  Constrained electronic-structure theories enable the construction of
effective low-energy models consisting of partially dressed particles. Since
the interpretation and physical content of these theories is not
straightforward, we investigate the minimal example of partially dressed
phonons in small molecules to explore the properties of constrained
density-functional perturbation theory (cDFPT). We show that the dipole
selection rules determine whether the partially dressed phonons satisfy
Goldstone's theorem and we proof that electronic screening always lowers the
phonon frequencies. We illustrate the theory with calculations for nitrogen and
benzene.
