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

Denis Jacquemin, Benoît Champagne, Jean-Marie André, Erik Deumens, Yngve Öhrn

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1430-1444
Number of pages15
JournalJournal of Computational Chemistry
Volume23
Issue number15
DOIs
Publication statusPublished - 30 Nov 2002

Keywords

  • Crystal-orbital
  • Integral calculation
  • Polymers

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