Optimized local basis set for Kohn-Sham density functional theory

  • Authors:

  • Lin Lin;Jianfeng Lu;Lexing Ying;Weinan E

  • Affiliations:

  • Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA;Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA;Department of Mathematics and ICES, University of Texas at Austin, Austin, TX 78712, USA;Department of Mathematics and PACM, Princeton University, Princeton, NJ 08544, USA and Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

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.