HOMO-LUMO gap and Charge transfer mechanism –
Molecular orbital analysis can provide very important information on electronic structure. The ability of molecules and clusters to participate in chemical reaction depends upon the energy gap which is known as HOMO [Highest Occupied Molecular Orbital] LUMO [Lowest Unoccupied Molecular Orbital] gap. The wide energy gap of clusters also decides the optical polarizability of the molecule[4]. A large value of HOMO-LUMO gap always indicate the closed shell electronic configuration[1-4] and the ability to take jump from lower state to higher state. The Egap of TM@Ge12 [TM = Co, Pd, Tc, and Zr] clusters are summarizes in table 3.
The results show that doping of 4d transition metal like Tc, Zr, and Pd have relatively large gap in compare to 3d transition metal Co. Here we obtain 1.96eV [Tc@Ge12], 1.96eV [Pd@Ge12], 1.86eV [Zr@Ge12], and 0.97eV [Co@Ge12] HOMO-LUMO gap for the most stable clusters. The stability of these clusters can be defined using closed shell electronic configuration and the contribution of π and σ bond. The energy gap of Tc and Pd doped germanium cluster is biggest among those of considered groups. On the off chance that we see the enhanced geometries of Tc and Pd doped germanium confine clusters, we found that both structure are impeccable hexagonal prism closed shell structure. It can likewise be finished up by the figure that there is π-π bond arrangement at the focal point of the HP ring and σ bond is framing at the ring side means among the germanium atoms. So also, in the Pd doped germanium cluster display 58 valence electron which is the sign of magic number. For Zr@Ge12 cluster, there are six down spin LUMO states of Ge12 confine that impeccably connect covalently with valence state electrons which is fundamentally the same as past examination by Vijay kumar et al. [19]. For our case the 4 valence electrons [4d25s2] of Zr totally share bonding with germanium enclosure and give huge HOMO-LUMO hole. It additionally shows that the HOMO and LUMO is roughly confined on the whole molecule. Because of this enormous energy gap, LUMO can scarcely gain electron from closed shell HOMO. So the enormous estimation of energy gap show lower reactivity in compound and photochemical procedure with electron move[59]. Based on above investigation, the cluster with huge energy can gap seen as building blocks of the novel materials.
In the next part of discussion, we describe the charge transfer mechanism by calculating the natural bond orbital analysis[43-44]. Since, among all the TM metals, studied in this work, only Pd (2.2) is more electronegative than germanium (2.01) on Pauling scale. It means the charge will always transfer from Pd to Ge atoms and in other TM atom; the charge will transfer from Ge atom to TM (Tc, Zr, and Co) atoms. The natural population analysis precisely determined the distribution of electrons in various sub shell of their atomic orbitals.
It is worth mentioning that the many body system properties like electronic geometry, dipole moment, polarizability are influenced by the atomic charges [60]. It can be seen from table 4, the most electronegative charge of -1.883e accumulated for Tc, whereas all germanium atoms gained positive charge. The electrostatic point of view tells us that most electronegative atoms have tendency to donate electron and electropositive atoms have inclination to accept electrons, it means here charge is transferring from Tc atom to germanium cage. Similarly, Pd atom plays a donor role in Pd@Ge12 cluster. In the Zr@Ge12 system, the charge accumulated by the Zr atom is -2.871 which again donate the electrons to Ge12 cage. The case of Co doped Ge12 cage is quite different. Here the charge is transferring from Ge12 cage to TM metal Co atom.