On the convergence of SCF algorithms for the Hartree-Fock equations

Eric Cancès; Claude Le Bris

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 4, page 749-774
  • ISSN: 0764-583X

Abstract

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The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting algorithm is proved to be well-posed and to converge provided the shift parameter is large enough. On the contrary, cases when the Roothaan algorithm is not well defined or fails in converging are exhibited. These mathematical results are confronted to numerical experiments performed by chemists.

How to cite

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Cancès, Eric, and Le Bris, Claude. "On the convergence of SCF algorithms for the Hartree-Fock equations." ESAIM: Mathematical Modelling and Numerical Analysis 34.4 (2010): 749-774. <http://eudml.org/doc/197609>.

@article{Cancès2010,
abstract = { The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting algorithm is proved to be well-posed and to converge provided the shift parameter is large enough. On the contrary, cases when the Roothaan algorithm is not well defined or fails in converging are exhibited. These mathematical results are confronted to numerical experiments performed by chemists. },
author = {Cancès, Eric, Le Bris, Claude},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Nonlinear eigenvalue problem; Hartree-Fock equations; self-consistent field; convergence analysis.; convergence analysis.},
language = {eng},
month = {3},
number = {4},
pages = {749-774},
publisher = {EDP Sciences},
title = {On the convergence of SCF algorithms for the Hartree-Fock equations},
url = {http://eudml.org/doc/197609},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Cancès, Eric
AU - Le Bris, Claude
TI - On the convergence of SCF algorithms for the Hartree-Fock equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 4
SP - 749
EP - 774
AB - The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting algorithm is proved to be well-posed and to converge provided the shift parameter is large enough. On the contrary, cases when the Roothaan algorithm is not well defined or fails in converging are exhibited. These mathematical results are confronted to numerical experiments performed by chemists.
LA - eng
KW - Nonlinear eigenvalue problem; Hartree-Fock equations; self-consistent field; convergence analysis.; convergence analysis.
UR - http://eudml.org/doc/197609
ER -

References

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Citations in EuDML Documents

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  1. Konstantin N. Kudin, Gustavo E. Scuseria, Converging self-consistent field equations in quantum chemistry – recent achievements and remaining challenges
  2. Antoine Levitt, Convergence of gradient-based algorithms for the Hartree-Fock equations
  3. Antoine Levitt, Convergence of gradient-based algorithms for the Hartree-Fock equations
  4. Heinz-Jürgen Flad, Reinhold Schneider, s∗-compressibility of the discrete Hartree-Fock equation
  5. Heinz-Jürgen Flad, Reinhold Schneider, -compressibility of the discrete Hartree-Fock equation
  6. Antoine Levitt, Convergence of gradient-based algorithms for the Hartree-Fock equations
  7. Eric Cancès, Gabriel Stoltz, Gustavo E. Scuseria, Viktor N. Staroverov, Ernest R. Davidson, Local Exchange Potentials for Electronic Structure Calculations
  8. Mathieu Lewin, Séverine Paul, A numerical perspective on Hartree−Fock−Bogoliubov theory

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