Chemical descriptors, convexity and structure of density matrices in molecular systems

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.