{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,3]],"date-time":"2023-09-03T01:51:17Z","timestamp":1693705877348},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,1,1]]},"abstract":"Abstract.<\/jats:title>\nThe Hartree\u2013Fock eigenvalue problem governed by the 3D integro-differential operator\nis the basic model in ab initio<\/jats:italic> electronic structure calculations.\nSeveral years ago the idea to solve the Hartree\u2013Fock equation by a\nfully 3D grid based numerical approach seemed to be a fantasy, and\nthe tensor-structured methods did not exist.\nIn fact, these methods evolved during the work on this challenging problem.\nIn this paper, our recent results on the topic are outlined\nand the black-box Hartree\u2013Fock solver by tensor numerical methods is presented.\nThe approach is based on the rank-structured calculation of the\ncore hamiltonian and of the two-electron integrals tensor\nusing the problem adapted basis functions discretized on $n\\times n\\times n$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> 3D Cartesian\ngrids. The arising 3D convolution transforms with the Newton kernel are\nreplaced by a combination of 1D convolutions and 1D Hadamard and scalar products.\nThe approach allows huge spatial grids, with $n^3\\simeq 10^{15}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>,\nyielding high resolution at low cost.\nThe two-electron integrals are computed via multiple factorizations.\nThe Laplacian Galerkin matrix can be computed \u201con-the-fly\u201d using the quantized\ntensor approximation of $O(\\log n)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> complexity.\nThe performance of the black-box solver in Matlab implementation is compatible with the benchmark\npackages based on the analytical (pre)evaluation of the multidimensional convolution integrals.\nWe present ab initio<\/jats:italic> Hartree\u2013Fock calculations of the ground state energy\nfor the amino acid molecules, and of the \u201cenergy bands\u201d for the model examples\nof extended (quasi-periodic) systems.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0023","type":"journal-article","created":{"date-parts":[[2013,11,7]],"date-time":"2013-11-07T20:11:38Z","timestamp":1383855098000},"page":"89-111","source":"Crossref","is-referenced-by-count":12,"title":["Black-Box Hartree\u2013Fock Solver by Tensor Numerical Methods"],"prefix":"10.1515","volume":"14","author":[{"given":"Venera","family":"Khoromskaia","sequence":"first","affiliation":[{"name":"1Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22\u201326, 04103 Leipzig, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/14\/1\/article-p89.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/cmam\/14\/1\/article-p89.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:47Z","timestamp":1614481427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0023\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,1]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0023","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,1]]}}}