The molecular structure is represented by an aggregate of atoms considered as a three-dimensional model required by means of the selection of a set of zinc and oxygen atoms to make the quantum calculations for obtaining a minimum energy structure using the methodology at the level of density functional theory (DFT). The Zn and O atoms with ionic bonds and well-defined interatomic distances form a ZnO molecular structure to be identified as the model whose morphology is an arrangement with a flat surface showing that the atoms also form hexagons at the centers of the whole structure, as the most representative structure of ZnO [22]. This model is designed for 24 zinc atoms and 24 oxygen atoms, the result of the DFT calculation shows an arrangement of hexagonal atoms as a monolayer, from this model another equal aggregate is considered for the interaction between atoms in parallel, that is to say, Zn with Zn and O with O, the result after the geometry optimization calculation determines the existence of a separation due to the repulsion between the two monolayers of atoms.
From this result, a different interaction position is selected by rotating a monolayer maintaining the parallel shape but interacting a Zn (Zinc) of the first monolayer with an O (oxygen) of the second monolayer. As a result of the geometry optimization calculation, it is obtained the minimum energy of the molecular structure, where an attractive interaction is observed when obtaining a cage-like three-dimensional model, due to the interaction of the two monolayers as shown in Fig. 1.
The minimum energy molecular structure from the results of the geometry optimization calculation uses the hybrid functional M06-2X with the set of base functions TZP (M06-2X/TZP) to form the aggregate that is displayed in two views locating the position of the atoms and their bonds, a regular formation in the center of hexagons is observed with a pronounced difference of the bonds located at the ends. The interatomic distance between the nuclei for all the bonds between Zn and O has an average value of 1.9 Å, another important value is the separation distance between layers, with an average of 2.37 Å. The distance value among extreme atoms is lower than the average central separation as observed in Fig. 1 side view.
The aggregate exhibits a hexagonal distribution in the central region on both the lower and upper monolayers, and at the ends they present irregular arrangements. The selection process consists of evaluating each Zn atom energetically when it is replaced point by point in the 24 sites of its Cartesian coordinates to determine which is the most probable site of substitution, choosing the one with the lowest energy to change the Zn atom by Al. The result shows that the label (32) is the correct one, with the rest of Zn-O remaining unsubstituted. Due to the characteristics containing an odd number of electrons, multiplicity 2 was used, maintaining charge 0. The atomic structure obtained after the substitution as a result of the geometry optimization calculation leads to the molecular structure with important changes when substituting aluminum. The morphological changes in the aggregate of atoms for the structure of ZnO are shown in Fig. 2b.
The substitution of aluminum in the atomic aggregate has produced structural modifications that are identified by changes in atomic positions when compared with pure ZnO. Such changes in the bond distance between Zn-O are due, on the one hand, to the electronic configuration of zinc and aluminum, generating different electronic distributions affected by the forces that aluminum exerts on oxygen as observed in the values of the properties evaluated for the substitution site. To use a hybrid functional allows to ensure good precision of the electronic and structural properties to be able to evaluate the electromagnetic forces due to aluminum, identifying that due to changes in the substitution sites, the number of atoms of the aggregate is counted, to determine that such substitution corresponds to 2% of the entire aggregate.
Table 1
The bond length for aluminum values with the near-neighbor oxygens as well as for the substituted zinc with the near-neighbor oxygens.
Interaction | Bond length (Å) | Interaction | Bond length (Å) |
Al(32) - O(33) | 1.78 | Zn(32) - O(33) | 1.98 |
Al(32) - O(38) | 1.78 | Zn(32) - O(38) | 1.98 |
Al(32) - O(31) | 1.72 | Zn(32) - O(31) | 1.98 |
Al(32) - O(6) | 1.87 | Zn(32) - O(6) | 2.21 |
Table 1 shows the bond length values of Al(32) - O(33) is 1.78 Å; Al(32) - O(38) is 1.78 Å; Al(32) - O(31) is 1.72 Å; Al(32) - O(6) is 1.87 Å, where 3 oxygens belong to one monolayer and O(6) to the other monolayer, observing that for bond lengths when compared with ZnO, the values increase when aluminum is replaced by zinc, indicating that the force exerted on the oxygens is greater than that of aluminum, determining that the bond value of the zinc with oxygens on average is 1.98 Å, when considering the distance between layers, the bond length of Zn(32) with O(6) is 2.21 Å. After calculating the minimum energy structure is observed that the bond length Al(32) – O(6) is 1.87 Å to form the tetrahedron as shown in Fig. 3.
Table 2
The values of bond lengths for aluminum with its near neighbors' oxygen prior to substitution using zinc and after substitution using aluminum.
Bond | Bond lengths | Bond | Bond lengths |
O(31) - Al(32) | 1.07 | Zn(26) - O(31) | 0.43 |
O(33) – Al(32) | 0.83 | Zn(35) – O(33) | 0.42 |
O(38) – Al(32) | 0.83 | Zn(29) – O(31) | 0.43 |
O(6) - Al(32) | 0.58 | Zn(40) – O(38) | 0.42 |
Zn(8) – O(6) | 0.43 | Zn(37) – O(38) | 0.38 |
Zn(29) – O(31) | 0.43 | Zn(20) – O(6) | 0.34 |
Zn(4) – O(6) | 0.43 | | |
Aluminum promotes the formation of a tetrahedral structure with a displacement of its center between the two layers, placing itself as an important atom to generate a new Zn-O-Al structure. The bond lengths between O(31) - Al(32) is 1.07; O(33) – Al(32) is 0.83; O(38) – Al(32) is 0.83; O(6) - Al(32) is 0.58; the latter due to the greater distance that existed when the zinc was with the oxygen Zn(8) – O(6) is 0.43; Zn(29) – O(31) is 0.43; Zn(4) – O(6) is 0.43; Zn(20) – O(6) is 0.34, these values determine that only one of the aluminum bonds has a value of order 1.0, the rest are less than 0.83 in the case of order Zn-O is of a lower order than the bonds of aluminum Al-O.
Table 3
The Electrostatic potential shows the values of aluminum with near-neighbor oxygens as well as prior to the substitution of zinc with near-neighbor oxygens.
Atom | ESP (esu/cm) |
Al(32) | -403.98 |
O(33) | -203.01 |
O(38) | -203.01 |
O(31) | -203.05 |
O(6) | -202.91 |
Zn(4) | -1289.36 |
Zn(8) | -1289.36 |
Zn(20) | -1289.4 |
Another property is the electrostatic potential, its values are shown in Table 3, which allows identifying by its values for each atom where Al(32) is -403.97 esu/cm; O(6) is -202.91 esu/cm; O(31) of -203.05 esu/cm; O(33) of -203.01 esu/cm; O(38) of -203.01 esu/cm; in the case of Zn(4) it is -1289.36 esu/cm; Zn(8) is -1289.36 esu/cm; Zn(20) is -1289.40. These values clearly determine the reason why electrostatic potentials influence an attraction between aluminum and oxygen.
The analysis of the frontier alpha molecular orbitals is associated with Zn(26) (s,py): in the same way for Zn(29) (s,py); Al(32) (pz) and Zn(16) (s), for 1.00 occupancy and for O(31) (s,py) with 0.000 occupancy orbitals, the energy difference is 0.00404 Ha, (0.10993 eV)(2.53514 Kcal/mole). Equivalently, for the Final Beta Molecular Orbital Analysis, they indicate that O(14), O(17), O(28), and O(42) (py, px) are the orbitals with occupancy 1.00 and for Al(32), Zn(26), Zn(29) (s, py) with occupancy 0.00 the energy difference is -0.20119 Ha, (-5.47466 eV)(-126.24865 Kcal/mol) clearly indicating that the part of the orbital frontier orbitals alpha molecules are those that promote these changes in a state of lower energy.
In a subsequent substitution of Zn by Al, as established in the experimental reports, a gap in the optical band due to the formation of holes is identified by the characterization of this material and the spectroscopic analysis, which exists in a 4% substitution, in this study. The aggregate is made up of 48 atoms that correspond to 2 aluminum atoms in the substitution, considering one in each layer, the results of the calculations persisting in the formation of a tetrahedral structure with centers in the aluminum, and this planar deformation allows the detection a Zn-Zn bond as shown in Fig. 4a). Spectroscopic results show that when Al is increased there is a decrease in grain size, also considering that said increase destroys morphology and that Al acts as nucleation centers.[22]
In this case, 2 aluminums use a closed shell calculation with multiplicity 1, obtained from the analysis of the frontier molecular orbitals that Zn(36) (s); similarly for Zn(37) (s); Al(32) (s); and the O(48) (s,pz); within the 2.00 occupancy this shows that the hole formed in this region of higher occupancy atoms, the 0.000 occupancy orbitals, are distributed with s orbitals; in the rest of the nearby neighboring atoms, and the energy difference is -0.10843 Ha, (-2.9506 eV)(-68.042 Kcal/mol).