  It has been predicted theoretically and found experimentally that magnetic
impurities induce localized bound states within the superconducting energy gap,
called Yu-Shiba-Rusinov (YSR) states. Combining symmetry analysis with
experimental findings provides a convincing argument for the energy splitting
and distribution of the YSR peaks, but the full details of the electronic
structure remain elusive and simple models with point scatterers lack the full
orbital complexity required to meet this challenge. In this work we combine a
Greens function based first-principles method, which incorporates a
phenomenological parameterization of the superconducting state, with orbitally
complex impurity potentials to make material-specific predictions of realistic
systems. We study the effect of 3d transition elements on the superconducting
energy gap of a Pb (001) surface. Not only do we find a good agreement with
experiment, we also show that the energetic position, strength and orbital
composition of the YSR states depend strongly on the chemical makeup of the
impurity and its position with respect to the surface. Such quantitative
results cannot be derived from simplified models but require full material
specific calculations.
