Ab initiocalculations of the structural and electronic properties ofHgmTenclusters

The structural and electronic properties of ${\mathrm{Hg}}_m{\mathrm{Te}}_n$ ($m\ne n=13$, 16, 19, and 28) clusters are calculated using density functional formalism and the pseudopotential method within the generalized gradient approximation. The initial structures of all the clusters are chosen to be fragments of bulk phase HgTe with $T_d$ symmetry. It is found that the relaxed structures of ${\mathrm{Hg}}_{13}{\mathrm{Te}}_{16}$ and ${\mathrm{Hg}}_{16}{\mathrm{Te}}_{19}$ retain their initial symmetry, whereas those of ${\mathrm{Hg}}_{16}{\mathrm{Te}}_{13},{\mathrm{Hg}}_{19}{\mathrm{Te}}_{16},{\mathrm{Hg}}_{19}{\mathrm{Te}}_{28}(={\mathrm{Hg}}_{16}{\mathrm{Te}}_{19}+12\mathrm{Te})$, and ${\mathrm{Hg}}_{28}{\mathrm{Te}}_{19}(={\mathrm{Hg}}_{16}{\mathrm{Te}}_{19}+12\mathrm{Hg})$, due to the Jahn-Teller distortions except for the last one, change to lower symmetries. However, it is apparent that the 12 additional Te atoms in the ${\mathrm{Hg}}_{19}{\mathrm{Te}}_{28}$ cluster act to stabilize the ${\mathrm{Hg}}_{19}{\mathrm{Te}}_{16}$ core, while the 12 additional Hg atoms in the ${\mathrm{Hg}}_{28}{\mathrm{Te}}_{19}$ cluster do not do so. It is also found that all the clusters studied here are initially semimetals with zero or very small highest occupied molecular orbital (HOMO) - lowest unoccupied molecular orbital (LUMO) gaps. However, after structural relaxation, ${\mathrm{Hg}}_{16}{\mathrm{Te}}_{13},{\mathrm{Hg}}_{19}{\mathrm{Te}}_{16},{\mathrm{Hg}}_{19}{\mathrm{Te}}_{28}$, and ${\mathrm{Hg}}_{28}{\mathrm{Te}}_{19}$ are semiconductors, while the other two clusters with unchanged symmetry are still semimetallic in nature. Therefore, as well as the size quantization, the symmetry of a cluster would seem to be another significant factor to determine its HOMO-LUMO gaps.