  We investigate the construction of approximated exchange-correlation
functionals by interpolating locally along the adiabatic connection between the
weak- and the strong-coupling regimes, focussing on the effect of using
approximate functionals for the strong-coupling energy densities. The gauge
problem is avoided by dealing with quantities that are all locally defined in
the same way. Using exact ingredients at weak coupling we are able to isolate
the error coming from the approximations at strong coupling only. We find that
the nonlocal radius model, which retains some of the non-locality of the exact
strong-coupling regime, yields very satisfactory results. We also use
interpolation models and quantities from the weak- and strong-coupling regimes
to define a correlation-type indicator and a lower bound to the exact
exchange-correlation energy. Open problems, related to the nature of the local
and global slope of the adiabatic connection at weak coupling, are also
discussed.
