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Journal of Chemical Physics / Volume 129 / Issue 12 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 129, 124106 (2008); http://dx.doi.org/10.1063/1.2974099 (12 pages)

The augmented Roothaan–Hall method for optimizing Hartree–Fock and Kohn–Sham density matrices

Stinne Høst1, Jeppe Olsen1, Branislav Jansík1, Lea Thøgersen1, Poul Jørgensen1, and Trygve Helgaker2

1The Lundbeck Foundation Center for Theoretical Chemistry, Department of Chemistry, University of Aarhus, DK-8000 Århus C, Denmark
2Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P. O. Box 1033 Blindern, N-0315 Oslo, Norway

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(Received 19 March 2008; accepted 30 July 2008; published online 24 September 2008)

We present a novel method for the optimization of Hartree–Fock and Kohn–Sham energies that does not suffer from the flaws of the conventionally used two-step Roothaan–Hall (RH) with direct inversion in iterative subspace (DIIS) acceleration scheme, improving the reliability of the optimization while reducing its cost. The key to its success is the replacement of the two separate steps of each RH/DIIS iteration by a single concerted step that fully exploits the Hessian information available from the previous iterations. It is a trust-region based method and therefore by design converges to an energy minimum. Numerical examples are given to illustrate that the algorithm is robust and cost efficient, converging smoothly to a minimum also in cases when the RH/DIIS algorithm fails to converge or when it converges to a saddle point rather than to a minimum. The algorithm is based on matrix multiplications and becomes linearly scaling for sufficiently large systems.

© 2008 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THEORY
    1. Newton’s method
    2. The Roothaan–Hall method
    3. The augmented RH method
    4. The RH/DIIS method
    5. Example: Local convergence
  3. TRUST-REGION OPTIMIZATION
    1. The direction of the step
    2. The length of the step
    3. Example: ARH trust-region optimization
    4. Example: Global convergence
  4. EFFICIENCY AND COMPUTATIONAL SCALING
  5. PERFORMANCE OF THE ARH ALGORITHM
    1. Hartree–Fock and Kohn–Sham optimizations
    2. The ground state of N -residue polyalanines
  6. CONCLUSION

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KEYWORDS and PACS

Keywords

HF calculations

PACS

  • 31.15.xr

    Self-consistent-field methods

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2974099

PUBLICATION DATA

ISSN

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

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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