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Bunge, Carlos F.
CarbÃ³Dorca, Ramon 

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  
http://hdl.handle.net/2072/101674  
eng  
American Institute of Physics  
Tots els drets reservats  
CÃ lcul de variacions
Electrons Matrius (MatemÃ tica) Funcions Calculus of variations Functions Matrices 

Selectdivideandconquer method for largescale configuration interaction  
info:eurepo/semantics/article  
Recercat 