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.
