Perturbative approximations to avoid matrix diagonalization

Péter R. Surján, Ágnes Szabados

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)


With the aim of developing linear-scaling methods, we discuss perturbative approaches designed to avoid diagonalization of large matrices. Approximate molecular orbitals can be corrected by perturbation theory, in course of which the Laplace transformation technique proposed originally by Almløf facilitates linear scaling. The first order density matrix P corresponding to a one-electron problem can be obtained from an iterative formula which preserves the trace and the idempotency of P so that no purification procedures are needed. For systems where P is sparse, the procedure leads to a linear scaling method. The algorithm is useful in course of geometry optimization or self-consistent procedures, since matrix P of the previous step can be used to initialize the density matrix iteration at the next step. Electron correlation methods based on the Hartree-Fock density matrix, without making reference to molecular orbitals are commented on.

Original languageEnglish
Title of host publicationChallenges and Advances in Computational Chemistry and Physics
Number of pages13
Publication statusPublished - Jan 1 2011

Publication series

NameChallenges and Advances in Computational Chemistry and Physics
ISSN (Print)2542-4491
ISSN (Electronic)2542-4483


  • Density matrix
  • Idempotency conserving iteration
  • Laplace-transform
  • Linear scaling

ASJC Scopus subject areas

  • Computer Science Applications
  • Chemistry (miscellaneous)
  • Physics and Astronomy (miscellaneous)

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  • Cite this

    Surján, P. R., & Szabados, Á. (2011). Perturbative approximations to avoid matrix diagonalization. In Challenges and Advances in Computational Chemistry and Physics (pp. 83-95). (Challenges and Advances in Computational Chemistry and Physics; Vol. 13). Springer.