We use the Gutzwiller Density Functional Theory to calculate ground-state properties and bandstructures of iron in its body-centered-cubic (bcc) and hexagonal-close-packed (hcp) phases. For a Hubbard interaction $U=9, {rm eV}$ and Hunds-rule coupling $J=0.54, {rm eV}$ we reproduce the lattice parameter, magnetic moment, and bulk modulus of bcc iron. For these parameters, bcc is the ground-state lattice structure at ambient pressure up to a pressure of $p_{rm c}=41, {rm GPa}$ where a transition to the non-magnetic hcp structure is predicted, in qualitative agreement with experiment ($p_{rm c}^{rm exp}=10ldots 15, {rm GPa}$). The calculated bandstructure for bcc iron is in good agreement with ARPES measurements. The agreement improves when we perturbatively include the spin-orbit coupling.
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