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Gold and Silver Clusters on TiO and ZrO (101) Surfaces: Role of Dispersion Forces Antonio Ruiz Puigdollers, Philomena Schlexer, and Gianfranco Pacchioni J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b04026 • Publication Date (Web): 15 Jun 2015 Downloaded from http://pubs.acs.org on June 16, 2015
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Gold and Silver Custers on TiO2 and ZrO2 (101) Surfaces: Role of Dispersion Forces
Antonio Ruiz Puigdollers, Philomena Schlexer, Gianfranco Pacchioni1 Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, via Cozzi, 55 20125 Milano, Italy
Abstract The adsorption of Ag and Au atoms and Ag4 and Au4 clusters on the stoichiometric TiO2 (anatase) and ZrO2 (tetragonal) (101) surfaces has been investigated using DFT+U calculations with and without the inclusion of van der Waals (VdW) forces. We have considered the role of VdW interactions on the physical properties of the adsorbed species using three different approaches: two variants of the pair-wise force field method proposed by Grimme (DFT+D2 and DFT+D2'), and the vdW-DF method where the vdW contribution is expressed directly as a function of the electron density. The results show that already at the level of metal atoms and small clusters the inclusion of vdW interactions can change the order of stability of various isomers and, more important, can result in major corrections to the adsorption energies. These, in turn, can affect other properties as for instance the structure and chemical reactivity of supported metal particles on oxides or their diffusion properties.
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1. Introduction Deposition of transition metal particles with nano and subnanometer size on various oxide materials is a topic of enormous interest for the investigation of the mechanisms of diffusion, nucleation and growth, and the stabilization of supported metal nanoparticles.1,2,3,4 These systems can find applications in very diverse fields, from the the study of optical and plasmonic properties to the design of magnetic systems at the nanoscale. However, one of the widest applications of supported metal clusters is in the field of heterogeneous catalysis.5,6 The possibility to grow, characterize and use metal nanoparticles or clusters of nanometer and sub-nanometer size is at the basis of the field known as nanocatalysis.7,8,9,10 Despite the large scientific and technological interest on these systems, no unified picture on the metal-support interaction exists yet. In fact, the bonding of metal nanostructures on solid supports (mostly oxides) depends on a large number of factors, like surface structure and termination, presence of surface or bulk defects, nature of the deposited metal, preparation conditions, etc. Theoretical investigations can contribute to interpret experimental data and to provide a more general understanding of the functioning of metal clusters and of the role of the support.11 The theoretical description of oxide-supported nanoparticles, however, is not free from limitations. The study requires a precise description of the electronic structure of the support, such as the electron localization and the band gap, which depend on the computational approach.12 The description of the metal cluster is complicated by the existence of multiple isomers, spin states and fluxionality. A gas-phase cluster has a large number of possible configurations and the situation can be even more complex when is deposited on a surface. The search of the global minimum structure is computationally expensive and implies the use of methods specifically designed for this purpose, like genetic algorithms13 or molecular dynamics.14 Moreover, the different local minima are often separated by small energy differences which facilitates the interconversion of one isomer into another. Thus, metal clusters are fluxional objects that at finite temperatures continously change shape and structure over the surface. On the other hand, the interaction between the metal cluster and the oxide support is central in determining the reaction mechanisms and catalytic properties. The description of the metal/oxide interface by electronic structure methods is largely based on the use of density functional theory, an approach that has produced several succesfull stories. However, only in the last years it has been recognized that dispersion forces, that for a long time have been considered as negligible in these problems, do play an important role.15 In this work we investigate the role of the van der Waals (vdW) forces on the structure and electronic properties of small metal clusters supported on two oxide surfaces. We make a comparative study of Au and Ag atoms and clusters, two metals which typically give different bonding with oxide surfaces, on two different reducible oxides, anatase TiO2 and tetragonal ZrO2 (101) surfaces. The anatase polymorph is not the most stable one for titania, showing at all temperatures higher free energy than rutile
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phase,16,17,18 but it is the most common phase in catalytic applications.19,20,21,22,23 Zirconia shows different stable phases in different temperature ranges. At room temperature the stable phase is monoclinic, but it has few practical applications.24 The tetragonal and cubic phases are stable only at high temperatures (from 1480 and 2650 K respectively) but have excellent mechanical, thermal, chemical and dielectrical properties.25,26 However, these structures can be obtained at lower temperatures by doping with impurities like Mg or Y cations.27,28 The (101) surface exposed for the deposition of the metal clusters is the most stable one in both a-TiO2 and t-ZrO2 oxides.29,30,31,32,33 The (101) surface of a-TiO2 and t-ZrO2 has been recently used to study the properties of supported Ru34 and Ni clusters.35 On the methodological site, we used the DFT+U approach to partly correct the problems related to the electronic structure of the oxide support, as explained in the computational part. The use of single atoms and small metallic clusters (tetramers) allows us to perform a full search of the optimal structures they can adopt when deposited on the two surfaces. The van der Waals forces are described in a first approach by means of the pairwise force field proposed by Grimme, DFT-D2.36 In this method, an inter-atomic long-range (C6 r-6) attractive term is added to the total DFT electronic energy. However, in the dispersive interaction between the adsorbate and more distant layers of the support the simple added term can not take into account the screening of the intermediate layers, resulting in an overestimation of the interaction energies.37 The C6 parameters and the vdW radii, R0, employed in this method are semiempirically determined for each atom in a neutral state. To circumvent ths problem, we used a slightly different approach where the parameters for the cations of the oxide are substituted by those of their precedent noble gases since the size of these atoms is closer to that of the ionic form (method referred to as DFT-D2').38 The third procedure here employed is the one implemented by Lundqvist39 and coworkers and later modified by Klimeš et al,40 which does not depend on external parameters and where the vdW contribution is directly expressed as a function of the electron density. The paper is structured as follows. A brief explanation of the computational details is first introduced (section 2). Then the results are reported and discussed starting from the binding properties and electronic structure of Au and Ag single atoms adsorbed on stoichiometric t-ZrO2 and a-TiO2 (101) surfaces; we first discuss the DFT results and then we analyze the role of the inclusion of vdW forces (section 3.1). This is followed by the description of the adsorption of Au and Ag tetramers on the same surfaces (section 3.2). The electronic properties of the supported clusters are discussed in § 3.3. In the final section the general conclusions are summarized.
2. Computational methods Periodic density functional theory (DFT) calculations were performed using the Vienna ab Initio Simulation Package (VASP 5.2)41,42 and the generalized gradient
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approximation (GGA) for the exchange-correlation functional. In particular, we used the Perdew, Burke and Ernzerhof (PBE) formulation.43 For oxides as TiO2 and ZrO2, the GGA approach suffers from the self-interaction error, which significantly affects the electronic structure and in particular the band gap. To partly circumvent this error, we use the GGA+U approach implemented by Dudarev et al. which consists in the definition of the effective Hubbard's parameter U.44,45 With this parameter the multiple occupation of d orbitals is penalized such that the underestimation of the band gap and electron delocalization is attenuated.46,47,48 In this work, we set the U parameter to 4 eV for Zr and 3 eV for Ti atoms. With these parameters, a good qualitative description of the electronic and geometric structures is given,49,50,51,52 giving 4.0 eV and 2.4 eV for the ZrO2 and TiO2 band gaps, respectively. To describe the electron-ion interactions, the Projector Augmented Wave (PAW) method is used.53,54 The O(2s, 2p), Ti(3s, 4s, 3p, 3d) and Zr(4s, 5s, 4p, 4d) for the oxides and Au(5d, 6s) and Ag(4d, 5s) for the adsorbates are described as valence electrons and consequently treated explicitly. The blocked Davidson iteration scheme is used for the electronic relaxations.55 In the geometric structure optimizations all ions are allowed to relax until ionic forces are smaller than |0.01| eV/Å. The calculation of the bulk structures is performed using a kinetic energy cut-off of 900 eV for TiO2 and 600 eV for ZrO2. A Г-centered Monkhorst-Pack k-point mesh is set to (8×8×4) for TiO2 and (8×8×8) for ZrO2. For subsequent structure optimizations, Г-point calculations are performed and the wavefunctions are expanded in a plane wave basis set up to a kinetic energy of 400 eV. To investigate the (101) surface, which is the most stable surface for both materials,29,30,31,32,33 we design slab models of five layers of MO2 (M=Ti or Zr), where the convergence of the surface energy and the band gap value is reached. All layers are fully relaxed in the calculations. A (3×1) surface supercell for TiO2 and a (3×2) supercell for ZrO2, of formula Ti60O120 and Zr60O120, respectively, are used for the deposition of single Au and Ag atoms. For the deposition of the Au and Ag tetramers a smaller (2×2) supercell is used for ZrO2 (Zr40O80). This supercell is sufficiently large to avoid an interaction between clusters in different replicas. To calculate the projected Density of States (PDOS), the set of k-points is adjusted to (3×3×1). This finer grid is also used to estimate the atomic charges, as described below. Adsorption energies (Eads) are calculated as defined in equation (1), where X = Ag, Au, n = 1, 4 and M = Ti, Zr. All components refer to structurally optimized systems. (1)
Eୟୢୱ ሺX୬ /MOଶ ሻ = EሺX ୬ /MOଶ ሻ − EሺX୬ ሻ − EሺMOଶ ሻ
Atomic charges are estimated with the Bader decomposition scheme.56 Effective Bader charges are defined as q = Zval - qBader , where Zval is the number of valence electrons and qBader is the computed Bader charge.
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The role of the vdW interactions is investigated by including the pair-wise force field implemented by Grimme (DFT-D2).36 In a variation of this approach, the van der Waals radii R0 and the C6 parameter for the Zr and Ti atoms are replaced with those corresponding to the preceding noble gas in the periodic table (Kr and Ar, respectively) since the size of these atoms is closer to that of Zr4+ and Ti4+ cations (DFT-D2').38 The third method used is the one proposed by Lundqvist39 where the vdW contribution is expressed directly as a function of the electron density (vdW-DF). In this work, the functional used for this third purpose is the optB86b-vdW density functional. Since the focus of the paper is on the structure and properties of neutral Au and Ag clusters supported on oxide surfaces, it is useful to check the effect of the dispersion interactions on the cohesive energy and lattice parameters of the respective metals, Table 1. Table 1 – Cohesive energies (Ec) and lattice parameters (a) of Au computed with various methods. PBE PBE+D2 Exp.57 Ec, eV a, Å Ec, eV a, Å Ec, eV a, Å Au 3.78 4.08 3.04 4.15 3.51 4.10 Ag 2.95 4.09 2.51 4.13 3.07 4.11
and Ag metals as vdW-DF Ec, eV a, Å 3.27 4.21 2.70 4.18
The results show that the cohesive energy of the metals is underestimated at the PBE level and that introducing dispersion at the PBE+D2 level produces a clear improvement. On the contrary, the vdW-DF functional on one hand slightly improves the cohesive energy but also results in much too large lattice constants. 3. Results and discussion 3. 1. Metal atom adsorption on t-ZrO2(101) and a-TiO2(101) Surfaces.
3.1.1 DFT-PBE results without vdW interactions For the deposition of single atoms we found two general stable adsorption positions on both a-TiO2 and t-ZrO2 (101) surfaces: (1) the bridge site and (2) the hollow site, shown in Fig. 1(a,c) and Fig. 1(b,d), respectively, for the Au case. On tetragonal ZrO2, the most stable adsorption site for both Au and Ag atoms is the bridge position, with adsorption energies of -0.90 eV (Au) and -0.34 eV (Ag), Table 2. Here the metal atom is coordinated to an O3c and a Zr7c ion, with bond distances 2.18 Å and 2.83 Å respectively for Au, and 2.30 Å and 3.02 Å respectively for Ag. This is similar to what is found for the Au and Ag adsorption on a c-ZrO2 (111) surface, which is equivalent to the t-ZrO (101) surface, where the most stable site is also the bridge position.58 The other stable adsorption site is the hollow position coordinated to an O3c
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and two Zr7c ions, Fig. 1(b). This is a less favorable position where the Au atom is bound with an adsorption energy of -0.69 eV, while Ag is bound by -0.28 eV. The distances with O3c and Zr7c are 2.22 Å and 3.22 Å respectively for Au, and 2.41 Å and 3.41 Å respectively for Ag. Not surprisingly, the weaker bond of Ag with the zirconia surface results in longer bond distances. The interaction between the Au adatom and the zirconia surface is mainly due to covalent mixing. A small depletion of electronic charge from the t-ZrO2 surface to the adsorbate is found (Bader charge of -0.16 |e|), Table 2. As can be seen in the PDOS plot, Fig. 2(a), the Au atom retains its open shell 6s1 configuration which excludes the occurrence of a net charge transfer to or from the adsorbed Au atom. Also the Ag atom, when deposited on zirconia, maintains the 5s1 configuration and charge neutrality; the interaction with the substrate is mainly due to polarization effects and to a small chemical mixing of the d states with the O 2p states of the support, Fig. 2(b).
a)
c)
b)
d)
Figure 1. Left: Au adsorption on t-ZrO2 (101); (a) side and top views of the bridge adsorption site; (b) side and top views of the hollow adsorption site. Right: Au adsorption on a-TiO2(101); (c) side and top views of the bridge adsorption site; (d) side and top views of the hollow adsorption site. For simplicity, only the first layer of both surfaces is shown in the top view of the structures. The two most stable adsorption sites found for Ag and Au atoms on the anatase TiO2 surface are the bridge position between an O2c and a Ti5c ions and the hollow site coordinated to two O2c and two O3c ions, Fig. 1(c,d). The bridge site is preferred for the Au atom, with Eads = -0.43 eV, Table 2. The corresponding bond lengths between Au and the O2c and Ti5c ions are 2.29 and 2.75 Å, respectively. These findings are in good agreement with those of Selloni et al.59 This Ti-O bridge position is also found to be the preferred site for Cu atoms on a-TiO2 (110),60,61 and for Pd atoms on a-TiO2 (101).62 However, the hollow site is the preferred one for the Ag adatom, with an Eads = -0.69 eV. The Ag-O bond lengths are 2.19 Å (O2c ions) and 2.87-2.99 Å (O3c ions). In the
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hollow site, the Ag atom lies in the same plane of the O ions and is therefore less protruding than in a bridge position, Fig. 1(d). In contrast to t-ZrO2, where the interaction of both Ag and Au atoms is due to polarization and covalent mixing effects independently of the adsorption site, on a-TiO2 the bonding is substantially different. On the bridge position, preferred for Au, the interaction with the a-TiO2 surface is dominated by the chemical mixing between the d states and the oxide O 2p levels, similar to the zirconia case. The Au and Ag atoms retain the ns1 configuration (n = 5 for Ag and n = 6 for Au), Fig. 2(c), and remain basically neutral, Table 2. This is no longer true when adsorption occurs on the a-TiO2 hollow position. The valence ns states of the adatoms are now above the Fermi level, as shown for Ag in Fig. 2(d). This is clearly indicative of a direct charge transfer of the ns1 valence electron to the oxide. The metal atoms lose completely their magnetic moment and become positively charged, with computed Bader charges +0.45 |e| (Au) and +0.67 |e| (Ag), Table 2. A spin density plot of the adatoms adsorbed on the a-TiO2 hollow reveals that the transferred electron is delocalized over the Ti atoms of the first three layers. Notice that this result is probably the consequence of the fact that no polaronic distortion has been introduced into the lattice. As shown for other studies, other solutions exist at similar energy where the transferred electron is localized on a single Ti ion.63,64,65 Table 2. PBE and PBE-D2 adsorption energies Eads, magnetic moments µ and effective Bader charges qX (X = Au and Ag) for Au and Ag atoms adsorbed on t-ZrO2 and a-TiO2 (101) surfaces. adsorption site
Eads (eV) PBE PBE-D2
|µ| (µB) X MO2
qX (|e|)
Au / t-ZrO2
bridge hollow
-0.90 -0.69
-1.27 -1.03
0.4 0.4
0.3 0.2
-0.16 -0.16
Ag / t-ZrO2
bridge hollow
-0.34 -0.28
-0.70 -0.72
0.2 0.2
0.2 0.2
0.01 0.00
Au / a-TiO2
bridge hollow
-0.43 -0.16
-0.66 -0.52
0.4 0.0
0.2 0.7
0.00 0.45
Ag / a-TiO2
bridge hollow
-0.24 -0.69
-0.46 -1.19
0.3 0.0
0.2 0.7
0.14 0.67
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a)
c)
b)
d)
Figure 2. Projected Density of States (PDOS) of the most stable adsorption sites. Left: (a) Au and (b) Ag on a Zr-O bridge site of t-ZrO2(101). Right: (c) Au on a-TiO2 (101) bridge site and (d) Ag on a-TiO2(101) hollow site. The zero of energy corresponds to the Fermi level. To rationalize the finding of the charge transfer, the various contributions to the adsorption energy need to be analyzed. The first term to be considered is the cost to ionize the metal adatom (ionization potential of the atom, IP(M)). The second is the energy gain associated to the transfer of one electron to the oxide support (electron affinity of the support, EA(MO2)). The adsorption energy can thus be written as Eads = IP(M) – EA(MO2) – Eint(M+/MO2-), where Eint is the electrostatic interaction between the charged systems. This latter term is difficult to evaluate precisely, but it can be assumed to be similar for Au+ and Ag+ species. Therefore, the main difference between the adsorption of Au and Ag atoms on the a-TiO2 hollow site will restrict to the IP(M) term. Since IP(Au) = 9.22 eV is considerably higher than IP(Ag) = 7.57 eV,66 the different adsorption properties can be related to a different atomic property: the higher cost required to ionize the Au atom destabilizes the hollow site and makes the bridge site preferred. On a similar basis, the different electron affinities of the two oxide surfaces can explain the absence of charge transfer when Au and Ag atoms are adsorbed on t-ZrO2. The electron affinity can be deduced from the position of the bottom of conduction band and the vacuum level in the oxide surface. In Fig. 3(a,b), we report the PDOS of the t-ZrO2 and a-TiO2 systems, respectively. The two oxides have different band gaps, mainly due to a different position of the bottom of the conduction band, which is at about -4.7 eV for a-TiO2 and at about -2.8 eV for t-ZrO2 with respect to the vacuum level. Thus, the energy gain
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when the oxide is reduced by addition of an extra electron is 1.9 eV higher for a-TiO2, favoring the charge transfer process. These results already allow to draw some general considerations. Contrary to what one could expect, there is no universal behavior when one considers Ag and Au adsorption on ZrO2 and TiO2 surfaces. In fact, Au is more strongly bound on t-ZrO2 than Ag, a fact that has been observed also on other oxides.63,67,68,69,70 On a-TiO2, on the contrary, Ag is more strongly bound than Au when deposition occurs on the hollow site, due to a completely different binding mechanism. The different behavior can be easily explained considering the lower ionization potential of Ag which leads to a more important charge transfer increasing thus the binding energy.
a)
b)
Figure 3. Projected Density of States of (101) surfaces of (a) t-ZrO2 and (b) a-TiO2. The zero of energy corresponds to the vacumm level.
3.1.2 DFT-PBE results with vdW interactions So far we have discussed the results of calculations that do not include vdW forces. Here we consider the effect of dispersion on the adsorption of single atoms, and we restrict the analysis to the DFT-D2 approach. Also at this level of theory two competing adsorption sites are found for the four X/MO2 systems (X = Au, Ag; M = Zr, Ti), Table 2. As expected, the adsorption energies are lowered (increased in absolute value) when the long-range terms are included, Table 2. However, the effect is not the same on Au or on Ag surface complexes. In fact, for Au the adsorption energies are increased (in absolute value) by about 50%. For Ag, on the contrary, the effect is more pronounced with an increase of the adsorption energies around 100%. The geometric structures change only slightly after inclusion of vdW forces, except for one case: upon deposition of Ag on the hollow site of a t-ZrO2, the adatom diffuses from the Zr-O-Zr bridge (no vdW) to the center of the ring (with vdW), coordinating the three O3c ions, Fig. 4. Thus, the preferred site for Ag adsorption on tZrO2 becomes the hollow position instead of the bridge, although the energy difference is small, 0.02 eV, Table 2. Apart from this case, the relative stabilities of the adsorption
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sites are maintained going from the DFT to the DFT-D2 method. The occurrence of a charge transfer at the hollow sites of a-TiO2 is found also at the DFT-D2 level. Also the computed magnetic moments and the Bader charges do not change in a significant way when the vdW interactions are included. To summarize, there are two competing sites on both t-ZrO2 and a-TiO2 for Au and Ag atoms adsorption: a bridge position and a hollow position. The adsorption is characterized by a covalent-polar bond, with chemical mixing between d states of the adsorbate and the O 2p states of the oxide. This is no longer true at the hollow positions of a-TiO2 where the bonding of the metal atoms has a charge transfer nature (one electron is transferred from the metal atom to the support). This picture is found both at the PBE and PBE-D2 levels, although some significant differences emerge. In particular, some change in the order of stability is found along with a non-uniform increase of the strength of the surface chemical bond (the vdW interactions affect the Ag bond strength more than the Au one).
PBE
PBE-D2
Figure 4. Side and top views of the structure of a Ag atom adsorbed on a t-ZrO2 hollow site. Left: no vdW forces; right: with vdW forces. 3. 2. Au4 and Ag4 adsorption on t-ZrO2(101) and a-TiO2(101) Surfaces. In this Section we discuss the adsorption properties of small Au and Ag clusters. Both Au4 and Ag4 in the gas-phase assume preferentially a rhombic structure.71,72 Therefore, we started by placing the two clusters in this initial geometry on the two surfaces and re-optimizing the entire system both with and without dispersion forces. Several starting orientations for the tetramers have been considered, and the final lowest structures obtained from this search are shown in Fig. 5. The adsorption energies computed with the different approaches employed are reported in Table 3.
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3.2.1 Adsorption on t-ZrO2, without vdW interactions Starting from the t-ZrO2 surface, we notice that the Au4 and Ag4 clusters assume three different two-dimensional structures, Fig. 5. The first and second configurations (isomers A and B) lose completely the initial rhombic arrangement of the gas-phase and form a Y-shaped structure, with the isomer A taking a tilted orientation (the cluster forms an angle of about 50° with the surface normal) and the isomer B taking a vertical orientation. On the contrary, in isomer C the rhombic structure is maintained. At the PBE level, the isomers A, B, and C are separated by no more than about 0.3 eV, and often the energy differences are much smaller, Table 3. Atoms in the clusters take preferably a position close to a Zr-O bridge, the preferred position when single Au and Ag atoms are deposited on t-ZrO2. Only in the vertical Y-shaped configuration (isomer B), one of the atoms interacting with the surface is bound in a hollow position between Zr7c-O3c- Zr7c ions. ZrO2
TiO2
Au4
Ag4
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Figure 5. Left: Side and top views of Au4 and Ag4 cluster adsorption on t-ZrO2(101). From top to bottom, isomers A, B and C. Right: Side and top views of Au4 and Ag4 cluster adsorption on a-TiO2(101). From top to bottom, isomers A and B. For simplicity, only the first layer of both surfaces is shown in the top view of the structures.
Table 3. Adsorption energies, in eV, of Au4 and Ag4 adsorbed on t-ZrO2 and a-TiO2 (101) surfaces, computed with and without the inclusion of van der Waals forces. Eads (eV) PBE-D2 PBE-D2'
isomer
PBE
Au4 / t-ZrO2
A B C
-2.49 -2.25 -2.19
-3.81 -3.27 -3.31
-3.51 -3.03 -3.07
-3.14 -2.77 -2.80
Ag4 / t-ZrO2
A B C
-1.34 -1.07 -1.15
unstable -2.09 -2.43
-2.17 unstable -2.10
-1.99 unstable -1.81
Au4 / a-TiO2
A B
-1.26 -1.55
-2.37 -2.39
-2.12 -2.19
-2.43 -2.48
Ag4 / a-TiO2
A B
-1.01 -1.05
-2.36 -2.02
-2.02 -1.77
-2.06 -1.85
vdW-DF
At the PBE level, both Au4 and Ag4 clusters adopt the tilted Y-shaped structure (isomer A) as preferred configuration, with adsorption energies of -2.49 eV (Au) and 1.34 eV (Ag). In the case of the Au tetramer, the structure is distorted and elongated in such a way it assumes a linear configuration more than a Y shape, Fig. 5. On the contrary, the relative stabilities of the isomers B and C is reversed going from Au4 to Ag4 (notice however that the two isomers at the PBE level are separated by only 0.06-0.07 eV, Table 3). For Ag4, the rhombic structure (isomer C), almost parallel to the surface, is preferred (Eads = -1.15 eV) compared to the isomer B that shows the cluster plane normal to the surface (0.08 eV higher in energy, Table 3). For Au4 the situation is reversed as isomer B (Y-shape, normal to the surface) is slightly preferred compared to isomer C (rhombus, tilted).
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3.2.2 Adsorption on t-ZrO2, with vdW interactions Considering Au4, when the vdW forces are included the preference for the tilted Yshaped configuration (isomer A) is maintained. The adsorption energy goes from -2.49 eV (PBE), to -3.81 eV (PBE-D2), -3.51 eV (PBE-D2') and -3.14 eV (vdW-DF). Clearly, there is a tendency of PBE-D2 to provide an upper bound to the strength of dispersion interactions, while vdW-DF gives the smallest correction. PBE-D2' lies in between. While there is no change in the order of stability as far as the most stable isomer is concerned, some changes are found for the other two isomers B and C. By including vdW forces, the tilted structure of the isomer C is pushed closer to the surface. This fact results in a more important contribution of the vdW terms compared to the vertical isomer B that is less affected. This effect leads to an inversion in the stability of isomers B and C at the PBE-D2 and PBE-D2' levels with respect to PBE, but not at the vdW-DF level, Table 3. Differently from Au4, the Ag tetramer is much more affected by the inclusion of dispersion forces. This is in line with the findings for the single atoms. First, instead of three local minima as found at the PBE level, only two are found after inclusion of vdW forces. With the PBE-D2' and vdW-DF approaches, the isomer B becomes unstable. With PBE-D2 the isomer A does not exist, but remains the most stable at PBE-D2' and vdW-DF levels. The adsorption energy goes from -1.34 eV (PBE) to -2.17 eV and -1.99 eV with PBE-D2' and vdW-DF approaches respectively. At PBE-D2 level the preferred structure is the rhombus (isomer C), with a binding energy of -2.43 eV, twice as large compared to the PBE level, Table 3. In short, the inclusion of the dispersion forces does not change the number of local minima for the deposition of Au4 on t-ZrO2 surface, nor the prediction of the most stable structure (isomer A). The adsorption energies are considerably lowered, and the strongest effect is found with the D2 correction (∆E from -1 to -1.3 eV). The vdW-DF approach provides the smallest corrections (∆E around -0.6 eV) while with the D2' approach ∆E is around -0.9 eV. While the prediction of the most stable isomer does not change with inclusion of vdW forces, the relative stability of isomers B and C does, but one should notice that these two isomers are almost isoenergetic. More relevant are the changes induced by vdW forces on Ag4 adsorption on t-ZrO2, Table 3. Here in fact the isomer A remains preferred at the D2' and vdW-DF levels, while at the D2 level this isomer is unstable and the preferred structure is the flat rhombus, isomer C. 3.2.3 Adsorption on a-TiO2, no vdW interactions Differently from zirconia, on anatase TiO2 the Au4 and Ag4 clusters only assume one of the two Y-shaped configurations, Fig. 5; the rhombic structure, most stable in gas phase, is not a minimum on the potential energy surface. The tilted Y-shaped configuration, isomer A, lies almost planar to the surface and the “Y” structure is oriented along the [100] direction. The bonding of this isomer to the surface is different for Au and Ag clusters. The gold tetramer is bound to the surface with two Au atoms coordinated to a
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bridge position, between Ti5c and O3c, and between Ti5c and O2c ions. The other two are bound to an O2c and an O3c sites, respectively. The silver tetramer adopts a deformed Y shape where one terminal Ag atom is coordinated to a Ti5c-O2c bridge site and to the closest O2c ion, and the other terminal Ag atom is placed on a hollow site between two O2c and one O3c ions. The vertical Y-shaped configuration (isomer B), shows the same kind of bonds between the cluster and the surface for the two metals, where one terminal atom is bound to a Ti5c-O2c bridge and to the closest O2c ion and the other terminal atom is on top of an O2c ion. On other titania surfaces also the rhombic structure has been found as a stable isomer, as for Au4 on rutile TiO2 (110)70 and Ag4 on anatase TiO2 (100).73 Moreover, a three-dimensional configuration with tetrahedral shape was reported as the most stable isomer for Ag4 on a-TiO2 (100)73 a-TiO2 (101)74 and r-TiO2 (110)70 surfaces. However, we have checked this structure and we found that it is unstable on a-TiO2 (101). This is true at all levels of theory considered (with and without vdW forces). The tetrahedral Ag4 structure transforms into a two-dimensional configuration upon geometry optimization. Also for Au4 we checked that the tetrahedral structure is unstable on the aTiO2 (101) surface. On titania, the PBE results (Table 3) show a preference for the vertical orientation of the Y-shaped configuration (isomer B) for both Au4 and Ag4 clusters, contrary to the zirconia case. The adsorption energy, -1.55 eV (Au4) and -1.05 eV (Ag4) indicates a stronger bonding for gold compared to silver, in line with the results obtained on zirconia, Table 3. However, for Ag4 the energy difference between the tilted (isomer A) and vertical (isomer B) configurations is 0.04 eV only (-1.01 eV versus 1.05 eV, respectively).
3.2.4 Adsorption on a-TiO2, vdW interactions As found for zirconia, the inclusion of the vdW forces has a stronger effect on the flatter isomer A due to the shorter distances with the surface. The binding energy of this isomer is therefore lowered in a more pronounced way, from -1.01 eV (PBE) to -2.36 eV (PBE-D2), -2.02 eV (PBE-D2') and -2.06 eV (vdW-DF) eV, in such a way that the order of stability of the two isomers is reversed. Once dispersion forces are included, the isomer A becomes the preferred structure, and the energy difference with isomer B increases to 0.34 eV (D2), 0.25 eV (D2') and 0.21 eV (vdW-DF). This effect is not observed for gold. The order of stability is maintained, with isomer B being more stable than isomer A, but the difference in energy between the two isomers, that was substantial in PBE, 0.29 eV, becomes negligible once vdW contributions are considered, 0.02 eV (D2), 0.07 eV (D2') and 0.05 eV (vdW-DF) eV. In general, as for zirconia, we observe that the vdW interactions increase the adsorption energies (in absolute value). This effect is probably overestimated at the PBE-D2 level while D2' and vdW-DF give corrections of similar magnitude. Most
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important, the relative stability of the isomers can change, in particular for silver, and the energies separating the various isomers are seriously affected.
3.2.5 Electronic structure and comparison of ZrO2 and TiO2 surfaces In this section we discuss the electronic structures of Au4 and Ag4 clusters supported on t-ZrO2 and a-TiO2 (101) surfaces. The PDOS curves are shown in Fig. 6(a-d), and refer to the most stable isomer obtained at the PBE level. While the energetics is clearly affected by the inclusion of vdW forces, the general features of the interaction are the same with and without vdW contributions. The valence states of Au4 are typically above the top of the valence band of the two oxides, in the band gap, Fig. 6(a,c); the electronic states of Ag4 appear mixed with the top of the O 2p valence band of both oxides, Fig. 6(b,d). Differently from the atomic case, where some adsorption sites on titania show the occurrence of a charge transfer to the support, for Au and Ag tetramers there is no sign of charge transfer. This is due to the closed shell nature of the two clusters, which implies a high ionization energy and a small electron affinity. Things could be radically different in the presence of a cluster with an odd number of atoms. In this case, in fact, the transfer of one electron to or from the cluster is much more likely. However, since the main interest in this work is the effect of vdW interactions, this is clearly easier to evaluate for chemical interactions that do not imply a direct charge transfer.
a)
c)
b)
d)
Figure 6. Projected density of states. Left: (a) Au4 and (b) Ag4 cluster adsorption on tZrO2(101). Right: (c) Au4 and (d) Ag4 cluster adsorption on a-TiO2(101). The zero of energy corresponds to the Fermi level.
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Table 4. Total effective Bader charges qX, X=Au4, Ag4, computed with and without the inclusion of van der Waals forces. qX (|e|) PBE-D2 PBE-D2'
isomer
PBE
Au / t-ZrO2
A B C
-0.30 -0.26 -0.26
-0.32 -0.26 -0.28
-0.32 -0.26 -0.28
-0.28 -0.24 -0.25
Ag / t-ZrO2
A B C
0.00 -0.04 0.00
-0.04 +0.01
0.00 0.00
+0.01 +0.02
Au / a-TiO2
A B
+0.06 +0.02
+0.06 +0.02
+0.07 +0.03
+0.07 +0.03
Ag / a-TiO2
A B
+0.33 +0.27
+0.36 +0.28
+0.36 +0.28
+0.36 +0.29
vdW-DF
This is further demonstrated by the analysis of the Bader charges, Table 4. The first observation is that these are always smaller than 0.3 |e|, sign of the fact that no net charge transfer occurs. Still, there is an accumulation of charge on the cluster or on the support, which depends on the metal and on the oxide, but not on the theoretical treatment. Au4 is partly negatively charged on ZrO2 with q(Au4) about -0.3 |e| for all isomers, and for all methods. This is completely different from the case where Au4 is deposited on TiO2: here the charges on Au are much smaller, and positive, q = +0.02/+0.07 |e|, Table 4. The Bader charges on Ag4 supported on ZrO2 are virtually zero, while when the same cluster is supported on TiO2 the charge on the cluster becomes positive, q ≈ +0.3 |e|. This shows (1) that the gold clusters have a stronger tendency to attract electronic charge, and (2) that, not surprisingly, titania is more reducible than zirconia. In general, the inclusion of the van der Waals forces has no important effects on the Bader charges, the largest difference being of 0.02 |e|.
4. Conclusions We have investigated the effect of vdW forces on the binding nature of single Au and Ag atoms and Ag4 and Au4 clusters on t-ZrO2 and a-TiO2 (101) surfaces. By inclusion of dispersion, the stability of the various isomers can change, with the Ag adsorbates more affected than the Au ones. Moreover, the adsorption energy is significantly increased when vdW forces are taken into account. These findings indicate that the bonding nature of neutral Ag and Au clusters on t-ZrO2 and a-TiO2 is characterized by a significant contribution of vdW interactions. These have been evaluated at various
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levels of theory. Even using the approach where the correction is smaller, i.e. the vdWDF method, the correction of the adsorption energies can go from a minimum of 20% up to 100%. In some cases, the order of stability of the various isomers can change depending on the level of treatment of vdW forces. This problem has to be taken into account when searches for global minima of supported clusters are performed, as the most stable isomer may not only be a function of the exchange-correlation functional used, but also of the inclusion of van der Waals forces. On the other hand, it is important to stress that the electronic structure of the supported clusters is not affected by the inclusion of dispersion forces.
Acknowledgements Financial support from the European Marie Curie Project CATSENSE and from the Italian MIUR (FIRB Project RBAP115AYN “Oxides at the nanoscale: multifunctionality and applications”) is gratefully acknowledged. We also thank the COST Action CM1104 “Reducible oxide chemistry, structure and functions”.
References 1
Libuda, J.; Freund, H. J. Molecular Beam Experiments on Model Catalysts. Surf. Sci. Rep. 2005, 57, 157-298. 2 Salmeron, M.; Schlogl, R. Ambient Pressure Photoelectron Spectroscopy: A New Tool for Surface Science and Nanotechnology. Surf. Sci. Rep. 2008, 63, 169-199. 3 Somorjai, G. A.; Park. J. Y. Molecular Surface Chemistry by Metal Single Crystals and Nanoparticles from Vacuum to High Pressure. Chem. Soc. Rev. 2008, 37, 2155-2162. 4 Bell, A. T. The Impact of Nanoscience on Heterogeneous Catalysis. Science 2003, 299, 16881691. 5 Campbell, C. T.; Sharp, J. C.; Yao, Y.; Karp, E. M.; Silbaugh, T. L. Insights into Catalysis by Gold Nanoparticles and Their Support Effects Through Surface Science Studies of Model Catalysts. Faraday Discuss. 2011, 152, 227-239. 6 Shaikhutdinov, S. K.; Meyer, R.; Naschitzki, M.; Baumer, M.; Freund, H. J. Surface Chemistry of Catalysis by Gold. Catal. Lett. 2003, 86, 211-219. 7 Li, Y.; Liu, Q.; Shen, W. Morphology-Dependent Nanocatalysis: Metal Particles. Dalton Trans. 2011, 40, 5811-5826. 8 Valden, M.; Lai, X.; Goodman, D. W. Onset of Catalytic Activity of Gold Clusters on Titania with the Appearance of Non-Metallic Properties. Science, 1998, 281, 1647-1650. 9 Zaera, F. Nanostructured Materials for Applications in Heterogeneous Catalysis. Chem. Soc. Rev. 2013, 42, 2746-2762. 10 Cuenya, B. R.; Behafarid, F. Nanocatalysis: Size-, and Shape-dependent Chemisorptions and Catalytic Reactivity Surf. Sci. Reports 2015, 70, 135-187. 11 Pacchioni, G. Electronic Interactions and Charge Transfers of Metal Atoms and Clusters on Oxide Surfaces, Phys. Chem. Chem. Phys., 2013, 15, 1737-1757. 12 Pacchioni, G. First Principles Calculations on Oxide-based Heterogeneous Catalysts and Photocatalysts: Problems and Avances, Catal. Lett., 2015, 145, 80-94. 13 Vilhelmsen, L. B.; Hammer, B. A Genetic Algorithm for First Principles Global Structure Optimization of Supported Nano Structures. J. Chem. Phys. 2014, 141, 044711. 14 Musolino, V.; Selloni, A.; Car, R. Structure and Dynamics of Small Metallic Clusters on an Insulating Meta-Oxide Surface: Copper on MgO(100). Phys. Rev. Lett. 1999, 83, 3242-3245.
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15
Carrasco, J.; Liu, W.; Michaelides, A.; and Tkatchenko, A. Insight Into the Description of Van der Waals Forces for Benzene Adsorption on Transition Metal (111) Surfaces, J. Chem. Phys., 2014, 140, 084704. 16 Gosh, T. B.; Dhabal, S.; Datta, A. K. On Crystallite Size Dependence of Phase Stability of Nanocrystalline TiO2. J. Appl. Phys. 2003, 94, 4577-4582. 17 Smith, S. J.; Stevens, R.; Liu, S. F.; Li, G. S.; Navrotsky, A.; Boerio-Goates, J.; Woodfield, B. F. Heat Capacities and Thermodynamic Functions of TiO2 Anatase and Rutile: Analysis of Phase Stability. Am. Mineral. 2009, 94, 236-243. 18 Hanaor, D. A. H.; Sorrell, C. C. Review of the Anatase to Rutile Phase Transformation. J. Mater. Sci. 2011, 46, 855-874. 19 Augustynski, J. The Role of the Surface Intermediates in the Photoelectrochemical Behavior of Anatase and Rutile TiO2. Electrochim. Acta 1993, 38, 43-46. 20 Linsebigler, A. L.; Lu, G. Q.; Yates, J. T. Photocatalysis on TiO2 Surfaces - Principles, Mechanisms, and Selected Results. Chem. Rev. 1995, 95, 735-758. 21 Hadjiivanov, K. I.; Klissurski, D. G. Surface Chemistry of Titania (Anatase) and TitaniaSupported Catalysts. Chem. Soc. Rev. 1996, 25, 61-69. 22 Kavan, L.; Gratzel, M.; Gilbert, S. E.; Klemenz, C.; Scheel, H. J. Electrochemical and Photoelectrochemical Investigation of Single-Crystal Anatase. J. Am. Chem. Soc. 1996, 118, 6716-6723. 23 Diebold, U.; Ruzycki, N.; Herman, G. S.; Selloni, A. One Step Towards Bridging the Materials Gap: Surface Studies of TiO2 Anatase. Catal. Today 2003, 85, 93-100. 24 Shukla, S.; Seal, S. Mechanisms of Room Temperature Metastable Tetragonal Phase Stabilisation in Zirconia. Int. Mater. Rev. 2005, 50, 45-64. 25 Dwivedi, A.; Cormack, A. N. A Computer-Simulation Study of the Defect Structure of Calcia-Stabilized Zirconia. Philos. Mag. 1990, 61, 1-22. 26 Kharton, V. V.; Marques, F. M. B.; Atkinson, A. Transport Properties of Solid Oxide Electrolyte Ceramics: A Brief Review. Solid State Ion. 2004, 174, 135-149. 27 Guo X. Low Temperature Stability of Cubic Zirconia. Phys. Status Solidi A 2000, 177, 191201. 28 Stefanovich, E. V.; Shluger, A. L.; Catlow C. R. A. Theoretical Study of the Stabilization of Cubic-Phase ZrO2 by Impurities. Phys. Rev. B 1994, 49, 11560-11571. 29 Hofmann, A.; Clark, S.J.; Oppel, M.; Hahndorf, I. Hydrogen Adsorption on the Tetragonal ZrO2 Surface: a Theoretical Study of an Important Catalytic Reactant. Phys. Chem. Chem. Phys. 2002, 4, 3500-3508. 30 Christensen, A.; Carter, E. A. First-Principles Study of the Surfaces of Zirconia. Phys. Rev. B 1998, 58, 8050-8064. 31 Haase, F.; Sauer, J. The Surface Structure of Sulfated Zirconia: Periodic Ab Initio Study of Sulfuric Acid Adsorbed on ZrO2(101) and ZrO2(001) J. Am. Chem. Soc. 1998, 120, 1350313512. 32 Eichler, A.; Kresse, G. First-Principles Calculations for the Surface Termination of Pure and Yttria-Doped Zirconia Surfaces. Phys. Rev. B 2004, 69, 045402. 33 Ganduglia-Pirovano, M.V.; Hofmann, A.; Sauer, J. Oxygen Vacancies in Transition Metal and Rare Earth Oxides: Current State of Understanding and Remaining Challenges. Surf. Sci. Rep. 2007, 62, 219-270. 34 Chen, H.-Y.; Tosoni, S.; Pacchioni, G. Adsorption of Ruthenium Atoms and Clusters on Anatase TiO2 and Tetragonal ZrO2 Surfaces: A Comparative DFT Study. J. Phys. Chem. C, 2015, published online (DOI: 10.1021/jp510468f). 35 Tosoni, S.; Chen, H.-Y.; Pacchioni, G. A DFT Study of Ni Clusters Deposition on Titania and Zirconia Surfaces. Surf. Sci. 2015, published online (DOI:10.1016/j.susc.2015.04.004). 36 Grimme, S. Semiempirical GGA-Type Density Funcrional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787-1799. 37 Mercurio, G.; McNellis, E. R.; Martin, L.; Hagen, S.; Leyssner, F.; Soubatch, S.; Meyer, J.; Wolf, M.; Tegeder, P.; Tautz, F. S.; et al. Structure and Energetics of Azobenzene on Ag(111): Benchmarking Semiempirical Dispersion Correction Approaches. Phys. Rev. Lett. 2010, 104,
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036102. 38 Tosoni, S.; Sauer, J. Accurate quantum chemical energies for the interaction of hydrocarbons with oxide surfaces: CH4/MgO(001), Phys. Chem. Chem. Phys. 2010, 12, 14330-14340 39 Dion, M.; Rydberg, H.; Schroder, E.; Langreth, D. C.; Lundqvist, B. I. Van der Waals Density Functional for General Geometries. Phys. Rev. Lett. 2004, 92, 246401. 40 Klimeš, J.; Bowler, D. R.; Michaelides, A. Chemical Accuracy for the Van der Waals Density Functional. J. Phys.: Condens. Matter 2010, 22, 022201. 41 Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. J. Comput. Mater. Sci 1996, 6, 15-50. 42 Kresse, G.; Furthmüller, J. Efficient Iterative Scheme for Ab-Initio Total Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169. 43 Perdew, J. P.; Burke, K.; Ernherhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868. 44 Anisimov, V. I.; Zaanen, J.; Andersen, O. K. Band Theory and Mott Insulators – Hubbard-U instead of Stoner-I. Phys. Rev. B 1991, 44, 943-954. 45 Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. ElectronEnergy-Loss Spectra and the Structural Stability of Nickel Oxide: An LSDA+U Study. Phys. Rev. B 1998, 57, 1505-1509. 46 Dagotto, E. Correlated Electrons in High-temperature Superconductors. Rev. Mod. Phys. 1994, 66, 763-840. 47 Moreira, I. de P. R.; Illas, F.; Martin, R. L. Effect of Fock Exchange on the Electronic Structure and Magnetic Coupling in NiO. Phys. Rev. B 2002, 65, 155102. 48 Rivero, P.; Moreira, I. de P. R.; Illas, F. Electronic Structure of Single-layered Undoped Cuprates from Hybrid Density Functional Theory. Phys. Rev. B 2010, 81, 205123. 49 Di Valentin, C.; Pacchioni, G.; Selloni A. Reduced and N-Type Doped TiO2: Nature of Ti3+ Species. J. Phys. Chem. C 2009, 113, 20543-20552. 50 Tosoni, S.; Lamiel-Garcia, O.; Fernandez Hevia, D.; Doña, J. M.; Illas, F. Electronic Structure of F-Doped Bulk Rutile, Anatase and Brookite Polymorphs of TiO2. J. Phys. Chem. C 2012, 116, 12738-12746. 51 Ortega, Y.; Lamiel-Garcia, O.; Fernandez Hevia, D.; Tosoni, S.; Oviedo, J.; San-Miguel, M. A.; Illas, F. Theoretical Study of the Fluorine Doped Anatase Surfaces. Surf. Sci. 2013, 618, 154-158. 52 Syzgantseva, O. A.; Calatayud, M.; Minot, C. Revealing the Surface Reactivity of Zirconia by Periodic DFT Calculations. J. Phys. Chem. C 2012, 116, 6636-6644. 53 Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953-17979. 54 Kresse, G.; Joubert, J. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758-1775. 55 Davidson, E. R. Methods in Computational Molecular Physics. Edited by Diercksen, G. H. F.; Wilson, S. NATO Advanced Study Institute C, 1993, 113, 95. 56 Bader, R. F. W. A Quantum Theory of Molecular Structure and its Applications. Chem. Rev. 1991, 91, 893-928. 57
Kittel C. Introduction to Solid State Physics.
58
Grau-Crespo, R.; Cruz Hernandez, N.; Sanz, J. F.; De Leeuw, N. H. Theoretical Investigation of the Deposition of Cu, Ag, and Au Atoms on the ZrO2 (111) Surface. J. Phys. Chem. C 2007, 111, 10448-10454. 59 Gong, X. Q.; Selloni, A.; Dulub, O.; Jacobson, P.; Diebold, U. Small Au and Pt Clusters at the Anatase TiO2(101) Surface: Behavior at Terraces, Steps, and Surface Oxygen Vacancies. J. Am. Chem. Soc. 2008, 130, 370-381. 60 Seriani, N.; Pinilla, C.; Crespo, Y. Presence of Gap States at Cu/TiO2 Anatase Surface: Consequences for the Photocatalytic Activity. J. Phys. Chem. C 2015, 119(12), 6696-6702. 61 Giordano, L.; Pacchioni, G.; Bredow, T.; Sanz, J. F. Cu, Ag, and Au Atoms Adsorbed on TiO2 (110): Cluster and Periodic Calculations. Surf. Sci. 2001, 471, 21.
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62
Zhang, J.; Zhang, M.; Han, Y.; Li, W.; Meng, X.; Zong, B. Nucleation and Growth of Palladium Clusters on Anatase TiO2 (101) Surface: a First Principle Study. J. Phys. Chem. C 2008, 112, 19506. 63 Bredow, T.; Aprà, E.; Catti, M.; Pacchioni, G. Cluster and Periodic Ab-Initio Calculations on K/TiO2 (110). Surf. Sci. 1998, 418, 150-165. 64 San Miguel, M. A.; Calzado, C. J.; Sanz, J. F. First Principles Study of Na Adsorption on TiO2 (110) Surface. Int. J. Quantum Chem. 1998, 70, 351-357. 65 San Miguel, M. A.; Calzado, C. J.; Sanz, J. F. Modeling Alkali Atoms Deposition on TiO2 (110) Surface. J. Phys. Chem. B, 2001, 105, 1794-1798 66 CRC Handbook of Chemistry and Physics, 91st Ed., CRC Press, Boca Raton 2010. 67 Yudanov, L.; Pacchioni, G.; Neyman, K.; Rösch, N. Systematic Density Functional Study of the Adsorption of Transition Metal Atoms on the MgO(001) Surface. J. Phys. Chem. B 1997, 101, 2786-2792. 68 Neyman, K.; Inntam, C.; Nasluzov, V. A.; Kosarev, R.; Rösch, N. Adsorprion of d-Metal Atoms on the Regular MgO(001) Surface: Density Functional Study of Cluster Models Embedded in An Elastic Polarizable Environment. Appl. Phys. A: Mater. Sci. Process. 2004, 78, 823-828. 69 Giordano, L.; Baistrocchi, M.; Pacchioni, G. Bonding of Pd, Ag and Au atoms on MgO(100) Surfaces and MgO/Mo(100) Ultra-Thin Films: A Comparative DFT Study. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72, 115403-11. 70 Pillay, D.; Hwang, G. S. Structure of Small Aun, Agn, and Cun Clusters (n=2-4) on Rutile TiO2 (110): A Density Functional Theory Study. J. Mol. Struct.: Theochem 2006, 771, 129-133. 71 Hakkinen, H.; Landman, U. Gold Clusters (AuN, 2 < ~N < ~10) and their Anions. Phys. Rev. B 2000, 62, R2287-R2290. 72 Wu, X.; Senapati, L.; Nayak, S. K.; Selloni, A.; Hajaligol, M. Growth and Structure of Small Gold Particles on Rutile TiO2 (110). J. Chem. Phys. B 2005, 72, 205422. 73 Mazheika, A. S.; Bredow, T.; Matulis, V. E.; Ivashkevich, O. A. Theoretical Study of Adsorption of Ag Clusters on the Anatase TiO2 (100) Surface. J. Phys. Chem. C 2011, 115, 17368-17377. 74 Yang, C.; Balakrishnan, N.; Bhethanabotla, V. R.; Joseph, B. Interplay Between Subnanometer Ag and Pt Clusters and Anatase TiO2 (101) Surface: Implications for Catalysis and Photocatalysis. J. Phys. Chem. C 2014, 118, 4702-4714.
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