  A detailed account of the implementation of equations of the Relativistic
Density Functional Theory (RDFT) using basis sets of APW/LAPW type with
flexible extensions provided by local orbitals is given. Earlier discoveries of
the importance of the High Derivative Local Orbital (HDLO) extension of
APW/LAPW basis set for enhancing the accuracy of DFT calculations are confirmed
using fully relativistic approach and $\alpha$-U as an example. High Energy
Local Orbitals (HELO's), however indispensable for GW calculations, are
considerably less efficient in enhancing the accuracy of DFT applications. It
is shown, that a simplified approach to the relativistic effects, namely,
considering them only inside the muffin-tin (MT) spheres, produces basically
identical results (as compared to fully relativistic approach) for the
electronic free energy of the five materials considered in this work. By
comparing the effect of the simplified approach on the electronic free energy
with its effect on the electronic kinetic energy we conclude that the
insensitivity of the free energy to the way we describe the relativistic
effects in the interstitial region is related to the variational property of
this quantity.
