  In order to explore the spin accumulation, evaluating the spin galvanic and
spin Hall effect, we utilize the semi-classical Boltzmann equation based on
input from the relativistic Korringa-Kohn-Rostoker Green's function method,
within the density functional theory. We calculate the spin accumulation
including multiple contributions, especially skew-scattering (scattering-in
term) and compare this to three different approximations, which include the
isotropic and anisotropic relaxation time approximation. For heavy metals, with
strong intrinsic spin-orbit coupling, we find that almost all the effects are
captured within the anisotropic relaxation time approximation. On the other
hand, in light metals the contributions from the vertex corrections
(scattering-in term) are comparable to the induced effect in anisotropic
relaxation time approximation. We put a particular focus on the influence of
the atomic character of the substitutional impurities on the spin accumulation
as well as the dependence on the impurity position. As impurities will break
space inversion symmetry of the thin film, this will give rise to both
symmetric and antisymmetric contributions to the spin accumulation. In general,
we find the impurities at the surface generate the largest efficiency of
charge-to-spin conversion in case of the spin accumulation. Comparing our
results to existing experimental findings for Pt we find a good agreement.
