  The exact static and time-dependent Kohn-Sham (KS) exchange-correlation (xc)
potential is extremely challenging to approximate as it is a local
multiplicative potential that depends on the electron density everywhere in the
system. The KS approach can be generalised by allowing part of the potential to
be spatially nonlocal. We take this nonlocal part to be that of unrestricted
Hartree-Fock theory. The additional local correlation potential in principle
ensures that the single-particle density exactly equals the many-body density.
In our case, the local correlation potential is predominantly nearsighted in
its dependence on the density and hence an (adiabatic) local density
approximation to this potential yields accurate ground-state properties and
real-time densities for one-dimensional test systems.
