文档介绍：Finite Difference Methods for Ab Initio
Electronic Structure and Quantum
Transport Calculations
of Nanostructures
Jean-Luc Fattebert a, Marco Buongiorno Nardelli b
aCenter for Applied puting ( CASC), Lawrence Livermore National
Laboratory, . Box 808, L-561, Livermore, CA 94551, USA
bDepartment of Physics, North Carolina State University, Raleigh, NC, and Center for
Computational Sciences ( CCS) putational Science and Mathematics Division,
Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA
E-mail address: fattebertl @ (J.-L. Fattebert)
1. Introduction
Among the numerical discretization methods used to solve the equations of density
functional theory (DFT), the most widely used are bination of atomic
orbitals (LCAO) - usually Gaussian-type orbitals (GTO) -, plane-waves (PW) and
finite differences (FD). Of these three methods, FD is the most recent and less
common. General fully 3D grid-based electronic structure representation using finite
differences as approximate numerical schemes for partial differential operators have
started being widely used in the last ten years only. However, real-space finite difference
approaches have already shown to be an efficient tool in a substantial number of large
scale electronic structure calculations. Among its various applications, we can cite
optical properties of surfaces (ScHMIDT, BECHSTEDT and BERNHOLC [2001]), surface
Computational Chemistry
Special Volume (C. Le Bris, Guest Editor) of
HANDBOOK OF NUMERICAL ANALYSIS, VOL. X
RG. Ciarlet (Editor)
2003 Elsevier Science .
571
572 J.-L. Fattebert and M. Buongiorno Nardelli
reconstruction (RAMAMOORTHY,BRIGGS and BERNHOLC [1998]), properties of GaN
surfaces (BUNGARO, RAPCEWICZ and BERNHOLC [1999]), excitation energies and
photoabsorption spectra of atoms and clusters (VASILIEV, OGUT and CHELIKOWSKY
[1999]), diffusion of oxygen ions in SiO2 (JIN and CHANG [2001]), first-principles
molecul