The concept of an atom in a molecule is undefined in quantum mechanics. Consequently, very useful properties like atomic charges, bond orders, and so on cannot be rigorously defined. There are many methods for defining these and other atomic quantities for atoms in a molecule. All of these methods are arbitrary and just try to satisfy principles that one might expect to be important.
One of the main strategies for defining atomic charges is based on partitioning the electron density into atomic regions and integrating the density of this atomic region.
A big reason one would want to define an atomic charge is to parameterize a force field. Force fields often work by calculating an energy for every atom in a system and then summing these atomic energies to get the total energy.
Have there been any attempts to directly define an atomic energy from a density partitioning scheme? In particular, is there any way to divide the total electronic energy of a molecular system into atomic components describing the electronic stabilization contributed by a particular atom?
This would be a rather strange quantity in many ways, but it is also a quantity commonly calculated in force fields, so even an approximate definition of this based on quantum mechanically calculated densities seems like it would be of interest.