  We have identified excitonic confinement in one-dimensional molecular chains
(i.e. polyacetylene and H$_2$) as the main driving force for the saturation of
the chain polarizability as a function of the number of molecular units. This
conclusion is based on first principles time--dependent density functional
theory calculations performed with a new derived exchange--correlation kernel.
The failure of simple local and semi--local functionals is shown to be related
to the lack of memory effects, spatial ultranonlocality, and self--interaction
corrections. These effects get smaller as the gap of the system reduces, in
which case such simple approximations do perform better.
