@article {Tasnádi:2007:1546-1955:1206,
title = "Solution of the Poisson Equation for Two Dimensional Periodic Structures in an Overlapping Localized Site Density Scheme",
journal = "Journal of Computational and Theoretical Nanoscience",
parent_itemid = "infobike://asp/jctn",
publishercode ="asp",
year = "2007",
volume = "4",
number = "6",
publication date ="2007-09-01T00:00:00",
pages = "1206-1217",
itemtype = "ARTICLE",
issn = "1546-1955",
eissn = "1546-1963",
url = "https://www.ingentaconnect.com/content/asp/jctn/2007/00000004/00000006/art00016",
doi = "doi:10.1166/jctn.2007.2399",
keyword = "SLABS, EWALD SUMMATION, POISSON EQUATION",
author = "Tasn{\’a}di, F.",
abstract = "Bertaut's equivalent electric density idea (E. F. Bertaut, Journal de Physique 39, 1331 (1978)) is applied to the case of two dimensional periodic continuous charge density distributions. The following derivation differs from what was introduced by Bertaut. The presented
method solves the Poisson equation for the scheme of overlapping localized site densities with periodic boundary conditions in the (x,y) plane and with the general finite voltage boundary condition in the perpendicular z-direction. As usual the long-range potential is calculated
in the Fourier space. For the K
0 case a Fourier transformation helps to calculate the solution in a three dimensional periodic sense, while for K
= 0 the required charge neutrality is the starting point. For both cases suitable representations
of the spherical harmonics are needed to arrive at expressions that are convenient for numerical implementation. In this localized density scheme an explicit relation can be derived between the finite voltage in z-direction and the z-component of the dipole density. The application
to band structure calculation is tested.",
}