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

Abstract

A set of simple analytic formulas is derived via electrostatics-based methods to accurately calculate the values of electron affinities An and ionization potentials In for n-carbon icosahedral fullerene molecules as a function of their average radii Rn. These formulas reproduce with accuracy the values of An, In, and their scaling with 1/Rn that were determined previously in detailed, computationally intensive density functional theory (DFT) calculations. The formula for An is derived from an enhanced image-charge model that treats the valence region of the icosahedral system as a quasispherical conductor of radius (Rn +δ), where δ=1/4W∞ is a small constant distance determined from the work function W∞ of graphene. Using this model, though, a formula for In that includes only electrostatics-like terms terms does not exhibit accuracy similar to the analogous formula for An. To make it accurate, a term must be added to account for the large symmetry-induced quantum energy gap in the valence energy levels (i.e., the HOMO-LUMO gap). An elementary two-state model based upon a quantum rotor succeeds in producing a simple expression that evaluates the energy gap as an explicit function of An. Adding this to the electrostatics-like formula for In gives a simple quantum equation that yields accurate values for In and expresses them as a function of An. Further, the simple equations for An and In yield much insight into both the physics of electron detachment in the fullerenes and the scaling with Rn of their quantum capacitances Cn = 1/(In − An).

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

“…Again, the electronegativity values found in ref. are close to those reported herein. As expected, the softness of the SWiF increases as the size of the single‐shell carbon nanoparticles increases whereas it decreases for double‐wall fullerenes because S is correlated to the inverse of the H‐L gap.…”

“…The regression coefficients associated to the above curves are equal to 0.998 and 0.968, respectively; nevertheless an exponential curve gives better regression coefficient. Atanasov and Ellenbogen recently calculated the H‐L gaps of single‐shell spherical‐like icosahedral fullerenes. The gaps were 1.14 eV and 0.63 eV for fullerenes with 180 and 720 carbons, respectively, and sizes almost equal to iC 180 and iC 720 (Table ).…”

“…Moreover, accurate electrostatics‐based formulas were used for calculating ionization potential and electron affinity of single‐shell fullerenes in ref. , which can be used for obtaining the electronegativity. Again, the electronegativity values found in ref.…”

“…Several theoretical works analyzed structures and electronic properties of spherical and polyhedral multi‐layer fullerenes . However, comparative studies on their electronic features as a function of nanoparticle size and number of concentric shells are scarce.…”

Why and When Is Electrophilicity Minimized? New Theorems and Guiding Rules

“…After the introduction of the [n]­fullerene ionization energy and electron affinity equations given above, Atanasov and Ellenbogen proposed the following equations for the accurate calculation of ionization energy ( I n ) and electron affinity ( A n ) of fullerenes using electrostatic methods and as a function of their average radii, R n . In the given equations, δ is a small constant distance determined with the help of the work function of graphene. In Table , ionization energy and electron affinity values calculated for C n -type fullerenes using the Atanasov and Ellenbogen equations are given in eV units.…”