A second generation of empirical potentials is produced for α-Fe within the framework of the magnetic potential formalism (Dudarev and Derlet 2005 J. Phys.: Condens. Matter 17 7097). This is a parameterization for bcc Fe fitted to a database of material parameters, including ab initio-derived point defect formation energies, third-order elastic constants, and ab initio-derived string potential data, the final two controlling, respectively, the thermal expansion properties and the core structure of the 1/2<111> screw dislocation. The potential produces a non-degenerate configuration for the relaxed 1/2<111> screw dislocation.