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In particular, for a model Hamiltonian representing a molecular system with an even number of electrons interacting via a two-body (Hubbard) interaction and a spin\u2013orbit coupling, we show that a meaningful nonzero Berry force emerges whenever there is spin unrestriction\u2014even though the Hamiltonian is real-valued and formally the on-diagonal single-surface Berry force must be zero. Moreover, if properly applied, this mean-field Berry force yields roughly the correct asymptotic motion for scattering through an avoided crossing. That being said, within the context of a ground-state calculation, several nuances do arise as far interpreting the Berry force correctly, and as a practical matter, the Berry force diverges near the Coulson\u2013Fischer point (which can lead to numerical instabilities). We do not address magnetic fields here.<\/jats:p>","DOI":"10.1063\/5.0093092","type":"journal-article","created":{"date-parts":[[2022,6,16]],"date-time":"2022-06-16T18:16:17Z","timestamp":1655403377000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["On the meaning of Berry force for unrestricted systems treated with mean-field electronic structure"],"prefix":"10.1063","volume":"156","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6445-7462","authenticated-orcid":false,"given":"Xuezhi","family":"Bian","sequence":"first","affiliation":[{"name":"Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8510-894X","authenticated-orcid":false,"given":"Tian","family":"Qiu","sequence":"additional","affiliation":[{"name":"Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4843-6324","authenticated-orcid":false,"given":"Junhan","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2170-2020","authenticated-orcid":false,"given":"Joseph E.","family":"Subotnik","sequence":"additional","affiliation":[{"name":"Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2022,6,16]]},"reference":[{"key":"2023081004583773100_c1","doi-asserted-by":"publisher","first-page":"8125","DOI":"10.1063\/1.466806","article-title":"Magnetic screening of nuclei by electrons as an effect of geometric vector potential","volume":"100","year":"1994","journal-title":"J. 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