Integral-direct electron correlation methods

Integral-direct implementations of Møller—Plesset perturbation theory up to fourth order (MP4(SDQ) without triple excitations), quadratic configuration interaction with single and double excitations (QCISD), coupled cluster (CCSD), multiconfiguration self-consistent field (MCSCF), second- and third-order multireference perturbation theory (MRPT2, MRPT3), and internally contracted multireference configuration interaction (MRCI) methods are described. All methods use the same three integral-direct kernels, namely direct calculation of Fock matrices, direct partial integral transformation, and direct evaluation of external exchange matrices. New algorithms for the latter two procedures are proposed and implemented, for which the memory requirement scales only linearly with basis set size. Test calculations with more than 500 basis functions are presented. It is demonstrated that integral prescreening can significantly reduce the scaling of the computational cost with molecular size N. For small polyglycine peptides (Gly)n (n = 1-4), we observe a scaling of N3 for the direct integral transformation (formal scaling N5), and N4 for the direct computation of the external exchange matrices (formal scaling N6).