The exact time-dependent Kohn-Sham (KS) exchange-correlation (xc) potential is not easily approximated due to its nonphysical properties; the burden of capturing xc effects solely within a multiplicative potential gives rise to pathological features, such as spatial steps. The generalization of the KS approach allows one to lessen this burden via an additional, more physical non-local potential. We present unrestricted Hartree-Fock (HF) theory -in which each electron occupies a distinct orbital regardless of its spin -as well as restricted HF, each with a corresponding additional multiplicative correlation potential which in principle ensures the single-particle electron density is exactly equal to the many-body density. The exact form of the local correlation potential when all electrons are permitted to occupy distinct orbitals is largely free from the pathological features which are present in the exact KS-xc potential. Hence we find that an (adiabatic) local density approximation to the correlation potential yields accurate ground-state properties and real-time dynamic densities for one-dimensional few-electron test systems -we compare our results to the exact many-body quantities.arXiv:1909.02510v1 [cond-mat.str-el]