  The electron energy and density matrices in molecular systems are convex in
respect of the number of particles. So that, the chemical descriptors based on
their derivatives present the hamper of discontinuities for isolated systems
and consequently higher order derivatives are undefined. The introduction of
the interaction between the physical domain with an environment induces a
coherent structure for the density matrix in the grand-canonical formulation
suppressing the discontinuities leading to the proper definitions of the
descriptors.
