Spatial Signatures of Electron Correlation in Least-Squares Tensor Hypercontraction

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Least-squares tensor hypercontraction (LS-THC) is an emerging method to reduce computational costs in quantum chemistry.
• Previous studies indicate LS-THC factorization is less accurate for wave function components (e.g., cluster amplitudes T̂₂ ) compared to Hamiltonian components.

Purpose of the Study:

• To investigate the source of errors in LS-THC, specifically within the real-space T̂₂ kernel.
• To identify and characterize a novel error feature in LS-THC representations.

Main Methods:

• Development of novel theoretical methods to analyze LS-THC errors.
• Examination of the LS-THC representation of the exchange-like correlation energy and T̂₂.

Main Results:

• Discovery of a consistent "correlation feature" in LS-THC errors across diverse molecular systems, wave functions, and basis sets.
• Identification of this feature's dependence on pairs of grid points near atoms with specific interpair distances (1-2 Bohr radii).

Conclusions:

• The identified
• correlation feature
• suggests the absence of a crucial
• pair point kernel
• in current LS-THC methods.
• These findings provide a roadmap for future LS-THC developments to enhance accuracy in quantum chemistry calculations.