  In this work we present the generalization of the model for chain formation
in break-junctions, introduced by Thiess {\it et al.} [\onlinecite{Alex08}], to
zigzag transition-metal chains with $s$ and $p$ impurities. We apply this
extended model to study the producibility trends for noble-metal chains with
impurities, often present in break junction experiments, namely, Cu, Ag and Au
chains with H, C, O and N adatoms. Providing the material-specific parameters
for our model from systematic full-potential linearized augmented plane-wave
first-principles calculations, we find that the presence of such impurities
crucially affects the binding properties of the noble-metal chains. We reveal
that both, the impurity-induced bond strengthening and the formation of zigzag
bonds, can lead to a significantly enhanced probability for chain formation in
break junctions.
