A two-orbital model for Fe-pnictide superconductors is investigated using computational techniques on two-dimensional square clusters. The hopping amplitudes are derived from orbital overlap integrals, or by band structure fits, and the spin frustrating effect of the plaquette-diagonal Fe-Fe hopping is remarked. A spin striped state is stable in a broad range of couplings in the undoped regime, in agreement with neutron scattering. Adding two electrons to the undoped ground state of a small cluster, the dominant pairing operators are found. Depending on parameters, two pairing operators were identified: they involve inter-xz-yz orbital combinations forming spin singlets or triplets, transforming according to the B_2g and A_2g representations of the D_4h group, respectively.
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