What Is an Atom in a Molecule?

A very interesting question and I have not really thought about before.
Comes from a forum disscusion thread
http://chem8.org/bbs/thread-650-1-1.html

Some contents in a paper read recently
jpca 2005 109 3957

Authors use "minimizing the information loss" method to obtain the definition of atom in a molecule (AIM). And validated the Hirshfeld AIM definition from information-theory viewpoint.

However, "Despite its utility, the atom in a molecule cannot be directly observed by experiment, nor can one measure enough properties of an atom in a molecule to define it unambiguously."

Therefore:"There are multiple ways to partition molecules into atoms that are consistent with various observed chemical trends and experimental data.""Chemical science is built upon the atom, and the atom in molecule is a vital, central chemical concept, yet forever elusive."

If AIM is not completely concrete how could electrons related to them be?This leads to Mulliken Population, NBO...