Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2019
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909550333919232 |
|---|---|
| author | Matthews, Devin A. |
| author_facet | Matthews, Devin A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_02120 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction Matthews, Devin A. Chemical Physics Computational Physics 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. |
| title | Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction |
| topic | Chemical Physics Computational Physics |
| url | https://arxiv.org/abs/1912.02120 |