  We present an efficient algorithm for one- and two-component relativistic
exact-decoupling calculations. Spin-orbit coupling is thus taken into account
for the evaluation of relativistically transformed (one-electron) Hamiltonian.
As the relativistic decoupling transformation has to be evaluated with
primitive functions, the construction of the relativistic one-electron
Hamiltonian becomes the bottleneck of the whole calculation for large
molecules. For the established exact-decoupling protocols, a minimal matrix
operation count is established and discussed in detail. Furthermore, we apply
our recently developed local DLU scheme [J. Chem. Phys. 136 (2012) 244108] to
accelerate this step. With our new implementation two-component relativistic
density functional calculations can be performed invoking the
resolution-of-identity density-fitting approximation and (Abelian as well as
non-Abelian) point group symmetry to accelerate both the exact-decoupling and
the two-electron part. The capability of our implementation is illustrated at
the example of silver clusters with up to 309 atoms, for which the cohesive
energy is calculated and extrapolated to the bulk.
