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A simplified density matrix minimization for linear scaling self-consistent field theory

J. Chem. Phys. 110, 2332 (1999); doi:10.1063/1.477969

Issue Date: 1 February 1999

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Matt Challacombe
Los Alamos National Laboratory, Theoretical Division, Group T-12, MS B268, Los Alamos, New Mexico 87545
A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tu-ring ma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree–Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. ©1999 American Institute of Physics.
History: Received 1 September 1998; accepted 7 October 1998
Permalink: http://link.aip.org/link/?JCPSA6/110/2332/1
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KEYWORDS and PACS

Keywords
PACS
  • 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
  • 02.60.-x
    Mathematical methods in physics Numerical approximation and analysis
  • YEAR: 1999

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0021-9606 (print)   1089-7690 (online)
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