Molecular Structures of ZnO by Aggregates of Atoms and Interaction of Two Monolayers

The first-principles calculations are useful for determining electronic and structural properties for a model that simulates a material composed of atomic clusters of ZnO through the analysis of interaction energies and charge distribution. The two-dimensional structural form of ZnO aggregates shows regularly flat hexagons obtained in models of 6, 27 and 54 atoms of Zinc and Oxygen. The structure of a three-dimensional system was determined by dynamics calculations by using the interaction of a pair of monolayers consisting of 108 atoms and as a result, a cage structure was formed from a cluster of Zn54 and O54 identifying only bond atoms at the ends that promote the union of monolayers. The stable structure shows modifications of the atomic bonds in whose centers hexagonal rings prevailed and at the arrangements of the end of triangles, squares, pentagons and even rings of 10 and 11 atoms were obtained. Atomic positions and charge distribution were analyzed based on the methodology used Density Functional Theory (DFT), with the becke88-LYP exchange and correlation functional.


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Abstract-The first-principles calculations are useful for determining electronic and structural properties for a model that simulates a material composed of atomic clusters of ZnO through the analysis of interaction energies and charge distribution. The two-dimensional structural form of ZnO aggregates shows regularly flat hexagons obtained in models of 6, 27 and 54 atoms of Zinc and Oxygen. The structure of a three-dimensional system was determined by dynamics calculations by using the interaction of a pair of monolayers consisting of 108 atoms and as a result, a cage structure was formed from a cluster of Zn54 and O54 identifying only bond atoms at the ends that promote the union of monolayers. The stable structure shows modifications of the atomic bonds in whose centers hexagonal rings prevailed and at the arrangements of the end of triangles, squares, pentagons and even rings of 10 and 11 atoms were obtained. Atomic positions and charge distribution were analyzed based on the methodology used Density Functional Theory (DFT), with the becke88-LYP exchange and correlation functional.

I. INTRODUCTION
The electronic properties as well as the behavior of atoms in molecules are studied by calculations of first principles. These calculations make it possible to know the electronic structure of a molecular system made up of a set of functions that depend on the atomic and spin positions [1]. Zinc oxide is a semiconductor of interest in the technological field for its applications [2,3,4]. During the last decades an increase in applications was observed due to the extensive study and development of research to obtain useful properties in technological development with important contributions [5,6]. This material is currently considered a semiconductor synthesized through a process of new techniques, where growth brings new physical properties, as well as technological applications [7][8][9][10]. Zinc oxide has different electronegativities of zinc and oxygen, and the most stable crystalline structure is the hexagonal wurzite type [11][12][13][14]. Zinc oxide has technological interest and especially in nanometer-level structures, because it is possible to obtain nanostructures in the form of nanoparticles, where different structures are observed in both form and type, generating various nanostructures in the form of nanoparticles, nanowires, nanofiber, as the main ones. This makes zinc oxide acquire great interest for the various nanosystems such as optoelectronic devices, biosensors, pigment for the production of paints, and in the pharmaceutical industry such as the field of cosmetics used as an ultraviolet radiation filter in products such as creams solar. In the electronic aspect they are also used as acoustic transducers, varistors, gas sensors, transparent electrodes and optical window for solar cells. [15][16][17][18][19].
In this report, structural properties were determined from atomic aggregates through geometry optimization calculations. The first results show that aggregates with hexagonal structure formation prevail. From a twodimensional system, the three-dimensional structure was generated. The development of molecular dynamics calculation was useful in the model of two interacting monolayers to obtain a stable structure. From the analysis of the structural results and the charge distribution, it was determined that various atomic arrangements occur in the peripheral zone of the monolayers where atomic clusters are identified for the ZnO, as a first approximation, structural forms resulting from the interaction between the two monolayers of hexagonal structure.

II. METHODOLOGY
In the theory of density functionalities where exchange energy is used in an atomic system, the behavior is asymptotic as an approximation to determine how the exchange energy affects density in addition to the corrected gradient presenting an asymptotic limit. appropriate under a single parameter that allows us to calculate the exact exchange energy implemented in the functional Becke 88 [20]. Lee-Yang-Parr (LYP) is another useful approximation for calculating correlation energy, which is expressed in terms of electronic density when considering a second-order operator to obtain the equation that calculates part of the density, as well as density of local kinetic energy expressed with expansions in the gradient, where the functional has elements to calculate energy and correlation potential [21]. The previous functionalities form a hybrid functional that constitutes the Becke88-LYP exchange and correlation Molecular Structures of ZnO by Aggregates of Atoms and Interaction of Two Monolayers Cristian E. García-López, Irineo-Pedro Z. Rivera, Benjamín Vargas-Arista, and Verónica Estrella-Suarez functional, being useful for the calculation of geometry optimization. In generals, the functional hybrids are considered as an approximation to obtain stable atomic structures, which allow to describe molecular electronic characteristics attached to experimental results from the level of DFT theory by including electronic correlation and spin-orbital corrections, in the non-local density approximation (NLDA). The non-local results favor the calculation of the electronic properties and the interaction energy for the molecules, presenting that the non-local is a better approximation in some molecular cases since it adequately explains the anisotropy for charge distribution attached to experimental values. The results of the geometry optimization calculations under this approximation scheme are used for molecules containing O and Zn atoms. The calculations involve all electrons in the DZVP basis set, considering neutral charge for the total system and multiplicity 1 to find baseline state. The electronic wave function is constructed from the approach when electrons are submerged in a field of static nuclei and the nuclei are considered as in a medium electronic field. Dynamics calculations are useful for knowing the favorable reaction mechanisms and for the formation of new molecular structures.

III. RESULTS AND DISCUSSIONS
A. Two-dimensional ZnO.
The structure of a first model was formed by 3 atoms of oxygen and 3 of zinc, atoms continue to be added in equal proportion to observe the two-dimensional shape of a molecular structure of 24 atoms, the number of atoms is increased again to obtain a molecular system with 54 atoms, as seen in Fig. 1. Optimization calculations were performed to determine a stable structure where it is observed that a priority direction is followed in regular arrangements prevailing exchanges between the oxygen atom and zinc atom favoring the flat hexagon type for the three models. In this stage, a relevant aspect is covered when determining the preferred direction from the structural point of view with stability associated with a minimum of energy by geometry optimization calculation results, as in the case shown in Fig. 1 c), with atoms of Zn27 and O27.

B. Molecular dynamics of the interaction between two monolayers of ZnO.
The above structures are used to form a three-dimensional structure taking into account the interaction of atoms by calculating DFT dynamics. The model of the molecule is selected from 2 molecular structures like the one shown in Fig. 1 c). The procedure consists in leaving a fixed molecule and the other giving it a speed with separation distance relatively considering that the initial position indicates a zero interaction of the monolayers The dynamic calculation as a result of the interaction when placed in parallel shows that the collision is totally repulsive moving the monolayers away, in the first result of the calculation developed giving the energy value of -2728839.1 eV, as shown in Fig. 2. The previous results propose to modify the initial position of the monolayers to carry out the interaction and obtain the three-dimensional structure. A monolayer was rotated so that the zinc atoms of a monolayer during the interaction are in the oxygen direction of the other monolayer to perform the dynamic calculation and consider this as the initial structure. For the interaction between monolayers, the energy values were obtained for each moment of time as reported in Fig. 3. The energy values obtained as a result of the dynamics are decreasing indicating that these values are associated with a different attraction interaction compared to the repulsive interaction obtained when they interacted in parallel. The values decrease to a minimum of -40 kcal/mol, instants later in 400 fs increase to a maximum of 10 kcal/mol, and then descend from -30 to -80 kcal/mol, comparing the structures at each instant of time it is observed that the maximums are associated to the reactions where a bond length modification for the extreme atoms of each monolayer is carried out. The structure resulting from the interaction of the two monolayers starting from the initial structure by dynamic calculation gives a value of -2728839.1 eV taking into account the same conditions of the parallel interaction, observing that there is an interaction that promotes a sandwich structure appreciating bond atoms at the ends determining that the central atoms of the two monolayers have minimal modifications preserving the representative hexagons whose energy value -2728846.2 eV, obtaining a value whose difference is -7 eV due to structural changes, as shown in Fig. 4. To determine the final structure by geometry optimization calculation for the two monolayers is made from the structure obtained by dynamics calculation is shaped like a sandwich, mentioning that the two monolayers do not change their flat shape. The result shows a final structure observing different types arising from one side of the dynamic interaction and the last calculation a stable structure as a three-dimensional molecule, where a small separation between centers of the monolayers is preserved describing a cage-like structure as shown in Fig. 5. Besides, different bonds for the Zn atoms represented by the larger atom and O represented by the smaller atom such as triangles Zn2 O1, squares Zn2 O2, pentagons Zn3 O2 were characterized in the figure of the final structure, and hexagons Zn3 O3. It is also observed that said interaction of the stable structure modifies the flat shape of the center of the monolayers.

C. Structural analysis and charge distribution for various structural forms of the ZnO.
The results of the interaction of the monolayers show different aggregates of O54 and Zn54 atoms, as shown in Fig.  5, where different atomic arrangements are observed at the ends. Atomic aggregates for the various forms of zinc oxide structure are analyzed to determine if there is an attachment to experimental results. The structures that form aggregates of atoms of hexagonal arrangements are according to the most stable hexagonal crystalline structure type wurzite.  The structure of our three-dimensional model shows a region of monolayers where they prevail with hexagonal arrangements mainly in the center but in contrast at the ends where there are no regular arrangements with existing atomic bonds with a triangular, square shape, until they reach structures with ten atoms attached. The bonds that appear in the first instance describe three atom bonds as seen in Fig. 6, identifying that an oxygen atom bonded to two zinc atoms prevails. In the next structure 4 bonds, two types that correspond to 2 oxygen and 2 zinc with different prevail, what varies are the angles which modify the separation distance between the two zinc atoms, identifying two different forms. In the case of 5 bonds, there are 2 oxygen and 3 zinc but having an excess of zinc there is a tendency of bonding between two zinc. Also, there is the case of 6 bonds in an equitable way, there are 3 oxygen and 3 zinc, with the sequence of one oxygen and one zinc, observing that the length of the bonds varies along with the angles that form between the atoms prevailing the hexagon.
The values in Table I shows the charge distribution, the bond length with the neighboring atom and the angle with the nearby neighbors where the oxygen with excess and the zinc with deficiency in the charge distribution reflected its effects on the length of the atomic bond as well as the angle between the different atoms. The irregular shapes of the final structure of Fig. 7 show that there is a further set of asymmetric figures formed by atoms of Zn as the largest atom and O the smallest atom that forms structures of seven bonds between Zn4 and O3, eight bonds between Zn4 and Zn4 O4 and ten bond between Zn5 and O5  Table II shows mainly by the bonds of atoms and angles that there is no regularly well-defined structure, so it is considered an irregular structure, detecting the variation between the angles of zinc-oxygen-zinc bond prevailing varied values in the angles for the structures of Fig. 7. In the case of ZnO structures that form pairs, Zn is well defined, followed by consecutive O. However, what is relevant in Fig. 7 and Table I is when the union between zinc and zinc only happens when the number of atoms is odd. The irregular ring-like formation of the final structure Fig. 4 has an eleven-sided structural asymmetric shape composed of Zn6 O5, with a Zn-Zn link protruding.

IV. CONCLUSIONS
The experimental research in the synthesized nanomaterial structures reports various structural forms, which implies explaining whether there is a way to understand the formation of these structures. The results allow the following conclusions to be made: In the process of describing the reaction phenomena that occur in an interaction, a flat structure that simulates a monolayer was considered and placed as an initial starting point, a speed was applied that showed the formation of a new structure. The physical environment of oxygen atoms has a direction with a preference for the formation of pairs of Zn54 and O54. In the analysis of the calculations for a two-layer model previously obtained by identifying aggregates of atoms where different molecular structures were obtained. The arrangements of atoms and the possible reaction mechanisms that occur when increasing the number of atoms with different tendencies depending on the direction is observed in the results that are assured there is generation of two-dimensional molecules that follow hexagons and are flat. In addition, continuing with the generation of a threedimensional molecule it is affirmed that different structural forms occur at the end concluding that for a threedimensional system the hexagons persist in the central part but the different structural forms of a nanomaterial are explained by the diversity of bonds that occur at the ends of this representative model of ZnO structures. The structural bonds with the number of odd atoms always have a zinc bond with zinc.