The partitioning of a charge distribution by surfaces exhibiting a local ze
ro flux in the gradient vector field of the electron density leads to an ex
haustive and disjoint division of the system into a set of mono-nuclear reg
ions or atoms, provided the only local attractors present in the system are
isolated nuclear attractors and the electronic energy is less than that re
quired to produce the plasma state. The existence of non-isolated attractor
s, whose limited occurrence is confined primarily to excited state charge d
istributions of one-electron systems, is shown to be readily encompassed wi
thin the topological theory of molecular structure, a theory whose purpose
is to relate a system's properties to the observed topology of its density
distribution. The zero-flux surface serves as the necessary boundary condit
ion for the application of Schwinger's principle oi stationary action to de
fine the physics of an atom in a molecule as an open system. Schwinger's pr
inciple requires the use of a special class of trial functions: those whose
variation is to be equated to the action of smooth, continuous changes in
the coordinates of the physical system caused by the action of generators o
f infinitesimal transformations, the very requirement needed to ensure the
applicability of the zero-flux surface condition as the defining constraint
of an open system.