Entanglement transmitted Through-Space

In a few recent articles, we have published the grounds of a theory that describes a new kind of entanglement occurring among two sets of virtual excitations involving one-particle molecular states or molecular orbitals (MO). Its first applications were focused to show a straight relationship between vicinal NMR J-couplings transmitted through covalent bonds and entangled excitations that involve the main coupling pathways. In this article, we show that such an entanglement also occurs when the set of excitations are connected through-space (TS). We have selected for its first application J-couplings that occurs among the following pairs of nuclei: Phosphorus-Phosphorus, Phosphorus-Carbon, and Nitrogen-Fluorine. We found that the linearity of the correlation between TS J-couplings and the entangled excitations is highly sensitive to the level of electron correlation included in the calculations within polarization propagators, with significant improvement from first-order or RPA to second-order or SOPPA, particularly for hydrogen-bonded systems.