The Zn12O12 cluster-assembled nanowires as a highly sensitive and selective gas sensor for NO and NO2

Motivated by the recent realization of cluster-assembled nanomaterials as gas sensors, first-principles calculations are carried out to explore the stability and electronic properties of Zn12O12 cluster-assembled nanowires and the adsorption behaviors of environmental gases on the Zn12O12-based nanowires, including CO, NO, NO2, SO2, NH3, CH4, CO2, O2 and H2. Our results indicate that the ultrathin Zn12O12 cluster-assembled nanowires are particularly thermodynamic stable at room temperature. The CO, NO, NO2, SO2, and NH3 molecules are all chemisorbed on the Zn12O12-based nanowires with reasonable adsorption energies, but CH4, CO2, O2 and H2 molecules are only physically adsorbed on the nanowire. The electronic properties of the Zn12O12-based nanowire present dramatic changes after the adsorption of the NO and NO2 molecules, especially their electric conductivity and magnetic properties, however, the other molecules adsorption hardly change the electric conductivity of the nanowire. Meanwhile, the recovery time of the nanowire sensor at T = 300 K is estimated at 1.5 μs and 16.7 μs for NO and NO2 molecules, respectively. Furthermore, the sensitivities of NO and NO2 are much larger than that of the other molecules. Our results thus conclude that the Zn12O12-based nanowire is a potential candidate for gas sensors with highly sensitivity for NO and NO2.

ZnO nanowires have attracted much interest in the past decade because of their various remarkable physical properties and potential applications not only in gas sensors but also in a number of emerging areas such as low-voltage and short-wavelength optoelectronics, photonics, and solar cells [24][25][26][27][28][29] . It is well known that the major advantage of using nanowires as gas sensors is the surface-to-volume ratio. That is to say, when the diameter of a nanowire is smaller, its surface-to-volume ratio would be higher, which lead to the electrical properties of the nanowires significantly more sensitive to the specific gas molecules 9 . Moreover, quantum confinement effects in ZnO nanowires are only expected for extremely small diameters as the bulk ZnO exciton Bohr radius of about 2.34 nm 30 , and the potential applications of ZnO nanowires as quantum electron devices require their radial confinement 31 . Therefore, the nanowires diameter is a key parameter in order to realize devices exploiting the quantum confinement effect in ZnO nanowires.
Although ZnO nanowires can be synthesized by many approaches, such as physical/chemical vapor deposition [32][33][34] and wet chemical processes 31,35,36 , high-quality ZnO nanowires with much smaller diameters still remain difficult to be synthesized. As we know, only few studies reported on the synthesis of ultrathin ZnO nanowires 32,[37][38][39] . For example, Yin et al. 37 have reported the synthesis of ultrathin, single-crystalline ZnO nanowires with an average diameter of 6 nm, which used micellar gold nanoparticles as catalyst templates. Stichtenoth et al. 32 also reported that the diameter of ultrathin ZnO nanowires can be down to about 4 nm.
In recent years, a "from the bottom up" approach of forming new materials (so-called cluster-assembled materials) of nanoscale dimensions using clusters as building blocks has been developed [40][41][42][43][44][45][46][47] . This approach has opened the pathway to accomplishing the synthesis of new nanoscale materials with tailed properties, indicating that the ZnO nanowires with unusual properties can be assembled by stable ZnO clusters. ZnO clusters have been extensively investigated theoretically and experimentally, and previous reports have demonstrated that Zn 12 O 12 cluster, as the smallest magic fullerene-like cluster, can be taken as a good candidate for the ideal building blocks for forming cluster-assembled materials [48][49][50][51][52][53][54][55] . Because of the diameter of fullerene-like Zn 12 O 12 cluster, which is defined as the distance between the most remote two atoms in cluster, is quite small (about 6.4 Å). As a consequence, the diameter of the ZnO nanowires which are assembled by Zn 12 O 12 cluster would be small, and their properties would be different from that of the traditional ZnO nanowires.
In this work, using first-principles calculations, we firstly demonstrated the feasibility of forming cluster-assembled nanowires based on Zn 12 O 12 cluster by investigating their structural stabilities and electronic properties. Then, we investigated the adsorption behaviors and electronic properties of gas molecules (including CO, NO, NO 2 , SO 2 , NH 3 , CH 4 , CO 2 , O 2 , and H 2 ) on the Zn 12 O 12 -based nanowires, to find out the possibility of using the Zn 12 O 12 -based nanowires as gas sensors for some certain gases detection.

Computational Methods
The spin-polarized density functional theory (DFT) implemented in the DMol 3 program 56,57 was performed for structural relaxation and electronic calculations. The generalized gradient approximation formulated by Perdew, Burke, and Ernzerhof (PBE) 58 with van der Waals (vdW) correction proposed by Tkatchenko and Scheffler (TS method) 59 was chosen to describe the exchange-correlation energy functional. Density-functional semi-core pseudopotentials (DSPPs) 60 fitted to all-electron relativistic DFT results, and double numerical basis sets supplemented with d polarization functions (i.e. the DND set) were selected. The charge transfer was analyzed based on Hirshfeld analysis 61 , which is based directly on the electron density as a function of space. A tetragonal supercell of 20 × 20 × L Å 3 was set for all calculations, where L is the length of translational periodicity. The Brillouin zone was sampled by 1 × 1 × 10 special k-points for structural relaxation, while 1 × 1 × 15 k-points for electronic structure calculations using the Monkhorst-Pack scheme 62 . In our previous studies, we have confirmed the reliability of the GGA-PBE and DND combination for predicting structural and electronic properties of (doped) ZnO clusters and cluster-assembled materials 50,63,64 .
The binding energy per ZnO (E b ) is defined as where E Zn , E O , and E (ZnO)n are the total energies of an isolated Zn atom, an isolated O atom, the corresponding (ZnO) n system, respectively, and n is the number of Zn or O atoms involved. To investigate the stability of the adsorption of molecules on Zn 12 O 12 -based nanowires, the adsorption energy (E ads ) is defined as where E (nanowire+molecule) , E (nanowire) and E (molecule) is the total energy of the system of molecule adsorbed on the nanowire, the corresponding pure nanowire and molecule, respectively.

Results and Discussion
The cluster-assembled nanowires based on Zn 12 O 12 . Recently, Zn 12 O 12 cluster has been probed by time-resolved photoelectron spectroscopy 52,53 , which further demonstrates that Zn 12 O 12 cluster is a promising building block for cluster-assembled materials with tailed properties. In previous work, we have proposed one growth path of Zn 12 O 12 cluster-cluster coalescence, and predicted that assembly can form by attaching a Zn 12 O 12 cage on a hexagonal site 50 . Further, Liu et al. 51 have characterized a family of Zn 12 O 12 cluster-assembled solid phases with novel structures and properties, and the most phases are formed by the hexagonal face coalescence. It is well known that Zn 12 O 12 cluster is a highly stable cluster with a cage structure with six isolated four-membered rings (4MRs) and eight six-membered rings (6MRs), which is shown in Fig. 1(a). Two most stable Zn 12 O 12 dimers are presented in Fig. 1(b and c). It can be seen that both two dimers are formed by the hexagonal face coalescence. However, what is different is that in the most stable one a 6MR of one monomer is connected with a 6MR of the other monomer, while in the second stable one a 6MR of one monomer is connected with a 4MR of the other monomer. Although the structures of the two dimers are different, the energy difference is very small (only 0.007 eV). These results are in good agreement with previous work 51 . On the basis of the two coalescence ways shown in dimers, we further investigated the Zn 12 O 12 tetramers. It is found that the wire-like structure of tetramers can be viewed as the coalescence of the two corresponding dimers, which is shown in Fig. 1  Based on the coalescence ways and characters of the dimers and tetramers, we can conclude that the Zn 12 O 12 -based nanowires can be formed by a translational symmetry arrangement. The segments of the two stable configurations of Zn 12 O 12 -based nanowires are shown in Fig. 1(f and g), named as nanowire-1 and nanowire-2, respectively. The calculated binding energy per ZnO (E b ) and the band energy gap are summarized in Table 1. It is clear that the structural geometry of the isolated Zn 12 O 12 monomer can be maintained in the assembled nanowires. This feature is similar to the cases of other cluster-assembled materials based on Zn 12 O 12 50,51 . From Table 1, it can be seen that the E b of the two nanowires are larger than that of monomer, dimers and tetramers, suggesting that the stability of Zn 12 O 12 -based nanostructures is strengthened because of the assembly continuing. The stability of the above discussed nanostructures (monomer, dimer, tetramer, and nanowire) is also demonstrated by their vibrational frequencies calculations. We found that these structures have no imaginary frequencies, indicating that they are real stable. The most stable nanowire is the nanowire-1, in which one 6MR of one monomer faces to a 6MR of adjacent monomer, which is the same as the coalescence way in the most stable dimer and tetramer.
The energy band structures for the two Zn 12 O 12 -assembled nanowires have been calculated and were plotted in Fig. 2. A direct gap of 2.102 eV is found for the most stable nanowire named as nanowire-1, whereas a direct gap of 2.159 eV is found for the second stable nanowire named as nanowire-2, indicating that both nanowires   67 , which shows that the electronic properties of the two Zn 12 O 12 -assembled nanowires are different from that of the traditional ZnO nanowires with wurtzite structures. Furthermore, the total and partial density of states (DOS) of the two Zn 12 O 12 -assembled nanowires were calculated to reach a deep understanding of the features in the band edges near the band gaps, which are also shown in Fig. 2 68 .
Although we have concluded that the two Zn 12 O 12 -assembled nanowires are real stable because of no imaginary frequencies, to develop their potential use as gas sensors, it also should figure out their thermodynamic stability. As a consequence, the thermodynamic stability of the most stable Zn 12 O 12 -based nanowire (i.e. nanowire-1) as an example was investigated using the first-principles Born-Oppenheimer molecular dynamics (BOMD) simulation within a NVT ensemble. The method of GGA-PBE and DND combination in the work was used for BOMD. The temperature was controlled by a Nosé-Hoover chain of thermostats. A simulation time of 8 ps with a time step of 1 fs was set, and the structural change was calculated at a constant temperature of 300 K. The variation in the energy as a function of time is shown in Fig. 3. It can be seen from Fig. 3 that no structural instability was observed at the temperature of 300 K. In addition, the total energies of the considered nanowire-1 during simulations also keep stable oscillation within a quite small range (no more than 0.001 eV), strongly supporting the fact that the structure of nanowire-1 is thermodynamic stable at room temperature. Based on the analysis of binding energy, dimerization energy, vibrational frequencies and thermodynamic stability, it is demonstrated that the assembly of Zn 12 O 12 cluster can form thermodynamic stable one-dimensional nanowires, which can be used as gas sensing materials. However, it is noting that the assembly of Zn 12 O 12 cluster is easier to form three-dimensional phases if there is no any extra restriction, which has been predicted by previous work 51,52 . Even so, our results provided a way to form the ultrafine ZnO nanowires through the assembly of Zn 12 O 12 cluster. For the experimental synthesis of ZnO nanowires by coalescence of Zn 12 O 12 cluster, the cluster evolution into nanowires can be through templating or aggregative mechanisms 69 , which should be similar to the case of single  CdTe nanoparticles (or clusters) evolution into nanowires 70,71 . We then investigated the feasibility of the thermodynamic stable Zn 12 O 12 -based nanowire-1 as a gas sensing material.
Adsorption of CO, NO, NO 2 , SO 2 , NH 3 , CH 4 , CO 2 , O 2 and H 2 . We started by investigating the adsorption geometries of nine gas molecules on the Zn 12 O 12 -based nanowire. To obtain the most stable configurations of each molecule adsorbed on the Zn 12 O 12 -based nanowire, we have considered the initial structures for the molecule-nanowire systems as many as possible. Figures 4 and 5 show the most stable and some low-lying structures of each molecule on the Zn 12 O 12 -based nanowire, and the corresponding results are listed in Table 2. It is found that different gas molecules prefer different adsorption geometries.
For the CO molecule adsorbed on the nanowire, it is found that the configuration of CO molecule located at the top of one Zn atom is the most stable as shown in Fig. 4(a), and the C atom is bonded with one Zn atom forming a Zn-C bond, whose bond length is 2.20 Å (i.e. adsorption distance). At this configuration the adsorption energy is −0.404 eV. The Zn-C bond length is larger than the average value listed in the Cambridge Structural Database (2.01 Å), but in agreement with that of zinc carbatrane compounds 72 . More importantly, the CO molecule can locate at the top of each Zn atom with little energy difference, compared with the most stable one. The CO molecule is also found that it can absorb on the nanowire with the configuration of the C atom located at the bridge of Zn-O bond, which is shown in Fig. 4(b). Its adsorption energy is −0.340 eV, a little higher (0.064 eV) than that of the most stable one. Similar to the most stable configuration of CO on the nanowire, the NO molecule prefers to locate at the top of an arbitrary Zn atom with the E ads of −0.367 ~ −0.355 eV, which is shown in Fig. 4(c-d). Although we have considered a lot of initial structures, no other kind of configurations is found for the NO adsorption.
For the most stable NO 2 adsorption, one O atom of NO 2 is bonded with a Zn atom with the bond length of 2.24 Å. Different geometries of NO 2 adsorption only reflect in the relative location between the molecule and nanowire, see Fig. 4(e-f). This is very similar to the case of NO 2 adsorption on ZnO nanotubes 11 , but different from the adsorption behaviors of NO 2 one other M 12 N 12 cluster-assembled nanowires 65 . Very different from the adsorption of NO 2 , the SO 2 molecule adopted the orientation of O-S-O parallel to one edge of Zn-O-Zn in the nanowire, and the configuration of SO 2 located on this edge is the most stable, as shown in Fig. 4(g), meanwhile one Zn-O bond is broken due to the interaction between the SO 2 and nanowire, which result in a large E ads of −1.281 eV, indicating strong interaction between the SO 2 and the nanowire. The structural deformation of the nanowire may be a limitation for its application as a gas sensor. In the second stable configuration as shown in Fig. 4(h), there are one O atom and S atom bonded with Zn and O atom, respectively. It is 0.209 eV higher in energy than that of the most stable one. For the NH 3 molecule adsorption, the N atom is directly bonded to one Zn atom with relatively large E ads of −1.187 eV. It is noted that for the most stable configuration of NH 3 adsorption, the bonded Zn atom is not located in the interaction region of Zn 12 O 12 monomers. When the N atom is bonded to the Zn atom that is located in the interaction region of Zn 12 O 12 monomers, the interaction between the molecule and nanowire would be weaken, as a matter of fact of the adsorption energy of −0.806 eV.
Based on the analysis of adsorption energy and bonding condition between the molecule and nanowire, it can be concluded that the CO, NO, NO 2 , SO 2 , and NH 3 molecules are all chemically adsorbed on the Zn 12 O 12 -based nanowire. Moreover, it can be seen from Table 2, because of the chemisorptions of CO, NO, NO 2 , SO 2 , and NH 3 , there are obvious charge transfers between the molecules and the Zn 12 O 12 -based nanowire, especially for CO, SO 2 , and NH 3 adsorption. Though the adsorption of NO and NO 2 result in very small charge transfers (less than 0.1 e), it should be noted that our results are obtained using the Hirshfeld method. Actually, almost all charge schemes give significantly larger atomic charges than Hirshfeld scheme, as a consequence, Hirshfeld charges are too small 73 .
Besides the above gas molecules, we also study the adsorption of CH 4 , CO 2 , O 2 and H 2 molecules on the Zn 12 O 12 -based nanowire. The most stable configurations of CH 4 , CO 2 , O 2 and H 2 on the nanowire are shown  We now turn to investigate the influence of gas adsorption on the electronic properties of the Zn 12 O 12 -based nanowire. Electronic band structures and total density of states (DOS) for the most stable configurations of each molecule adsorbed on the Zn 12 O 12 -based nanowire as well as local DOS (LDOS) of the corresponding molecules are shown in Figs 6 and 7, and the corresponding band-gap widths are summarized in Table 2. Compared with the band structures and DOS of the pure Zn 12 O 12 -based nanowire, it can be seen that the adsorption of a single CO, NH 3 , CH 4 , CO 2 , and H 2 molecule per supercell does not introduce any impurity states in the band gap, resulting in a little change of the band gap widths. Similar results were also reported on the adsorption of CO, H 2 and NH 3   11 . Although the charge transfer from the CO molecule to the nanowire does lead the CO molecule to introduce some impurity states within the conduction band, which is located at about 2.5 eV above the Fermi level, it is not expected that the adsorption of NH 3 , CH 4 , CO 2 , and H 2 molecules hardly enhance the electronic conductance of the Zn 12 O 12 -based nanowire, which would block the applications of the Zn 12 O 12 -based nanowires as gas sensors for CO, NH 3 , CH 4 , CO 2 , and H 2 detection. For the adsorption of the SO 2 molecule as shown in Fig. 6(b), LDOS analysis shows that SO 2 adsorption will produce fully occupied states, which are strongly hybridized with the original "bulk" states in the valence bands, and these states are nonlocalized. These results indicate that the interaction between the SO 2 molecule and the nanowire is very strong, which is in agreement with the biggest adsorption energy (−1.281 eV). It is very difficult for the fully occupied states resulted from SO 2 to influence the electronic conductance of the Zn 12 O 12 -based nanowire. From the above analysis, it can be concluded that, although CO, SO 2 , and NH 3 gases are chemisorbed on the nanowire with reasonable E ads and apparent charge transfer, the electronic properties, especially the electronic conductance of the nanowire indeed are not influenced by the adsorption of CO, SO 2 , and NH 3 . This may indicate that the charge transfer does not affect the electronic conductivity of the nanowire, which is very different from that of ZnO surfaces 74 .
However, for the adsorption of NO and NO 2 molecules, it is found that these both molecules adsorption does introduce impurity states in the band gap, and especially some certain unoccupied local states in the conduction as shown in Fig. 7, resulting in the decrease of the original band gap. More importantly, the Fermi level is shifted to original conduction bands for NO adsorption. From this perspective, we do expect that these impurity states and unoccupied local states that produced by NO molecule adsorption can change the conductance of the Zn 12 O 12 -based nanowire. Although the mid-gap states produced by NO 2 may not change the conductance of the Zn 12 O 12 -based nanowire, as mentioned above, NO 2 (the same as NO) behaves as a charge acceptor because of the charge transfer (0.02 e) from the nanowire to the molecule. The charge transfer behavior may influence the electronic conductance of the Zn 12 O 12 -based nanowire, which would be consistent with the experimental findings in that the electronic conductance of ZnO nanowires changes when exposed to NO 2 13 .
It is known that DFT-GGA not only greatly underestimates the band gaps of bulk ZnO, but also of low-dimensional ZnO structures 11,17 , and the hybrid functional or DFT + U can give a quantitatively more accurate band gaps of the ZnO structures 11,17 . However, previous work have found that the overall features of the band structures calculated by using different hybrid functional or DFT + U are nearly the same as that based on the DFT-GGA method 11,17,51,67,68 . Thus, we used the DFT-HSE06 hybrid functional 75 to recalculate the band structures of the most stable configuration of the Zn 12 O 12 -based nanowire without and with NO adsorption, respectively (see Supporting Information Figure S1). The calculated band gaps of the Zn 12 O 12 -based nanowire without and with NO adsorption are 3.438 and 1.110 eV, respectively, much larger than that obtained from GGA-PBE. Compared with the band structures that calculated by GGA-PBE, one can find that the two functional predict similar dispersion features for both valence and conduction bands. These results are in agreement with previous work 11,17,51,67,68 . Since both DFT-HSE06 and GGA-PBE calculations show that the band gap of the Zn 12 O 12 -based nanowire is larger than that of the bulk ZnO (the calculated band gap value of 0.94 eV), we may expect that the qualitatively correct trend in the band structure can still be drawn from the GGA-PBE calculation. More importantly, as discussed below, the results are valuable for comparative studies on the change of band gaps because of the molecule adsorption.
The possibility of the Zn 12 O 12 -based nanowire as gas sensors. In general, a good commercial sensor should face the following challenges: sensor sensitivity, selectivity, stability, and speed (response and recovery rate), namely the "4 s". Next, we would discuss the possibility of the Zn 12 O 12 -based nanowire as a gas sensor for some certain gas detection, that is, whether the gas sensors based on the Zn 12 O 12 -based nanowire can exhibit better performances.
As mentioned above, the Zn 12 O 12 -based nanowire is particularly thermodynamic stable at room temperature. After the NO and NO 2 molecules adsorption, it is found that there is no structural deformation in Zn 12 O 12 -based nanowire, further indicating the stability of Zn 12 O 12 -based nanowire for the adsorption of NO and NO 2 .
If the Zn 12 O 12 -based nanowire is indeed effective as a gas sensor for certain gas detection, the molecular gases would be chemically adsorbed on the Zn 12 O 12 -based nanowire with apparent E ads . As above discussed, CO, NO, NO 2 , SO 2 , and NH 3 molecules are all chemisorbed on the nanowire with reasonable E ads , but CH 4 , CO 2 , O 2 and H 2 molecules are only physically adsorbed on the nanowires with small E ads and little charge transfer, indicating that the nanowire is incapable for sensing CH 4 , CO 2 , O 2 and H 2 gases. Furthermore, the conductivity under a certain temperature can be estimated by the following equation: g where σ is the electric conductivity of the configurations, E g is the band gap value of the configurations, k is the Boltzmann's constant, and T is the thermodynamic temperature. As the equation is shown that the conductivity is controlled by exp (−E g /kT) under a certain temperature, a change of electronic conductance would be observed by experiment. Therefore the changes of electronic conductance of the nanowire before and after the adsorption can be used to differentiate the molecules because of the change of E g . It is found that the adsorption of CO, SO 2 , and NH 3 molecules makes the change of band gap of Zn 12 O 12 -based nanowire be very small, indicating the adsorption of these molecules hardly has any impact on the electric conductivity of the nanowire. This is consisting with the analysis of band structures and DOS. However, the adsorption of NO and NO 2 changes the band gap widths of the nanowire as obvious as from 2.106 eV for pure nanowire to 0.525 and 0.259 eV, respectively. Therefore, the NO and NO 2 molecules can be detected by calculating the conductivity change in the Zn 12 O 12 -based nanowire before and after the adsorption process. If the Zn 12 O 12 -based nanowire cannot detect the NO and NO 2 molecules because of the change of conductance, it also can be concluded by using a completely new transduction principle, which is the exploitation of magnetic instead of electrical properties modifications due to surface-gas interaction in the active material 6,76 . Our results show that the Zn 12 O 12 -based nanowire is non-magnetic. The spin density of the most stable configurations of NO 2 (or NO) adsorbed on the Zn 12 O 12 -based nanowire is shown in Fig. 8. The adsorption of NO (or NO 2 ) molecule introduces spin polarization in the Zn 12 O 12 -based nanowire with a magnetic moment of approximately 1 μ B , indicating that magnetic properties of the Zn 12 O 12 -based nanowire is changed obviously due to the adsorption of NO (or NO 2 ) molecule. Furthermore, the magnetic moment is mainly located at the NO 2 (or NO) molecule, and chiefly originates from the 2p states of N and O atoms. However, the net spin polarization of the Zn 12 O 12 -based nanowire is not modified due to the adsorption of the other considered molecules. In this regard of the change of magnetic properties, the Zn 12 O 12 -based nanowire can be viewed as a highly sensitive gas detection technique based on the measurement of the local magnetic moment in the Zn 12 O 12 -based nanowire using various experimental methods such as AFM or SQUID magnetometry [77][78][79] .
Furthermore, the strong interaction between the molecules and the Zn 12 O 12 -based nanowire also block the applications of the nanowire as a gas sensor. This is because that strong adsorption would make the molecules desorbed from the nanowire very difficultly, and the devices would suffer a longer recovery time. The transition state theory gives the relation between the recovery time (τ) and the adsorption energy (E ads ) as follows: where ν 0 is the attempt frequency, k is the Boltzmann's constant, and T is the temperature. Supposing all the considered molecules have the same order of magnitude for the attempt frequency as NO 2 (ν 0 = 10 12 s −1 ) 80 . We can estimate that the strong adsorption energies of SO 2 and NH 3 on the nanowire (more than −1 eV) would match a recovery time of much more than 12 hours at T = 300 K, which further shows that the Zn 12 O 12 -based nanowire is not suitable as a reusable sensor for SO 2 and NH 3 gases. Because of the adsorption energy of −0.367 and −0.430 eV for NO and NO 2 , we can obtain the recovery time of the Zn 12 O 12 -based nanowire sensor at T = 300 K to be 1.5 μs and 16.7 μs, respectively, indicating the rapid response of the Zn 12 O 12 -based nanowire to NO and NO 2 gases. Experimentally, one of the most important parameters for sensing a gas is sensitivity (S), which is defined as follows: 74 where k is the Boltzmann's constant and T is the temperature. E g0 is the band gap of the Zn 12 O 12 -based nanowire with gas adsorption, and E g is the band gap of the pure Zn 12 O 12 -based nanowire. It is obvious that the sensitivity would grow exponentially with a decrease in E g . Yuan et al. 74 have investigated the sensitivity of the ZnO surface using the above equation, which has been modified by taking account of environmental influence. The sensitivities of H 2 , NH 3 and ethanol at 573 K they estimated are in agreement with experimental data. Although there are no experimental data that can used to compare with our calculated results, and the GGA-PBE calculations underestimate the band gap widths of semiconductors, we can estimate the trend of sensitivities of different molecules on the Zn 12 O 12 -based nanowire at room temperature. It can be concluded that the sensitivities of NO and NO 2 gases are much larger than that of other gases because of the larger difference value of band gaps of the nanowire before and after adsorption of NO and NO 2 . This shows that the Zn 12 O 12 -based nanowire can be a highly sensitive gas sensor for NO and NO 2 detection.

Conclusions
In conclusion, using first-principles calculations based on density functional theory, firstly, we investigated the structural and electronic properties of cluster-assembled nanowires based on Zn 12 O 12 cluster, then investigated the structures, energetics, charge transfer and electronic properties of the most stable Zn 12 O 12 -based nanowire adsorbed by environmental gases, including CO, NO, NO 2 , SO 2 , NH 3 , CH 4 , CO 2 , O 2 and H 2 . Our results indicate that the ultrathin ZnO nanowires can be assembled by the coalescence of stable Zn 12 O 12 cluster. The Zn 12 O 12 -based nanowires have semiconducting properties with direct energy gaps, and are particularly stable at room temperature. The CO, NO, NO 2 , SO 2 , and NH 3 molecules are all chemisorbed on the Zn 12 O 12 -based nanowire with reasonable adsorption energies, but CH 4 , CO 2 , O 2 and H 2 molecules are only physically adsorbed on the nanowire with small E ads and little charge transfer. The electronic properties of the Zn 12 O 12 -based nanowire present dramatic changes after the adsorption of the NO and NO 2 molecules, especially their electric conductivity, however, the other molecules adsorption hardly change the electronic properties of the nanowire. Furthermore, The adsorption of NO (or NO 2 ) molecule introduces spin polarization in the Zn 12 O 12 -based nanowire with a magnetic moment of approximately 1 μ B , indicating that magnetic properties of the Zn 12 O 12 -based nanowire is changed obviously due to the adsorption of NO (or NO 2 ) molecule. Meanwhile, the strong adsorption of SO 2 and NH 3 makes their recovery times be much longer than 12 hours, which precludes its applications for SO 2 and NH 3 sensors, however, the recovery time of the nanowire sensor at T = 300 K is 1.5 μs and 16.7 μs for NO and NO 2 molecules, respectively. Furthermore, the sensitivities of NO and NO 2 are much larger than that of the other molecules. Therefore, synthetically considering the adsorption energies, charge transfer, the change of electric conductivity and magnetic properties, sensitivities and recovery time, we can conclude that the Zn 12 O 12 -based nanowire is a potential candidate for gas sensors with highly sensitivity for NO and NO 2 .