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This paper focuses on four isomers, namely the X2PO4I (X = Pb, Sn, Ba, and Sr) series. For the first time, the paper\u2019s attention is paid to the changes in electronic structure, as well as refractive indices and birefringence, with and without the inclusion of spin\u2013orbit effects in this series. The first-principles results show that spin\u2013orbit effects of the 5p and 6p states found in these compounds lead to splitting of the bands, narrowing of the band gap, enhancement of the lone-pair stereochemistry, and enhancement of the refractive indices and birefringence. Moreover, a comparison of the lone-pair electron phosphates, X2PO4I (X = Pb and Sn), and the isomeric alkaline earth metal phosphates, X2PO4I (X = Ba and Sr), reveals that changes in the band structure have a greater effect on the enhancement of the birefringence than the slight enhancement of the lone-pair stereochemical activity. This study has important implications for a deeper understanding of the optical properties of crystals and the design of novel optical materials.<\/jats:p>","DOI":"10.3390\/nano14070617","type":"journal-article","created":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T05:44:36Z","timestamp":1711950276000},"page":"617","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["The Spin\u2013Orbit Effect on the Electronic Structures, Refractive Indices, and Birefringence of X2PO4I (X = Pb, Sn, Ba and Sr): A First-Principles Investigation"],"prefix":"10.3390","volume":"14","author":[{"given":"Xudong","family":"Leng","sequence":"first","affiliation":[{"name":"Xinjiang Key Laboratory of Solid State Physics and Devices, School of Physical Science and Technology, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mei","family":"Hu","sequence":"additional","affiliation":[{"name":"Xinjiang Key Laboratory of Solid State Physics and Devices, School of Physical Science and Technology, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1801-2638","authenticated-orcid":false,"given":"Qun","family":"Jing","sequence":"additional","affiliation":[{"name":"Xinjiang Key Laboratory of Solid State Physics and Devices, School of Physical Science and Technology, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiming","family":"Duan","sequence":"additional","affiliation":[{"name":"Xinjiang Key Laboratory of Solid State Physics and Devices, School of Physical Science and Technology, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Henglei","family":"Chen","sequence":"additional","affiliation":[{"name":"Xinjiang Key Laboratory of Solid State Physics and Devices, School of Physical Science and Technology, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiuhua","family":"Cui","sequence":"additional","affiliation":[{"name":"Xinjiang Key Laboratory of Solid State Physics and Devices, School of Physical Science and Technology, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e2118675119","DOI":"10.1073\/pnas.2118675119","article-title":"Synergistic dual conversion reactions assisting Pb-S electrochemistry for energy storage","volume":"119","author":"Xu","year":"2022","journal-title":"Proc. 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