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 $U$, Neel 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.
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