  A new method is presented that allows for efficient evaluation of spin-orbit
coupling (SOC) in density-functional theory calculations. In the so-called
second-variational scheme, where Kohn-Sham functions obtained in a
scalar-relativistic calculation are employed as a new basis for the
spin-orbit-coupled problem, we introduce a rich set of local orbitals as
additional basis functions. Also relativistic local orbitals can be used. The
method is implemented in the all-electron full-potential code \exciting. We
show that, for materials with strong SOC effects, this approach can reduce the
overall basis-set size and thus computational costs tremendously.
