Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure.
Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.
Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
Erik P
EP
Hoy
Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
David A
DA
Mazziotti
D000473:Alkanes / Q000737:chemistry; D004583:Electrons; D006858:Hydrofluoric Acid / Q000737:chemistry; D017665:Hydroxyl Radical / Q000737:chemistry; D008697:Methane / Q000737:chemistry; D008956:Models, Chemical
D000473:Alkanes; D017665:Hydroxyl Radical; D008697:Methane; D006858:Hydrofluoric Acid