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We analyze two approaches to the problem: the one-step approach, where both effects are treated simultaneously, and the two-step state interaction approach. We report an implementation of the ab initio density matrix renormalization group with a one-step treatment of the SOC effect, which can be compared to prior two-step treatments on an equal footing. Using a dysprosium octahedral complex and bridged dimer as benchmark systems, we identify characteristics of problems where the one-step approach is beneficial for obtaining the low-energy spectrum.<\/jats:p>","DOI":"10.1063\/5.0107805","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T16:05:05Z","timestamp":1664467505000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":19,"title":["A comparison between the one- and two-step spin\u2013orbit coupling approaches based on the <i>ab initio<\/i> density matrix renormalization group"],"prefix":"10.1063","volume":"157","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0086-0388","authenticated-orcid":false,"given":"Huanchen","family":"Zhai","sequence":"first","affiliation":[{"name":"Division of Chemistry and Chemical Engineering, California Institute of Technology , Pasadena, California 91125, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8009-6038","authenticated-orcid":false,"given":"Garnet Kin-Lic","family":"Chan","sequence":"additional","affiliation":[{"name":"Division of Chemistry and Chemical Engineering, California Institute of Technology , Pasadena, California 91125, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2022,10,26]]},"reference":[{"key":"2023102600035802700_c1","doi-asserted-by":"publisher","first-page":"1648","DOI":"10.1039\/c3cc48866g","article-title":"Beyond the anisotropy barrier: Slow relaxation of the magnetization in both easy-axis and easy-plane Ln (trensal) complexes","volume":"50","year":"2014","journal-title":"Chem. 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