  We propose exchanging the energy functionals in ground-state DFT with
physically equivalent exact force expressions as a new promising route towards
approximations to the exchange-correlation potential and energy. In analogy to
the usual energy-based procedure, we split the force difference between the
interacting and auxiliary Kohn-Sham system into a Hartree, an exchange, and a
correlation force. The corresponding scalar potential is obtained by solving a
Poisson equation, while an additional transverse part of the force yields a
vector potential. These vector potentials obey an exact constraint between the
exchange and correlation contribution and can further be related to the
atomic-shell structure. Numerically, the force-based local-exchange potential
and the corresponding exchange energy compare well with the numerically more
involved optimized effective-potential method. Overall, the force-based method
has several benefits when compared to the usual energy-based approach and opens
a route towards numerically inexpensive non-local and (in the time-dependent
case) non-adiabatic approximations.
