13C and 19F nucleus–electron correlation and self-energies

We present a theoretical and numerical study of the correlation between electrons and the fermionic 13C and 19F nuclei. We use the random-phase approximation (RPA) as a valuable tool in obtaining these correlation energies. A special connection between the RPA and second-order perturbation theory for the inter-fermionic interaction is outlined. Subsequently, Green's function-based GW self-energies are evaluated for the nuclear densities. The strong influence of self-interaction errors is demonstrated, and vertex corrections are shown to be strictly necessary to obtain reasonable results. The theoretical and technical requirements for a quantum mechanical treatment of 13C and 19F nuclei are also addressed in this study, thereby facilitating further research in this area.