Integral algorithm and density matrix integration scheme for ab initio band structure calculations on polymeric systems

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

A new program for band structure calculations of periodic one-dimensional systems has been constructed. It is distinguishable from other codes by the efficient two-electron integral evaluation and the integration schemes of the density matrix in the first Brillouin zone. The computation of polymeric two-electron integrals is based on the McMurchie Davidson algorithm and builds batches of the different cell indices included in the polymeric system. Consequently it presents efficient scaling with respect to the number of unit cells taken into account. Our algorithm takes into account fully the polymeric symmetry rather than the molecular symmetry. A semidirect procedure where only exchange integrals are computed at each SCF cycle is proposed in order to maintain balance between computation time and disk space. In addition, the integration of the density matrix over a large number of cell indices can be performed by different methods, such as Gauss-Legendre, Clenshaw-Curtis, Filon, and Alaylioglu-Evans-Hyslop. This last scheme is able to obtain an accuracy of 10-13 a.u. on each individual density matrix element for all cell indices with only 48 k-points.

langue originaleAnglais
Pages (de - à)1430-1444
Nombre de pages15
journalJournal of Computational Chemistry
Volume23
Numéro de publication15
Les DOIs
étatPublié - 30 nov. 2002

Empreinte digitale

Band Structure
Density Matrix
Band structure
Cell
Electrons
Electron
Symmetry
Periodic Systems
One-dimensional System
Legendre
Gauss
Batch
Scaling
Cycle
Unit
Evaluation

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abstract = "A new program for band structure calculations of periodic one-dimensional systems has been constructed. It is distinguishable from other codes by the efficient two-electron integral evaluation and the integration schemes of the density matrix in the first Brillouin zone. The computation of polymeric two-electron integrals is based on the McMurchie Davidson algorithm and builds batches of the different cell indices included in the polymeric system. Consequently it presents efficient scaling with respect to the number of unit cells taken into account. Our algorithm takes into account fully the polymeric symmetry rather than the molecular symmetry. A semidirect procedure where only exchange integrals are computed at each SCF cycle is proposed in order to maintain balance between computation time and disk space. In addition, the integration of the density matrix over a large number of cell indices can be performed by different methods, such as Gauss-Legendre, Clenshaw-Curtis, Filon, and Alaylioglu-Evans-Hyslop. This last scheme is able to obtain an accuracy of 10-13 a.u. on each individual density matrix element for all cell indices with only 48 k-points.",
keywords = "Crystal-orbital, Integral calculation, Polymers",
author = "Denis Jacquemin and Beno{\^i}t Champagne and Jean-Marie Andr{\'e} and Erik Deumens and Yngve {\"O}hrn",
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language = "English",
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pages = "1430--1444",
journal = "Journal of Computational Chemistry",
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Integral algorithm and density matrix integration scheme for ab initio band structure calculations on polymeric systems. / Jacquemin, Denis; Champagne, Benoît; André, Jean-Marie; Deumens, Erik; Öhrn, Yngve.

Dans: Journal of Computational Chemistry, Vol 23, Numéro 15, 30.11.2002, p. 1430-1444.

Résultats de recherche: Contribution à un journal/une revueArticle

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AU - André, Jean-Marie

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N2 - A new program for band structure calculations of periodic one-dimensional systems has been constructed. It is distinguishable from other codes by the efficient two-electron integral evaluation and the integration schemes of the density matrix in the first Brillouin zone. The computation of polymeric two-electron integrals is based on the McMurchie Davidson algorithm and builds batches of the different cell indices included in the polymeric system. Consequently it presents efficient scaling with respect to the number of unit cells taken into account. Our algorithm takes into account fully the polymeric symmetry rather than the molecular symmetry. A semidirect procedure where only exchange integrals are computed at each SCF cycle is proposed in order to maintain balance between computation time and disk space. In addition, the integration of the density matrix over a large number of cell indices can be performed by different methods, such as Gauss-Legendre, Clenshaw-Curtis, Filon, and Alaylioglu-Evans-Hyslop. This last scheme is able to obtain an accuracy of 10-13 a.u. on each individual density matrix element for all cell indices with only 48 k-points.

AB - A new program for band structure calculations of periodic one-dimensional systems has been constructed. It is distinguishable from other codes by the efficient two-electron integral evaluation and the integration schemes of the density matrix in the first Brillouin zone. The computation of polymeric two-electron integrals is based on the McMurchie Davidson algorithm and builds batches of the different cell indices included in the polymeric system. Consequently it presents efficient scaling with respect to the number of unit cells taken into account. Our algorithm takes into account fully the polymeric symmetry rather than the molecular symmetry. A semidirect procedure where only exchange integrals are computed at each SCF cycle is proposed in order to maintain balance between computation time and disk space. In addition, the integration of the density matrix over a large number of cell indices can be performed by different methods, such as Gauss-Legendre, Clenshaw-Curtis, Filon, and Alaylioglu-Evans-Hyslop. This last scheme is able to obtain an accuracy of 10-13 a.u. on each individual density matrix element for all cell indices with only 48 k-points.

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