Structure-dependence of the magnetic moment in small palladium clusters: Surprising results from the M06-L Meta-GGA functional

摘要

The size- and structure-dependence of the magnetic moment in Pd_n clusters (n = 13, 19, 38) was studied with density functional theory. We compare the Becke-Perdew gradient-corrected exchange-correlation functional with the parameterized meta-generalized gradient approximation functional by Zhao and Truhlar (M06-L). Although the former functional shows the expected quenching of the clusters' magnetic moment with increasing nuclearity, the latter one predicts a strongly increasing magnetic moment. In a series of fixed-spin calculations with the two functionals at different geometries, we observe a strong dependence of the magnetic moment on the cluster structure, where the untypically long metal-metal bonds predicted by the M06-L functional are a dominant influence on the stability of the high-spin cluster configurations. Furthermore, we observe differing behavior of the two functionals with respect to the magnetic moment as particular bonds in the cluster are strained, indicating that, in addition to the structural contribution, the description of exchange-correlation energy in the M06-L functional may intrinsically favor high magnetic moments in these Pd clusters.