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,...,S(R). S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds tao 0 identical with{Tao 0(egy),Tao 0(etc.)}; the CI coefficients in S0 remain always free to vary. S1 accommodates Ks with attributes above tao 1 < or = tao 0. An eigenproblem of dimension d0 + d1 for S0 + S1 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 > or = 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 {tao j;j = 0,1,2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S0 + 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 mu hartree accuracy is achieved for an eigenproblem of order 24 x 10(6), involving 1.2 x 10(12) nonzero matrix elements, and 8.4 x 10(9) Slater determinants.
Bunge
Carlos F
CF
Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, México 01000, México. bunge@fisica.unam.mx
Carbó-Dorca
Ramon
R