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_1S_2,...,S_R.S_0,of dimension d_0,contains all configurations K with attributes (energy contributions,etc.) above thresholds T_0 ident to {T_0~(egy),T_0~(etc)};the CI coefficients in S_0 remain always free to vary.S1 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_1(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 muhartree 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.