Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory

Lin Lin, Sihong Shao, Weinan E

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt2, Au2, TlF, and Bi2Se3 indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.

Original languageEnglish (US)
Pages (from-to)205-217
Number of pages13
JournalJournal of Computational Physics
StatePublished - Jul 5 2013

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


  • Dirac-Kohn-Sham equations
  • Iterative methods
  • Relativistic density functional theory
  • Spectral pollution
  • Spin-orbit coupling
  • Variational collapse


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