By means of ab initio calculations in conjunction with the random-phase approximation (RPA) within the full-potential linearized augmented plane wave method, we study the screening of the Coulomb interaction in ${\mathrm{Nb}}_x\mathrm{Co}$ ($1\le x\le 9$) clusters. In addition, these results are compared with pure bcc Nb bulk. We find that for all clusters the on-site Coulomb interaction in RPA is strongly screened, whereas the intersite nonlocal Coulomb interaction is weakly screened and for some clusters it is unscreened or even antiscreened. This is in strong contrast with pure Nb bulk, where the intersite Coulomb interaction is almost completely screened. Furthermore, constrained RPA calculations reveal that the contribution of the Co $3d \to 3d$ channel to the total screening of the Co $3d$ electrons is small. Moreover, we find that both the on-site and intersite Coulomb interaction parameters decrease in a reasonable approximation linearly with the cluster size and for clusters having more than 20 Nb atoms a transition from 0D to 3D screening is expected to take place.

• Received 19 September 2017
• Revised 29 November 2017

DOI:https://doi.org/10.1103/PhysRevB.97.045121