Asymptotic equivalence of the shell-model and local-density descriptions of Coulombic systems confined by radially symmetric potentials in two and three dimensions

被引：10

作者：

Cioslowski, Jerzy ^{[1
,2
]}

Albin, Joanna ^{[1
]}

机构：

[1] Univ Szczecin, Inst Phys, PL-70451 Szczecin, Poland

[2] Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany

来源：

JOURNAL OF CHEMICAL PHYSICS | 2013年 / 139卷 / 11期

关键词：

WIGNER CRYSTAL ISLAND; CHARGING SPECTRUM; PARTICLES; CLUSTERS; THERMODYNAMICS; SIMULATION; FORMULA; ENERGY; DOTS;

D O I：

10.1063/1.4821217

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

Asymptotic equivalence of the shell-model and local-density (LDA) descriptions of Coulombic systems confined by radially symmetric potentials in two and three dimensions is demonstrated. Tight upper bounds to the numerical constants that enter the LDA expressions for the Madelung energy are derived and found to differ by less than 0.5% from the previously known approximate values. Thanks to the variational nature of the shell-model approximate energies, asymptotic expressions for other properties, such as mean radial positions of the particles and number densities, are also obtained. A conjecture that generalizes the present results to confining potentials with arbitrary symmetries is formulated. (C) 2013 AIP Publishing LLC.

引用

页数：6