Partial Density of states –
In order to investigate the electronic properties, variation in the HOMO-LUMO gap and chemical bonding nature due to TM metal doping in Ge12 cage cluster, we have performed subtleties examination of the atomic orbital to examine the contribution of different TM’s (s, p, or d) and Ge (s, p) orbital’s by calculating partial density of states (PDOS). The DOS is acquired by utilizing GaussSum programming [41]. It very well may be seen that the partial density of states means the number of different states where the electrons are allowed to occupy at a particular energy level can be significantly change when the Ge12 cluster are doped with Tc, Pd, Zr, and Co atoms. As shown in the figure 6, the density of states of pure Ge12 cluster, the position of spin up and spin down DOS are same but after the doping of TM’s (Tc, Pd, Zr, and Co) the spin up and spin down states in DOS exhibit the presence of electronic polarization.
The PDOS provide basic analysis of the interaction between the TM’s atom orbital’s and germanium cage. The peak of spin up and spin down near the Fermi level define the localization domains and corresponds to chemically reactive regions. The charge transfer between the TM atoms and the germanium cage generate the electric field, on the basis of this charge transfer, polarization can be explained. Study of natural bond orbital analysis [Supplementary Information] explain that electronic states near the Fermi level mainly come from 4s, 4p orbital’s of germanium cage and 4d orbital of TM atoms. As we can see in table 2 [SI] that there are 4s1.604p2.38 orbital contributions of Ge atom and 4d9.55 orbital contribution of Pd atom are mainly dominated near the Fermi level of Ge12Pd system. These all contribution has shown in alpha dos in the PDOS figure 6 and the p-d hybridization is mostly responsible for localized electrons near the Fermi level. Similarly, In Ge12Tc, there is 4s1.55, 4p2.30 orbital of Ge atom 4d7.63 orbital of Tc atom are contributing near the Fermi level and it is also clear from the PDOS.