{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T23:22:05Z","timestamp":1772234525004,"version":"3.50.1"},"reference-count":35,"publisher":"AIP Publishing","issue":"18","funder":[{"DOI":"10.13039\/501100005416","name":"Norges Forskningsr\u00e5d","doi-asserted-by":"publisher","award":["287950"],"award-info":[{"award-number":["287950"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]},{"name":"UNINETT Sigma2","award":["NN4654k"],"award-info":[{"award-number":["NN4654k"]}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,11,14]]},"abstract":"<jats:p>Non-adiabatic coupling matrix elements (NACMEs) are important in quantum chemistry, particularly for molecular dynamics methods such as surface hopping. However, NACMEs are gauge dependent. This presents a difficulty for their calculation in general, where there are no restrictions on the gauge function except that it be differentiable. These cases are relevant for complex-valued electronic wave functions, such as those that arise in the presence of a magnetic field or spin\u2013orbit coupling. In addition, the Berry curvature and Berry force play an important role in molecular dynamics in a magnetic field and are also relevant in the context of spin\u2013orbit coupling. For methods such as surface hopping, excited-state Berry curvatures will also be of interest. With this in mind, we have developed a scheme for the calculation of continuous, differentiable NACMEs as a function of the molecular geometry for complex-valued wave functions. We demonstrate the efficacy of the method using the H2 molecule at the full configuration\u2013interaction (FCI) level of theory. In addition, ground- and excited-state Berry curvatures are computed for the first time using FCI theory. Finally, Berry phases are computed directly in terms of diagonal NACMEs.<\/jats:p>","DOI":"10.1063\/5.0229854","type":"journal-article","created":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T10:46:38Z","timestamp":1731408398000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Non-adiabatic coupling matrix elements in a magnetic field: Geometric gauge dependence and Berry phase"],"prefix":"10.1063","volume":"161","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6722-0022","authenticated-orcid":false,"given":"Tanner","family":"Culpitt","sequence":"first","affiliation":[{"name":"Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison 1 , 1101 University Ave., Madison, Wisconsin 53706,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0019-4330","authenticated-orcid":false,"given":"Erik I.","family":"Tellgren","sequence":"additional","affiliation":[{"name":"Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo 2 , P.O. Box 1033 Blindern, N-0315 Oslo,","place":["Norway"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6572-8738","authenticated-orcid":false,"given":"Laurens D. M.","family":"Peters","sequence":"additional","affiliation":[{"name":"Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo 2 , P.O. Box 1033 Blindern, N-0315 Oslo,","place":["Norway"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5032-8392","authenticated-orcid":false,"given":"Trygve","family":"Helgaker","sequence":"additional","affiliation":[{"name":"Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo 2 , P.O. 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