Capacitance: A property of nanoscale materials based on spatial symmetry of discrete electrons

Discrete charge dielectric model of electrostatic energy

“…Used in the treatment of spherical quantum dots, the discrete charge dielectric model has played a centrol role in the identification of a classical electrostatic "fingerprint" of the periodic table of elements. 12,13 The "fingerprint" Coulomb repulsion, U C , is schematically represented by a mutually-directed arrow between q 1 and q 2 indicating mutual energy distribution. Likewise, for direct polarizations, U dir , energy is mutually shared between each point charge, q i , and its respectively polarized surface charge element, q i .…”

“…The discrete charge dielectric model has been used for numerical evaluations in recent studies concerning the capacitance of few-electron spherical quantum dots [10][11][12][13] and "meta-atoms" 14 , cited as leading to charge carrier localization near quantum dot surfaces 15 and played a central role in the discovery of a classical electrostatic fingerprint of atomic structure. 12,13 The present model represents a redevelopment and generalization of a previously published interactions picture initially used to evaluate the electrostatic energy of a silicon sphere containing one or two electrons embedded in a uniform silicon dioxide environment. 16,17 Exclusion of one-half of the "self-polarization" interaction energy term in the original picture is shown to be inconsistent with the current formulation in which a more appropriate description, "direct polarization," is used to both eliminate confusion with self-interaction or self energy -interaction of a point charge with its own potentialand to differentiate it from indirect polarization interactions ("polarizations" in the original picture) which are not directly involved in the polarization of the dielectric.…”

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).…”

Correspondences between the classical electrostatic Thomson problem and atomic electronic structure

“…15 However, electrostatic treatments of three-dimensional artificial atoms have fallen short of yielding any observable shell-filling patterns. 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.…”