Discrete charge dielectric model of electrostatic energy

Abstract

Studies on nanoscale materials merit careful development of an electrostatics model concerning discrete point charges within dielectrics. The discrete charge dielectric model treats three unique interaction types derived from an external source: Coulomb repulsion among point charges, direct polarization between point charges and their associated surface charge elements, and indirect polarization between point charges and surface charge elements formed by other point charges. The model yields the potential energy, U (N ), stored in a general N point charge system differing from conventional integral formulations, 1/2 E · DdV and 1/2 ρΦdV , in a manner significant to the treatment of few electron systems.

Correspondences between the classical electrostatic Thomson problem and atomic electronic structure

“…3 as the unit Thomson radius constraint is relaxed to minimize the sum of all electrostatic interaction terms within the sphere. 18 This suggests that a screening parameter is important to future developments as it is involved in the spherical jellium model 48 which presumes a "uniform" positive background charge within a spherical volume (cf. the "plum pudding" model) to neutralize the total charge of the system.…”

“…2 Recently, similarities between classical electrostatic properties of spherical quantum dots and the distribution of empirical ionization energies of neutral atoms were reported for N ≤ 32 electrons 16,17 when evaluated using the discrete charge dielectric model. 18 The present paper builds on this previous work by identifying numerous correspondences between the electrostatic Thomson Problem of distributing equal point charges on a unit sphere and atomic electronic structure.…”

“…Energies inFig. 3 associated with N =4,10,12,18,20,30,36,48, 54, 56, 70, 80, and 88 exhibit this trait. The few exceptions to this trend, N =2, 38, and 86, are indiscernible from the rising global trend of the distribution.…”

Capacitance, the Next of Kin to Chemical Softness and Density of States, an Unexpected Perk of Being the “Middle Child”

“…In case of discrete charge elements, d q = e , the quantum capacitance expression would be in order, which refers either to the right- or to the left-hand side process (to one electron charge increment or deduction) and has been advocated to come without one-half factor . Nevertheless, the quantity given here has the self-capacitance nature, and it is based on continuum inhomogeneous charge distribution, to which the one-half formalism applies , (similarly, as it occurs in the textbook integration approach to classical charging energy). Hence, by analogy to classical charging energy and in compliance with functional differentiation (variational derivative of energy with respect to density), the local capacitance is expressed as In a very straightforward model, the “chemical energy” in atoms or molecules is stored in the electric field, generated by electric charge (similarly to the macroscopic capacitors).…”

Discrete transformations in the Thomson Problem

“…The Thomson Problem treated within a dielectric sphere, (20)(21)(22) using an appropriate model for discrete charges in the presence of dielectrics (24) these disparities become more pronounced as shown in Fig. 5 (solid circles).…”