Meshfree implementation for the real‐space electronic‐structure calculation of crystalline solids

A meshfree formulation of the Schrodinger equation having periodic potential is presented. The conventional meshfree shape function is modified to express properly the periodicity of Bravais lattice. Then, it is applied to the electronic-structure calculation of crystalline solids in real space. Numerical examples are the Kronig–Penney model potential and the empirical pseudopotentials of diamond and zinc-blende semiconductors. Results prove that the meshfree method is a promising one to be used as a real-space technique for the calculations of electronic structures. Copyright © 2004 John Wiley & Sons, Ltd.

[1]  Kyeongjae Cho,et al.  Wavelets in all-electron density-functional calculations , 1999 .

[2]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[3]  L. Freund,et al.  The influence of strain on confined electronic states in semiconductor quantum structures , 2001 .

[4]  Li,et al.  Moving least-square reproducing kernel methods (I) Methodology and convergence , 1997 .

[5]  Wing Kam Liu,et al.  Meshfree and particle methods and their applications , 2002 .

[6]  C. M. Goringe,et al.  Basis functions for linear-scaling first-principles calculations , 1997 .

[7]  C. Y. Fong,et al.  Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach , 1999, cond-mat/9903313.

[8]  J. Q. Broughton,et al.  Concurrent coupling of length scales: Methodology and application , 1999 .

[9]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[10]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[11]  Erich Wimmer,et al.  Full-potential self-consistent linearized-augmented-plane-wave method for calculating the electronic structure of molecules and surfaces: O 2 molecule , 1981 .

[12]  J. Pask,et al.  Finite-element methods in electronic-structure theory , 2001 .

[13]  T. Beck.  Real-space mesh techniques in density-functional theory , 2000, cond-mat/0006239.

[14]  D. Tekleab,et al.  Strain-induced electronic property heterogeneity of a carbon nanotube , 2001 .

[15]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[16]  Finite element analysis of strain effects on electronic and transport properties in quantum dots and wires , 1998, cond-mat/9806029.

[17]  C. Pryor.  Eight-band calculations of strained InAs/GaAs quantum dots compared with one-, four-, and six-band approximations , 1997, cond-mat/9710304.

[18]  Tsukada,et al.  Adaptive finite-element method for electronic-structure calculations. , 1996, Physical review. B, Condensed matter.

[19]  Marvin L. Cohen,et al.  Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-blende Structures , 1966 .

[20]  D. Sander,et al.  The correlation between mechanical stress and magnetic anisotropy in ultrathin films , 1999 .

[21]  Ted Belytschko,et al.  ON THE COMPLETENESS OF MESHFREE PARTICLE METHODS , 1998 .