Tensor hypercontraction. II. Least-squares renormalization.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• The electron repulsion integral (ERI) tensor is crucial for quantum chemistry calculations.
• Accurate computation of the ERI tensor is computationally intensive.
• Previous tensor hypercontraction (THC) methods, like PARAFAC-THC, faced limitations.

Purpose of the Study:

• To introduce a novel and efficient least-squares tensor hypercontraction (LS-THC) representation for the ERI tensor.
• To develop an improved algorithm for generating THC factors.
• To assess the accuracy and efficiency of LS-THC for quantum chemistry applications.

Main Methods:

• Developed LS-THC by least-squares renormalization of spatial quadrature over the 1/r(12) operator.
• Derived an analytical formula for LS-THC factors.
• Applied LS-THC to MP2 calculations using conventional and density-fitted integrals.
• Investigated computational scaling as O(N(5)) for exact integrals and O(N(4)) for density-fitted integrals.

Main Results:

• LS-THC provides an efficient O(N(4)) computational approach.
• Grid fitting errors in LS-THC are negligible, even with sparse grids.
• LS-THC introduces minimal additional error compared to density fitting errors.
• The method demonstrates high accuracy for MP2 calculations.

Conclusions:

• LS-THC offers a robust, efficient, and accurate O(N(4)) method for quantum chemistry.
• LS-THC is broadly applicable to various quantum chemistry methods beyond MP2 and MP3.
• The developed analytical formula simplifies the generation of THC factors, enhancing computational feasibility.