3.1. Free Zn12O12 monomer and dimer
The optimized geometries of Zn12O12 and (Zn12O12)2 nanowire are presented in Fig. 1. The Zn12O12 nanocluster, as illustrated in Fig. 1a, is composed of six Zn2O2 and eight Zn3O3 rings with a Th symmetry point group. Consistent with the tetragonal isolated rule for small fullerenes 50, this cage structure has been determined to be the most stable isomer of the Zn12O12 system due to the maximum separation of the four-membered rings. Zn12O12 has two distinct Zn-O bonds: one shared by a hexagon and a tetragon and the other by two hexagons. The average bond lengths are 1.98 and 1.91 Å, respectively, which are consistent with those found in the other DFT/B3LYP studies 34. The Hirshfeld charge density analysis of Zn12O12 reveals that the Zn and O atoms have positive and negative charges of 0.39 |e|, respectively. The estimated binding energy of -7.33 eV per ZnO in Zn12O12 agrees well with the experimental value of -7.52 eV 51. It is worth mentioning that the binding energy of Zn12O12 per ZnO is higher than that of B12N12 (ca. -6.27 eV per BN), owing to the distinct nature of chemical bonds of these systems. In fact, because the electronegativity difference between Zn (1.6) and O (3.4) is bigger than that between B (2.0) and N (3.0), more ionic Zn‒O bonds are expected in Zn12O12. Also, the current DFT/PBE calculations provide a Γ-point band gap of 2.46 eV between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), representing that this material has semiconducting electrical properties. Meanwhile, this value is almost consistent with the value of 2.53 eV obtained in the previous DFT studies 27, indicating that the DFT approach employed here can successfully reproduce the overall structural characteristics and chemical bonding of Zn12O12 cluster.
The ZnO nanowire was formed by connecting two Zn12O12 clusters and then optimizing at the PBE/DNP level. In this system, Zn12O12 clusters are coupled to one another by 6-membered rings, as in previous computational investigations 27. This structure is shown to be slightly more stable than other possible structures formed by connecting two Zn12O12, i.g., through coupling of 6-/4- or 4-/4-membered rings. The binding energy of the (Zn12O12)2 system per ZnO is predicted to be -6.37 eV, which is smaller than the value for the Zn12O12 monomer. The dimerization energy for (Zn12O12)2, defined as Edimerization=(ED-2Em)/2 where ED and Em are the energies of Zn12O12 dimer and monomer, respectively, is -2.22 eV, showing that the assembling two Zn12O12 monomers is energetically favorable. Furthermore, the HOMO-LUMO energy gap of (Zn12O12)2 is 2.17 eV, which is about 0.3 eV less than that of Zn12O12 monomer. Considering that a narrow HOMO-LUMO gap suggests lesser kinetic stability, (Zn12O12)2 has more chemical reactivity than Zn12O12. These findings are consistent with previous comparable theoretical investigations 27.
The adsorption of N2O and CH4 was studied in detail to explore the surface reactivity and catalytic activity of Zn12O12 monomer and dimer in the CH4 oxidation process. Figures 1c and d show the most stable N2O configurations on Zn12O12 and (Zn12O12)2, in which N2O is oriented toward the Zn atom of the cluster from its O-site. The corresponding adsorption energies are about − 0.20 eV, showing that N2O adsorption should be classified as a physisorption (Table 1). This finding is further supported by negligible electron-transfer from the cluster to N2O, indicating that N2O is only weakly activated on the ZnO systems. Similarly, the very small adsorption energies reported for CH4 in Table 1 imply that this molecule is only weakly attached to the Zn12O12 and (Zn12O12)2 clusters, as also evidenced by the negligible charge-transfers and large binding distances. As a result, neither Zn12O12 nor (Zn12O12)2 can be employed as a potential catalyst for the oxidation of CH4 by N2O.
Table 1
Calculated adsorption energies (Eads, eV) and amounts of charges shifted (QCT, e) for the adsorption of N2O and CH4 on pristine and Al-doped ZnO clusters
cluster | | N2O | | CH4 |
| Eads | QCT | | Eads | QCT |
Zn12O12 | | -0.19 | + 0.05 | | -0.12 | -0.03 |
(Zn12O12)2 | | -0.21 | + 0.07 | | -0.13 | -0.03 |
AlZn11O12 | | -0.77 | -0.25 | | -0.13 | -0.04 |
(AlZn11O12)2 | | -1.80 | -0.43 | | -0.17 | -0.03 |
3.2. A single Al atom doped Zn12O12 cluster and nanowire
The adsorption of CH4 and N2O molecules on the catalyst surface initiates the CH4 oxidation reaction; thus, a stable and strong adsorption is required to sufficiently activate these molecules. Because pristine Zn12O12 and (Zn12O12)2 fails to properly activate these molecules, the surface activity of these systems was improved by replacing a Zn atom with a single Al atom. Figure 2a depicts the optimized geometry of AlZn11O12 cluster. The doped Al atom in AlZn11O12 is positively charged by 0.45 |e| (based on the Hirshfeld analysis) and the calculated Al‒O bond distances are about 1.75 Å. According to our DFT calculations, the resulting AlZn11O12 cluster has an Eform value of -1.78 eV, showing that the Al atom is stably incorporated into the Zn12O12 cluster. We note that this formation energy value is greater (more negative) than the comparable value for AlZn12O11 (ca. +5.03 eV), which is formed by substituting an Al atom for an O atom in Zn12O12. Hence, the (AlZn11O12)2 dimer was formed by connecting two optimized AlZn11O12 clusters through their hexagon face, and its most energetically stable structure is shown in Fig. 2b. The dimerization energy of (AlZn11O12)2 is calculated to be -2.66 eV, which is 0.44 eV more than the corresponding value obtained for pristine (Zn12O12)2. This implies that the addition of the Al impurities improves the stability of the ZnO cluster. Considering the Hirshfeld charge density analysis results, the three- and four-coordinated Al atom in AlZn11O12 dimer has a positive charge of 0.43 and 0.36 |e|, respectively. The average Al‒O bond distance is about 1.77 Å, which is 12% shorter than the Zn‒O bond distance. The Al-doping has also a considerable impact on the HOMO-LUMO energy gaps of these systems. In particular, our calculations demonstrate that the HOMO-LUMO gap of (Zn12O12)2 decreases by 1.65 eV after Al-doping. All of these results clearly suggest that Al-doping significantly alters the properties of the Zn cluster. As a result, it seems that the addition of Al impurities significantly influences the surface reactivity and adsorption behavior of the ZnO clusters.
As Fig. 2c indicates, N2O molecule is adsorbed onto AlZn11O12 via forming an Al‒N chemical bond with an Eads value of -0.77 eV (Table 1). The N‒O and N‒N bond lengths of the adsorbed N2O are stretched by 1.42 and 1.17 Å, respectively, which are 0.23 and 0.03 Å longer than the corresponding values in the isolated N2O (1.19 Å (N-O) and 1.14 Å (N-N)). Given the Hirshfeld analysis, 0.25 electrons are shifted from AlZn11O12 to N2O, causing the elongation of the N‒O bond. On the other hand, it is found that when N2O approaches the Al atom of (AlZn11O12)2 from its O end, it spontaneously dissociates into a N2 molecule and an O atom connected to the Al atom. This interesting phenomenon has also been observed in other investigations 52 and may be explained in terms of the significant charge-transfer from the (AlZn11O12)2 into the LUMO of the N2O. According to the frontier molecular orbital (FMO) theory 53, the energy difference between the electron donor’s HOMO/SOMO and the electron acceptor’s LUMO determines the degree of orbital contact and electron transfer in a donor-acceptor complex. To understand this, we depict the SOMO isosurface and energy of AlZn11O12 and (AlZn11O12)2 as well as those of LUMO of N2O in Fig. 3. For comparison, those of pristine Zn12O12 and (Zn12O12)2 are also represented in the same figure. According to Fig. 3, the energy difference between the HOMO of Zn12O12 dimer and LUMO of N2O is smaller than that of Zn12O12 monomer, indicating that former system is a better electron donor than latter. After the Al-doping, the SOMO of these clusters shifts to a lower energy state, and consequently, the energy gap between the SOMO of clusters and the LUMO of N2O narrows, and electron transport between these species improves. As evident, such a decrease in the energy difference is more important for the AlZn11O12 dimer than monomer. Hence, AlZn11O12 dimer should be most suitable and promising system to activate N2O molecule.
The adsorption of CH4 on AlZn11O12 and (AlZn11O12)2 surface is also studied. Figures 2e and f show the most stable configurations of CH4 over the latter systems. It is found that CH4 adsorbs weakly over these systems as evidenced by the long binding distances and low adsorption energies (see Table 1). Nevertheless, compared to the pristine Zn12O12 and (Zn12O12)2, the addition of the Al atom makes a significant increase in the adsorption energies. On the other hand, the adsorption energies of CH4 over AlZn11O12 and (AlZn11O12)2 is less than those of N2O, indicating that the tendency of N2O to occupy the Al site is larger than that of CH4.
3.3. Oxidation of CH4 to methanol
Considering the above results, now we turn to study the oxidation of CH4 by N2O over the Al-doped ZnO systems. As previously noted, N2O is attached to the Al atom of AlZn11O12 from its O site. The bent structure of adsorbed N2O clearly shows that this molecule is activated on the Al atom. Figure 4a shows the potential energy diagram of CH4 oxidation over AlZn11O12 nanocluster. To proceed the reaction, CH4 progressively approach the adsorbed N2O molecule and this elongates the N‒O bond and finally by supplying an activation energy of 0.48 eV, N2O is separated into a N2 and an activated O atom (*O). The formed *O species acquires a negative charge (-0.42 |e|), associated with a very large negative Eads value (-4.35 eV). Next, CH4 further approaches the *O and the intermediate state IM-1 forms. The adsorption energy of CH4 on the *O-adsorbed AlZn11O12 is about − 0.10 eV. In the next step, the C‒H bond of CH4 is constantly elongated until the H atom is added to the *O and an O‒H bond is obtained on the Al atom. The latter reaction is exothermic and needs an activation barrier of 0.41 eV, which seems to be easily supplied at normal temperatures. The whole CH4 oxidation process on the AlZn11O12 is exothermic by 2.98 eV, indicating that the formation of final product is thermodynamically favored. Notably, the adsorption energy of the formed methanol is calculated to be about − 0.58 eV, demonstrating that it is easily detached from the catalyst surface and hence a new CH4 oxidation reaction can be initiated.
As noted earlier, N2O is unstable over the (AlZn11O12)2 surface since it can easily decompose into a N2 molecule and an activated *O remained on the Al atom. Hence the N2O decomposition is barrier-less on the (AlZn11O12)2. After the leaving N2 molecule due to its small adsorption energy, the remaining *O moiety is ready to interact with CH4. Figure 4b shows the corresponding potential energy surface. As clear, the C-H bond of CH4 in IS-3 can be broken and the H atom is shifted to the *O (IM-3). The latter step is exothermic (-1.13 eV), but needs an activation barrier of 0.29 eV. This activation barrier is lower than those reported for FeO+-ZSM-5 (0.82 eV) 54, Fe- and Co-ZSM-5 clusters (0.69 and 0.65 eV) 55, FeO-doped BN sheet (0.91 eV) 56, CoN3-doped graphene (0.83 eV) 6, and Co-embedded graphene (0.56 eV) 57. In the next, the CH3 radical reacts with the *OH moiety to form a methanol molecule. This reaction step is also exothermic (-2.05 eV) and requires a barrier energy of 0.31 eV. Finally, the formed CH3OH flies from the catalyst surface due to its low adsorption energy. Overall, the calculated results indicate that the activation barrier for the oxidation of methane over (AlZn11O12)2 nanowire is smaller than those of AlZn11O12, confirming the higher catalytic performance of the former system.
3.4. Overoxidation of methanol
Overoxidation of methanol on the catalyst surface, as demonstrated in earlier experimental and theoretical investigations 6, 58, 59, is one of the most significant side reactions during methane oxidation. In this process, the generated methanol first interacts with the activated *O to make methoxy (CH3O) and OH moieties, and then the CH3O interacts with the *OH to produce water (H2O) and formaldehyde (CH2O) molecules:
CH3OH + *O → CH3O + *OH (3)
CH3O + *OH → CH2O + H2O (4)
The process described above is illustrated in full in Fig. 5, along with a potential energy diagram. The findings show that there is no energy barrier for the first dehydrogenation of methanol over AlZn11O12 cluster and (AlZn11O12)2 nanowire. This is to be expected given that the presence of a negative O species readily dissociates the ionic O‒H bond. In order to interact with the *OH, the generated CH3O molecule is then reoriented on the catalyst. However, because of the high energy barrier and fairly nonpolar nature of the C‒H bond, dehydrogenation of CH3O is nearly impossible. Furthermore, the bigger catalytic activity of (AlZn11O12)2 than AlZn11O12 is confirmed by the predicted lower activation barrier of this process.
In summary, whereas the dehydrogenation of CH3OH over *O-functionalized ZnO systems is barrier-free, overoxidation is nearly impossible on these catalysts due to the large activation barrier for the dehydrogenation of CH3O to give formaldehyde molecule. Therefore, CH3OH should be removed from the reactor to optimize methanol production efficiency and prevent its dehydrogenation.