62We analyze the physical grounds of common approaches used to model the dependency of the ground state energy on the number of electrons in molecular systems (E vs. N models). We elaborate on a recent result indicating that smooth interpolation models are inconsistent with the popular grand ensemble approach to open quantum systems, and we illustrate this discrepancy using the parabolic and exponential E vs. N models. Unlike most previous considerations of this problem, we explicitly account for the possibility of degenerate ground states and nonconvexity of the energy.