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

摘要

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 S-0,S-1,S-2,...,S-R. S-0, of dimension d(0), contains all configurations K with attributes (energy contributions, etc.) above thresholds T-0 equivalent to{T (egy)(0),T (etc.)(0)}; the CI coefficients in S-0 remain always free to vary. S-1 accommodates Ks with attributes above T-1 <= T-0. An eigenproblem of dimension d(0)+d(1) for S-0+S-1 is solved first, after which the last d(1) rows and columns are contracted into a single row and column, thus freezing the last d(1) CI coefficients hereinafter. The process is repeated with successive S-j(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 {T-j;j=0,1,2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S-0+S-1 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 24x10(6), involving 1.2x10(12) nonzero matrix elements, and 8.4x10(9) Slater determinants. (c) 2006 American Institute of Physics.