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International Journal for Multiscale Computational Engineering

年間 6 号発行

ISSN 印刷: 1543-1649

ISSN オンライン: 1940-4352

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Indexed in

LINEAR SCALING SOLUTION OF THE ALL-ELECTRON COULOMB PROBLEM INSOLIDS

巻 10, 発行 1, 2012, pp. 83-99
DOI: 10.1615/IntJMultCompEng.2011002201
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要約

We present a linear scaling formulation for the solution of the all-electron Coulomb problem in crystalline solids. The resulting method is systematically improvable and well suited to large-scale quantum mechanical calculations in which the Coulomb potential and energy of a continuous electronic density and singular nuclear density are required. Linear scaling is achieved by introducing smooth, strictly local neutralizing densities to render nuclear interactions strictly local, and solving the remaining neutral Poisson problem for the electrons in real space. Although the formulation includes singular nuclear potentials without smearing approximations, the required Poisson solution is in Sobolev space H1, as required for convergence in the energy norm. We employ enriched finite elements, with enrichments from isolated atom solutions, for an efficient solution of the resulting Poisson problem in the interacting solid. We demonstrate the accuracy and convergence of the approach by direct comparison to standard Ewald sums for a lattice of point charges and demonstrate the accuracy in all-electron quantum mechanical calculations with an application to crystalline diamond.

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によって引用された
  1. Rufus Nelson D., Kanungo Bikash, Gavini Vikram, Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements, Physical Review B, 104, 8, 2021. Crossref

  2. Rufus Nelson D., Gavini Vikram, Ionic forces and stress tensor in all-electron density functional theory calculations using an enriched finite-element basis, Physical Review B, 106, 8, 2022. Crossref

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