Large-scale semidefinite programs in electronic structure calculation

Mituhiro Fukuda, Bastiaan J. Braams, Maho Nakata, Michael L. Overton, Jerome K. Percus, Makoto Yamashita, Zhengji Zhao

Research output: Contribution to journalArticlepeer-review


It has been a long-time dream in electronic structure theory in physical chemistry/chemical physics to compute ground state energies of atomic and molecular systems by employing a variational approach in which the two-body reduced density matrix (RDM) is the unknown variable. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual state of this new application of SDP as well as the formulation of these SDPs, which can be arbitrarily large. Numerical results using parallel computation on high performance computers are given. The RDM method has several advantages including robustness and provision of high accuracy compared to traditional electronic structure methods, although its computational time and memory consumption are still extremely large.

Original languageEnglish (US)
Pages (from-to)553-580
Number of pages28
JournalMathematical Programming
Issue number2-3
StatePublished - Mar 2007


  • Computational chemistry
  • Large-scale optimization
  • N-representability
  • Parallel computation
  • Reduced density matrix
  • Semidefinite programming relaxation

ASJC Scopus subject areas

  • Software
  • General Mathematics


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