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

Denis Jacquemin1, Benoît Champagne, Jean-Marie André

  • 1Laboratoire de Chimie Théorique Appliquée, Facultés Universitaires Notre-Dame de la Paix, rue de Bruxelles, 61, B-5000 Namur, Belgium. denis.jacquemin@fundp.ac.be

Journal of Computational Chemistry
|October 9, 2002
PubMed
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A new program efficiently calculates band structures for periodic 1D systems using advanced integral evaluation and density matrix integration. It scales well with system size and leverages polymeric symmetry for faster computations.

Area of Science:

  • Computational Physics
  • Materials Science
  • Quantum Chemistry

Background:

  • Accurate band structure calculations are crucial for understanding and designing materials.
  • Existing computational codes often face challenges with scaling and symmetry in periodic systems.

Purpose of the Study:

  • To develop a novel program for efficient band structure calculations of periodic one-dimensional systems.
  • To improve computational efficiency and accuracy compared to existing methods.

Main Methods:

  • Utilizes the McMurchie Davidson algorithm for efficient computation of polymeric two-electron integrals.
  • Employs advanced integration schemes for the density matrix, including Gauss-Legendre, Clenshaw-Curtis, Filon, and Alaylioglu-Evans-Hyslop.
  • Incorporates a semidirect procedure for SCF cycles and leverages polymeric symmetry.

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Main Results:

  • Demonstrates efficient scaling with the number of unit cells in polymeric systems.
  • Achieves high accuracy (10^-13 a.u.) with the Alaylioglu-Evans-Hyslop scheme using only 48 k-points.
  • Balances computation time and disk space effectively.

Conclusions:

  • The new program offers a significant advancement in calculating band structures for 1D periodic systems.
  • Its efficiency and accuracy make it a valuable tool for materials research and development.
  • The integration schemes and algorithmic improvements provide a robust solution for complex systems.