{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T13:08:39Z","timestamp":1788872919555,"version":"build-2803163510"},"reference-count":106,"publisher":"American Chemical Society (ACS)","issue":"17","license":[{"start":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T00:00:00Z","timestamp":1787788800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T00:00:00Z","timestamp":1787788800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T00:00:00Z","timestamp":1787788800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NSFC)","doi-asserted-by":"crossref","award":["22233001"],"award-info":[{"award-number":["22233001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NSFC)","doi-asserted-by":"crossref","award":["22473013"],"award-info":[{"award-number":["22473013"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We report the state-averaged spin\u2013orbit driven similarity renormalization group second-order perturbation theory (SA-SO-DSRG-PT2) for efficient computations of spin\u2013orbit coupling (SOC) effects in multireference systems. This approach adopts a set of multiconfigurational reference states obtained with a spin-free relativistic Hamiltonian and introduces SOC during the perturbative treatment of dynamical correlation. Specifically, the zeroth-order Hamiltonian is defined from the spin-free Hamiltonian, while the remaining spin-free contributions and the spin-dependent Hamiltonian enter as first-order perturbations in the DSRG transformation. This formulation generates an SOC-containing SA-DSRG-PT2 effective Hamiltonian while largely preserving the computational cost of the conventional spin-free theory. Two spin-dependent Hamiltonians are examined: the first-order Douglas\u2013Kroll\u2013Hess spin\u2013orbit Hamiltonian with mean-field approximated two-electron contributions and the spin-dependent part of the one-electron X2C Hamiltonian with the screened-nuclear spin\u2013orbit approximation. Benchmarks on main-group atoms and diatomic molecules, transition-metal elements, trivalent lanthanide cations, and actinide dioxide cations show consistent accuracy across the periodic table for both spin-dependent Hamiltonians. Applications to Co(II) single-ion magnets, including systems described with up to 1790 basis functions, further highlight the promise of SA-SO-DSRG-PT2 for efficient SOC calculations in large open-shell molecules.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c01381","type":"journal-article","created":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T19:50:33Z","timestamp":1788292233000},"page":"8910-8923","source":"Crossref","is-referenced-by-count":0,"title":["Simultaneous Treatment\nof Electron Correlation and\nSpin\u2013Orbit Coupling with State-Averaged Driven Similarity Renormalization\nGroup Second-Order Perturbation Theory"],"prefix":"10.1021","volume":"22","author":[{"given":"Meng","family":"Wang","sequence":"first","affiliation":[{"name":"Beijing Normal University , , ,","place":["Beijing, China, 100875"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0059-4174","authenticated-orcid":true,"given":"Chenyang","family":"Li","sequence":"additional","affiliation":[{"name":"Beijing Normal University , , ,","place":["Beijing, China, 100875"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,8,27]]},"reference":[{"key":"2026090808094341500_cit1","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1021\/ar50140a002","article-title":"Relativity and the periodic system of elements","volume":"12","author":"Pyykko\u0308","year":"1979","journal-title":"Acc. 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