Regional virial relations for arbitrary subsystems of particles of a molecule with nuclear motion quantum mechanically described

The partition of a molecule in different regions where virial relations are fulfilled has been proved in the literature to be a fruitful scheme for the description of molecular properties. However, the conceptual importance of this approach is somewhat diminished by the fact that nuclei are considered to occupy successive fixed positions. We show that this restriction can in fact be relaxed when such partitions of molecules are considered. The conditions that density functions must fulfill on the surfaces of such regions, when the nuclear motion is taken into account, are found. Using these conditions, we have examined general cases where the nuclear motion may introduce important modifications of the surfaces defined by the usual condition of zero flux on the one‐particle density corresponding to the fixed nuclei model. Finally a further generalization is introduced by considering partitions of subsystems of particles of the system.