Molecular Response Properties, Electron Correlation, and Quantum Entanglement

There is an ever-increasing interest in studying the properties and main characteristics of entangled atomic and molecular quantum states. As a matter of fact, merging two different areas of research like information theory and quantum physics/chemistry gives new insights to understand from a different framework some of the most basic quantum phenomena. In line with this, the calculation and analysis of the electronic origin of some molecular response properties, like the NMR J-coupling, require the consideration of electron correlation (quantum and classical) and the fact that some response properties could arise from nonlocal interactions. In the case of J-couplings, the change of energy due to the flip-flop of one nuclear magnetic dipole moment that is influenced (directly or indirectly) by the flip-flop of another one has its correlate in the NMR spectra. Besides, from a theoretical perspective, this J-coupling interaction is described and calculated using the electronic framework. In the past few years, we started the development of a theory that introduces a new kind of entanglement that occurs among pairs of excitations of molecular orbitals (MOs). In this work, we give the most general expression of such a theory showing that the entanglement is not dependent on the spin-dependence of the external perturbations. We applied this theory to the analysis of vicinal J-couplings between fluorine nuclei in 1,2-difluoroethane, and we show that there is an entanglement between electron-spin-dependent mechanisms (known as FC and SD) and electron-spin-independent mechanisms (PSO). This entanglement remains lightly dependent on the degree of electron correlation considered (up to the higher RPA level), which confirms previous explanations regarding the physical origin of the empirical Karplus rule. Besides, we show new results for the vicinal J(H, H) coupling in ethane that confirm a direct relationship between the Karplus rule and the entanglement among some coupling pathways that contain a couple of excitations of MOs that are close to the coupled nuclei.