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

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Materials Science

Background:

• Tensor factorization of the 2-electron integral matrix reduces computational scaling in ab initio electronic structure methods.
• Cholesky factorization is the simplest positive semidefinite factorization for the 2-electron integral matrix.

Purpose of the Study:

• Introduce a generalized family of positive semidefinite factorizations.
• Evaluate the performance of these generalized factorizations in electronic structure calculations.

Main Methods:

• Implementation of generalized positive semidefinite factorizations within the parametric 2-RDM method.
• Application to inorganic molecules, alkane chains, and potential energy curves.

Main Results:

• The generalized factorization retains the accuracy and size extensivity of the Cholesky factorization.
• Performance is maintained even with multi-reference correlation present.
• The method shows potential for low-scaling ab initio electronic structure methods.

Conclusions:

• Generalized positive semidefinite factorizations offer a promising avenue for efficient electronic structure calculations.
• This approach can achieve computational costs comparable to Hartree-Fock and density functional theories.
• The method is suitable for treating electron correlation in complex systems.