  The physical regions (domains or basins) within the molecular structure are
open systems that exchange charge between them and consequently house a
fractional number of electrons (net charge). The natural framework describing
the quantum states for these domains is the density matrix (DM) in its
grand-canonical version which corresponds to a convex expansion into a set of
basis states of an integer number of electrons. In this report, it is shown
that the solution for these quantities is supported by the DM expansion into
three states of different number of particles, the neutral and two (edge) ionic
states. The states and the average number of particles in the domains
(fractional occupation population) are determined by the coefficients of the
expansion in terms of the fundamental transference magnitudes revealing the
donor/acceptor character of the domains by which the quantum accessible states
are discussed.
