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In this work, we introduce, for the first time, the scalar Hamiltonians derived from the Dirac\u2013Coulomb\u2013Gaunt and Dirac\u2013Coulomb\u2013Breit operators based on spin separation in the Pauli quaternion basis. While the widely used spin-free Dirac\u2013Coulomb Hamiltonian includes only the direct Coulomb and exchange terms that resemble nonrelativistic two-electron interactions, the scalar Gaunt operator adds a scalar spin\u2013spin term. The spin separation of the gauge operator gives rise to an additional scalar orbit-orbit interaction in the scalar Breit Hamiltonian. Benchmark calculations of Aun (n = 2\u20138) show that the scalar Dirac\u2013Coulomb\u2013Breit Hamiltonian can capture 99.99% of the total energy with only 10% of the computational cost when real-valued arithmetic is used, compared to the full Dirac\u2013Coulomb\u2013Breit Hamiltonian. The scalar relativistic formulation developed in this work lays the theoretical foundation for the development of high-accuracy, low-cost correlated variational relativistic many-body theory.<\/jats:p>","DOI":"10.1063\/5.0144359","type":"journal-article","created":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T06:07:24Z","timestamp":1683180444000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":19,"title":["Scalar Breit interaction for molecular calculations"],"prefix":"10.1063","volume":"158","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7680-3972","authenticated-orcid":false,"given":"Shichao","family":"Sun","sequence":"first","affiliation":[{"name":"Department of Chemistry, University of Washington 1 , Seattle, Washington 98195, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0150-082X","authenticated-orcid":false,"given":"Jordan","family":"Ehrman","sequence":"additional","affiliation":[{"name":"Department of Chemistry, University of Washington 1 , Seattle, Washington 98195, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9655-7927","authenticated-orcid":false,"given":"Tianyuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Chemistry, University of Washington 1 , Seattle, Washington 98195, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0528-6186","authenticated-orcid":false,"given":"Qiming","family":"Sun","sequence":"additional","affiliation":[{"name":"AxiomQuant Investment Management LLC 2 , Shanghai 200120, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5682-3132","authenticated-orcid":false,"given":"Kenneth G.","family":"Dyall","sequence":"additional","affiliation":[{"name":"Dirac Solutions 3 , Portland, Oregon 97229, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7341-6240","authenticated-orcid":false,"given":"Xiaosong","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Chemistry, University of Washington 1 , Seattle, Washington 98195, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2023,5,4]]},"reference":[{"key":"2024050400020497200_c1","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1098\/rspa.1961.0139","article-title":"Relativistic self-consistent fields","volume":"262","year":"1961","journal-title":"Proc. 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