Toward a formulation of a CISS theory with the inclusion of two-particle relativistic effects, electron-phonon coupling, and electron-electron correlation. An application to NMR-based chiral discrimination.

The current status of the theoretical foundations of the Chiral-Induced Spin Selectivity (CISS) effect has substantially improved from its original one-electron formulation. However, there is a need to improve the inclusion of electron-vibrational interaction, the exchange and correlation effects arising from electron-electron interactions, and non-Born-Oppenheimer 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-Pauli many-particle Hamiltonian. In particular, we determine in this context the effect that including non-Born-Oppenheimer components arising in a Taylor expansion of the electron-nuclear potential has on the spin-orbit coupling term of this Hamiltonian. We also consider in this framework the electron-electron exchange and correlation effects and propose some practical approximations based on non-relativistic approaches. Finally, we extend the application of the Breit-Pauli Hamiltonian to describe nuclear-nuclear spin interactions and discuss the possibility of explaining enantiomeric selectivity in cross-polarization nuclear magnetic resonance experiments.