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Conference Paper: Selfconsistent solution of KohnSham equation by realspace finitedifference method
Title  Selfconsistent solution of KohnSham equation by realspace finitedifference method 

Authors  
Issue Date  2015 
Publisher  IEEE. The Journal's web site is located at http://www.ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000033 
Citation  The 2015 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting (APS/URSI 2015), Vancouver, BC., Canada, 1924 July 2015. In IEEE Antennas and Propagation Society International Symposium Digest, 2015, p. 8787 How to Cite? 
Abstract  Electronicstructure calculations play a fundamental role in predicting important physical (optical, electrical, etc) properties of condensed matter. Based on density functional theory (DFT), KohnSham (KS) equation replaces the interacting manybody (electrons) problem by an equivalent set of selfconsistent singleparticle equations. Different from welladopted basis set approach, we present a realspace finitedifference method to discretize the KS equation where the Laplacian operator is represented by highorder differences. After spatial discretization, a derived nonlinear eigenvalue problem is solved by a selfconsistent field (SCF) iteration scheme with the update of electron density and potentials. In spite of the simplicity and versatility of the finitedifference method, one has to perform largescale calculations of both eigenvalue and electrostatic problems at each iteration step. For eigenvalue problems, we minimize the Rayleigh quotients by the conjugate gradient method; and find minimum eigenvalues of interest through subspace diagonalization without GramSchmidt procedure. For obtaining electrostatic potentials, we use Dirichlet boundary condition to truncate the computational domain after inserting electron density and Gaussian compensating charge density together into Poisson's equation. Then a preconditioned Krylov subspace solver is employed to solve the Poisson's equation. A threedimensional quantum dot with few spinpolarized electrons (each electron has spin up) is simulated by the realspace DFT incorporating local spin density (LSD) approximation. Wave function, electron density, eigenenergy, and total energy are calculated and compared to published results. The realspace finitedifference method produces reliable simulation results with a high computational efficiency. This work is fundamentally important to quantummechanical abinitio calculation. 
Persistent Identifier  http://hdl.handle.net/10722/217367 
ISBN  
ISSN 
DC Field  Value  Language 

dc.contributor.author  Sha, WEI   
dc.contributor.author  Chen, YP   
dc.contributor.author  Dai, QI   
dc.contributor.author  Chew, WC   
dc.date.accessioned  20150918T05:57:34Z   
dc.date.available  20150918T05:57:34Z   
dc.date.issued  2015   
dc.identifier.citation  The 2015 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting (APS/URSI 2015), Vancouver, BC., Canada, 1924 July 2015. In IEEE Antennas and Propagation Society International Symposium Digest, 2015, p. 8787   
dc.identifier.isbn  9781479978175   
dc.identifier.issn  15223965   
dc.identifier.uri  http://hdl.handle.net/10722/217367   
dc.description.abstract  Electronicstructure calculations play a fundamental role in predicting important physical (optical, electrical, etc) properties of condensed matter. Based on density functional theory (DFT), KohnSham (KS) equation replaces the interacting manybody (electrons) problem by an equivalent set of selfconsistent singleparticle equations. Different from welladopted basis set approach, we present a realspace finitedifference method to discretize the KS equation where the Laplacian operator is represented by highorder differences. After spatial discretization, a derived nonlinear eigenvalue problem is solved by a selfconsistent field (SCF) iteration scheme with the update of electron density and potentials. In spite of the simplicity and versatility of the finitedifference method, one has to perform largescale calculations of both eigenvalue and electrostatic problems at each iteration step. For eigenvalue problems, we minimize the Rayleigh quotients by the conjugate gradient method; and find minimum eigenvalues of interest through subspace diagonalization without GramSchmidt procedure. For obtaining electrostatic potentials, we use Dirichlet boundary condition to truncate the computational domain after inserting electron density and Gaussian compensating charge density together into Poisson's equation. Then a preconditioned Krylov subspace solver is employed to solve the Poisson's equation. A threedimensional quantum dot with few spinpolarized electrons (each electron has spin up) is simulated by the realspace DFT incorporating local spin density (LSD) approximation. Wave function, electron density, eigenenergy, and total energy are calculated and compared to published results. The realspace finitedifference method produces reliable simulation results with a high computational efficiency. This work is fundamentally important to quantummechanical abinitio calculation.   
dc.language  eng   
dc.publisher  IEEE. The Journal's web site is located at http://www.ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000033   
dc.relation.ispartof  IEEE Antennas and Propagation Society International Symposium Digest   
dc.rights  IEEE Antennas and Propagation Society International Symposium Digest. Copyright © IEEE.   
dc.rights  ©2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.   
dc.title  Selfconsistent solution of KohnSham equation by realspace finitedifference method   
dc.type  Conference_Paper   
dc.identifier.email  Sha, WEI: shawei@hkucc.hku.hk   
dc.identifier.email  Chen, YP: ypchen@hku.hk   
dc.identifier.email  Chew, WC: wcchew@hkucc.hku.hk   
dc.identifier.authority  Sha, WEI=rp01605   
dc.identifier.authority  Chew, WC=rp00656   
dc.description.nature  link_to_OA_fulltext   
dc.identifier.doi  10.1109/USNCURSI.2015.7303371   
dc.identifier.hkuros  254126   
dc.identifier.spage  87   
dc.identifier.epage  87   
dc.publisher.place  United States   
dc.customcontrol.immutable  sml 151119   