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Conference Paper: Self-consistent solution of Kohn-Sham equation by real-space finite-difference method

TitleSelf-consistent solution of Kohn-Sham equation by real-space finite-difference method
Authors
Issue Date2015
PublisherIEEE. 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, 19-24 July 2015. In IEEE Antennas and Propagation Society International Symposium Digest, 2015, p. 87-87 How to Cite?
AbstractElectronic-structure calculations play a fundamental role in predicting important physical (optical, electrical, etc) properties of condensed matter. Based on density functional theory (DFT), Kohn-Sham (KS) equation replaces the interacting many-body (electrons) problem by an equivalent set of self-consistent single-particle equations. Different from well-adopted basis set approach, we present a real-space finite-difference method to discretize the KS equation where the Laplacian operator is represented by high-order differences. After spatial discretization, a derived nonlinear eigenvalue problem is solved by a self-consistent field (SCF) iteration scheme with the update of electron density and potentials. In spite of the simplicity and versatility of the finite-difference method, one has to perform large-scale 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 Gram-Schmidt 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 three-dimensional quantum dot with few spin-polarized electrons (each electron has spin up) is simulated by the real-space DFT incorporating local spin density (LSD) approximation. Wave function, electron density, eigen-energy, and total energy are calculated and compared to published results. The real-space finite-difference method produces reliable simulation results with a high computational efficiency. This work is fundamentally important to quantum-mechanical ab-initio calculation.
Persistent Identifierhttp://hdl.handle.net/10722/217367
ISBN
ISSN

 

DC FieldValueLanguage
dc.contributor.authorSha, WEI-
dc.contributor.authorChen, YP-
dc.contributor.authorDai, QI-
dc.contributor.authorChew, WC-
dc.date.accessioned2015-09-18T05:57:34Z-
dc.date.available2015-09-18T05:57:34Z-
dc.date.issued2015-
dc.identifier.citationThe 2015 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting (APS/URSI 2015), Vancouver, BC., Canada, 19-24 July 2015. In IEEE Antennas and Propagation Society International Symposium Digest, 2015, p. 87-87-
dc.identifier.isbn978-1-4799-7817-5-
dc.identifier.issn1522-3965-
dc.identifier.urihttp://hdl.handle.net/10722/217367-
dc.description.abstractElectronic-structure calculations play a fundamental role in predicting important physical (optical, electrical, etc) properties of condensed matter. Based on density functional theory (DFT), Kohn-Sham (KS) equation replaces the interacting many-body (electrons) problem by an equivalent set of self-consistent single-particle equations. Different from well-adopted basis set approach, we present a real-space finite-difference method to discretize the KS equation where the Laplacian operator is represented by high-order differences. After spatial discretization, a derived nonlinear eigenvalue problem is solved by a self-consistent field (SCF) iteration scheme with the update of electron density and potentials. In spite of the simplicity and versatility of the finite-difference method, one has to perform large-scale 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 Gram-Schmidt 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 three-dimensional quantum dot with few spin-polarized electrons (each electron has spin up) is simulated by the real-space DFT incorporating local spin density (LSD) approximation. Wave function, electron density, eigen-energy, and total energy are calculated and compared to published results. The real-space finite-difference method produces reliable simulation results with a high computational efficiency. This work is fundamentally important to quantum-mechanical ab-initio calculation.-
dc.languageeng-
dc.publisherIEEE. The Journal's web site is located at http://www.ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000033-
dc.relation.ispartofIEEE Antennas and Propagation Society International Symposium Digest-
dc.rightsIEEE 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.titleSelf-consistent solution of Kohn-Sham equation by real-space finite-difference method-
dc.typeConference_Paper-
dc.identifier.emailSha, WEI: shawei@hkucc.hku.hk-
dc.identifier.emailChen, YP: ypchen@hku.hk-
dc.identifier.emailChew, WC: wcchew@hkucc.hku.hk-
dc.identifier.authoritySha, WEI=rp01605-
dc.identifier.authorityChew, WC=rp00656-
dc.description.naturelink_to_OA_fulltext-
dc.identifier.doi10.1109/USNC-URSI.2015.7303371-
dc.identifier.hkuros254126-
dc.identifier.spage87-
dc.identifier.epage87-
dc.publisher.placeUnited States-
dc.customcontrol.immutablesml 151119-

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