An efficient solver for large structured eigenvalue problems in relativistic quantum chemistry

Toru Shiozaki*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalisation of matrices of dimension N > 10, 000 is now routine on a single computer node. Such matrices appear frequently in relativistic quantum chemistry owing to the time-reversal symmetry. The implementation is based on a blocked version of the Paige–Van Loan algorithm, which allows us to use the Level 3 BLAS subroutines for most of the computations. Taking advantage of the symmetry, the program is faster by up to a factor of 2 than state-of-the-art implementations of complex Hermitian diagonalisation; diagonalising a 12, 800 × 12, 800 matrix took 42.8 (9.5) and 85.6 (12.6) minutes with 1 CPU core (16 CPU cores) using our symmetry-adapted solver and Intel Math Kernel Library's ZHEEV that is not structure-preserving, respectively. The source code is publicly available under the FreeBSD licence.

Original languageEnglish (US)
Pages (from-to)5-12
Number of pages8
JournalMolecular Physics
Issue number1-2
StatePublished - Jan 17 2017


  • Relativistic
  • diagonalisation
  • quaternion

ASJC Scopus subject areas

  • Biophysics
  • Molecular Biology
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry


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