### 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 language | English |
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Pages (from-to) | 1430-1444 |

Number of pages | 15 |

Journal | Journal of Computational Chemistry |

Volume | 23 |

Issue number | 15 |

DOIs | |

Publication status | Published - 30 Nov 2002 |

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### Keywords

- Crystal-orbital
- Integral calculation
- Polymers

### Cite this

*Journal of Computational Chemistry*,

*23*(15), 1430-1444. https://doi.org/10.1002/jcc.10146

}

*Journal of Computational Chemistry*, vol. 23, no. 15, pp. 1430-1444. https://doi.org/10.1002/jcc.10146

**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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Integral algorithm and density matrix integration scheme for ab initio band structure calculations on polymeric systems

AU - Jacquemin, Denis

AU - Champagne, Benoît

AU - André, Jean-Marie

AU - Deumens, Erik

AU - Öhrn, Yngve

PY - 2002/11/30

Y1 - 2002/11/30

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.

KW - Crystal-orbital

KW - Integral calculation

KW - Polymers

UR - http://www.scopus.com/inward/record.url?scp=0037202604&partnerID=8YFLogxK

U2 - 10.1002/jcc.10146

DO - 10.1002/jcc.10146

M3 - Article

AN - SCOPUS:0037202604

VL - 23

SP - 1430

EP - 1444

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

SN - 0192-8651

IS - 15

ER -