A Critical Analysis of Least-Squares Tensor Hypercontraction Applied to MP3
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866909550339162112 |
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| author | Matthews, Devin A. |
| author_facet | Matthews, Devin A. |
| contents | The least-squares tensor hypercontraction (LS-THC) approach is a promising method of reducing the high polynomial scaling of wavefunction methods, for example those based on many-body perturbation theory or coupled cluster. Here, we focus on LS-THC-MP3, and identify four variants with differing error and efficiency characteristics. The performance of LS-THC-MP3 is analyzed for regular test systems with up to 40 first-row atoms. We also analyze the size-extensivity/size-consistency and grid- and basis set-dependence of LS-THC-MP3. Overall, the errors observed are favorably small in comparison with standard density fitting, and a more streamlined method of generating grids via pruning is suggested. Practical crossover (the point at which LS-THC-MP3 is cheaper than the canonical method) is achieved around 240 correlated electrons. Despite several drawbacks of LS-THC that have been identified: a small but non-zero size-consistency error, poor description of angular correlation, and potentially large increase of error with basis set size, the results show that LS-THC has significant potential for practical application to MP3 and other wavefunction methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2011_13044 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Critical Analysis of Least-Squares Tensor Hypercontraction Applied to MP3 Matthews, Devin A. Chemical Physics The least-squares tensor hypercontraction (LS-THC) approach is a promising method of reducing the high polynomial scaling of wavefunction methods, for example those based on many-body perturbation theory or coupled cluster. Here, we focus on LS-THC-MP3, and identify four variants with differing error and efficiency characteristics. The performance of LS-THC-MP3 is analyzed for regular test systems with up to 40 first-row atoms. We also analyze the size-extensivity/size-consistency and grid- and basis set-dependence of LS-THC-MP3. Overall, the errors observed are favorably small in comparison with standard density fitting, and a more streamlined method of generating grids via pruning is suggested. Practical crossover (the point at which LS-THC-MP3 is cheaper than the canonical method) is achieved around 240 correlated electrons. Despite several drawbacks of LS-THC that have been identified: a small but non-zero size-consistency error, poor description of angular correlation, and potentially large increase of error with basis set size, the results show that LS-THC has significant potential for practical application to MP3 and other wavefunction methods. |
| title | A Critical Analysis of Least-Squares Tensor Hypercontraction Applied to MP3 |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2011.13044 |