Structural and Electronic Properties of Zno nanoclusters: a b3lyp dft study

Calculation and results 
Stability of structures.During the optimization of the ZnO nanoclusters, different types of forty 
possible structures including the linear chains, rings, planer and three-dimensional ones have been 
considered. Each structure having minimum energy is achieved by relaxing the atomic positions. 
We find convergence in the system energy up to 10
-7
meV and the forces of 10
-3
eV/Å on each 
atom. The stability of nanocluster depends upon the binding energy of the nanocluster. We subtract 
the total energy of a nanocluster from the sum of the energies of all the isolated atoms present in the 
nanocluster and divide the resultant quantity by the number of atoms. We name this as the binding 
energy (BE) per atom. For a more precise calculation, we have calculated the harmonic vibrational 
frequencies and the corresponding zero point energy (ZPE) which is subtracted from the calculated 
BE. The final binding energy (FBE) = BE - ZPE. For a specific chemical formula Zn
m
O
n
, the 
configuration possessing the maximum value of BE is named as the most stable structure. All the 
most stable structures are present ed in Fig. 1. 
(a) ZnO Linear (b) ZnO
2 
Linear (c) Zn
2
O Triangular
(d) ZnO
3
Rhombus (e) Zn
2
O
2
Rhombus (f) Zn
3
O
Trigonal
Fig. 1 Optimized structures of ZnO nanoclusters. 
( All the bond lenths are in A
0
) 
The computed O – O, Zn – O and Zn – Zn bond lengths are 1.20, 1.93 and 2.28 Å, respectively for 
the two atoms nanoclusters. The present calculated value of O – O bond length is in excellent 
agreement with the experimental value of 1.21 Å [25]. 
The symmetry, multiplicity of the ground state and the BEs are given for all the optimized 
structures in Table 1, where the most stable structures have been depicted in bold letters. The BEs 
reported by others have also been included for comparison. During the optimization of each 
structure, we have selected the ground state with minimum energy and the multiplicity of the 
ground state has been shown in Table 1. Each nanocluster is now discussed below: 
ZnO.The ground state of the ZnO nanocluster as shown in Fig. 1 is triplet state. The present 
computed FBE of 0.42 eV is quite close to that of Matxain et. al [18]. Others [19, 20, 21] have 
obtained higher values. Our computed value for Zn – O bond length of 1.93 Å is slightly higher 
than those reported by others [19, 20, 21]. No experimental data is available for comparison.