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Linear-scaling implementation of molecular electronic self-consistent field theory
KTH, School of Biotechnology (BIO), Theoretical Chemistry (closed 20110512).
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2007 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 126, no 11, 85-98 p.Article in journal (Refereed) Published
Abstract [en]

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Lowdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall (LS-TRRH) method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix (including a boxed fitting of the electron density), LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF (LS-TRSCF) method. The LS-TRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point.

Place, publisher, year, edition, pages
2007. Vol. 126, no 11, 85-98 p.
Keyword [en]
renormalization-group method, fast multipole method, density-matrix, hartree-fock, exchange matrix, convergence acceleration, large systems, basis-sets, computation, optimization
URN: urn:nbn:se:kth:diva-16475DOI: 10.1063/1.2464111ISI: 000245120400012ScopusID: 2-s2.0-34047190981OAI: diva2:334517
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2011-07-13Bibliographically approved

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Salek, Pawel
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Theoretical Chemistry (closed 20110512)
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