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. Last, 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, to C 60, to graphene.

From small fullerenes to the graphene limit: A harmonic force‐field method for fullerenes and a comparison to density functional calculations for Goldberg–Coxeter fullerenes up to C980

“…This is the main reason why we used this class of fullerenes (up to C 980 ) to obtain the graphene limit. For a recent interesting discussion on smooth scaling of fullerene properties toward the graphene limit see Lewis et al…”

Simple, accurate electrostatics-based formulas for calculating ionization potentials, electron affinities, and capacitances of fullerenes

“…Further, carbon particles are at the heart of a number of important electrical energy storage innovations [3,4], while more such innovations are essential to develop and improve a wide variety of other advanced technology products. Thus, it is important to establish a firmer foundation for our prior analysis [5] of how fullerenes store charge and electrical energy, how much they can store, and how that quantity or capacitance varies as carbon particles in practical applications are shrunk to the nanoscale to achieve much greater aggregate surface areas. Additionally, the invariance of the local electronic structure and the quasispherical global structure of fullerenes C n as they vary in carbon number n and average radius R n makes them ideal for investigating the nature and scaling of quantum properties, such as electron detachment energies.…”

“…Motivated by this coupling of practical concerns and long-term fundamental concerns [5][6][7][8][9], we develop here a very simple set of equations for accurately calculating the values of the electron affinity A n and the ionization potential I n for an icosahedral fullerene as a function of R n . We employ these equations to analyze the scaling of A n and I n with 1/R n .…”

DFT study on electronic properties of single‐ and double‐shell icosahedral fullerenes

“…In addition, the electronegativity of iC 180 and iC 720 were compared with those reported in ref. , referred to icosahedral fullerenes with the same number of carbons and very similar diameters. The values of the electronegativity calculated in this work were 5.13 eV and 4.94 eV for iC 180 and iC 720 , respectively, in excellent agreement with the literature values of 5.19 eV and 4.98 eV .…”

“…, referred to icosahedral fullerenes with the same number of carbons and very similar diameters. The values of the electronegativity calculated in this work were 5.13 eV and 4.94 eV for iC 180 and iC 720 , respectively, in excellent agreement with the literature values of 5.19 eV and 4.98 eV . Moreover, accurate electrostatics‐based formulas were used for calculating ionization potential and electron affinity of single‐shell fullerenes in ref.…”