Accurate relativistic density functional calculations for the solid-state of metallic francium.

Bulk properties of the heaviest known Group 1 element francium are investigated by using density functional theory within the projector augmented wave method including scalar relativistic and spin-orbit corrections as well as zero-point vibrational effects. The accuracy of our method is tested for lithium and sodium where we find that the PBEsol functional describes the properties of these elements extremely well. This gives confidence for the accurate prediction of the cohesive energy differences between the different proposed phases of francium. We find that francium fits nicely within the periodic trend of the Group 1 metals with a predicted low temperature close packed structure (hcp or fcc or Barlow mixtures between those two), and with the bcc phase being slightly less stable.