Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure

Journal Article · Fri Aug 14 04:00:00 EDT 2015 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4928064· OSTI ID:22493498

Hoy, Erik P.

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.

• OSTI ID: 22493498
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 6 Vol. 143; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
ACCURACY
ALKANES
DENSITY FUNCTIONAL METHOD
DIAGRAMS
ELECTRON CORRELATION
ELECTRONIC STRUCTURE
ELECTRONS
FACTORIZATION
HARTREE-FOCK METHOD
INTEGRALS
MOLECULES
POTENTIAL ENERGY
POTENTIALS
TENSORS