Cholesky decomposition within local multireference singles and doubles configuration interaction

A local multireference singles and doubles configuration interaction method in which Cholesky vectors are used in place of conventional two-electron integrals has been developed (CD-LMRSDCI). To reduce the overall cost associated with our linear scaling LMRSDCI method presented earlier [T. S. Chwee, J. Chem. Phys. 128, 224106 (2008)], we adopt a two-pronged approach. First, localized orthogonal virtual orbitals, introduced by Subotnik [J. Chem. Phys. 123, 114108 (2005)], are substituted for nonorthogonal projected atomic orbitals. This obviates the need for contraction with overlap matrices and simplifies our working formalism. In addition, we restructure the rate-limiting step of our LMRSDCI algorithm to be driven by the search for two-electron integrals instead of configuration state functions. The shift necessitates a flexible way of processing the four-indexed two-electron integrals, which is facilitated by use of two-indexed Cholesky vectors. Our restructured LMRSDCI method is an order of magnitude faster and has greatly reduced storage requirements so that we are able to apply it to molecules containing up to 50 heavy atoms. However, generation of the Cholesky vectors and their subsequent transformation to the molecular orbital (MO) basis is not linear scaling. Together with assembling the MO integrals from the Cholesky vectors, these now constitute the rate-limiting steps in our method.