  The electronic parameters and, in particular, the isotropic electrostatic
polarizability (IEP) of sub-nanoscale magnesium clusters were studied in an
expanded set of 1237 structurally unique isomers found in the course of direct
global DFT optimization of the structure of Mg2-Mg32 clusters at the BP86
level, as well as using global optimization based on DFT-calibrated MTP
potential for some larger structures. The calculation of the polarizability at
the same DFT level reveals an unusual property of the IEP - the dependence of
the IEP of the most favorable isomers on the cluster nuclearity n is linear
with a high correlation coefficient, and its value for each n is close to the
minimum value among all found isomers of a given nuclearity. These features
take place independently on the cluster structure which allows hypothesizing
that the energetic favorability of a cluster structure is connected to their
polarizability. A possible explanation of the observed dependence, its
significance for quantum chemistry, and the possibility of practical
application are discussed.
