  We present two methods of calculating the spatial entanglement of an
interacting electron system within the framework of density-functional theory.
These methods are tested on the model system of Hooke's atom for which the
spatial entanglement can be calculated exactly. We analyse how the strength of
the confining potential affects the spatial entanglement and how accurately the
methods that we introduced reproduce the exact trends. We also compare the
results with the outcomes of standard first-order perturbation methods. The
accuracies of energies and densities when using these methods are also
considered.
