  The self-energy-functional approach proposed recently is applied to the
single-band Hubbard model at half-filling to study the Mott-Hubbard
metal-insulator transition within the most simple but non-trivial
approximation. This leads to a mean-field approach which is interesting
conceptually: Trial self-energies from a two-site single-impurity Anderson
model are used to evaluate an exact and general variational principle. While
this restriction of the domain of the functional represents a strong
approximation, the approach is still thermodynamically consistent by
construction and represents a conceptual improvement of the ``linearized DMFT''
which has been suggested previously as a handy approach to study the critical
regime close to the transition. It turns out that the two-site approximation is
able to reproduce the complete (zero and finite-temperature) phase diagram for
the Mott transition. For the critical point at T=0, the entire calculation can
be done analytically. This calculation elucidates different general aspects of
the self-energy-functional theory. Furthermore, it is shown how to deal with a
number of technical difficulties which appear when the self-energy functional
is evaluated in practice.
