Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction

A new method for generating fitting grids for least squares tensor hypercontraction (LS-THC) is presented. This method draws inspiration from the related interpolative separable density fitting (ISDF) technique but uses only a pivoted Cholesky decomposition of the metric matrix, S, already computed as a matter of course in LS-THC. The size and quality of the resulting grid are controlled by a user-defined cutoff parameter and the size of the starting grid. Additionally, the Cholesky-based method provides an alternative and possible more numerically stable method for performing the least-squares fit. The quality of the grids produced is evaluated for LS-DF-THC-MP2 calculations on retinal and benzene, the former with a large starting grid and small cc-pVDZ basis set, and the latter with a wide range of grids and basis sets. The error and grid size are found to be well-controlled by either the cutoff parameter (with a large starting grid) or the starting grid size (with a tight cutoff) and highly predictable. The Cholesky-based method is also able to generate unique grids tailored to different charge distributions, for example the (ab vertical bar, (ai vertical bar, and (ij vertical bar distributions that arise in the molecular orbital integrals. While only the (ail grid directly affects the MP2 energy, the relative sizes of the other grids are examined.