A spectrum slicing method for the Kohn-Sham problem

Grady Schofield, James R. Chelikowsky, Yousef Saad

Research output: Contribution to journalArticle

38 Scopus citations


Solving the Kohn-Sham equation, which arises in density functional theory, is a standard procedure to determine the electronic structure of atoms, molecules, and condensed matter systems. The solution of this nonlinear eigenproblem is used to predict the spatial and energetic distribution of electronic states. However, obtaining a solution for large systems is computationally intensive because the problem scales super-linearly with the number of atoms. Here we demonstrate a divide and conquer method that partitions the necessary eigenvalue spectrum into slices and computes each partial spectrum on an independent group of processors in parallel. We focus on the elements of the spectrum slicing method that are essential to its correctness and robustness such as the choice of filter polynomial, the stopping criterion for a vector iteration, and the detection of duplicate eigenpairs computed in adjacent spectral slices. Some of the more prominent aspects of developing an optimized implementation are discussed.

Original languageEnglish (US)
Pages (from-to)497-505
Number of pages9
JournalComputer Physics Communications
Issue number3
StatePublished - Mar 1 2012


  • Hermitian eigenproblem
  • Kohn-Sham equation
  • Polynomial filtering
  • Sparse parallel eigensolver
  • Spectrum slicing

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