A reduced basis method applied to the Restricted Hartree–Fock equations

Yvon Maday; Ulrich Razafison

doi:10.1016/j.crma.2007.11.015

Numerical Analysis

A reduced basis method applied to the Restricted Hartree–Fock equations
[Une méthode de base réduite appliquée aux équations Restricted Hartree–Fock]

Présenté par : Olivier Pironneau

Yvon Maday ^1,² ; Ulrich Razafison ¹

¹ UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
² Division of Applied Mathematics, Brown University 182 George Street, Providence, RI 02912, USA

Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 243-248.

Résumé
Abstract

Dans cette Note, nous décrivons une méthode d'approximation par bases réduites pour les calculs de structures électroniques en chimie quantique basées sur le modèle Restricted Hartree–Fock. Nous présentons des résultats numériques montrant que la méthode permet des réductions de complexité et potentiellement de coûts de calculs.

In this Note, we describe a reduced basis approximation method for the computation of some electronic structure in quantum chemistry, based on the Restricted Hartree–Fock equations. Numerical results are presented to show that this approach allows for reducing the complexity and potentially the computational costs.

Reçu le : 2007-05-19
Accepté le : 2007-11-22
Publié le : 2008-01-30

DOI : 10.1016/j.crma.2007.11.015

Affiliations des auteurs :

Yvon Maday ^{1, 2} ; Ulrich Razafison ¹

¹ UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
² Division of Applied Mathematics, Brown University 182 George Street, Providence, RI 02912, USA

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     title = {A reduced basis method applied to the {Restricted} {Hartree{\textendash}Fock} equations},
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     doi = {10.1016/j.crma.2007.11.015},
     language = {en},
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Yvon Maday; Ulrich Razafison. A reduced basis method applied to the Restricted Hartree–Fock equations. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 243-248. doi : 10.1016/j.crma.2007.11.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.11.015/

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É. Polack; A. Mikhalev; G. Dusson; B. Stamm; F. Lipparini An approximation strategy to compute accurate initial density matrices for repeated self-consistent field calculations at different geometries, Molecular Physics, Volume 118 (2020) no. 19-20 | DOI:10.1080/00268976.2020.1779834
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Yvon Maday A Priori and A Posteriori Error Analysis in Chemistry, Encyclopedia of Applied and Computational Mathematics (2015), p. 5 | DOI:10.1007/978-3-540-70529-1_255
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Valentín de la Rubia Reliable Reduced-Order Model for Fast Frequency Sweep in Microwave Circuits, Electromagnetics, Volume 34 (2014) no. 3-4, p. 161 | DOI:10.1080/02726343.2014.877735
Yvon Maday h−P Finite Element Approximation for Full-Potential Electronic Structure Calculations, Partial Differential Equations: Theory, Control and Approximation (2014), p. 349 | DOI:10.1007/978-3-642-41401-5_14
Maël Bosson; Sergei Grudinin; Stephane Redon Block‐adaptive quantum mechanics: An adaptive divide‐and‐conquer approach to interactive quantum chemistry, Journal of Computational Chemistry, Volume 34 (2013) no. 6, p. 492 | DOI:10.1002/jcc.23157
Michele Penna; Francesco Bertazzi; Michele Goano, 2010 14th International Workshop on Computational Electronics (2010), p. 1 | DOI:10.1109/iwce.2010.5677941
V. de la Rubia; U. Razafison; Y. Maday Reliable Fast Frequency Sweep for Microwave Devices via the Reduced-Basis Method, IEEE Transactions on Microwave Theory and Techniques, Volume 57 (2009) no. 12, p. 2923 | DOI:10.1109/tmtt.2009.2034208

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