A Schwarz inequality for complex basis function methods in non-Hermitian quantum chemistry
A generalization of the Schwarz bound employed to reduce the scaling of quantum-chemical calculations is introduced in the context of non-Hermitian methods employing complex-scaled basis functions. Non-Hermitian methods offer a treatment of molecular metastable states in terms of L2-integrable wave...
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Veröffentlicht in: | The Journal of chemical physics 2019-11, Vol.151 (18), p.184104-184104 |
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creator | Thompson, Travis H. Ochsenfeld, Christian Jagau, Thomas-C. |
description | A generalization of the Schwarz bound employed to reduce the scaling of quantum-chemical calculations is introduced in the context of non-Hermitian methods employing complex-scaled basis functions. Non-Hermitian methods offer a treatment of molecular metastable states in terms of L2-integrable wave functions with complex energies, but until now, an efficient upper bound for the resulting electron-repulsion integrals has been unavailable due to the complications from non-Hermiticity. Our newly formulated bound allows us to inexpensively and rigorously estimate the sparsity in the complex-scaled two-electron integral tensor, providing the basis for efficient integral screening procedures. We have incorporated a screening algorithm based on the new Schwarz bound into the state-of-the-art complex basis function integral code by White, Head-Gordon, and McCurdy [J. Chem. Phys. 142, 054103 (2015)]. The effectiveness of the screening is demonstrated through non-Hermitian Hartree-Fock calculations of the static field ionization of the 2-pyridoxine 2-aminopyridine molecular complex. |
doi_str_mv | 10.1063/1.5123541 |
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Non-Hermitian methods offer a treatment of molecular metastable states in terms of L2-integrable wave functions with complex energies, but until now, an efficient upper bound for the resulting electron-repulsion integrals has been unavailable due to the complications from non-Hermiticity. Our newly formulated bound allows us to inexpensively and rigorously estimate the sparsity in the complex-scaled two-electron integral tensor, providing the basis for efficient integral screening procedures. We have incorporated a screening algorithm based on the new Schwarz bound into the state-of-the-art complex basis function integral code by White, Head-Gordon, and McCurdy [J. Chem. Phys. 142, 054103 (2015)]. The effectiveness of the screening is demonstrated through non-Hermitian Hartree-Fock calculations of the static field ionization of the 2-pyridoxine 2-aminopyridine molecular complex.</description><identifier>ISSN: 0021-9606</identifier><identifier>EISSN: 1089-7690</identifier><identifier>DOI: 10.1063/1.5123541</identifier><identifier>CODEN: JCPSA6</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Algorithms ; Basis functions ; Field ionization ; Integrals ; Mathematical analysis ; Metastable state ; Organic chemistry ; Pyridoxine ; Quantum chemistry ; Screening ; Tensors ; Upper bounds ; Wave functions</subject><ispartof>The Journal of chemical physics, 2019-11, Vol.151 (18), p.184104-184104</ispartof><rights>Author(s)</rights><rights>2019 Author(s). Published under license by AIP Publishing.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c360t-f17525f87b852a327e3928fc85f2be94a1c64a1c4850c4d5ab00eceba2a4ee003</citedby><cites>FETCH-LOGICAL-c360t-f17525f87b852a327e3928fc85f2be94a1c64a1c4850c4d5ab00eceba2a4ee003</cites><orcidid>0000-0001-5919-424X ; 0000-0002-4189-6558</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jcp/article-lookup/doi/10.1063/1.5123541$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,776,780,790,4498,27901,27902,76127</link.rule.ids></links><search><creatorcontrib>Thompson, Travis H.</creatorcontrib><creatorcontrib>Ochsenfeld, Christian</creatorcontrib><creatorcontrib>Jagau, Thomas-C.</creatorcontrib><title>A Schwarz inequality for complex basis function methods in non-Hermitian quantum chemistry</title><title>The Journal of chemical physics</title><description>A generalization of the Schwarz bound employed to reduce the scaling of quantum-chemical calculations is introduced in the context of non-Hermitian methods employing complex-scaled basis functions. Non-Hermitian methods offer a treatment of molecular metastable states in terms of L2-integrable wave functions with complex energies, but until now, an efficient upper bound for the resulting electron-repulsion integrals has been unavailable due to the complications from non-Hermiticity. Our newly formulated bound allows us to inexpensively and rigorously estimate the sparsity in the complex-scaled two-electron integral tensor, providing the basis for efficient integral screening procedures. We have incorporated a screening algorithm based on the new Schwarz bound into the state-of-the-art complex basis function integral code by White, Head-Gordon, and McCurdy [J. Chem. Phys. 142, 054103 (2015)]. The effectiveness of the screening is demonstrated through non-Hermitian Hartree-Fock calculations of the static field ionization of the 2-pyridoxine 2-aminopyridine molecular complex.</description><subject>Algorithms</subject><subject>Basis functions</subject><subject>Field ionization</subject><subject>Integrals</subject><subject>Mathematical analysis</subject><subject>Metastable state</subject><subject>Organic chemistry</subject><subject>Pyridoxine</subject><subject>Quantum chemistry</subject><subject>Screening</subject><subject>Tensors</subject><subject>Upper bounds</subject><subject>Wave functions</subject><issn>0021-9606</issn><issn>1089-7690</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp90MtKAzEUBuAgCtbqwjcIuFFh6kkymcuyFLVCwYW6cTNk0oSmzCRtklHr0zulRUHBzTmb71z4ETonMCKQsRsy4oQynpIDNCBQlEmelXCIBgCUJGUG2TE6CWEJACSn6QC9jvGTXLwL_4mNVetONCZusHYeS9euGvWBaxFMwLqzMhpncaviws1Dr7F1Npkq35pohMX9rI1di-VCtSZEvzlFR1o0QZ3t-xC93N0-T6bJ7PH-YTKeJZJlEBNNck65LvK64FQwmitW0kLLgmtaqzIVRGbbkhYcZDrnogZQUtWCilQpADZEl7u9K-_WnQqx6u9L1TTCKteFijLCocx5znp68YsuXedt_91WsZQBzWmvrnZKeheCV7paedMKv6kIVNuUK1LtU-7t9c4GaaLYJvSN35z_gdVqrv_Dfzd_AYkTixc</recordid><startdate>20191114</startdate><enddate>20191114</enddate><creator>Thompson, Travis H.</creator><creator>Ochsenfeld, Christian</creator><creator>Jagau, Thomas-C.</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0001-5919-424X</orcidid><orcidid>https://orcid.org/0000-0002-4189-6558</orcidid></search><sort><creationdate>20191114</creationdate><title>A Schwarz inequality for complex basis function methods in non-Hermitian quantum chemistry</title><author>Thompson, Travis H. ; Ochsenfeld, Christian ; Jagau, Thomas-C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c360t-f17525f87b852a327e3928fc85f2be94a1c64a1c4850c4d5ab00eceba2a4ee003</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algorithms</topic><topic>Basis functions</topic><topic>Field ionization</topic><topic>Integrals</topic><topic>Mathematical analysis</topic><topic>Metastable state</topic><topic>Organic chemistry</topic><topic>Pyridoxine</topic><topic>Quantum chemistry</topic><topic>Screening</topic><topic>Tensors</topic><topic>Upper bounds</topic><topic>Wave functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Thompson, Travis H.</creatorcontrib><creatorcontrib>Ochsenfeld, Christian</creatorcontrib><creatorcontrib>Jagau, Thomas-C.</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><jtitle>The Journal of chemical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Thompson, Travis H.</au><au>Ochsenfeld, Christian</au><au>Jagau, Thomas-C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Schwarz inequality for complex basis function methods in non-Hermitian quantum chemistry</atitle><jtitle>The Journal of chemical physics</jtitle><date>2019-11-14</date><risdate>2019</risdate><volume>151</volume><issue>18</issue><spage>184104</spage><epage>184104</epage><pages>184104-184104</pages><issn>0021-9606</issn><eissn>1089-7690</eissn><coden>JCPSA6</coden><abstract>A generalization of the Schwarz bound employed to reduce the scaling of quantum-chemical calculations is introduced in the context of non-Hermitian methods employing complex-scaled basis functions. Non-Hermitian methods offer a treatment of molecular metastable states in terms of L2-integrable wave functions with complex energies, but until now, an efficient upper bound for the resulting electron-repulsion integrals has been unavailable due to the complications from non-Hermiticity. Our newly formulated bound allows us to inexpensively and rigorously estimate the sparsity in the complex-scaled two-electron integral tensor, providing the basis for efficient integral screening procedures. We have incorporated a screening algorithm based on the new Schwarz bound into the state-of-the-art complex basis function integral code by White, Head-Gordon, and McCurdy [J. Chem. Phys. 142, 054103 (2015)]. The effectiveness of the screening is demonstrated through non-Hermitian Hartree-Fock calculations of the static field ionization of the 2-pyridoxine 2-aminopyridine molecular complex.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/1.5123541</doi><tpages>8</tpages><orcidid>https://orcid.org/0000-0001-5919-424X</orcidid><orcidid>https://orcid.org/0000-0002-4189-6558</orcidid></addata></record> |
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subjects | Algorithms Basis functions Field ionization Integrals Mathematical analysis Metastable state Organic chemistry Pyridoxine Quantum chemistry Screening Tensors Upper bounds Wave functions |
title | A Schwarz inequality for complex basis function methods in non-Hermitian quantum chemistry |
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