  The role of frustration and interaction strength on the half-filled Hubbard
model is studied on the square lattice with nearest and next-nearest neighbour
hoppings t and t' using the Variational Cluster Approximation (VCA). At
half-filling, we find two phases with long-range antiferromagnetic (AF) order:
the usual Neel phase, stable at small frustration t'/t, and the so-called
collinear (or super-antiferromagnet) phase with ordering wave-vector $(\pi,0)$
or $(0,\pi)$, stable for large frustration. These are separated by a phase with
no detectable long-range magnetic order. We also find the d-wave
superconducting (SC) phase ($d_{x^2-y^2}$), which is favoured by frustration if
it is not too large. Intriguingly, there is a broad region of coexistence where
both AF and SC order parameters have non-zero values. In addition, the physics
of the metal-insulator transition in the normal state is analyzed. The results
obtained with the help of the VCA method are compared with the large-U
expansion of the Hubbard model and known results for the frustrated J1-J2
Heisenberg model. These results are relevant for pressure studies of undoped
parents of the high-temperature superconductors: we predict that an insulator
to d-wave SC transition may appear under pressure.
