Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Determination of the chemical potential and HOMO/LUMO orbitals in density purification methods
KTH, School of Biotechnology (BIO), Theoretical Chemistry.
2006 (English)In: Chemical Physics Letters, ISSN 0009-2614, E-ISSN 1873-4448, Vol. 432, no 4-6, 591-594 p.Article in journal (Refereed) Published
Abstract [en]

Several density purification methods have been proposed to achieve linear scaling in Hartree-Fock and Kohn-Sham calculations. However, only the density is found, while in the traditional diagonalization method the orbitals are also obtained. This could be seen as a drawback as in many cases one would like at least the HOMO and LUMO orbitals and their orbital energies. In this letter, we show how a value for the chemical potential can be obtained as a by-product of density purification methods at negligible cost. Once the chemical potential is known, MO's around the HOMO-LUMO gap can be calculated with the Spectral Transformation Lanczos method.

Place, publisher, year, edition, pages
2006. Vol. 432, no 4-6, 591-594 p.
Keyword [en]
Chemical analysis, Cost effectiveness, Orbits, Purification
National Category
Theoretical Chemistry
Identifiers
URN: urn:nbn:se:kth:diva-6545DOI: 10.1016/j.cplett.2006.10.090ISI: 000243067000039Scopus ID: 2-s2.0-34547868145OAI: oai:DiVA.org:kth-6545DiVA: diva2:11287
Note
QC 20101123. Uppdaterad från In press till Published (20101123).Available from: 2006-12-11 Created: 2006-12-11 Last updated: 2010-11-23Bibliographically approved
In thesis
1. Sparse Matrices in Self-Consistent Field Methods
Open this publication in new window or tab >>Sparse Matrices in Self-Consistent Field Methods
2006 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis is part of an effort to enable large-scale Hartree-Fock/Kohn-Sham (HF/KS) calculations. The objective is to model molecules and materials containing thousands of atoms at the quantum mechanical level. HF/KS calculations are usually performed with the Self-Consistent Field (SCF) method. This method involves two computationally intensive steps. These steps are the construction of the Fock/Kohn-Sham potential matrix from a given electron density and the subsequent update of the electron density usually represented by the so-called density matrix. In this thesis the focus lies on the representation of potentials and electron density and on the density matrix construction step in the SCF method. Traditionally a diagonalization has been used for the construction of the density matrix. This diagonalization method is, however, not appropriate for large systems since the time complexity for this operation is σ(n3). Three types of alternative methods are described in this thesis; energy minimization, Chebyshev expansion, and density matrix purification. The efficiency of these methods relies on fast matrix-matrix multiplication. Since the occurring matrices become sparse when the separation between atoms exceeds some value, the matrix-matrix multiplication can be performed with complexity σ(n).

A hierarchic sparse matrix data structure is proposed for the storage and manipulation of matrices. This data structure allows for easy development and implementation of algebraic matrix operations, particularly needed for the density matrix construction, but also for other parts of the SCF calculation. The thesis addresses also truncation of small elements to enforce sparsity, permutation and blocking of matrices, and furthermore calculation of the HOMO-LUMO gap and a few surrounding eigenpairs when density matrix purification is used instead of the traditional diagonalization method.

Place, publisher, year, edition, pages
Stockholm: Bioteknologi, 2006. x, 38 p.
Keyword
sparse matrix, self-consistent field, Hartree-Fock, Density Functional Theory, Density Matrix Purification
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-4219 (URN)978-91-7178-534-3 (ISBN)978-91-7178-534-5 (ISBN)
Presentation
2006-12-15, FD41, AlbaNova, Roslagstullsbacken 21, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20101123Available from: 2006-12-11 Created: 2006-12-11 Last updated: 2010-11-23Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Rubensson, Emanuel
By organisation
Theoretical Chemistry
In the same journal
Chemical Physics Letters
Theoretical Chemistry

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 57 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf