Perturbative approximations to avoid matrix diagonalization

Péter R. Surján, A. Szabados

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

Abstract

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
PublisherSpringer
Pages83-95
Number of pages13
DOIs
Publication statusPublished - Jan 1 2011

Publication series

NameChallenges and Advances in Computational Chemistry and Physics
Volume13
ISSN (Print)2542-4491
ISSN (Electronic)2542-4483

Fingerprint

scaling
molecular orbitals
approximation
Laplace transformation
Molecular orbitals
matrices
purification
iteration
electrons
perturbation theory
Electron correlations
Correlation methods
optimization
Purification
geometry
Geometry
Electrons

Keywords

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

ASJC Scopus subject areas

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

Cite this

Surján, P. R., & Szabados, A. (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. https://doi.org/10.1007/978-90-481-2853-2_4

Perturbative approximations to avoid matrix diagonalization. / Surján, Péter R.; Szabados, A.

Challenges and Advances in Computational Chemistry and Physics. Springer, 2011. p. 83-95 (Challenges and Advances in Computational Chemistry and Physics; Vol. 13).

Research output: Chapter in Book/Report/Conference proceedingChapter

Surján, PR & Szabados, A 2011, Perturbative approximations to avoid matrix diagonalization. in Challenges and Advances in Computational Chemistry and Physics. Challenges and Advances in Computational Chemistry and Physics, vol. 13, Springer, pp. 83-95. https://doi.org/10.1007/978-90-481-2853-2_4
Surján PR, Szabados A. Perturbative approximations to avoid matrix diagonalization. In Challenges and Advances in Computational Chemistry and Physics. Springer. 2011. p. 83-95. (Challenges and Advances in Computational Chemistry and Physics). https://doi.org/10.1007/978-90-481-2853-2_4
Surján, Péter R. ; Szabados, A. / Perturbative approximations to avoid matrix diagonalization. Challenges and Advances in Computational Chemistry and Physics. Springer, 2011. pp. 83-95 (Challenges and Advances in Computational Chemistry and Physics).
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