Tensor structured coupled cluster methods
| dc.contributor.advisor | Scuseria, Gustavo | en_US |
| dc.creator | Schutski, Roman | en_US |
| dc.date.accessioned | 2019-05-17T14:16:09Z | en_US |
| dc.date.available | 2019-05-17T14:16:09Z | en_US |
| dc.date.created | 2018-05 | en_US |
| dc.date.issued | 2018-02-26 | en_US |
| dc.date.submitted | May 2018 | en_US |
| dc.date.updated | 2019-05-17T14:16:09Z | en_US |
| dc.description.abstract | A constant goal of quantum chemistry is devising accurate and computationally effective methods for molecular simulations. In this work an application of tensor decompositions in the context of highly accurate coupled cluster theory, which is often considered a "gold standard", is investigated. The scheme we develop is aimed to mitigate the steep growth of the computational cost with the system size, and hence to overcome the "curse of dimensionality" common in many potent methods in electronic structure. We show how to reduce the computational effort of the restricted coupled cluster with singles and doubles (RCCSD) by two orders of magnitude by introducing alternative parameterizations of the method using "canonical polyad decomposition" (CPD) and "tensor hypercontraction" (THC) formats. After describing CPD and THC formats in detail, we demonstrate how to cast regular index based tensors into a decomposed form. The number of parameters and the accuracy of these representations depend on the expansion length (rank) of the approximation. We investigate the dependence of rank upon the size of the system and a target accuracy and show it to be low for typical tensors in electronic structure. We then provide a generic procedure to reformulate any coupled cluster method using tensor decompositions. Two specific approximate methods, THC-RCCSD and CPD-RCCSD, are derived. We demonstrate the accuracy of these new approaches by calculating energies of a large set of organic molecules, as well as by simulations of Hubbard models. Finally, it is shown how the restriction of the number of parameters in approximate coupled cluster can improve the accuracy in the challenging strong correlation regime. We conclude by discussing a connection of our findings to other new developments in the coupled cluster theory and propose possible extensions of our approach. | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.citation | Schutski, Roman. "Tensor structured coupled cluster methods." (2018) Diss., Rice University. <a href="https://hdl.handle.net/1911/105665">https://hdl.handle.net/1911/105665</a>. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/105665 | en_US |
| dc.language.iso | eng | en_US |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | en_US |
| dc.subject | coupled cluster | en_US |
| dc.subject | tensor decompositions | en_US |
| dc.subject | tensor hypercontraction | en_US |
| dc.subject | canonical decomposition | en_US |
| dc.subject | low-cost method | en_US |
| dc.title | Tensor structured coupled cluster methods | en_US |
| dc.type | Thesis | en_US |
| dc.type.material | Text | en_US |
| thesis.degree.department | Chemistry | en_US |
| thesis.degree.discipline | Natural Sciences | en_US |
| thesis.degree.grantor | Rice University | en_US |
| thesis.degree.level | Doctoral | en_US |
| thesis.degree.major | Quantum chemistry | en_US |
| thesis.degree.name | Doctor of Philosophy | en_US |
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