Finally, I would like to mention that, unlike ground-state DFT, TDDFT is very poorly understood mathematically. 684 685. Lammert provides a counterexample of a convex and lower semicontinuous function with a (unique) subdifferential that is not differentiable. Thus, this illustrates that convexity and lower semicontinuity are not enough to establish "F = -v", even for variations that stay within the domain of the density functional F[ρ] -that is, Lieb's set of N-representable densities I N .