  Interpolating the exchange-correlation energy along the density-fixed
adiabatic connection of density functional theory is a promising way to build
approximations that are not biased towards the weakly correlated regime. These
interpolations can be done at the global (integrated over all spaces) or at the
local level, using energy densities. Many features of the relevant energy
densities as well as several different ways to construct these interpolations,
including comparisons between global and local variants, are investigated here
for the analytically solvable Hooke's atom series, which allows for an
exploration of different correlation regimes. We also analyze different ways to
define the correlation kinetic energy density, focusing on the peak in the
kinetic correlation potential.
