Optimized local basis set for Kohn-Sham density functional theory

Lin Lin, Jianfeng Lu, Lexing Ying, Weinan E

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12 Scopus citations


We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn-Sham density functional theory for both insulating and metallic systems. The optimized local basis functions are obtained by solving a minimization problem in an admissible set determined by a large number of primitive basis functions. Using the optimized local basis set, the electron energy and the atomic force can be calculated accurately with a small number of basis functions. The Pulay force is systematically controlled and is not required to be calculated, which makes the optimized local basis set an ideal tool for ab initio molecular dynamics and structure optimization. We also propose a preconditioned Newton-GMRES method to obtain the optimized local basis functions in practice. The optimized local basis set is able to achieve high accuracy with a small number of basis functions per atom when applied to a one dimensional model problem.

Original languageEnglish (US)
Pages (from-to)4515-4529
Number of pages15
JournalJournal of Computational Physics
Issue number13
StatePublished - May 1 2012

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Discontinuous Galerkin
  • Electronic structure
  • Kohn-Sham density functional theory
  • Molecular dynamics
  • Optimized local basis set
  • Preconditioning
  • Pulay force
  • Trace minimization


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