Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Least-squares tensor hypercontraction (LS-THC) is a computational method used in quantum chemistry.
• Generating fitting grids is crucial for the efficiency and accuracy of LS-THC calculations.
• Existing methods for grid generation can be computationally intensive or lack flexibility.

Purpose of the Study:

• To introduce a new, efficient method for generating fitting grids for LS-THC.
• To leverage Cholesky decomposition for improved numerical stability and control over grid generation.
• To evaluate the performance and predictability of the new method.

Main Methods:

• A Cholesky decomposition of the metric matrix (S) is employed, inspired by interpolative separable density fitting (ISDF).
• Grid size and quality are controlled via a user-defined cutoff parameter and the initial grid size.
• The method was tested on LS-DF-THC-MP2 calculations for retinal and benzene using various basis sets.

Main Results:

• The Cholesky-based method effectively controls fitting grid size and quality, offering predictable outcomes.
• Numerical stability is potentially improved compared to existing least-squares fitting techniques.
• Unique grids can be generated for different charge distributions, such as (ab|, (ai|, and (ij|.

Conclusions:

• The new Cholesky decomposition approach provides a robust and controllable method for generating LS-THC fitting grids.
• This method enhances numerical stability and allows for tailored grids, improving computational efficiency in quantum chemical studies.
• The predictability of error and grid size offers significant advantages for practical applications.