  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 is
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 is 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|,
(ai|, and (ij| distributions that arise in the molecular orbital integrals.
While only the (ai| grid directly affects the MP2 energy, the relative sizes of
the other grids are examined.
