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However, there is a need to improve the inclusion of electron\u2013vibrational interaction, the exchange and correlation effects arising from electron\u2013electron interactions, and non-Born\u2013Oppenheimer coupling to enhance the predictive power of the theory and its agreement with experiments. In an attempt to overcome these difficulties, we advance in the present work a microscopic quantum mechanical treatment of CISS based on the relativistic Breit\u2013Pauli many-particle Hamiltonian. In particular, we determine in this context the effect that including non-Born\u2013Oppenheimer components arising in a Taylor expansion of the electron\u2013nuclear potential has on the spin\u2013orbit coupling term of this Hamiltonian. We also consider in this framework the electron\u2013electron exchange and correlation effects and propose some practical approximations based on non-relativistic approaches. Finally, we extend the application of the Breit\u2013Pauli Hamiltonian to describe nuclear\u2013nuclear spin interactions and discuss the possibility of explaining enantiomeric selectivity in cross-polarization nuclear magnetic resonance experiments.<\/jats:p>","DOI":"10.1063\/5.0272982","type":"journal-article","created":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T11:32:52Z","timestamp":1758713572000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Toward a formulation of a CISS theory with the inclusion of two-particle relativistic effects, electron\u2013phonon coupling, and electron\u2013electron correlation. An application to NMR-based chiral discrimination"],"prefix":"10.1063","volume":"163","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1381-7194","authenticated-orcid":false,"given":"Eduardo V.","family":"Lude\u00f1a","sequence":"first","affiliation":[{"name":"School of Physical Sciences and Nanotechnology, Yachay Tech University 1 , Urcuqui,","place":["Ecuador"]},{"name":"Chemistry Center, Venezuelan Institute for Scientific Research, IVIC 2 , Apartado 21827, Caracas 1020A,","place":["Venezuela"]},{"name":"Donostia International Physics Center, DIPC 3 , Paseo Manuel de Lardizabal, 4, 20018 Donostia-San Sebastian,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8980-9751","authenticated-orcid":false,"given":"Jesus M.","family":"Ugalde","sequence":"additional","affiliation":[{"name":"Donostia International Physics Center, DIPC 3 , Paseo Manuel de Lardizabal, 4, 20018 Donostia-San Sebastian,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2711-3588","authenticated-orcid":false,"given":"Xabier","family":"Lopez","sequence":"additional","affiliation":[{"name":"Donostia International Physics Center, DIPC 3 , Paseo Manuel de Lardizabal, 4, 20018 Donostia-San Sebastian,","place":["Spain"]},{"name":"Department of Chemistry, Euskal Herriko Univertsitatea 4 , Donostia,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4151-5628","authenticated-orcid":false,"given":"Louis-S.","family":"Bouchard","sequence":"additional","affiliation":[{"name":"Department of Chemistry and Biochemistry, University of California Los Angeles 5 , 607 Charles E. 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