  The phase stability of the various crystalline structures of the super-heavy
element Copernicium was determined based on the first-principles calculations
with different levels of the relativistic effects. We utilized the Darwin term,
mass-velocity, and spin-orbit interaction with the single electron framework of
the density functional theory while treating the exchange and correlation
effects using local density approximations. It is found that the spin-orbit
coupling is the key component to stabilize the body-centered cubic ($bcc$)
structure over the hexagonal closed packed ($hcp$) structure, which is in
accord with Sol. Stat. Comm. 152 (2012) 530, but in contrast to Sol. Stat.
Comm. 201 (2015) 88, Angew. Chem. 46 (2007) 1663, Handbook of Elemental Solids
Z=104-112 (Springer 2015). It seems that the main role here is the correct
description of the semi-core relativistic $6p_{1/2}$ orbitals. The all other
investigated structures, i.e. face-centered cubic ($fcc$), simple cubic ($sc$)
as well as rhombohedral ($rh$) structures are higher in energy. The criteria of
mechanical stability were investigated based on the calculated elastic
constants, identifying the phase instability of $fcc$ and $rh$ structures, but
surprisingly confirm the stability of the energetically higher $sc$ structure.
In addition, the pressure-induced structural transition between two stable $sc$
and $bcc$ phases has been detected. The ground-state $bcc$ structure exhibits
the highest elastic anisotropy from single elements of the Periodic table. At
last, we support the experimental findings that Copernicium is a metal.
