  The $\kappa$-(ET)$_2$X layered conductors (where ET stands for BEDT-TTF) are
studied within the dimer model as a function of the diagonal hopping $t^\prime$
and Hubbard repulsion $U$. Antiferromagnetism and d-wave superconductivity are
investigated at zero temperature using variational cluster perturbation theory
(V-CPT). For large $U$, N\'eel antiferromagnetism exists for $t' < t'_{c2}$,
with $t'_{c2}\sim 0.9$. For fixed $t'$, as $U$ is decreased (or pressure
increased), a $d_{x^2-y^2}$ superconducting phase appears. When $U$ is
decreased further, the a $d_{xy}$ order takes over. There is a critical value
of $t'_{c1}\sim 0.8$ of $t'$ beyond which the AF and dSC phases are separated
by Mott disordered phase.
