Energy dependence with the number of particles: Density and reduced density matrices functionals

The energy of a physical domain within a molecular system considered as a quantum open system is analyzed as a functional of the electron distribution dependence with the number of particles. Our attention is focused upon the constrained-search functionals of the electron density, the 1- and 2-reduced density matrices (1-, 2-RDMs) for grand-canonical states. It is shown that functionals of the 2-RDM depend on the number of particles if the ground state energy is not a convex function of them.