  We present here novel insight into exchange-correlation functionals in
density functional theory, based on the viewpoint of optimal transport. We show
that in the case of two electrons and in the semiclassical limit, the exact
exchange-correlation functional reduces to a very interesting functional of
novel form, which depends on an optimal transport map $T$ associated with a
given density $\rho$. Since the above limit is strongly correlated, the limit
functional yields insight into electron correlations. We prove the existence
and uniqueness of such an optimal map for any number of electrons and each
$\rho$, and determine the map explicitly in the case when $\rho$ is radially
symmetric.
