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

Abstract

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 Au_n cluster deposition-modified TiO₂NTs. It is of great significance to investigate the mechanism of Au_n 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 Au_n (n = 1, 8, 13) clusters supported on TiO₂NTs were investigated by DMOL3. Based on published research results, the most stable adsorption configurations of Au_n (n = 1, 8, 13) clusters supported with TiO₂NTs were obtained. The adsorption energy increased as the number of Au adatoms increased linearly. The Au_n 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.

1. 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 TiO₂, 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 m²/g) and the large band gap of TiO₂ (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 TiO₂ and increase the surface area of TiO₂ materials. As is well known to us, among the nanostructures, namely simple assemblies of nanoparticles, one-dimensional (1D) nanostructures (nanorods, nanowires, and nanotubes) have a relatively large surface area. Accordingly, the TiO₂ nanotubes (TiO₂NTs) constructed by anatase are a promising structure with a large surface area of 328 m²/g [29]. Furthermore, TiO₂NTs have a smaller band gap than the bulk powders and strong adsorption capacity, which will be desired to improve the photocatalytic properties and photoelectricity conversion effects, and have attracted considerable attention. A 3D random network of nanoparticles with more particle boundaries is more beneficial for transporting charge carriers than 1D nanostructures. Therefore, the collection of photogenerated charge carriers should be enhanced for adopted 1D nanostructure materials [30,31,32,33].

Although the smaller band gap of TiO₂NTs was beneficial in the absorbing of visible lights [34], they clearly required more solar energy than modified nanotubes. In order to enhance the visible light sensitivity of TiO₂ photocatalyst materials, many efforts have been made. The main modification methods are the organic dye photosensitive process, noble metal deposition, metal ion doping, the semiconductor coupling method, and so on. Metal nanoparticles (NPs) have considerably better photostability than semiconductor quantum dots, which usually suffer from anodic corrosion [26,35,36]. Some metal elements such as Au, Pt, Ag, Cu, and Fe have been employed to tune the electronic structure and enhance the catalytic activity of TiO₂NTs [4,37,38,39,40,41,42,43,44]. Among various metal clusters, the Au cluster is considered as one of the most promising candidates owing to its high conductivity, good stability in the air, and controllability of the electrical properties. In contrast to the noble character of bulk Au, the Au cluster/metal oxide system (such as Au/TiO₂) has been extensively studied due to the unique catalytic activity of this system. Recently, Zhi and co-workers [37] demonstrated that an Au nanoparticle–TiO₂ nanotube junction was formed by using bovine serum albumin as a biotemplate, with the Au nanoparticles formed in the tube channels and even in the space between the tube bottom and the Ti substrate, which show highly improved electrochemical conductivity and act as electrode materials to achieve the enhanced direct electrochemistry of heme proteins. Shao et al. [38] reported plasmonic Au particles loaded on anodic TiO₂ nanotube films exhibiting about 145% enhancement of the photocurrent and 37% reduction in response time. Chen et al. [39] synthesized the TiO₂ nanotube-supported Pt/Au nanoparticles by means of the photo-assisted deposition approach. The studies have shown that TiO₂NT-supported Pt/Au nanoparticles exhibit very high electrocatalytic activity toward formic acid oxidation when the Au composition is between 30% and 50%. Zhao et al. [4] prepared Au (or Pt) loaded on TiO₂ nanotubes by means of the photo-deposition method for the degradation of methyl orange. The Au-loaded sample with an adsorption peak in the visible range becomes a visible light photocatalyst. In addition, other researchers [40,41,42,43,44] combined Au nanoparticles with other metal-loaded TiO₂NTs to achieve high catalytic performance.

For Au nanoparticles supported on TiO₂ nanotube systems, numerous investigations have been performed through many experiments. By contrast, the theoretical research providing important insights into the properties and mechanisms of real catalyst systems is scarce and significant. The purpose of this work is to investigation the micromechanisms of energy and charge transport in the nano-junction consisting of TiO₂NTs and Au_n clusters by building a nanostructure catalyst model. In this work, we report our results of first principles DFT calculation of Au_n clusters supported on the anatase TiO₂NT surface. The TiO₂NTs were obtained by rolling up a TiO₂ (101) surface, which was prepared by cleaving anatase bulk TiO₂ perpendicular to the [1 0 1] direction. The anatase (101) surface was selected due to its thermodynamic stability [45,46,47,48]. In adsorption experiments, we adopted a single Au atom to test the adsorption sites of the TiO₂NT surface. For the catalytic performance of Au, nanoparticles were defined by three major factors: contact structure, support selection, and particle size [49]. The 3D conformations are better suited for adsorption on a surface and concomitant oxidation and reduction reactions compared with planar conformations [7,50]. The measurements of CO oxidation using the temperature-programmed reaction by A. Sanchez [51] showed that the smallest gold cluster that catalyzes the reaction is Au₈. Similar results were obtained by Hannu Häkkinen [52] and Bokwon Yoon [53]. Based on previous research [49,50,51,52,53,54], the adsorptive conformation of Au₈ biplanar was adopted in our study. Atomic clusters show both electronic and geometric magic numbers, and 13 is a common magic number for many transition-metal clusters, including Au [55,56]. 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 Au₁₃ 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 Au₁₃ 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 Au₁₃ cluster. After the geometric optimization without symmetry being restricted, an energy-stable Au₁₃ cuboctahedral structure was obtained. In order to understand the driving mechanism that determines the morphology and charge transport of TiO₂NT-supported Au_n nanoparticles, the structural and electronic properties of the adsorption systems were studied.

2. 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 TiO₂NT (6,0). The supercell included 32 titanium and 64 oxygen atoms with the crystal form of (TiO₂)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 TiO₂ anatase, TiO₂NT, 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 TiO₂ 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 TiO₂ 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 exchange-correlation 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 TiO₂NT models were constructed by rolling up one (101) layer of the anatase structure in the $\left[\overline{1}01\right]$ 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 $\left[\overline{1}01\right]$ 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 TiO₂NT (6,0) can be represented as P42/mmc (D4H-9).

According to the work of Vittadini and Selloni on TiO₂ (101) surface adsorption of Au clusters [3], the adsorption energies for Au_n clusters are as follows:

$$E_{{\mathrm{Au}}_n}^{\mathrm{ads}}=-\left(E_{{\mathrm{Au}}_n/{\mathrm{TiO}}_2\mathrm{NT}}-E_{{\mathrm{TiO}}_2\mathrm{NT}}-E_{{\mathrm{Au}}_n}\right)$$

(1)

where $E_{{\mathrm{Au}}_n/{\mathrm{TiO}}_2\mathrm{NT}}$ ($E_{{\mathrm{TiO}}_2\mathrm{NT}}$) represents the energy of the nanotube with (without) the adsorbate, and $E_{{\mathrm{Au}}_n}$ denotes the energy of the gas-phase cluster.

We also define a cohesive energy to obtain information about the clustering energetics:

$$E_{{\mathrm{Au}}_n}^{\mathrm{clu}}=-\left(E_{{\mathrm{Au}}_n/{\mathrm{TiO}}_2\mathrm{NT}}-E_{{\mathrm{TiO}}_2\mathrm{NT}}-n{E}_{\mathrm{Au}}\right)/n$$

(2)

where E_Au is the total energy of a free Au atom. $E_{{\mathrm{Au}}_n}^{\mathrm{ads}}=E_{{\mathrm{Au}}_n}^{\mathrm{clu}}$, when a single Au adatom is on the TiO₂NT 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 TiO₂NTs.

3. Results and Discussion

3.1. Structures of Anatase TiO₂ Nanotubes

The cross-sectional and side view of the optimized TiO₂NT (6,0) are shown in Figure 1. In the TiO₂NT (6,0), both the inner and outer walls were terminated with the two-fold-coordinated 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 TiO₂NT (6,0).

3.2. Structures of Au₁/TiO₂NTs

Two different stable adsorption structures were found for a single Au adatom on the TiO₂NT (6,0) surface, as shown in Figure 2: a symmetric bridging site between two edge 2cO atoms in the $\left[\overline{1}01\right]$ 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. Adsorption and clustering energies of Au₁ and atomic Mulliken charges of Au and TiO₂NT surface atoms for the Au₁/TiO₂NT system in different configurations ^a.

Configuration	Energy	Mulliken Charge (a.u.)
	${\mathit{E}}_{\mathbf{A}{\mathbf{u}}_1}^{\mathbf{a}\mathbf{d}\mathbf{s}}\left(\mathbf{eV}\right)$	Au	3cO 1	2cO 1	3cO 2	2cO 2	5cTi 1	5cTi 2	5cTi 3
Bare TiO2NT			−0.966	−0.779	−0.965	−0.779	1.714	1.714	1.713
Au1(O,O)	0.20	−0.060	−0.958	−0.770	−0.958	−0.770
Au1(O,Ti)	0.49	−0.075			−0.940		1.732	1.731	1.676

^a The superscripts on O and Ti indicate to which Au atom they are bounded.

. 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 TiO₂NT 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 5cTi³, which generally indicated the loss of electrons. This is consistent with Au adsorption on the anatase TiO₂ (101) surface [3].

The DOS plots of bare TiO₂NT and the adsorption system, and the PDOS plots of the Au adatom and the oxygen atoms and titanium atoms of TiO₂ 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 TiO₂NT 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 TiO₂NT 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 TiO₂NTs, the TiO₂NTs 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 TiO₂NTs to red shift.

The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) along with the energy gap of bare TiO₂NTs and the adsorption system are shown in Figure 4. In the two adsorption configurations, the Au atoms are supported on the TiO₂NT 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 3$d_{x^2-y^2}$ 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 TiO₂NT 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 TiO₂NTs to gold nano-clusters.

3.3. Structures of Au₈/TiO₂NT

Figure 6 shows four different configurations of Au₈ clusters adsorbed on the TiO₂NT surface. The structures of Au₈ 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. Adsorption and clustering energies of Au₈ and atomic Mulliken charges of Au and TiO₂NT surface atoms for the Au₈/TiO₂NT system in different configurations ^a.

Configuration	Energy					Mulliken Charge (a.u.)
	${\mathit{E}}_{\mathbf{A}{\mathbf{u}}_8}^{\mathbf{a}\mathbf{d}\mathbf{s}}\left(\mathbf{eV}\right)$	${\mathit{E}}_{\mathbf{A}{\mathbf{u}}_8}^{\mathbf{c}\mathbf{l}\mathbf{u}}(\mathbf{eV}/\mathbf{atom})$	Au8	3cO 1	2cO 1	2cO 2	3cO 2	2cO 3	5cTi 1	5cTi 2	5cTi 3	5cTi 4	5cTi 5
Bare TiO2NT				−0.966	−0.779	−0.779	−0.966	−0.779	1.717	1.714	1.718	1.714	1.713
Au8-A(2cO, 3cO, 2cO)	1.11	2.12	−0.321		−0.836		−0.965	−0.809	1.720	1.834		1.766	1.892
Au8-B(2cO,5cTi)	0.86	2.09	−0.293			−0.851	−0.960					1.815	1.803
Au8-C(2cO,2cO,3cO)	0.81	2.09	−0.424	−0.993	−0.826	−0.758		−0.843	1.926	1.874	1.716	1.783	1.905
Au8-D(2cO,2cO,3cO)	0.72	2.07	−0.343	−0.987		−0.818		−0.817	1.733	1.769	1.751	1.783	1.870

^a The superscripts on O and Ti indicate to which Au atom they are bound.

. Au_{8-A(2cO,3cO,2cO)} is the most stable configuration for the Au₈/TiO₂NT systems, as shown in Figure 6(A-a,A-b). In this structure, three Au atoms as an adsorption layer bond to TiO₂NT surface atoms, and the oxygen atoms of the TiO₂NT 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 Au₈ biplanar binding to the TiO₂NT 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 TiO₂NT 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 Au₈ biplanar parallel to the axial of TiO₂NTs. 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 TiO₂NT surface’s deformation; the 3cO atoms which bonded with Au adatoms were pulled off of the surface of TiO₂NT. Meanwhile, the other 3cO atoms which have no relation with the Au₈ clusters were “pushed” into a slightly concave formation. This phenomenon can be found in Figure 6. According to Table 2, the Au₈ clusters in four structures were negatively charged. Based on analysis of Au nanocluster size with Mulliken atomic charge and adsorption energy, for Au₈ clusters, not only transfer charges but also adsorption energies were increased, with clusters enlarging. Compared to Au₁ 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 Au₈ 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 TiO₂NT surface atoms were analyzed in detail. Apart from a few TiO₂NT surface atoms, there are two main trends in atomic charge redistribution after the adsorption of Au₈ clusters: electron transfer to oxygen atoms, and titanium losing electrons and showing greater positive charge.

PDOSs of Au₈ clusters as well as the associated TiO₂NT 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 Au₈ 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 TiO₂NTs almost disappears in all four adsorption systems. This indicates that metallization of the nanojunction Au₈-TiO₂NT 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 Au₈ clusters adsorb on the TiO₂NT 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 Au₈–TiO₂NT nanojunction was below 1.10 eV; Au₈ clusters narrowed the band gap of the system more efficaciously than a single Au adatom. From the EDD contour maps of the Au₈ adsorption system in Figure 5e,f, it can be found that Au₈ clusters obtained electrons from TiO₂NTs. In addition to the electron cloud distribution in Au₈ nanoclusters, the Au atoms which have direct bonding with TiO₂NT surface atoms show obvious electron accumulation, such as a Au_8-C structure, as shown in Figure 5f.

3.4. Structures of Au₁₃/TiO₂NT

Au₁₃ 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. Au₁₃ clusters possessing the more stable configuration of cuboctahedrons were selected to construct the Au₁₃/TiO₂NT system. Three stable adsorption configurations for Au₁₃/TiO₂NTs were obtained. The investigated configurations for the three adsorption systems are displayed in Figure 9. We can find that the condition of TiO₂NT 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 TiO₂NT axial, Au₁₃ 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. Adsorption and clustering energies of Au₁₃and atomic Mulliken charges of Au and TiO₂NT surface atoms for the Au₁₃/TiO₂NT system in different configurations ^a.

Configuration	Energy						Mulliken Charge (a.u.)
	${\mathit{E}}_{\mathbf{A}{\mathbf{u}}_{13}}^{\mathbf{a}\mathbf{d}\mathbf{s}}\left(\mathbf{eV}\right)$	${\mathit{E}}_{\mathbf{A}{\mathbf{u}}_{13}}^{\mathbf{c}\mathbf{l}\mathbf{u}}(\mathbf{eV}/\mathbf{atom})$	Au13	3cO 1	2cO 1	3cO 2	2cO 2	3cO 3	2cO 3	5cTi 1	5cTi 2	5cTi 3	5cTi 4	5cTi 5	5cTi 6
Bare TiO2NT				−0.966	−0.779	−0.965	−0.779	−0.966	−0.779	1.717	1.714	1.718	1.714	1.713	1.717
Au13-A(2cO,2cO)	3.12	2.28	−0.225		−0.870				−0.833	1.788	1.794			1.819
Au13-B(2cO,3cO,2cO,3cO)	2.23	2.21	−0.322	−0.996			−0.809	−0.929	−0.830	1.736		1.761	1.805	1.848	1.727
Au13-C(3cO,2cO)	1.6	2.19	−0.171		−0.854	−0.934				1.762	1.791		1.737	1.778

^a The superscripts on O and Ti indicate to which Au atom they are bound.

). In Au_{13-B(2cO,3cO,2cO,3cO)}, the absorbed Au₁₃ cluster is similar to a cage-like structure [67,68], with four Au atoms directly bonding to the TiO₂NT surface. Since the cage-like structure covers less area of the TiO₂ 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 Au₁₃ 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. Au₁₃ is adsorbed with a three-coordination oxygen atom and a two-coordination bridge oxygen atom, as shown in Figure 9C. The interaction of the Au₁₃ 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 TiO₂NT are summarized in Table 3. Au₁₃/TiO₂NT systems have greater adsorption energy than Au₈ and Au₁ 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 Au₁ and Au₈, the Au₁₃ clusters became negative after being absorbed on TiO₂NTs. However, the number of electrons transferred experiences no change. The interatomic charge distributions of related TiO₂NT surface atoms are shown in Table 3. The two main trends of atomic charge redistribution after the adsorption of Au₁₃ clusters are: electron transfer to oxygen atoms and titanium losing electrons and showing a more positive charge, except for a few TiO₂NT surface atoms, which is similar to the Au₈ 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 Au₁₃ clusters and connecting surface atoms of TiO₂NT 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 Au₁₃ cluster adsorbed onto the TiO₂NT 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. Au₁₃ 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 Au₈/TiO₂NT 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.

4. Conclusions

In summary, Au_n/TiO₂NTsystems 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 TiO₂NT. Our results show that a single Au adatom prefers the top position of 3cO as well as the bridging 2cO–2cO site of the TiO₂NT surface. Adsorbed Au₈ maintains a distorted biplanar configuration. The strong interaction between Au_n and atoms of the nanotube surface causes deformation of TiO₂NT. Au₁₃ 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 TiO₂NTs. This causes TiO₂NTs 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 TiO₂NT/Au_n cluster, as a potential photoelectric device, possesses better energy and charge transmission performance.