Analytic Löwdin alpha-function method for two-center electron-repulsion integrals over slater-type orbitals
Using the Löwdin alpha‐function method in which displaced orbitals are expanded in spherical harmonics, two‐center, two‐electron repulsion integrals of the Coulomb, hybrid, and exchange type are done analytically using Slater‐type orbitals. Computer algebra and integer arithmetic are used to obtain...
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| Veröffentlicht in: | Journal of computational chemistry 1991-12, Vol.12 (10), p.1217-1222 |
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| container_title | Journal of computational chemistry |
| container_volume | 12 |
| creator | Jones, Herbert W. |
| description | Using the Löwdin alpha‐function method in which displaced orbitals are expanded in spherical harmonics, two‐center, two‐electron repulsion integrals of the Coulomb, hybrid, and exchange type are done analytically using Slater‐type orbitals. Computer algebra and integer arithmetic are used to obtain analytic results and avoid cancellation errors by the generation of rational matrix elements for C, E, and F matrices that are used to express the α‐function. The formula for the exchange integral is kept simple by reversing the order of integration over each part of a split quadrant. Only two basic integrals are used that are first efficiently evaluated by using look‐up tables and then used repeatedly. |
| doi_str_mv | 10.1002/jcc.540121008 |
| format | Article |
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Computer algebra and integer arithmetic are used to obtain analytic results and avoid cancellation errors by the generation of rational matrix elements for C, E, and F matrices that are used to express the α‐function. The formula for the exchange integral is kept simple by reversing the order of integration over each part of a split quadrant. Only two basic integrals are used that are first efficiently evaluated by using look‐up tables and then used repeatedly.</description><identifier>ISSN: 0192-8651</identifier><identifier>EISSN: 1096-987X</identifier><identifier>DOI: 10.1002/jcc.540121008</identifier><identifier>CODEN: JCCHDD</identifier><language>eng</language><publisher>New York: John Wiley & Sons, Inc</publisher><subject>Atomic and molecular physics ; Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations) ; Electronic structure of atoms, molecules and their ions: theory ; Exact sciences and technology ; Physics</subject><ispartof>Journal of computational chemistry, 1991-12, Vol.12 (10), p.1217-1222</ispartof><rights>Copyright © 1991 John Wiley & Sons, Inc.</rights><rights>1992 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2678-dc9b726be6dd9b2ff652ec299e0b94e554ac13648fc750e18bd1f79a87a693373</citedby><cites>FETCH-LOGICAL-c2678-dc9b726be6dd9b2ff652ec299e0b94e554ac13648fc750e18bd1f79a87a693373</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fjcc.540121008$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fjcc.540121008$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=5080674$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Jones, Herbert W.</creatorcontrib><title>Analytic Löwdin alpha-function method for two-center electron-repulsion integrals over slater-type orbitals</title><title>Journal of computational chemistry</title><addtitle>J. Comput. Chem</addtitle><description>Using the Löwdin alpha‐function method in which displaced orbitals are expanded in spherical harmonics, two‐center, two‐electron repulsion integrals of the Coulomb, hybrid, and exchange type are done analytically using Slater‐type orbitals. Computer algebra and integer arithmetic are used to obtain analytic results and avoid cancellation errors by the generation of rational matrix elements for C, E, and F matrices that are used to express the α‐function. The formula for the exchange integral is kept simple by reversing the order of integration over each part of a split quadrant. Only two basic integrals are used that are first efficiently evaluated by using look‐up tables and then used repeatedly.</description><subject>Atomic and molecular physics</subject><subject>Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations)</subject><subject>Electronic structure of atoms, molecules and their ions: theory</subject><subject>Exact sciences and technology</subject><subject>Physics</subject><issn>0192-8651</issn><issn>1096-987X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1991</creationdate><recordtype>article</recordtype><recordid>eNp9kM1OxCAUhYnRxPFn6b4LtyjQAmVpRh1_JhoTjcYNoRQUxbYBxnFezBfwxcSMmbhydXNzvnPuzQFgD6MDjBA5fNH6gFYIk7zVa2CEkWBQ1PxhHYwQFgTWjOJNsBXjC0KopKwaAX_UKb9IThfTr89567pC-eFZQTvrdHJ9V7yZ9Ny3he1DkeY91KZLJhTGG51C38FghpmPP6DLwlNQPhb9eyaiVxmEaTGYog-NS1nZARs2D7P7O7fB3enJ7fgMTq8n5-OjKdSE8Rq2WjScsMawthUNsZZRYjQRwqBGVIbSSmlcsqq2mlNkcN202HKhaq6YKEtebgO4zNWhjzEYK4fg3lRYSIzkT1UyVyVXVWV-f8kPKmrlbVCddnFloqhGjFcZ40ts7rxZ_J8pL8bjvwd-H3IxmY-VU4VXyXjJqby_msjLCbl9vDxm8qb8BtDei-w</recordid><startdate>199112</startdate><enddate>199112</enddate><creator>Jones, Herbert W.</creator><general>John Wiley & Sons, Inc</general><general>Wiley</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>199112</creationdate><title>Analytic Löwdin alpha-function method for two-center electron-repulsion integrals over slater-type orbitals</title><author>Jones, Herbert W.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2678-dc9b726be6dd9b2ff652ec299e0b94e554ac13648fc750e18bd1f79a87a693373</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1991</creationdate><topic>Atomic and molecular physics</topic><topic>Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations)</topic><topic>Electronic structure of atoms, molecules and their ions: theory</topic><topic>Exact sciences and technology</topic><topic>Physics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jones, Herbert W.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Journal of computational chemistry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jones, Herbert W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analytic Löwdin alpha-function method for two-center electron-repulsion integrals over slater-type orbitals</atitle><jtitle>Journal of computational chemistry</jtitle><addtitle>J. Comput. Chem</addtitle><date>1991-12</date><risdate>1991</risdate><volume>12</volume><issue>10</issue><spage>1217</spage><epage>1222</epage><pages>1217-1222</pages><issn>0192-8651</issn><eissn>1096-987X</eissn><coden>JCCHDD</coden><abstract>Using the Löwdin alpha‐function method in which displaced orbitals are expanded in spherical harmonics, two‐center, two‐electron repulsion integrals of the Coulomb, hybrid, and exchange type are done analytically using Slater‐type orbitals. Computer algebra and integer arithmetic are used to obtain analytic results and avoid cancellation errors by the generation of rational matrix elements for C, E, and F matrices that are used to express the α‐function. The formula for the exchange integral is kept simple by reversing the order of integration over each part of a split quadrant. Only two basic integrals are used that are first efficiently evaluated by using look‐up tables and then used repeatedly.</abstract><cop>New York</cop><pub>John Wiley & Sons, Inc</pub><doi>10.1002/jcc.540121008</doi><tpages>6</tpages></addata></record> |
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| ispartof | Journal of computational chemistry, 1991-12, Vol.12 (10), p.1217-1222 |
| issn | 0192-8651 1096-987X |
| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Atomic and molecular physics Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations) Electronic structure of atoms, molecules and their ions: theory Exact sciences and technology Physics |
| title | Analytic Löwdin alpha-function method for two-center electron-repulsion integrals over slater-type orbitals |
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