here, aggregates of bucky-like cages could lead to interesting dielectric properties. To achieve high capacitance at the nanoscale, one needs a material medium that polarizes strongly in the presence of an external electric field, while not allowing the passage of electric current.…”

“…Thus, a good spread of n-type structures is possible with these Ge n F n nanocages, and it appears that those of 3 – 6 are ideal. The quasi-classical molecular capacitance C q was calculated − , according to eq (see Methods) in units of fundamental positive charges per volt, from the inverse of the difference between the ionization potential and the electron affinity. The capacitance (0.158–0.242 eV –1 ) increases with molecular size from 1 to 13 , in good correlation with the literature for molecular wires and large polyatomic bucky-like cages. , Although not explored here, aggregates of bucky-like cages could lead to interesting dielectric properties.…”

“…The differences in energy between the open-shell and closed-shell structures yielded the vertical electron affinities (EA V ) and ionization potentials (IPv). The molecular capacitance [73][74][75]82 (C) was calculated from the inverse differences between the ionization energy (IE) and the electron affinity (EA), as in eq 1.…”

Photoinduced Charge Separation in the Carbon Nano-Onion C60@C240

“…As can be seen, the INDO/S results are in better agreement with the observed electronic spectra than the TD-DFT data. A detailed comparison of experimental and computational data for several fullerenes can be found in ref . Also, the INDO/S scheme reproduces observed spectroscopic parameters of C 240 better than the TD-DFT BLYP/TZP calculation .…”

“…The vibrational modes of C 60 and C 240 in C 60 @C 240 are clearly recognizable, with small shifts that reflect the small geometrical deformations of C 60 and C 240 . When an external electric field is applied, the outer C 240 shell of the onion essentially shields the inner C 60 cage (the reduction in the C 60 polarizability after inclusion in C 240 was found to be about 75%), which makes C 60 @C 240 a near-perfect Faraday cage. , DFT estimates of the structures, ionization potentials, and electron affinities were recently reported for large fullerenes (up to C 2160 ) …”