We present results of a study of small stoichiometric $Cd_{n}Te_{n}$ ($1{leq}n{leq}6$) clusters and few medium sized non-stoichiometric $Cd_{m}Te_{n}$ [($m,n= 13, 16, 19$); ($m{ eq}n$)] clusters using the Density Functional formalism and projector augmented wave method within the generalized gradient approximation. Structural properties {it viz.} geometry, bond length, symmetry and electronic properties like HOMO-LUMO gap, binding energy, ionization potential and nature of bonding {it etc.} have been analyzed. Medium sized non-stoichiometric clusters were considered as fragments of the bulk with T{$_{d}$} symmetry. It was observed that upon relaxation, the symmetry changes for the Cd rich clusters whereas the Te rich clusters retain their symmetry. The Cd rich clusters develop a HOMO-LUMO gap due to relaxation whereas there is no change in the HOMO-LUMO gap of the Te rich clusters. Thus, the symmetry of a cluster seems to be an important factor in determining the HOMO-LUMO gap.
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