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We find that the approximation error decreases exponentially with TT-rank for all systems studied and identify quantized tensor train as the most efficient TT format. Furthermore, we identify quasi-periodic and symmetric structures\u2014including graphene, graphite layers, and polyalanine helices\u2014as particularly favorable candidates exhibiting sublinear rank growth with system size. The tensor train approach automatically compresses quasi-symmetries and systems with symmetry defects, which makes it an attractive approach for materials science applications. TT-Cross-Orth enforces orthogonality during the decomposition, thereby improving stability and reducing the number of function evaluations compared to standard TT-Cross. These findings establish an empirical foundation for the development of scalable tensor network methods for HF and DFT.<\/jats:p>","DOI":"10.1063\/5.0327459","type":"journal-article","created":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T14:21:58Z","timestamp":1791901318000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Tensor train compression of molecular orbitals"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-5629-6237","authenticated-orcid":false,"given":"Ruslan A.","family":"Mallaev","sequence":"first","affiliation":[{"name":"Terra Quantum AG , St. Gallen 9000,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9524-948X","authenticated-orcid":false,"given":"Dmitry","family":"Morozov","sequence":"additional","affiliation":[{"name":"Terra Quantum AG , St. Gallen 9000,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dmitry","family":"Zheltkov","sequence":"additional","affiliation":[{"name":"Terra Quantum AG , St. Gallen 9000,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7912-1750","authenticated-orcid":false,"given":"Michael R.","family":"Perelshtein","sequence":"additional","affiliation":[{"name":"Terra Quantum AG , St. Gallen 9000,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3555-6263","authenticated-orcid":false,"given":"Roman","family":"Ellerbrock","sequence":"additional","affiliation":[{"name":"Terra Quantum AG , St. Gallen 9000,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,13]]},"reference":[{"key":"2026101310205517900_c1","doi-asserted-by":"publisher","first-page":"7498","DOI":"10.1021\/acs.chemrev.2c00704","article-title":"Computational approaches for organic semiconductors: From chemical and physical understanding to predicting new materials","volume":"123","year":"2023","journal-title":"Chem. 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