Entanglement is at the core of quantum physics and so, one may conjecture that it should have some influence on atomic and molecular response properties. The usual way of treating entanglement is by applying information theory via the von Newman entropy. Given that the principal propagator is the operator that contains the physical information that arises due to the transmission of the effects of two external perturbations through the electronic framework of a quantum system, it should have in it the information necessary to quantify the likely entanglement among molecular orbital excitations. In this article we first propose a proper density matrix and from it, the way to quantify entangled excitations by using information theory. The NMR J-couplings are among the best candidates to learn about the potentialities of this formalism. We applied this new tool to analyze the famous Karplus rule and found a relationship between the dihedral angular dependence and the entanglement. We also found that the entangled excitations are related to electron correlation. The new formalism can be applied to all other response properties.

In modern physics, the entanglement between quantum states is a well-established phenomenon. Going one step forward, one can conjecture the likely existence of an entanglement between excitations of one-particle quantum states. Working with a density matrix that is well defined within the polarization propagator formalism, together with information theory, we found that the quantum origin of, at least, few molecular response properties can be described by the entanglement between two pairs of virtual excitations of molecular orbitals (MOs). With our model, we are able to bring new insights into the electronic mechanisms that are behind the transmission, and communication, of the effects of a given perturbation to the whole electronic system described by the Hamiltonian of an unperturbed quantum system. With our entanglement model, we analyzed the electronic origin of the Karplus rule of nuclear magnetic resonance spectroscopy, a well-known empirical phenomenon, and found that this rule is straightforwardly related to the behavior of entangled MO excitations. The model compound used to show it is the H2O2 molecule.