Ab Initio Study of Structural and Electronic Properties of (ZnO)_{ n } “Magical” Nanoclusters n = (34, 60)
- Rostyslav Bovhyra^{1}Email author,
- Dmytro Popovych^{1},
- Oleg Bovgyra^{2} and
- Andrew Serednytski^{1}
Received: 29 December 2016
Accepted: 16 January 2017
Published: 25 January 2017
Abstract
Density functional theory studies of the structural and electronic properties of nanoclusters (ZnO)_{ n } (n = 34, 60) in different geometric configurations were conducted. For each cluster, an optimization (relaxation) of structure geometry was performed, and the basic properties of the band structure were investigated. It was established that for the (ZnO)_{34} nanoclusters, the most stable are fullerene-like hollow structures that satisfy the rule of six isolated quadrangles. For the (ZnO)_{60} nanoclusters, different types of isomers, including hollow structures and sodalite-like structures composed from (ZnO)_{12} nanoclusters, were investigated. It was determined that the most energetically favorable structure was sodalite-type structure composed of seven (ZnO)_{12} clusters with common quadrangle edges.
Keywords
Background
Wide-gap semiconductors are perspective materials to use in optoelectronic systems, ultraviolet lasers, field emitters, and other devices of new generation. It is said that not only the composition but also the nature of the nanostructures give new properties to the material. Atomic clusters and fullerenes are the building blocks of the new nanostructured materials which are a subject of intensive research with the prospect of applications in optoelectronics. Special interest is given to the clusters of zinc oxide which, with its variety of interesting physical and chemical properties, such as anisotropic crystalline structure, semiconducting properties even with a wide band gap, amphoteric chemical properties, piezoelectric properties, biocompatibility, and high exciton energy, is quite unique [1, 2]. A large number of studies have been devoted to understand its structure, processes of formation and properties, and the behavior of its nanoparticles [3–5]. Thin films and nanostructures based on ZnO, are candidates for creating ultrathin displays, UV emitters and switches [6, 7], and gas sensors [8].
The main methods of studying the electronic properties of atomic clusters are quantum mechanics methods, such as restricted and unrestricted Hartree-Fock method, the density functional theory, and molecular dynamics. To address this problem is to use theoretical methods to study model clusters, particularly in structures that lie between molecular and bulk. Nonetheless, the structure design still allows for many geometric possibilities to exist, and it is challenging to find a true global minimum energy structure.
Numerous theoretical studies of (ZnO)_{ n } clusters have explored optimized geometries for a range of cluster sizes, and a prevalent theoretical observation shows that a fullerene-like structures are more stable in the case for smaller-sized clusters, while a wurtzite-like structure shows increased stability for larger clusters [9]. A core-cage structure for (ZnO)_{34} has been proposed as the most stable in [10, 11], while [12] have predicted the hollow cage structures formed by (ZnO)_{2} squares and (ZnO)_{3} hexagons. In the case of (ZnO)_{60}, the studies [13, 14] revealed an energetically preferred sodalite motif, while nested cage configuration was predicted to be the most stable in [10, 11]. Such differences indicate that there is a strong dependence of the calculated binding energy on the details of the computational framework adopted.
This paper presents a theoretical investigation of structural and electronic properties of clusters (ZnO)_{ n } (n = 34, 60), within the density functional theory, in different geometric configurations to establish which type of structure is the most energetically favorable.
Methods
Ab initio calculations within density functional were performed, which have been successfully used for studying properties of nanoscale structures such as nanotubes and nanowires [15–18]. For structural models, the optimization (relaxation) of the geometry (finding the equilibrium of ions coordinates, in which the full electronic energy of the system is minimal) was carried. Optimization was calculated using the effective algorithm of delocalized internal coordinates [19]. The convergence of the relaxation procedures deemed reached when the magnitude of forces acting on atoms was less than 0.05 eV/Å.
For describing the exchange-correlation energy of the electronic subsystem, the generalized gradient approximation (GGA) in a parameterization of Perdew, Burke, and Ernzerhof was used [20]. It is known that the use of this approach in the calculation leads to underestimation of the quantitative value of the binding energy. On the other hand, an alternative description of the exchange-correlation interaction within local density approximation (LDA) leads to overestimation of the energy values compared to the experimental data. Using GGA in this paper makes it possible to argue that if calculation results say that the cluster model is stable, then the real system will be stable as well. Electronic functions of electrons were divided in the basis of atomic orbitals, including d-orbitals. Core electrons had been described using effective potential with regard to relativistic corrections. Integration in the first Brillouin zone was conducted in the Monkhorst-Pack k-point set [21].
Results and Discussion
There were also sodalite-like structures composed of structural units of (ZnO)_{12}. For each cluster, geometry optimization was performed and band structure properties were analyzed.
Geometry parameters of (ZnO)_{34} and (ZnO)_{60} nanoclusters
Isomer | d, Å in quadrangles | d, Å in hexagons | D, Å | α, in quadrangles | α, in hexagons |
---|---|---|---|---|---|
(ZnO)_{34-28} | 1.945–1.984 | 1.886–1.984 | 14.827 | 84.761–91.960 | 113.612–132.058 |
(ZnO)_{34-43} | 1.938–1.994 | 1.881–1.994 | 13.013 | 85.315–93.708 | 117.331–122.628 |
(ZnO)_{34-15} | 1.938–1.992 | 1.912–1.992 | 13.018 | 84.791–93.952 | 107.145–128.283 |
(ZnO)_{60-sodalite} | 1.931–2.284 | 1.884–2.284 | 15.659 | 83.927–97.183 | 106.583–134.193 |
(ZnO)_{60-25} | 1.963–1.968 | 1.896–1.968 | 16.342 | 85.782–92.117 | 109.977–129.234 |
(ZnO)_{60-24} | 1.964–1.970 | 1.890–1.970 | 16.112 | 85.622–92.846 | 110.167–129.060 |
For all clusters, the maximum value of interatomic distance between Zn and O atoms is set for joint edge between quadrangle and hexagon. For angle values, we established that smaller angles correspond to oxygen atoms and bigger angles correspond to zinc atoms.
Electronic properties of (ZnO)_{34} and (ZnO)_{60} nanoclusters
Isomer | E _{total}/ZnO, eV | ΔE/ZnO, eV | E _{b}/ZnO, eV | E _{g}, eV |
---|---|---|---|---|
(ZnO)_{34-A} | –50461.66 | 0 | –6.764 | 2.275 |
(ZnO)_{34-B} | –50461.64 | 0.02 | –6.748 | 2.151 |
(ZnO)_{34-C} | –50461.62 | 0.04 | –6.724 | 2.048 |
(ZnO)_{34-W} | –50461.54 | 0.12 | –6.645 | 1.124 |
(ZnO)_{60-sodalite} | –50461.744 | 0 | –6.847 | 1.93 |
(ZnO)_{60-A} | –50461.734 | 0.01 | –6.836 | 2.184 |
(ZnO)_{60-B} | –50461.732 | 0.012 | –6.835 | 2.4 |
(ZnO)_{60-W} | –50461.699 | 0.045 | –6.802 | 0.982 |
The valence band of each cluster between −7.0 and −4.0 eV consist mainly from 3d states of Zn and O 2p states. The bands between −4.0 and 0 eV are composed from O 2p states, Zn 3d states, and in smaller scale, Zn 3p and 3s states. The conduction band, on the other hand, between 1 and 5 eV consists mainly from Zn 4s and O 2p and O 2s states.
The valence band of each cluster between −7.0 and −4.0 eV, like in the case with (ZnO)_{34} nanoclusters, is composed from 3d states of Zn and O 2p states. The bands between −4.0 and 0 eV consist mainly from O 2p states, Zn 3d states, and in smaller scale, Zn 3p and 3s states. The conduction band between 1 and 5 eV consists mainly from Zn 4s and O 2p and O 2s states.
Conclusions
Density functional theory studies of the structural and electronic properties of (ZnO)_{ n } (n = 34, 60) nanoclusters were performed. Optimization of structure geometry, as well as the band structure research, was performed. It was established that for the (ZnO)_{34} nanoclusters, the most stable are the fullerene-like hollow structures that satisfy the rule of six isolated quadrangles. For the (ZnO)_{60} nanoclusters, different types of isomers, including hollow structures and sodalite-like structures composed from (ZnO)_{12} nanoclusters, were investigated. It was determined that the most energetically favorable structure was the sodalite-type structure composed of seven (ZnO)_{12} clusters with common quadrangle edges.
Declarations
Authors’ Contribution
All the authors took part in solving the problem under study. They read and approved the final manuscript.
Competing Interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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