Electronic Properties
In this piece of our proposed work, we will talk about the electronic properties of germanium confine containing a transition metal atom dependent on determined (a) average binding energy [BE], (b) HOMO-LUMO gap and charge transfer mechanism and (c) partial density of states.
Binding energy - To get knowledge about the relative stability of clusters we calculate the average binding energy of the TM@Ge12 [TM = Co, Pd, Tc, and Zr] clusters. The average binding energy can be defined using below mathematical formation:
\begin{equation} BE=\frac{\left[E_{\text{TM}}+12\times E_{\text{Ge}}-E_{TMGe12}\right]}{n}\nonumber \\ \end{equation}
Where ETM, EGe and ETMGe12 are the ground state energy of transition metal, germanium and TM doped germanium confine individually. Here ”n” characterizes the total number of atoms in the cage. In our current work the n = 13 for all figuring as [n = 12 Ge and 1 TM atom]. The binding energy, HOMO-LUMO gap, charge on TM metal particle, bond length of Ge-TM, relative energy (ΔE) appeared in table 3. We analyze the binding energy of TM@Ge12 [TM = Co, Pd, Tc, and Zr] clusters and found that the Tc metal encapsulated germanium confine gives most stable structure. The remaining are in the order of Zr > Pd > Co. The average binding energy of TM doped germanium cage cluster with the correlation of pure Ge12 cluster is appeared in figure 3.
The magnitude of binding energy of the clusters gives the information about the strength of the chemical bonding in the clusters. The binding energy value of pure germanium cluster is 2.062eV in HP ring obtained using the present method is consistent with our previous reports[1-4]. The average binding energy values of TM encapsulated germanium cage are 2.45 eV, 2.40 eV, 2.25 eV, and 2.23 eV for Tc, Zr, Pd, and Co respectively. It means the doping of 4d transition metal Tc, and Zr gives most stable structure rather than 3d transition metal Co atom.
It tends to be seen that the doping of 3d and 4d transition metal in pure Ge12 cage cluster can improve the dependability of pure germanium cluster. The value of binding energy given by other research group [49] of Tc@Ge12 is around 3.02 eV with BPW91/LANL2DZ level of theory. Our worth is less a direct result of the utilizing ECP basis set and a reasonable B3LYP functional. Essentially, the binding energy value of Zr doped Ge12 cluster is well predictable with past reports[16]. All the determined parameters like average binding energy, HOMO-LUMO hole, bond length of Ge-TM, and the relative energy (ΔE) contrast between stable isomers are appeared in table 3.
Here, we have also calculated the binding energy for all other isomers presented in figure2. We can easily see the variation of binding energy as the structures are changing. The comparisons of all other isomers are shown in figure 4. The biding energy of Co doped germanium atom in hexagonal prism [HP] and hexagonal anti-prism are nearly same but the icosahedral and bicapped pentagon prism both are relatively less stable with the difference of 0.04eV and 0.06eV respectively. On the other hand, in Pd@Ge12, the binding energy difference between HP and HAP geometries is around 0.02eV. The difference is quite large in icosahedral case which is around 0.07eV. Similarly if we see the case of Tc and Zr doped germanium cage clusters, the binding energy difference is more as we move towards HP-HAP-IH-BPP geometries. We can conclude that the symmetry stability depend on the 3d and 4d transition metal. In the case of 3d transition metal, the metal encapsulated hexagonal anti-prism is stable geometries whereas in 4d transition metal we get hexagonal prism as a minimum energy structure as we predicted in our previous reports [2, 4].