Energy level reordering and stability of MPb12 clusters: An interplay between geometry and electronic structure

The electronic energy level spectrum provides a convenient overall view of the cluster electronic structure and bonding. Fig. 2 shows a comparison of energy spectrum for MPb12 clusters as obtained from the Kohn-Sham energy states after broadening with a Gaussian. It is seen that when the central Pb atom is replaced by C, the ordering of the energy levels remained similar with a shift in the Kohn-Sham energy states towards higher binding energy (more negative). This leads to the larger energy gap of 2.0 eV for CPb12. The stabilization of the energy levels by replacing Pb with C could be due to a small charge transfer from the peripheral atoms to the central atom as shown in Fig. 4. Based on the energy level ordering of Pb13 and CPb12 clusters (Fig. 2), it can be imagined that a substitution on central Pb atom by divalent impurity with smaller electronegativity (will transfer electron charge from centre to peripheral) as compared to Pb should result in a larger energy gap than CPb12. Indeed, a very large energy gap of MPb12 clusters was found when the central atom of Pb13 is replaced by Mg. The widening of the energy gap of MgPb12 cluster is due to the splitting of higher angular momentum 1g18 orbital into 1g10 and 1g8 as can be seen in Fig. 2.