Molecular Response Properties, Electron Correlation, and Quantum Entanglement

Abstract

There is an ever-increasing interest in studying theproperties and main characteristics of entangled atomic andmolecular quantum states. As a matter of fact, merging twodifferent areas of research like information theory and quantumphysics/chemistry gives new insights to understand from adifferent framework some of the most basic quantum phenomena.In line with this, the calculation and analysis of the electronicorigin 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 propertiescould 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 isdescribed and calculated using the electronic framework. In the past few years, we started the development of a theory thatintroduces a new kind of entanglement that occurs among pairs of excitations of molecular orbitals (MOs). In this work, we give themost general expression of such a theory showing that the entanglement is not dependent on the spin-dependence of the externalperturbations. We applied this theory to the analysis of vicinal J-couplings between fluorine nuclei in 1,2-difluoroethane, and weshow 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 (upto 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 theentanglement among some coupling pathways that contain a couple of excitations of MOs that are close to the coupled nuclei.