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Select-divide-and-conquer method for large-scale configuration interaction

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,...,SR. S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds T0={T0egy, T0etc.}; the CI coefficients in S0 remain always free to vary. S1 accommodates KS with attributes above T1≤T0. An eigenproblem of dimension d0+d1 for S0+S 1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j≥2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson’s eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {Tj;j=0, 1, 2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S 0+S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One μhartree accuracy is achieved for an eigenproblem of order 24 × 106, involving 1.2 × 1012 nonzero matrix elements, and 8.4×109 Slater determinants

© Journal of Chemical Physics, 2006, vol. 125, núm. 1

American Institute of Physics

Author: Bunge, Carlos F.
Carbó-Dorca, Ramon
Date: 2006
Abstract: A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,...,SR. S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds T0={T0egy, T0etc.}; the CI coefficients in S0 remain always free to vary. S1 accommodates KS with attributes above T1≤T0. An eigenproblem of dimension d0+d1 for S0+S 1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j≥2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson’s eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {Tj;j=0, 1, 2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S 0+S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One μhartree accuracy is achieved for an eigenproblem of order 24 × 106, involving 1.2 × 1012 nonzero matrix elements, and 8.4×109 Slater determinants
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Citation: Bunge, Carlos F., i Carbó-Dorca, Ramon (2006). Select-divide-and-conquer method for large-scale configuration interaction. Journal of Chemical Physics 125 (1), 014108. Recuperat 27 desembre 2010, a http://link.aip.org/link/JCPSA6/v125/i1/p014108/s1
ISSN: 0021-9606 (versió paper)
1089-7690 (versió electrònica)
Document access: http://hdl.handle.net/10256/3200
Language: eng
Publisher: American Institute of Physics
Collection: Reproducció digital del document publicat a: http://dx.doi.org/10.1063/1.2207621
Articles publicats (D-Q)
Is part of: © Journal of Chemical Physics, 2006, vol. 125, núm. 1
Rights: Tots els drets reservats
Subject: Càlcul de variacions
Electrons
Matrius (Matemàtica)
Funcions
Calculus of variations
Functions
Matrices
Title: Select-divide-and-conquer method for large-scale configuration interaction
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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