DFT Investigations of Aun Nano-Clusters Supported on TiO2 Nanotubes: Structures and Electronic Properties

TiO2 nanotubes (TiO2NTs) are beneficial for photogenerated electron separation in photocatalysis. In order to improve the utilization rate of TiO2NTs in the visible light region, an effective method is to use Aun cluster deposition-modified TiO2NTs. It is of great significance to investigate the mechanism of Aun clusters supported on TiO2NTs to strengthen its visible-light response. In this work, the structures, electronic properties, Mulliken atomic charge, density of states, band structure, and deformation density of Aun (n = 1, 8, 13) clusters supported on TiO2NTs were investigated by DMOL3. Based on published research results, the most stable adsorption configurations of Aun (n = 1, 8, 13) clusters supported with TiO2NTs were obtained. The adsorption energy increased as the number of Au adatoms increased linearly. The Aun clusters supported on TiO2NTs carry a negative charge. The band gaps of the three most stable structures of each adsorption system decreased compared to TiO2NTs; the valence top and the conduction bottom of the Fermi level come mainly from the contribution of 5d and 6s-Au. The electronic properties of the 5d and 6s impurity orbitals cause valence widening and band gap narrowing.


Introduction
The research on nanostructure models of metal clusters supported on well-ordered metal oxide surfaces is significant, providing important insights into the properties and mechanisms of real catalyst systems, and thus has been conducted extensively over the past few years [1][2][3][4][5][6][7][8][9][10][11][12][13]. In these model systems, the nature and strength of the interaction between the metal clusters and the support materials not only govern the nucleation and stability of the metal clusters, but also control the geometric and electronic structure of the resulting cluster/oxide interface, which are in turn critical to the catalytic activity of oxide-supported metal clusters [1,2]. Titanium dioxide has attracted worldwide attention due to its potential applications in a wide variety of products, such as photocatalysis [14,15], solar cells [16][17][18], and designing nanostructure architectures [19][20][21][22][23], due to its excellent gas sensitivity, moisture sensitivity, dielectric effect, photoelectric conversion and photocatalytic properties, chemical stability, nontoxicity, and relatively low cost. Among the three different polymorphs of TiO 2 , rutile, anatase, and brookite, the anatase phase has been extensively studied over the last few decades due to its technological applications and photocatalysis [24]. However, the low surface area (ca. 50 m 2 /g) and the large band gap of TiO 2 (about 3.2 eV in the anatase phase [25]) limit its light absorption to only 5% of the solar spectrum [26][27][28], restricting its applications. In order to make more use of solar energy to increase the photocatalytic efficiency, it is more beneficial for absorbing visible light to reduce the band gap of TiO 2 and increase the surface area of TiO 2 materials. As is well known to us, among the nanostructures, namely simple assemblies of nanoparticles, onedimensional (1D) nanostructures (nanorods, nanowires, and nanotubes) have a relatively large surface area. Accordingly, the TiO 2 nanotubes (TiO 2 NTs) constructed by anatase are a promising structure with a large surface area of 328 m 2 /g [29]. Furthermore, TiO 2 NTs For Au n nanoclusters with 11 to 14 atoms, there appears to be a transition from 2D to 3D structures [57]. The work of J. Oviedo suggested that the most stable structure of Au 13 comprises face-centered cubes or icosahedrons [55]. Ghazal Shafai et al. [57] selected the lowest-energy isomers for four types of cluster: planar, flake, cuboctahedron, and icosahedrons. The results show that there is no energy barrier between the icosahedron and the cuboctahedron configurations. Under the principle of three-dimensional configuration, we adopted a face-centered cubic and icosahedron structure for the original structures of the Au 13 cluster. After optimization, the icosahedrons deformed into a distorted face-centered cubic structure, which is consistent with results of [57]. Therefore, we used a cuboctahedron as the initial configuration of the Au 13 cluster. After the geometric optimization without symmetry being restricted, an energy-stable Au 13 cuboctahedral structure was obtained. In order to understand the driving mechanism that determines the morphology and charge transport of TiO 2 NT-supported Au n nanoparticles, the structural and electronic properties of the adsorption systems were studied.

Methodology
The geometric structures of the bare nanotube and bare Au n clusters are shown in Figure 1. All the calculations were performed using the semi-core pseudopotential method within the DFT framework. Exchange and correlation terms were considered within the generalized gradient approximation (GGA) with a Perdew-Burke-Ernzerof (PBE) functional [58], the all-electron double numerical basis set with a polarized function (DNP), as implemented in Dmol3 code [59,60]. A tetragonal supercell with the size of 40 Å × 40 Å × c Å was set, where the parameter c was 11 Å, equal to the minimum periodic unit length of the TiO 2 NT (6,0). The supercell included 32 titanium and 64 oxygen atoms with the crystal form of (TiO 2 ) 32 . The Brillouin zone was sampled by 4*4*2 [61] special k-points using the Monkhorst Pack [62] scheme for geometrical optimizations and the electronic properties calculation of TiO 2 anatase, TiO 2 NT, and adsorption systems, respectively. A spin-restricted formalism was employed even in the presence of unpaired electrons, as the geometrical optimization is extremely sensitive to the details of the computational approach. The calculated bulk anatase TiO 2 lattice parameters (a = b = 3.8283 Å, c = 9.5734 Å, u = 0.2080 Å, where u = d ap /c is the internal coordinate and d ap is the Ti-O top bond length) agree well with the experiments [25,63]. The calculated band gap of pure anatase TiO 2 is 2.77 eV, which is smaller than the experimental value, 3.2 eV [25]. This is due to the fact that density functional theory does not consider the electronic exchangecorrelation potential discontinuity, which results in the basic band gap width being smaller than the experimental value by about 30-50%, generally. This does not affect the analysis of the electronic structure. The initial single-walled anatase TiO 2 NT models were constructed by rolling up one (101) layer of the anatase structure in the 101 direction [30,34,64,65]. The (101) layer has 12 atoms (four titanium and eight oxygen atoms) in the unit cell and with the basic vectors V and U in the [010] and 101 directions, respectively. The nanotubes were obtained by rolling up the layer in ways in which the chiral vectors (6,0) = 6 V became the circumferences of the nanotube. The 1D line symmetry group of the nanotube TiO 2 NT (6,0) can be represented as P42/mmc (D4H-9).
According to the work of Vittadini and Selloni on TiO 2 (101) surface adsorption of Au clusters [3], the adsorption energies for Au n clusters are as follows: where E Au n /TiO 2 NT (E TiO 2 NT ) represents the energy of the nanotube with (without) the adsorbate, and E Au n denotes the energy of the gas-phase cluster. We also define a cohesive energy to obtain information about the clustering energetics: where E Au is the total energy of a free Au atom. E ads Au n = E clu Au n , when a single Au adatom is on the TiO 2 NT surface. Electronic structure analyses, including Mulliken charge and density of states (DOS), the partial density of states (PDOS), as well as deformation density, energy gap, and molecular orbital, were performed with DMOL3 of Materials Studio package (MS, version 8.0 Accelrys Software Inc., San Diego, CA, USA). These analyses were used to help us understand the nature of bonding and the interaction between Au n clusters and anatase TiO 2 NTs.

Structures of Anatase TiO 2 Nanotubes
The cross-sectional and side view of the optimized TiO 2 NT (6,0) are shown in Figure 1. In the TiO 2 NT (6,0), both the inner and outer walls were terminated with the two-foldcoordinated oxygen atoms (2cO). In addition to 2cO atoms, three-fold-coordinated oxygen atoms (3cO) as well as five-fold-coordinated (5cTi) atoms are also exposed on the surface of the TiO 2 NT (6,0).

Structures of Au 1 /TiO 2 NTs
Two different stable adsorption structures were found for a single Au adatom on the TiO 2 NT (6,0) surface, as shown in Figure 2: a symmetric bridging site between two edge 2cO atoms in the 101 direction, Au 1(O,O) , and the other right on top of a 3cO atom, as well as bonding to three 5cTi atoms, Au 1(O,Ti) . The adsorption energies of Au in these two configurations are listed in Table 1. For the two stable configurations, the adsorption energy of Au 1(O,Ti) is 0.49 eV. Au 1(O,Ti) is significantly more stable than Au 1(O,O) , which has an adsorption energy of about 0.20 eV. To illustrate the charge of adsorbed clusters and the charge distributions of clusters and related TiO 2 NT surface atoms, Mulliken charge analysis was employed. The Mulliken charges of Au and the nanotube surface atoms that directly associated with the Au adatom are shown in Table 1. Apparently, Au became negatively charged by receiving electrons in both configurations. Both types of O atoms binding to Au directly became less negative, and most 5cTi atoms became more positive, except for 5cTi 3 , which generally indicated the loss of electrons. This is consistent with Au adsorption on the anatase TiO 2 (101) surface [3].  The DOS plots of bare TiO 2 NT and the adsorption system, and the PDOS plots of the Au adatom and the oxygen atoms and titanium atoms of TiO 2 nanotube, are shown in Figure 3 and are used to further illustrate bonding characteristics. For the projection of 2p orbitals of oxygen, 3d orbitals of titanium and 5d orbitals of gold showed the major contribution to the PDOS in the energy range of interest. Therefore, projections of individual orbitals along with the DOS are shown. The zero on the energy axis of the plots corresponds to the Fermi level of the bare TiO 2 NT and is at the top of the valence band, marked with a red dashed line in the figures. As presented in Figure 3a, the bare TiO 2 NT is semiconducting, and the valence band mostly has a contribution by the O 2p orbital (red line in Figure 3a) with a small contribution from the Ti 3d orbital (blue line in Figure 3a). The conduction band is dominated by the Ti 3d orbital. The electron density contributed by the O 2s orbital in the low energy region from −0.8 Ha to −0.5 Ha has little effect on the electron structure regarding the Fermi level. Therefore, in the following parts, we do not discuss this any further. According to Figure 3b,c, after an Au atom was adsorbed on TiO 2 NTs, the TiO 2 NTs retained some semiconductor properties. The Fermi level moved close to the bottom of conduction band, and the valence band had mostly an O 2p character, but a new small peak of the Au 5d atom arose at the top of it. Correspondingly, a smaller peak of Au 6s appeared in the bottom of the conduction band at the zero of the energy axis. Compared with Au 1(O,O) , the Au 5d peak arose in the valence band separately. The valence band of Au 1(O,Ti) contributed by the Au 5d peak, overlapped well with the O 2p and Ti 3d. It is thus more likely to cause electron transfer. The contribution of the Au 5d and 6s orbitals at the top valence band and bottom conduction band causes valence band broadening and band gap narrowing, which causes the adsorption band edge of TiO 2 NTs to red shift. . The black curve is the sum of PDOS of O atoms, Ti atoms, and Au atoms from the optimized bare TiO 2 NT (6,0)/Au systems, while the red curve indicates the 2p orbital of oxygen atoms, the dark green curve indicates the 2s orbital of oxygen atoms, the blue curve represents the 3d orbital of titanium atoms, the light green curve denotes the 5d orbital of gold atoms, and the magenta curve represents the 5s orbital of gold atoms, respectively. The Fermi level of bare TiO 2 NTs is set at 0 eV, as denoted in the red dashed line.
The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) along with the energy gap of bare TiO 2 NTs and the adsorption system are shown in Figure 4. In the two adsorption configurations, the Au atoms are supported on the TiO 2 NT surface, reducing the energy gap from 2.704 eV to 1.979 eV and 2.592 eV, respectively. Further analysis shows that the d orbital of Au adatoms has an evident contribution to the HOMO orbital. The results are the same as the previous analysis of DOS. This leads to the energy of HOMO (Au 1(O,O) ) rising from −7.171 eV to −6.494 eV.
Meanwhile, the major feature of HOMO is that the Au 5d orbital as well as the O 2p orbital replaced the main contribution of O 2p. The energy of LUMO (Au 1(O,O) ) decreases from −4.467 eV to −4.515 eV. The 3d x 2 −y 2 orbital of Ti gives the contribution to the bottom of the conduction band. The character of the 6s orbital of Au was not obviously observed in the LUMO orbital. The bonding characteristics of the adsorption system are further demonstrated in the electron deformation density (EDD) contour maps in Figure 5. The EDD contour maps were defined as the total density by subtracting the isolated atoms' electron density. Compared with the Au 1(O,O) , which has no significant bonding between Au atoms, and 2cO atoms deposited on the TiO 2 NT surface, the Au 1(O,Ti) has an obvious depletion of electron density when the 3cO 2p orbital is aligned with the Au-3cO bond direction. Additionally, the Au atom was surrounded by a small number of electrons, which indicated the electron transfer from TiO 2 NTs to gold nano-clusters.  Figure 6 shows four different configurations of Au 8 clusters adsorbed on the TiO 2 NT surface. The structures of Au 8 in the four adsorption systems still maintain the biplanar conformation. The adsorption energy and Mulliken charge analysis for all these structures are listed in Table 2. Au 8-A(2cO,3cO,2cO) is the most stable configuration for the Au 8 /TiO 2 NT systems, as shown in Figure 6(A-a,A-b). In this structure, three Au atoms as an adsorption layer bond to TiO 2 NT surface atoms, and the oxygen atoms of the TiO 2 NT surface which interacted with the Au 8-A were 2cO, 3cO, and 2cO, respectively. In the structure shown in Figure 6(B-a,B-b), Au 8-B(2cO,5cTi) has an adsorption energy of about 0.86 eV, slightly smaller than Au 8-A , which has an adsorption energy of 1.11 eV. For the adsorption configuration of Au 8-B , similar to Au 8-A , there was an adsorption layer consisting of three Au atoms from the side direction of original Au 8 biplanar binding to the TiO 2 NT directly. The third structure, Au 8-C(2cO,2cO,3cO) , which is displayed in Figure 6(C-a,C-b), is almost as stable as Au 8-B . The energy difference between the two structures is merely 0.05 eV. In Au 8-C , the adsorption layer is made up by four Au atoms as the bottom layer connecting with the TiO 2 NT surface. Both the bottom and top layer are part of the rhombus. The fourth structure, Au 8-D(2cO,2cO,3cO) , is a result of the relaxation by five Au atoms of Au 8 biplanar parallel to the axial of TiO 2 NTs. Au 8-D , as a local minimum, has similar binding sites to Au 8-C , and is evidently less stable than the three previous structures. Noticeably, the adsorption of Au adatoms caused the TiO 2 NT surface's deformation; the 3cO atoms which bonded with Au adatoms were pulled off of the surface of TiO 2 NT. Meanwhile, the other 3cO atoms which have no relation with the Au 8 clusters were "pushed" into a slightly concave formation. This phenomenon can be found in Figure 6. According to Table 2, the Au 8 clusters in four structures were negatively charged. Based on analysis of Au nanocluster size with Mulliken atomic charge and adsorption energy, for Au 8 clusters, not only transfer charges but also adsorption energies were increased, with clusters enlarging. Compared to Au 1 absorption systems with a charge of about −0.060 au and −0.075 au, respectively, there was a remarkable increase in the electron transfer to Au 8 clusters. The maximum charge is −0.424 au for the Au 8-C structure. This phenomenon suggested that more charge transfer will be required to enlarge the size of Au n nanoclusters to a certain degree. The interatomic charge distributions of related TiO 2 NT surface atoms were analyzed in detail. Apart from a few TiO 2 NT surface atoms, there are two main trends in atomic charge redistribution after the adsorption of Au 8 clusters: electron transfer to oxygen atoms, and titanium losing electrons and showing greater positive charge.

Structures of Au 8 /TiO 2 NT
PDOSs of Au 8 clusters as well as the associated TiO 2 NT surface atoms in all four adsorption structures are plotted in Figure 7. The mixing between the O 2p orbital and Au 5d6s states spans the whole energy range of the valence band. Compared with the PDOS of a single Au adatom, the intensity of Au 8 clusters at the Fermi level was greatly increased. The Au clusters' 6s states make a dominating contribution to the states for the gap and are closely related to the Fermi level. The fact is that the energy gap of bare TiO 2 NTs almost disappears in all four adsorption systems. This indicates that metallization of the nanojunction Au 8 -TiO 2 NT system occurs, and therefore further increases tunnelling currents [66].
For more detailed analysis, the molecular orbital diagrams of HOMO and LUMO along with band gaps of the adsorption systems are shown in Figure 8. As the Au 8 clusters adsorb on the TiO 2 NT surface, the contribution of metal clusters to the HOMO and the LUMO of the Fermi level is increased. As in the analysis of DOS, the band gap of the Au 8 -TiO 2 NT nanojunction was below 1.10 eV; Au 8 clusters narrowed the band gap of the system more efficaciously than a single Au adatom. From the EDD contour maps of the Au 8 adsorption system in Figure 5e,f, it can be found that Au 8 clusters obtained electrons from TiO 2 NTs. In addition to the electron cloud distribution in Au 8 nanoclusters, the Au atoms which have direct bonding with TiO 2 NT surface atoms show obvious electron accumulation, such as a Au 8-C structure, as shown in Figure 5f.  A-a,B-a,C-a,D-a), respectively. The side vies of four adsorption geometries are shown as (A-b,B-b,C-b,D-b), respectively.

Structures of Au 13 /TiO 2 NT
Au 13 clusters in the gas phase have two stable 3D arrangements: icosahedrons and cuboctahedrons. There is no energy barrier between these two configurations. In our study, the icosahedrons deformed into a distorted face-centered cubic structure after geometry optimization. Au 13 clusters possessing the more stable configuration of cuboctahedrons were selected to construct the Au 13 /TiO 2 NT system. Three stable adsorption configurations for Au 13 /TiO 2 NTs were obtained. The investigated configurations for the three adsorption systems are displayed in Figure 9. We can find that the condition of TiO 2 NT surface oxygen atoms which bind with the cluster is similar to the Au 8- A(2cO,3cO,2cO) . For the Au 13-A(2cO,2cO) configuration, in which the cluster is parallel to the TiO 2 NT axial, Au 13 bonded to two oxygen atoms on the nanotube surface and possessed the conformation with Au atoms spreading on the outside of nanotube surface, which is energetically preferred (see Table 3). In Au 13-B(2cO,3cO,2cO,3cO) , the absorbed Au 13 cluster is similar to a cage-like structure [67,68], with four Au atoms directly bonding to the TiO 2 NT surface. Since the cage-like structure covers less area of the TiO 2 nanotube than the flat geometry does, the density of the interfacial sites of the former is less than that of the latter. Although the cage-like structure is slightly less energetically favored than one of the geometries considered here, when the interface is considered as the controlling parameter, the cage-like Au 13 nanoclusters can be expected to be more active than the other one for catalytic reactions. For optimized Au 13-C(3cO,2cO) configuration, it also presents as a cage-like configuration. Au 13 is adsorbed with a three-coordination oxygen atom and a two-coordination bridge oxygen atom, as shown in Figure 9C. The interaction of the Au 13 with the nanotube surface was further analyzed with Mulliken charges. The adsorption energy for these structures and the Mulliken charges on the Au atoms and the binding atoms of TiO 2 NT are summarized in Table 3. Au 13 /TiO 2 NT systems have greater adsorption energy than Au 8 and Au 1 systems (see Table 3). This indicates that increasing the number of Au atoms can enhance the stabilization of the adsorption system and the size scope of Au clusters according to the results of this study for the Au nanoclusters. According to Table 3, with previous Mulliken charge analysis results of Au 1 and Au 8 , the Au 13 clusters became negative after being absorbed on TiO 2 NTs. However, the number of electrons transferred experiences no change. The interatomic charge distributions of related TiO 2 NT surface atoms are shown in Table 3. The two main trends of atomic charge redistribution after the adsorption of Au 13 clusters are: electron transfer to oxygen atoms and titanium losing electrons and showing a more positive charge, except for a few TiO 2 NT surface atoms, which is similar to the Au 8 system. For further details, we integrated Mulliken charge analysis with deformation density (see Figure 5g,h); noticeably, there are significant electrons missing on the three coordination oxygen atoms, while the connected Au atoms obtain electrons, which are highlighted using a red dashed line in the EDD contour maps in Figure 5h. Figure 10 shows the PDOS of Au 13 clusters and connecting surface atoms of TiO 2 NT along with the DOS of adsorption system. 5d-Au has a contribution to the top of the valence band and overlaps well with the O 2p orbital for all three adsorption structures. With the electron density of 5d6s-Au being raised, the contribution from Au atoms in the valence band and the conduction band was more and more obvious. The Au 13 cluster adsorbed onto the TiO 2 NT surface will have an excellent performance in electron transport. The HOMO and LUMO orbital diagrams of adsorption systems, as shown in Figure 11, visually illustrate the orbital analysis results given the density of states. Au 13 nanoclusters contribute to the valence band and the conduction band, along with the increase in the number of gold atoms. HOMO and LUMO orbitals are mainly provided by the Au nanoclusters. Compared with the Au 8 /TiO 2 NT system, the system's energy is further decreased, particularly for the Au 13-A configuration, which downgraded the energy gap to 0.049 eV, far below the maximum energy value of the visible light absorption.

Conclusions
In summary, Au n /TiO 2 NTsystems are studied using density functional theory to characterize the effect of the adsorption of Au n (n = 1, 8, 13) clusters on the geometric and electronic structures of anatase TiO 2 NT. Our results show that a single Au adatom prefers the top position of 3cO as well as the bridging 2cO-2cO site of the TiO 2 NT surface. Adsorbed Au 8 maintains a distorted biplanar configuration. The strong interaction between Au n and atoms of the nanotube surface causes deformation of TiO 2 NT. Au 13 is adsorbed in a cage-like structure and has a tendency to spread out on the wetted nanotube surface.
The adsorption energy is increased as the number of Au atoms increases linearly, and increases in the size of Au n clusters are conducive to stabilizing the load systems. The peaks at the Fermi level of the valence top and the conduction bottom come mainly from the contribution of 5d6s-Au atoms. The 5d6s orbital of impurities' electronic state density caused valence widening and band gap narrowing. The band gap of the three most stable structures of adsorption systems Au 1-A (2.592 eV), Au 8-A (1.100 eV), and Au 13-A (0.049 eV) decreased compared to bare TiO 2 NTs. This causes TiO 2 NTs to achieve a visible light response. Molecular orbital diagrams intuitively verify the obviously increasing contribution to HOMO and LUMO orbitals with the increase in gold atoms. Our present results serve as a possible indicator that the nanojunction TiO 2 NT/Au n cluster, as a potential photoelectric device, possesses better energy and charge transmission performance.