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].