  The adiabatic connection curve of density functional theory (DFT) is
accurately calculated beyond the physical interaction strength for Hooke's
atom, two interacting electrons in a harmonic well potential. Extrapolation of
the accurate curve to the infinite coupling limit agrees well with the strictly
correlated electron (SCE) hypothesis but the approach to this limit is more
complex. The interaction strength interpolation is shown to be a good, but not
perfect, fit to the adiabatic curve. Arguments about the locality of
functionals and convexity of the adiabatic connection curve are examined in
this regime.
