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Bunge, Carlos F.
CarbÃ³Dorca, Ramon 

2006  
A selectdivideandconquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (HartreeFock or similar) and suitable correlation orbitals (natural or localized orbitals), a large Nelectron 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 T1â‰¤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(jâ‰¥2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidsonâ€™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 largedimensional 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 matrixelement evaluation becomes rate determining. One Î¼hartree accuracy is achieved for an eigenproblem of order 24 Ã— 106, involving 1.2 Ã— 1012 nonzero matrix elements, and 8.4Ã—109 Slater determinants  
application/pdf  
Bunge, Carlos F., i CarbÃ³Dorca, Ramon (2006). Selectdivideandconquer method for largescale configuration interaction. Journal of Chemical Physics 125 (1), 014108. Recuperat 27 desembre 2010, a http://link.aip.org/link/JCPSA6/v125/i1/p014108/s1  
00219606 (versiÃ³ paper) 10897690 (versiÃ³ electrÃ²nica) 

http://hdl.handle.net/10256/3200  
eng  
American Institute of Physics  
ReproducciÃ³ digital del document publicat a: http://dx.doi.org/10.1063/1.2207621 Articles publicats (DQ) 

Â© Journal of Chemical Physics, 2006, vol. 125, nÃºm. 1  
Tots els drets reservats  
CÃ lcul de variacions
Electrons Matrius (MatemÃ tica) Funcions Calculus of variations Functions Matrices 

Selectdivideandconquer method for largescale configuration interaction  
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