{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:26:40Z","timestamp":1760243200115,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2014,3,14]],"date-time":"2014-03-14T00:00:00Z","timestamp":1394755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>A new approach to solving the Time-Dependent Self-Consistent-Field equations is developed based on the double quotient formulation of Tsiper 2001 (J. Phys. B). Dual channel, quasi-independent non-linear optimization of these quotients is found to yield convergence rates approaching those of the best case (single channel) Tamm-Dancoff approximation. This formulation is variational with respect to matrix truncation, admitting linear scaling solution of the matrix-eigenvalue problem, which is demonstrated for bulk excitons in the polyphenylene vinylene oligomer and the (4,3) carbon nanotube segment.<\/jats:p>","DOI":"10.3390\/computation2010001","type":"journal-article","created":{"date-parts":[[2014,3,14]],"date-time":"2014-03-14T13:18:11Z","timestamp":1394803091000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations"],"prefix":"10.3390","volume":"2","author":[{"given":"Matt","family":"Challacombe","sequence":"first","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}]}],"member":"1968","published-online":{"date-parts":[[2014,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1757","DOI":"10.1002\/cphc.200900268","article-title":"Charge-transfer excitations and time-dependent density functional theory: Problems and some proposed solutions","volume":"10","author":"Autschbach","year":"2009","journal-title":"ChemPhysChem"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"144108","DOI":"10.1063\/1.3243819","article-title":"An improved long-range corrected hybrid functional with vanishing Hartree-Fock exchange at zero interelectronic distance (LC2gau-BOP)","volume":"131","author":"Song","year":"2009","journal-title":"J. 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