{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T19:35:59Z","timestamp":1770752159714,"version":"3.50.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2011]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, the tensor-structured numerical evaluation of the Coulomb and exchange \n\t\t\toperators in the Hartree-Fock equation is supplemented by the usage of recent quantized-TT \n\t\t\t(QTT) formats. It leads to O(log n) complexity at computationally extensive stages in the \n\t\t\trank-structured calculation with the respective 3D Hartree and exchange potentials discretized \n\t\t\ton large n\u00d7n\u00d7n Cartesian grids. The numerical examples for some volumetric organic molecules \n\t\t\tconfirm that the QTT ranks of these potentials are nearly independent of the one-dimension \n\t\t\tgrid size n. Thus, paradoxically, the complexity of the grid-based evaluation of the Coulumb \n\t\t\tand exchange matrices becomes almost independent of the grid size, being regulated only by \n\t\t\tthe structure of a molecular system. As a result, the grid approximation of the Hartree-Fock \n\t\t\tequation allows to gain the high resolution with a guaranteed accuracy.<\/jats:p>","DOI":"10.2478\/cmam-2011-0018","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T16:10:16Z","timestamp":1366042216000},"page":"327-341","source":"Crossref","is-referenced-by-count":18,"title":["QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations"],"prefix":"10.2478","volume":"11","author":[{"given":"Venera","family":"Khoromskaia","sequence":"first","affiliation":[{"name":"1Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany."}]},{"given":"Boris","family":"Khoromskij","sequence":"additional","affiliation":[{"name":"1Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany."}]},{"given":"Reinhold","family":"Schneider","sequence":"additional","affiliation":[{"name":"2TU Berlin, Strasse des 17.Juni 136, D-10623 Berlin, Germany."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/11\/3\/article-p327.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2011-0018\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:56Z","timestamp":1619101316000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/11\/3\/article-p327.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2011-0018","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2011]]}}}