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Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations

J. Chem. Phys. 106, 5569 (1997); doi:10.1063/1.473579

Issue Date: 1 April 1997

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John M. Millam and Gustavo E. Scuseria
Center for Nanoscale Science and Technology, Rice Quantum Institute, and Department of Chemistry, Mail Stop 60, Rice University, Houston, Texas 77005-1892
Advances in the computation of the Coulomb, exchange, and correlation contributions to Gaussian-based Hartree–Fock and density functional theory Hamiltonians have demonstrated near-linear scaling with molecular size for these steps. These advances leave the [script O](N3) diagonalization bottleneck as the rate determining step for very large systems. In this work, a conjugate gradient density matrix search (CG-DMS) method has been successfully extended and computationally implemented for use with first principles calculations. A Cholesky decomposition of the overlap matrix and its inverse is used to transform to and back from an orthonormal basis, which can be formed in near-linear time for sparse systems. Linear scaling of CPU time for the density matrix search and crossover of CPU time with diagonalization is demonstrated for polyglycine chains containing up to 493 atoms and water clusters up to 900 atoms. ©1997 American Institute of Physics.
History: Received 18 October 1996; accepted 31 December 1996
Permalink: http://link.aip.org/link/?JCPSA6/106/5569/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.Ew
    Electronic structure of atoms, molecules and their ions: theory Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations) Density-functional theory
  • 31.15.Ne
    Electronic structure of atoms, molecules and their ions: theory Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations) Self-consistent-field methods
  • 02.10.Sp
    Mathematical methods in physics Logic, set theory, and algebra Linear and multilinear algebra; matrix theory (finite and infinite)
  • YEAR: 1996-97

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (46)
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