Surface: A Combined Density Functional Theory and Scan

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

From the Terrace Contraction to the Hexameric Sulfur Phase in the Au(100) Surface: A Combined Density Functional Theory and Scanning Tunneling Microscopy Study Ransel Barzaga, Javier Alberto Martinez Pons, Mario H. Farias, and Mayra Paulina Paulina Hernandez J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b12316 • Publication Date (Web): 22 Apr 2019 Downloaded from http://pubs.acs.org on April 22, 2019

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The Journal of Physical Chemistry

From the Terrace Contraction to the Hexameric Sulfur Phase in the Au(100) Surface: A Combined Density Functional Theory and Scanning Tunneling Microscopy Study Ransel Barzaga,†¶ Javier A. Martínez,† Mario H. Farías and Mayra P. Hernández†*

† Instituto de Ciencia y Tecnología de Materiales (IMRE), Universidad de La Habana, Zapata y G, El Vedado, Plaza de la Revolución, La Habana 10400, Cuba

¶ Departamento de Química Módulo 13, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain

Universidad

Nacional Autónoma de México (UNAM), Centro de Nanociencias y

Nanotecnología (CNyN). Campus Ensenada, Km 107 Carretera Tijuana-Ensenada. Ensenada, Baja California 22800, Mexico

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ABSTRACT: The lifting of the Au (100) quasi-hexagonal reconstruction by atoms or molecules leaves a rough surface with islands, terraces and vacancies where different patterns of adsorbates can appear. Although the roughness of the (1 × 1)Au(100) surface has been well characterized, to our knowledge there are not theoretical studies considering its effect in the formation of adsorbate patterns, for instance in the case of sulfur adsorption. In this study, we have combined DFT calculations and STM measurements in order to explore the structural effects induced on the terrace when the sulfur adsorption takes place on the island and vacancy. Models predict a decrease of the Au-Au bond length in the terrace, if the terrace has an appropriate size, when the simultaneous adsorption of sulfur structure ( 2 × 2) occurs on island and vacancy. According to our predictions, this process of gold bond length contraction on the terrace can affect the formation of the sulfur structure on it. STM images reveal regions where the ( 2 × 2) structure is observed on island and vacancy, while a different structure, denoted as hexamer, appear on the terrace. Results from our calculations considering the roughness of

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the (1 × 1)-Au(100) surface and the gold bond contraction agree well with these experimental observations.

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1. INTRODUCTION

The reconstruction of the Au(100) surface has been denoted as a quasi-hexagonal (5 × 20) or 𝑐(26 × 48) lattice with a 25% more dense arrangement of gold atoms than the (1 × 1) surface1-3. The lifting of this hex-reconstruction by atoms and molecules leave a strong corrugate pattern on the Au(100) surface4-8. The transition from the more densely packed hex-reconstruction to (1 × 1) surface produces different domains on the Au(100) surface9-10. Three main features can be identified on the (1 × 1)-Au(100) surface: vacancies, terraces and islands5, 11. A previous theoretical study based on Dispersive-corrected Density Functional Theory (D-DFT) resolved the distortion of the ( 2 × 2) structure considering a surface expansion mechanism of the islands12. As it was demonstrated by HernándezTamargo et al., the strong chemisorption of sulfur atoms in the island provokes the lateral movement of gold atoms expanding the Au-Au bond. Under this approach, they reproduced the nearest sulfur-sulfur distance observed experimentally by Scanning Tunneling Microscopy (STM)11. However, the surface expansion mechanism only accounts for the island in the (1 × 1)-Au(100) surface, while terrace and vacancy were 4


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not considered in this study. Other studies instead focus in calculating the sulfur adsorption energy as a function of surface position or exploring the diffusion of sulfur adatoms along the surface13-14. Nevertheless, there are not theoretical studies considering a realistic description of the sulfur adsorption on roughness of (1 × 1)Au(100) surface. The Au-Au expansion process of gold atoms on the island provokes strong structural changes which can affect the nearby domains like the terrace. Therefore, it is likely that the terrace displays also structural modifications caused by the Au-Au expansion. Reactivity and binding of adsorbates depend crucially on the structural modifications produced in the metal surface15. The formation of different sulfur structures on the terrace should reflect these structural changes on terraces. In order to obtain an adequate description of the structural surface changes on the terrace, we have combined first principles calculations and STM measurements. Density Functional Theory calculations have been carried out to analyze the relative stability of sulfur structure on the terrace when it is structurally affected by the sulfur adsorption on the island and vacancy. We have examined the terrace in our 5



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calculations after the simultaneous formation of the sulfur ( 2 × 2) structure on the island and vacancy, and a decreasing of the Au-Au bond length has been observed on appropriated terrace size. This behavior has been denoted as gold bond contraction of the terrace. Furthermore, the gold bond contraction was also accompanied by a gold bond expansion of the terrace. Both processes, gold bond expansion and contraction, occurred simultaneously on the terrace. A deep exploration of STM images revealed regions where the sulfur ( 2 × 2) structure was adsorbed on the island and vacancy, while a different structure appeared on the terrace. This sulfur structure has been previously described as an arrangement of six sulfur atoms, and denoted as hexamer. Considering the roughness of the (1 × 1)Au(100) surface and bond contraction, we have been able to achieve a good agreement between experiments and calculations.

2. EXPERIMENTAL METHODS

Computational Methods. Periodic DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP 5.4.4)16-17. The semi-empirical method of Grimme 6


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(DFT-D2)18-19 was used to take into account van der Waals (vdW) interactions, applying the gold coefficients calculated by Toyoda et al. (C6 = 47.81 J nm6 mol-1, R0 = 1.497 Å)20 and the sulfur coefficients reported by Grimme (C6 = 5.57 J nm6 mol-1, R0 = 1.683 Å)18. The vdW interactions were only considered for atoms located up to 15 Å from each other. Exchange and correlation have been described using the generalized gradient approximation (GGA)21-22 employing the functional of Perdew, Burke and Ernzerhof (PBE)23-24. The ion-electron interactions were described through the projector augmented wave method (PAW)25-26. The one-electron Kohn-Sham wavefunctions were expanded in a plane-wave basis set with a 500 eV cutoff energy. The Monkhorst-Pack method27 was used for the numerical integration in the reciprocal space of the (2 2 × 8 2) and (2 2 × 10 2) supercells, with a grid of k-points 8 × 1 × 1. Supercells with a larger periodicity were described by one Г-point only grid. Electron smearing was introduced following the Methfessel-Paxton technique28 with a

σ = 0.2 eV, all the energies reported here were extrapolated to 0 K. The gold surface was modelled by five-layer and six-layer slabs for the supercells (2 2 × 8 2) and (2 2 × 10 2), respectively with a vacuum of ~20 Å from the topmost layer to minimize 7



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interactions between periodic images. Relaxation was allowed in the three uppermost layers of these supercells. In the case of (6 2 × 12 2) and (6 2 × 14 2) supercells a four-layer slab was employed, keeping the bottom layer fixed. During geometry optimization all atomic positions of adsorbates and gold layers were relaxed until the force reached 0.01 eV ∙ Å-1. The electronic iteration threshold was set to an energy of 10-5 eV for each ionic step. The calculated gold lattice constant was 4.16 Å, which corresponds to a Au-Au bond length of 2.94 Å, in good agreement with previous DFT calculations under similar computational conditions12, 29. A dipole correction along the surface normal has been included in all calculations for correcting the error introduced from the periodic boundary conditions. The adsorption energy per sulfur atom in the slab, Eads, was defined by the equation: 𝐸𝑎𝑑𝑠 = (𝐸𝑆𝑛 𝑠𝑙𝑎𝑏 ― 𝐸𝑠𝑙𝑎𝑏 ― 𝑛𝐸𝑆0) 𝑛

………………………(1)

where 𝐸𝑆𝑛 𝑠𝑙𝑎𝑏 is the energy of 𝑛 sulfur atoms adsorbed in the slab, 𝐸𝑠𝑙𝑎𝑏 is the energy of the clean gold slab, and 𝐸𝑆0 is the energy of an isolated sulfur atom at the center of a 20 × 21 × 22 Å3 simulation box. Spin polarization was considered for calculating the isolated sulfur atom. 8


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The adsorption energy for further deposition of m sulfur atoms in a slab with n preadsorbed sulfur atoms was calculated according to the following equation: 𝐸𝑎𝑑𝑠 = (𝐸𝑆𝑛 + 𝑚 𝑠𝑙𝑎𝑏 ― 𝐸𝑆𝑛/𝑠𝑙𝑎𝑏 ― 𝑚𝐸𝑆0) 𝑚

………………………(2)

where 𝐸𝑆𝑛 + 𝑚 𝑠𝑙𝑎𝑏 is the adsorption energy produced by the deposition of n+m sulfur atoms in the slab and 𝐸𝑆𝑛/𝑠𝑙𝑎𝑏 is the adsorption energy for the n preadsorbed sulfur atoms. We have also computed the charge allocated on the slab after the adsorption of n+m sulfur atoms, for both (2 2 × 8 2) and (2 2 × 10 2) supercells, by using the quantum theory of atoms in molecules (QTAM) by R. Bader30 as implement by Henkelman et al.31-33. The constant current STM images were simulated with the

p4vasp34 software within the Tersoff-Hamman approach35 using the portioned charge density generated with VASP. The bias voltage of the experimental STM images was reproduced by considering the states within the range EF ± 13.4 meV (EF denotes the Fermi energy). Sample Preparation. An Au(100) single-crystal with 12 mm in diameter and 2 mm thickness (MaTecK Inc.) was used as substrate. The single crystal surface was prepared 9



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by the electrochemical polishing process in 1 M H2SO4. It were then rinsed with 5 M HCl and abundant deionized water. The thermally induced reconstructed Au(100) surface, which is also known as the Au(100)-(hex) surface, was prepared by annealing in a hydrogen flame for several seconds, followed by cooling in air for approximately 3 min. K2DTC2pz was synthetized following the method described by reference 11. K2DTC2pz solution was prepared by dissolving 0.4 g of K2DTC2pz salt, in 10 cm3 of 1 M NaOH solution. The Au(100) substrate was immersed into a K2DTC2pz solution during 24 h. After immersion, the modified gold substrate was rinsed with water and then dried under nitrogen flow. STM Imaging. A home-made STM in air system was used to acquire the STM images in the constant current mode. Tungsten tips were used to obtain the images with a 13.4 mV bias voltage, 3.5 nA tunneling current and 10.1-15.26 Hz frequencies. The tips were prepared by electrochemical etching of tungsten wire (Alpha Aesar 99.95%, diameter 0.25 mm) in 6 M NaOH solution. For the analysis of the images the software WSxM36 was utilized.

3. RESULTS AND DISCUSSION

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The lifting of the Au(100) hex-reconstruction during sulfur adsorption provokes a roughness surface formed by island, terraces and vacancies under a (1 × 1) periodicity4-8. Previous theoretical works reveal that sulfur adsorbs most strongly in the four-fold coordination site forming a monoatomic phase13-14. The maximum occupation of the four-fold sites in the (1 × 1)-Au(100) surface occurs for an intermediate level of coverage appearing the sulfur

( 2 × 2) pattern 12.

Figure 1. Schematic representation of the sulfur adsorption in island and vacancy on the (1 × 1)-Au(100) surface. T1-T2 and T3-T4 models are represented in (2 2 × 8 2) and (2 2 × 10 2) supercells, respectively. The island, terrace, vacancy and bulk layers of Au(100) are identified as dark gray, gray, light gray and white balls, respectively and the sulfur atoms in red. All the models consider that six sulfur atoms were adsorbed on the island and four on the vacancy forming the sulfur ( 2 × 2) structure.

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We studied the relative stability of the reconstruction lifting of the (1 × 1)-Au(100) surface when the adsorption of the sulfur atoms forming the ( 2 × 2) pattern ocurrs on the island and vacancy. With this goal, we observed the behavior of the absorption energy of the sulfur atoms on island and vacancy. Six sulfur atoms were placed on the island and four on the vacancy. Figure 1 illustrates four models, which were labeled as T1-T2 and T3-T4 for the (2 2 × 8 2) and (2 2 × 10 2) supercells, respectively. The terrace size of T1-T2 models was 10.39 Å and for T3-T4 models was 18.70 Å. As first step, we have carried out the structural optimization of sulfur atoms adsorption. After full optimization, the adsorption energy per sulfur atom was evaluated in island and vacancy. Figure 1 shows an increasing of the adsorption energy with the sulfur coverage, independently of the terrace size. This is caused by the lateral movement of gold atoms, which is allowed on the island when the sulfur atoms are adsorbed12, but for the vacancy this movement is limited. T1 and T2 models, corresponding to adsorbed sulfur atoms on island, reported the lowest energy of adsorption, being the most stable configurations. Also, these absorption energies of the T1 and T2 models are close to each other, indicating that the terrace size did not affect the stability of the sulfur absorption on islands. However, T3 and T4 models behaved differently from previous ones. These absorption energies were different between them, being T4 model, which had the larger terrace, the most stable configuration. The adsorption stability of sulfur atoms diminished with the decrease of terrace size, which was likely provoked by the proximity between the island and 12


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vacancy. If the total disappearance of the terrace will occur from the reconstruction lifting, then, the process of the sulfur absorption will be very unstable, reaching a Au-S bond breaking point. Finally, the increasing of absorption energy indicates the weakening of the goldsulfur interaction, which may be due to structural effects induced by the adsorption of sulfur atoms on the island and the vacancy. In order to analyse the structural changes in the terraces provoked by the sulfur adsorption on the islands and on the vacancies, we focused in the changes of the AuAu bond length produced by terrace size effects (the proximity of islands and vacancies). We used the (6 2 × 12 2) and (6 2 × 14 2) supercells shown in Figure 2. Before the geometry optimization, the terrace size values were 20.80 Å for H1 and 29.12 Å for H2. In all cases, an island of thirty-eight gold atoms with fifteen sulfur atoms adsorbed in the four-fold sites was placed in the (1 × 1)-Au(100) surface. The vacancy was described as a region of thirty-six gold atoms with ten sulfur atoms on it. Sulfur atoms were first placed on the island and keeping the island covered, the vacancy was then filled of sulfur atoms. Each step implied a geometry optimization of the models. Figure 2 also show the correlation of the Au-Au bond length with the distance from the middle point between each pair of atoms from the center of terrace (DTcenter). The black dot in Figure 2 represents the 13



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center of terrace. The dash line in the charts of Figure 2 represents the theoretical Au-Au bond length in a perfect (1 × 1)-Au(100) surface (2.940 Å). The Au-Au bond lengths from the center of terrace towards the island were described by positive values and towards the vacancy by negative values. We have grouped the Au-Au bond lengths in three ranges, from 2.930 to 2.940 Å, above 2.940 Å and below 2.929 Å. The variation of the Au-Au bond lengths was evaluated by the amount of the bonds above 2.940 Å or below 2.929 Å with respect to the amount between 2.930 to 2.940 Å. After the sulfur adsorption, the terrace size decreased for both models. The occurrence of sulfur adsorption on islands or islands and vacancies modified the terrace size differently, as can be seen in Figure 2.

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Figure 2. Representation of the (6 2 × 12 2) and (6 2 × 14 2) supercells corresponding H1 model and H2 model. The terrace size after the sulfur adsorption is depicted to the left of each model. The identifier colors of the island, terrace, vacancy, bulk layers of Au(100) and sulfur atoms coincide with Figure 1. It is also depicted the island and the vacancy with sulfur atoms adsorbed on it forming the ( 2 × 2) structure. The black dot indicates the center of terrace. The dash line points out at zero value (DTcenter = 0). The positive and negative distances respect to dash line are also represented in the models. In the charts, the Au-Au bond lengths above 2.940 Å are represented in orange dots, instead those between 2.930-2.940 Å and below 2.929 Å are depicted in blue and dark yellow dots, respectively.

The Table 1 summarizes the fraction for each range of Au-Au bond lengths. We consider

that the fraction 𝑐𝑜𝑛𝑡𝑟𝑎𝑐 =

𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑏𝑜𝑛𝑑𝑠 < 2.929 Å 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑏𝑜𝑛𝑑𝑠 2.940 ― 2.930Å

of the terrace and 𝑒𝑥𝑝𝑎𝑛 =

allows the evaluation of the gold bond contraction

𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑏𝑜𝑛𝑑𝑠 > 2.940 Å 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑏𝑜𝑛𝑑𝑠 2.940 ― 2.930Å

the gold bond expansion of the terrace. Table 1

shows the changes on the terrace structural properties provoked by: (i) terrace size and (ii) the sulfur adsorption on islands and vacancies. It is a fact, that the sulfur adsorption caused

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the reduction of the terrace size. As consequence, the Au-Au bond lengths should be modified, as can be seen in Table 1. The maximum 𝑐𝑜𝑛𝑡𝑟𝑎𝑐 corresponds to the smaller terrace size (20.58 Å), for which the island and vacancy were covered by sulfur atoms. Also, the 𝑒𝑥𝑝𝑎𝑛 value is greater than the contrac value after the sulfur adsorption occurred on the islands, which means that the expansion process is predominant over the contraction when there is only sulfur adsorption on the islands. On the other hand, the non-adsorption of the sulfur atoms in the vacancy produced a lateral movement of the gold atoms of the terrace, which also contributed to increment of the bond length Au-Au. The highest values of contrac and expan are observed for the smallest terrace size. This behavior can be explained because an increase in the terrace size benefits the relaxation of the Au-Au bonds. Probably, a big enough terrace will allow the strong relaxation of the Au-Au bonds with the disappearance of the structural terrace effects induced by the sulfur adsorption. On the contrary, the reduction of the terrace size combined with the sulfur adsorption on islands and vacancies provoked the decreasing of Au-Au bond lengths of the terrace. These modifications in the surface structure should provoke a change in the surface 16


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reactivity according to the predictions of previous DFT calculations, which have shown that a reduction in the lattice constant of late-transition metal can diminish the reactivity of the surface37-38.

Table 1. Values of the 𝒄𝒐𝒏𝒕𝒓𝒂𝒄 and the 𝒆𝒙𝒑𝒂𝒏 for All the Models in Figure 2 The terrace size before optimization is also included. H1 (terrace size = 20.80 Å) H2 (terrace size = 29.12 Å)

𝑐𝑜𝑛𝑡𝑟𝑎𝑐 𝑒𝑥𝑝𝑎𝑛

Island

Island-

Island

Island-vacancy

(H1a)

vacancy

(H2a)

(H2b)

0.67 1.11

(H1b) 0.84 0.79

0.47 0.72

0.49 0.51

The gold bond contraction requires that a terrace, with an appropriate size, is surrounded by islands and vacancies, which are covered by sulfur atoms forming the ( 2 × 2) structure. In principle, this gold bond contraction should also affect the sulfur atom adsorption on the terraces provoking the formation of a pattern different to the ( 2 × 2) on island and vacancy. Figure 3 shows STM images of reconstruction lifting of the modified surface Au(100) by sulfur adsorption. The characteristic reconstruction lifting is visible at low magnification as the corrugated surface layer, where vacancies, terraces and islands can be observed (Figure 3a). Figure 3b shows the formation of different sulfur atom structure at the modified gold surface.

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Figure 3. Unfiltered STM images of the reconstruction lifting of the modified surface Au(100) by sulfur adsorption. (a) 50 nm × 50 nm. (b) 20 nm × 20 nm. (c) 14 nm × 14 nm. Zooming in at the squared area showing the sulfur structures on the four regions of the (1 × 1)Au(100) surface. The black arrow highlights a bright region where non-periodicity was observed after the adsorption of sulfur on the surface Au(100). The height profile along the line I and schematic of the proposed model for the arrangement of sulfur structures are drawn (red balls ( 2 × 2), yellow balls hexamer).

The zooming in at the squared area of Figure 3b was explored along the line of profile I distinguishing four regions on the modified gold surface (Figure 3c). Region 2 was described as the terrace, region 1 and 3 as the island and the vacancy, respectively and the deep regions around the vacancies were labeled as region 4. It is also noticed in Figure 3c (black arrow) the appearance of a bright region with several spots distributed on the surface, in which no 18


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periodicity was observed. We have attributed these bright spots to an excess of sulfur atoms forming polymeric structures similarly to the previous report presented by Jiang et al8. The island (region 1) and vacancy (region 3) revealed a square-like pattern of four points, which can be resolved as a ( 2 × 2) structure. Instead on the terrace (region 2) appeared another arrangement with a different structure. Our previous STM measurements have depicted this arrangement as a rectangular structure composed of six atoms, denoted as hexamer11. An average drop in height of 0.11 ± 0.02 nm was observed between regions 1 and 2, which was similar to the height between regions 3 and 4. A previous report has explained the formation of sulfur multilayers with a difference in height of 0.07 ± 0.02 nm between adjacent layers11, which is lower than the value in our observations. Therefore, we can conclude that hexamer is an adlayer of sulfur atoms. However, the height of 0.27 ± 0.02 nm, between regions 2 and 3, could be explained considering that the sulfur atoms of the hexamers are not at the same height (see line profile of Figure 3).

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Figure 4. Filtered high resolution images of the sulfur ( 2 × 2) structures and hexamer on the (1 × 1)-Au(100) surface. (1) island 3.6 nm × 3.2 nm. (2) terrace 3.5 nm × 3.6 nm. (3) vacancy 3.3 nm × 3.0 nm. (4) deep 3.5 nm × 3.4 nm. Height profiles along the lines corresponded to directions A and B.

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Figure 4 shows the high resolution STM images. In it can be observed sulfur structures in the four regions of the modified gold surface. The profiles along the directions A and B in regions 1 and 3 showed the periodicities of individual atoms in the ( 2 × 2) structure. The characteristic height (~0.8 Å) of the adlayer of sulfur atoms forming the ( 2 × 2) structure was also noticed11. On the other hand, the line profiles of hexamers (regions 2 and 4) revealed elevations and depressions inside the pattern, indicating a difference in height of sulfur atoms. This can be also related with the bright and dark spots observed in Figure 4 inside the hexameric pattern. We have proposed a theoretical model for the arrangement of sulfur dimers in the terrace of the hexamer structure. Therefore, T2 and T4 models (Figure 1) were employed to arrange the sulfur dimers in the terrace. This approach allowed us to consider simultaneously the ordering of sulfur dimers and the contraction of terrace. Models also explained drop in height differences measured between sulfur layers (see Figure 3).

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Figure 5. Representation of the sulfur dimers arrangement into hexamer structures after full optimization of T2/S and T4/S models. Top view (Left) and side view (Right). Sulfur atoms on islands and vacancies (red balls), sulfur dimers on terraces (yellow balls) and gold surface domains are represented: island (dark gray balls), terrace (gray balls), vacancy (light gray balls) and Au(100) bulk layers (white balls). The dimers along the [010] direction are labeled as A and B while dimers C correspond to the ones along the [001] direction. The sulfur atoms of dimers A,B are denoted as 2 and 1, respectively.

Figure 5 displays the hexamer models upon optimization of sulfur dimers arranged in a rectangle shape (see T2/S and T4/S). Two sulfur dimers were placed along the [010] direction (A, B) and the other dimers (C) along the [001] direction. Dimers A and B had one sulfur atom bonded to the terrace surface and the other above it, instead dimer C was directly on the terrace surface. In addition, the sulfur atom of dimer A and B bonded to the surface was adsorbed almost on bridge position, while in the case of dimer C was close to top position. During geometry optimization the dimers A and B got closer to each other, which was an evidence of the lateral interaction between the dimers. It should be noted that we have tested different arrangements of sulfur dimers for the hexamer, but only the model showed in Figure 22


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5 is consistent with the experimental data (see Figure S4 in Supporting Information). Furthermore, the structural optimization of a model with a combination of sulfur atoms and sulfur dimers resulted in the dimerization of sulfur atoms (see Figure S3 in Supporting Information).

Figure 6. Comparison between simulated and experimental STM images of the hexamer structure. Experimental images size: (Top) 2.5 × 2.7 nm2 (Bottom) 2.6 × 1.7 nm2. The hexamer model (yellow balls) along with the sulfur atoms (red balls) of the ( 2 × 2) structure are inserted in the STM images.

Figure 6 shows that simulated STM images reproduced the features of the hexamer structure, which are: a rectangular-like shape and bright, dark zones inside the pattern. The good agreement between experiment and simulation was achieved with the comparison of the hexamer model and the line profiles in Figure 4. According to the hexamer model, dimers A,B have one sulfur atom represented closer to the surface 23



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and the other atom, brighter point in the STM images, is more separated from the surface. Instead, the sulfur atoms of the dimer C are very close to the surface. The dimers A,B are more bright than the dimer C probably due to the specific orientation of sulfur atoms in the dimers. The arrangement of dimers A,B diminished the interaction between the sulfur atoms and the surface. In consequence, the brightness increased respect to dimer C. This arrangement was caused by the effect of terrace contraction, which limited the packing of dimers A,B leaving one sulfur atom separated from the surface. Additionally, we have included the simulation of a STM image of the terrace border (see Figure 6 top). This image shows a similar alignment between the sulfur atoms of the ( 2 × 2) structure (red balls) in the vacancy and the hexamer, which indicates that terrace contraction occurred along the [010] direction. Table 2 summarizes the energetic and structural parameters of the hexamer models after full optimization. The larger negative adsorption energy observed for T2/S model indicated a higher stability of the hexamer structure respect to T4/S model. The sulfur dimers (A, B, C) exhibited Au-S distances within the range of the bond lengths for sulfur dimers adsorbed on the Au(111) surface reported in other DFT studies29,

39.

24


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Dimers A and B had a S-S distance of 1.98 Å, which differs slightly from the S-S distance (2.00 – 2.04 Å) of sulfur dimers on the Au(111) surface29, 39 (see Table 2). The sulfur atom of the dimer more separated from the surface could have a weak interaction with the gold atoms, which enhanced the bond between the sulfurs of the dimer, shortening the S-S distance. On the other hand, the SC-SC distance of dimer C agrees very well with those observed in sulfur dimers adsorbed on the Au(111) surface29. The SA2-SB2 distance of 2.20 Å has been also reported for weakly bonded sulfur atoms in cyclo-octasulfur oxide molecule40. We also made a direct comparison with experimental width and length of hexamer pattern from STM measurements (see Table 2). The hexamer width was defined as the average distance along the [001] direction and the length along the [010] direction. Small deviations were observed between the theoretical width and length of hexamer models and the STM data, as seen in Table 2. We attribute this behavior on the structural parameters to the variability of the Au-Au bond length, which is strongly dependent on the terrace size. The difference in height between the adjacent layers of ( 2 × 2) structures and hexamer was also evaluated in T2/S and T4/S models. The drop in height from the sulfur atoms of

( 2 × 2) structure on the island to the ones of dimer C on the terrace (SC) was

25



Page 26 of 68

defined as HeightC. Similarly, the height between sulfur atoms SA1,SB1 of dimers A,B and structure ( 2 × 2) on the vacancy has been labeled as HeightA1B1. Both parameters were compared with the experimental values obtained from the line profile in Figure 3. Non-significant differences were observed between HeightC and the experimental measurements for models T2/S and T4/S. However, HeightA1B1 from T4/S model showed a better agreement with the experimental values in comparison to T2/S model. This indicates that in T4/S model a better description of the experiments is achieved, allowing the hexamer-hexamer packing observed in the STM images.

26


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Table 2. Adsorption Energy (Eads) and Structural Parameters of Hexamer Model (Hex) Average values of distances S-Au, S-S, width and length of the hexamer. HeightC represents the drop in height between the ( 2 × 2) structure on island and dimer C on terrace, while HeightA1B1 describes the difference in height from SA1,SB1 atoms and ( 2 × 2) structure on the vacancy. T2/S

T4/S

Eads (eV/atom)

-3.62

-3.46

SA1-Au (Å)

2.38

2.39

SB1-Au (Å)

2.38

2.39

SC-Au (Å)

2.37

2.39

SA1-SA2 (Å)

1.97

1.98

SB1-SB2 (Å)

1.97

1.98

SC-SC (Å)

2.03

2.02

SA2-SB2 (Å)

2.20

2.19

width (Å)

2.58

2.58

Reference value

2.39 – 2.48[a] [b]

2.02 – 2.04[a][b]

2.6 ± 0.2[c] 3.3 ± 0.2[d]

length (Å)

4.85

4.81

4.1 ± 0.2[c] 4.9 ± 0.2[d]

HeightC (Å)

1.03

1.02

1.1 ± 0.2[d]

HeightA1B1 (Å)

3.10

2.96

2.7 ± 0.2[d]

[a] DFT, VASP Sulfur dimers on the Au(111) surface Reference 29. [b] DFT, VASP Sulfur dimers on the Au(111) surface Reference 39. [c] Experimental values Reference 11. [d] Experimental values current work.

The Bader charge analysis30 allows to examine the charge transfer during the formation of hexamer structure, the results are compiled in Table 3. The total charges allocated in all the gold atoms of the terrace before and after the formation of hexamer are denoted as Terrace clean and Terrace+Hexamer, respectively. The total charge of the sulfur atoms of the hexamer structures taking into account the gold atoms of the terrace is represented as Terrace+Hexamer 27



Page 28 of 68

(S atoms). In addition, the charge over each sulfur atom of the hexamer is included, the notations remained according to Figure 5. An increment of the charge on the gold atoms of the terraces in both models (Terrace clean) is observed after the formation of hexamer, which suggests a charge transfer from the surface to hexamer. The difference in charge of gold atoms observed between models is provoked by the different amount of gold atoms. However, the total charge of the hexamer was similar for the models T2 and T4 (-0.28

e- vs -0.29 e-). This result was expected because the T4 model has a larger terrace size than in the T2 model and consequently a higher number of hexamers can be located on it. The charge over each sulfur atom of the hexamer structure has been calculated in order to reveal the interactions between the sulfur dimers and the terrace surface. The results have been compared with the charge on the sulfur atoms of an isolated sulfur dimer.

The

charges of the sulfur atoms in the isolated sulfur dimer are of ± 0.06 e-. We started our analysis from the dimer C, which was the sulfur dimer directly adsorbed on the terrace near top sites. A net charge transfer close to -0.10 e- per sulfur atom is noticed after the adsorption of dimer C in T2 and T4 models (see SC). However, the charge transfer 28


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in dimers A and B behaves differently. SA1 and SB1 are the atoms of dimers A and B adsorbed directly on the terrace close to bridge sites. The negative charge in SA1 and SB1 of -0.07 e- (T2) and -0.08 e- (T4) highlights the charge transfer from the terrace of almost -0.14 e- per sulfur atom. In comparison to SC in Table 3, these atoms have a stronger charge transfer from the surface. Nevertheless, the other sulfur atoms SA2,SB2 of the dimers A and B, that are separated from the surface, show a loss of negative charge with respect to the isolated dimer of -0.14 e- and -0.03 e- for SA2 and SB2, respectively. This means that in the case of SA2 and SB2 the charge transfer occurs from the sulfur atoms towards the surface. Consequently, this creates a counterbalancing charge distribution that binds SA2 and SB2 atoms.

29



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Table 3. Bader Charges of the Terrace Clean and Covered with the Hexamer, along with the Charges per Sulfur Atoms of Dimers A, B and C within the Hexamer Structure* T2

T4

-0.31 e-

-0.68 e-

+0.12 e-

+0.29 e-

Terrace+Hexamer

-0.28 e-/per

-0.29 e-/per hexamer

(S atoms)

hexamer

SA1 SB1

-0.07 e-

-0.08 e-

SA2

+0.08 e-

+0.08 e-

SB2

-0.03 e-

-0.02 e--

SC

-0.16 e-

-0.16 e-

SC

-0.03 e-

-0.03 e-

Terrace clean (Au atoms) Terrace+Hexamer (Au atoms)

*The Bader charge on the individual sulfur atoms of a sulfur dimer in a 20 × 21 × 22 simulation box is +0.06 e- and 0.06 e-, respectively.

In order to gain further insights into S–Au bonding interactions from the contracted terrace we have also analyzed the projected density of states (PDOS). Changes in the 5d states of the gold atoms for the contracted terrace were considered taking into account that bonding in gold surfaces is dominated by d-d coupling. T2, T4 and H2b models have been employed for the electronic structure calculations. T2 and T4 models have been selected in order to find a trend in the electronic structure from a more to a less contracted terrace, while H2b allowed to include a model where the contraction of terrace is not a predominant effect. Figure 7 displays the d-projected density of states (d-PDOS) of the terraces in T2, T4 and H2b models has been compared with the electronic structure of the unreconstructed Au(100) 30


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surface, which was labeled as flat surface. All graphics have been rescaled respect to the flat surface for a better comparison. The d-band center has been calculated in order to understand the difference in reactivity of hexamer structure in T2/S and T4/S models (see Table 2) using the approach described by Kitchin et al.41. The value is depicted in the top-right corner of each graphic of Figure 7. We have also analyzed the contributions of the different d orbitals to the total 5d band according to its orientation respect to the [100] crystallographic direction. The schematic representation of the d orbitals along the [100] direction is depicted in Figure 7.

31



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Figure 7. (a) Comparison between the total d-PDOS of flat surface (dark green color) and of the terrace in T2, T4 and H2b models (black color). The d-band center energy for T2, T4 and H2b models is depicted in the top-right corner of the graphics. (b) The

32


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deconvolution of the d states according to their orientation on the Au(100) surface is represented for T2, T4 and H2b models. A schematic representation of the orientation of the atomic d orbitals wavefunctions along the different crystallographic directions is also included.

The total 5d states for T2 model exhibited the disappearance of the well-defined peaks in comparison to the flat surface. Figure 7a shows an overlapping of the 5d states in the bonding edge from -6.5 to 0 eV caused by the decrease of the bond length between the gold atoms in the terrace. Instead, the increment of terrace size in T4 attenuated the gold bond contraction, which produced softening in the 5d states and provoking the 5d states electronic structure of model T4 to resemble the flat surface. The major similarities in the bonding edge were noticed for model H2b, with the appearance of six defined peaks at energy values close to those observed for the flat surface. These observations confirm our predictions that as the terrace size increases, it behaves as a Au(100) surface without bond contraction. In the antibonding edge, above 0 eV, the d-PDOS of all models maintained a similar behavior with respect to the flat surface. The absence of significant differences between the antibonding edge 33



Page 34 of 68

of the flat surface and T2, T4, H2b models suggest that the effect of gold bond contraction does not change the antibonding states. It is also observed an energy upshift of the d-band center42, with the decreasing of terrace size. The displacement of the d-band center energy can be directly related with the reactivity of a metal surface38. Previous studies have demonstrated that an energy downshift or upshift of the d-band center can decrease or increase the adsorbates-surface interaction43-45. Therefore, the higher stability of the hexamer structure in T2 model (see Table 2) is due to the higher d-band center energy. Figure 7b shows the deconvolution of the d-PDOS according to the orbitals orientation in the Au(100) surface. The modifications in the total distribution of 5d states for all models were mainly produced by the 5dz2, 5dxz and 5dyz orbitals, which are parallel to the [100] direction. The 5dz2, 5dxz, 5dyz and 5dx2-dy2, 5dxy states show a decreasing of the PDOS near the Fermi energy, from 0 to -2 eV, as the terrace size increases, which indicates a broadening of the band41. This means that as the terrace size decreases and consequently the bond contraction increases, the 5d band becomes narrower.

34


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Figure 8. PDOS of Au(5d,6s,6p) states of terrace and the S(3s,3p) states of the hexamer.

The Au(5d,6s,6p) projections of the clean terrace are shown in shadow

gray and in solid line after the formation of the hexamer. The Au(5d║) and Au(5d┴) notations represent the 5dz2, 5dxz, 5dyz and 5dx2-dy2, 5dxy states, respectively. Zooming from -17 to -10 eV are inset in the graphics using a scaling factor for the intensity, which is indicated in the graphics.

Figure 8 shows the PDOS curves of the Au(5d,6s,6p) and S(3s,3p) states when the hexamer structure was formed on terraces of the T2 and T4 models. The 5dz2, 5dxz, 5dyz states were labeled as 5d║ (parallel) and 5dx2-dy2, 5dxy states as 5d┴ (perpendicular) according to the 35



Page 36 of 68

crystallographic orientation in the Au(100) surface. The Au(5d┴,5d║,6s,6p) projections show slight modifications after the hexamer adsorption. The biggest changes are seen in Au(6p). A widening of the band toward higher energy is observed for the T2 model, while a narrowing occurs for T4. The S(3s,3p) projections of hexamer between -9 and -17 eV are mainly associated with σ states of the sulfur dimers, which interact with the terrace gold atoms producing the multiple peaks observed in the Au(5d┴,6s,6p) projections (see zoomings in Figure 8). Furthermore, the σ states related to the S(3s) projection, denoted as σS-S, does not show antibonding states shifted above the Fermi level. This is an indication that the σS-S states have a small contribution to the Au-S bonding46. The states of the S(3p) projection in the energy range from -19 to -7 eV are associated to a weak coupling of s and p orbitals of the sulfur dimers. The contribution of these states to the Au-S bonding is almost negligible. Whereas the peaks of the S(3p) projection from -8 to 4 eV are related to the σP-P and  bonding and * antibonding states of the sulfur dimers. The mixing between the σP-P,  and the Au(5d,6s,6p) states is noticeable due to the appearance of σP-P* antibonding states above the Fermi level in the S(3p) projection. In fact, for T2, these antibonding states reach energy values up to almost 6 eV. This behavior is caused by the narrowing of the terrace 5d band of the T2 model before the formation of hexamer (see Figure 7)

46-47.

Moreover, it is also observed that the

intensity of the bonding edge of the Au(5d┴) and the Au(5d║) states decrease below -2 eV, which was caused by the S-Au interaction. The multiple peaks of low intensity observed near the upper edge of Au(5d┴) and Au(5d║) states, above -2 eV, appear due to

36


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participation of several d orbitals in the S–Au bonding after the formation of hexamer48. In addition, a small broadening and downshift of the bonding and antibonding levels of the Au(6s) states can be observed for T2 and T4. All these modifications in the Au(5d,6s,6p) and S(3p) states indicate chemisorption of hexamer structure upon the terrace, which is more intense for T246. In order to obtain a deeper understanding of the interaction between the terrace and hexamer, the gold slab and sulfur atoms were removed, hence keeping only the hexamer inside the vacuum, the PDOS projections were calculated without further optimization. In this case, there were key differences between the hexamer inside vacuum and on the contracted terraces of T2 and T4. The contribution of each sulfur dimer to hexamer-terrace interaction has been compared for the hexamer inside vacuum and on the contracted terrace for which we have focused in the S(3s,3p) projections. Figure 9 shows that the S(3s) projection of hexamer inside vacuum (black dash line) has different peaks, which have been attributed to σS-S states of the sulfur dimers forming the hexamer. The S(3s) projection of hexamer maintained the well-defined peaks after the interaction with the terrace (black solid line), but with a downshift in energy accompanied by an intense peak. The decomposition of the S(3s) projection

37



Page 38 of 68

into the contribution of the sulfur dimers allows assigning the σS-S states to each peak. Four σS-S states are assigned to the sulfur dimers A and B, otherwise dimer C exhibits two σS-S states. Normally the σS-S states split into bonding and antibonding, just like it is observed in dimer C. Nevertheless, we were unable to separate the σS-S states of sulfur dimers A and B, indicating a strong coupling between these two species. Probably the four molecular states of dimers A and B resulted from the linear combination of individual σS-S states, which occurs due to the specific arrangement of hexamer structure49. According to the position in energy 1σ, 2σ, 3σ can be described as bonding states, while 4σ*, 5σ*, 6σ* like antibonding states. The charge density isosurfaces (CDIs), not included, also show the bonding/antibonding character of each σS-S states (see Figure S5 in Supporting Information). Non-significant differences are observed for these states in the terraces of T2 and T4 models. The main alteration after the adsorption of sulfur dimers is an intensity reduction of 4σ*, 5σ* and 6σ* states, as result from the electron donation towards the Au(5d┴,6s,6p) states of the terrace46 (see zoomings in Figure 8 and Figure 9).

38


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Figure 9. PDOS of hexamer S(3s) projection of T2 and T4 models: in vacuum and after the formation on the terrace. The different σS-S states from the combination of sulfur dimers A+B and C are also represented inside the vacuum and after the adsorption.

Further insight in the strong coupling between dimers A and B was attained with the decomposition of the 1σ, 3σ, 4σ* and 6σ* states into atomic s orbital contributions. For this purpose the spd and site projected wave function character of each state obtained from the PDOS was analyzed. Table 4 summarizes the average fractional breakdown

39



Page 40 of 68

of each molecular state into atomic s orbital contributions from the sulfur atoms of dimers A and B. The sulfur atoms notation remains according to Figure 5. From the coefficients in Table 4 it can be observed that 1σ bonding state is mostly due to the contribution of sulfur atoms SA2 and SB2, which are separated from the terrace surface. On the other hand, 3σ bonding state has more contribution from the atomic s orbital of sulfur atoms SA1 and SB1. The 4σ* and 6σ* antibonding states have the opposite trend in the atomic contributions respect to 1σ and 3σ. All these states are occupied and delocalized around the sulfur atoms of dimers A and B, giving rise to strong sulfursulfur interactions. In fact, 1σ and 6σ* states were responsible of the bonding between SA2 and SB2 atoms (see Table 2 and Figure S5 in Supporting Information). Therefore, it can be conclude that sulfur dimers A and B form one building block due to the interaction of these σS-S states.

Table 4. Fractional Breakdown into Atomic s Orbital Contributions of the σ States of Sulfur Dimers A and B Adsorbed on the Terrace 1σ

SA2

SA1

SB2

SB1

0.216

0.103

0.216

0.103 40


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3σ

0.129

0.191

0.129

0.191

4σ*

0.098

0.195

0.098

0.195

6σ*

0.179

0.127

0.179

0.127

Features of the interaction between sulfur dimers of hexamer analyzing the S(3px,py,pz) projections inside vacuum and after the adsorption are presented in Figure 10. The specific orientation of sulfur dimers A and B made impossible to explain the molecular states in terms of σP-P and π states. Therefore, we opted to compare the S(3px,py,pz) projections of dimer C, which have pure σP-P and π states, with dimers A,B. Inside vacuum, dimer C exhibits peaks which can be assigned as the σPXPX,

πPY-PY and πPZ-PZ molecular states. Instead, multiple peaks appear in the A+B

projections due to the coupling between px, py and pz orbitals of these sulfur dimers, forming molecular states with a partial σ or π character. At energies below -9 eV, all the projections of A+B and the px of C show small peaks related to a weak s-p interaction between the sulfur dimers (soft line). The py and pz projections of dimer C were interpreted as the double degenerated πPY-PY and πPZ-PZ molecular states. The position of the peaks observed for the py and pz projections of A+B coincide but with different intensities. We have described these projections as molecular states with a 41



Page 42 of 68

stronger 𝜋 character than A+B(px) projection. It can be stated that the S(3px,py,pz) projections inside vacuum also show the coupling between sulfur dimers A and B, as it was previously observed for the σS-S states (see Figure 9).

Figure 10. PDOS of the S(3p) projection decomposed in the px, py and pz states for the

combination of sulfur dimers: A+B and C. In soft line are represented the

projections inside the vacuum and the ones after the adsorption in bold line.

42


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The A+B and C projections after adsorption showed a broadening of all the molecular states due to the interaction with the Au(5d,6s,6p). In addition, bonding and antibonding states appeared after the coupling with Au(5d) states, although most of the antibonding states were below the original molecular states. The interaction between sulfur dimers and the surface of terrace should have given rise to bonding and antibonding states below and above the original molecular states. This behavior can be explained by a two steps process, first the coupling of molecular states with the 5d band of the surface generated the bonding/antibonding states, which then were downshifted in energy by the charge transfer from the surface46. The molecular states involved in this charge transfer are the π* antibonding states.

Previous reports

highlight that this charge transfer is the reason of the elongation of sulfur-sulfur bonds in the sulfur dimers after the adsorption on the surface (S-S bond isolated dimer 1.90 Å)29. The elongation of sulfur-sulfur bond in our case, with 1.98 Å for dimers A,B and 2.02 Å for dimer C, also confirmed this charge transfer process (see Table 2). However, the charge transfer occurred differently for dimers A,B and C owing to its orientation on the surface of terrace. The orientation of sulfur dimers A,B has also an 43



Page 44 of 68

effect in the Au-S bonding and it can be noticed in the px projection of the PDOS curves. In C(px) the disappearance of the two molecular states after adsorption can be distinguished (soft vs bold line), one around -4 eV which hybridizes with the Au(5d) states and the other about 3 eV that is broadened as a result of the coupling with the Au(6s,6p). In contrast for A+B(px) the molecular states after adsorption still show defined peaks in the bonding and antibonding regions. This shows a weaker hybridization and coupling with the Au(5d,6s,6p) states for the dimers A and B compared to dimer C, which is a direct consequence of their orientation. In the case of the projections A+B(py,pz) and C(py,pz) the hybridization of the molecular states is quite noticeable. The attractive interaction between the π states of sulfur dimers and Au(5d) is reflected in the broadening of all py,pz projections. Moreover, we were able to extract information about the effect of terrace size on the strength of sulfur dimersterrace interaction from the PDOS antibonding region. The A+B and C projections showed more antibonding states above the Fermi level, around 0-5 eV, for T2 model than T4. The higher in energy the antibonding states are the stronger is the bond between the surface and adsorbates47. Therefore, this is another indication of the 44


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stronger S-Au bonding of sulfur dimers in T2, which is the more contracted terrace. The affinity of sulfur dimers for the surface of terrace was just caused by the Au-Au bond contraction. Normally, sulfur atoms are more reactive than sulfur dimers in the Au(100) surface12. Hence, it is likely that bond contraction unfavored the adsorption of the sulfur atoms and enhanced that of the sulfur dimers.

4. CONCLUSIONS

In this work, we have investigated the structural effects over the terrace induced by the simultaneous adsorption of sulfur ( 2 × 2) structure on island and vacancy using DFT calculations and STM measurements. Our calculations predict a contraction of the Au-Au bond length on the terrace when sulfur atoms are adsorbed on the island and vacancy. Furthermore, from the calculations we also conclude that the Au-Au bond contraction can modify the sulfur adsorption, if the terrace has the appropriate size, forming different sulfur patterns. STM images reveal that the terrace exhibits a different sulfur pattern when it is surrounded by islands and vacancies covered with the ( 2 × 2) structure. This pattern on the terrace is described as a rectangular-like 45



Page 46 of 68

structure composed of six sulfur atoms, and denoted as hexamer. STM and DFT data show that the hexamer structure is actually conformed by the arrangement of three sulfur dimers. The correlation between experiments and calculations is achieved when two of the sulfur dimers in the hexamer have been arranged with one sulfur atom separated from the terrace surface. Bader charge analysis allows explaining the orientation of these sulfur dimers on the basis of two processes: a terrace-sulfur dimer charge transfer and a sulfur dimer-terrace charge transfer back. Both processes maximize the sulfur-gold bonding, the sulfur-sulfur interactions and the sulfur-gold long range interactions. In addition, the analysis of PDOS shows that despite the hexamer structure is described as the arrangement of three sulfur dimers, two of them form a single unit. Finally, the PDOS also predict that the bond contraction modifies the reactivity of the terrace, likely increasing the preference for the dimers with respect to the sulfur atoms. The present study illustrated the importance of taking into account the surroundings of a domain when analyzing the structural effects induced by the adsorption.

46


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ASSOCIATED CONTENT Supporting Information. Analysis of the Au-Au bond length in models T2 and T4. Grid values and total charge per layer of slab for the Bader atomic charges calculation. Geometry optimization of the arrangement of sulfur dimers and sulfur atoms in model T2. Hexamer structure adsorbed on a flat Au(100) surface. Charge density isosurfaces of the σS-S states in model T4. Modelling of the hexamer structure using S-Au-S units as building blocks.

AUTHOR INFORMATION Corresponding Author *Email: [email protected]

ACKNOWLEDGEMENTS The authors would like to gratefully thank the generous allocation of computer time at Centro de Computación Científica at the Universidad Autónoma de Madrid (CCCUAM). R.B. acknowledges Fundación Carolina, España for a PhD fellowship. (J.A.M) acknowledges a grant from Centro Latinoamericano de Física (CLAF) and the Abdus Salam International Centre for Theoretical Physics (ICTP). Also, one of the authors (M.P.H.) is very grateful to DGAPA-UNAM for a 4-month fellowship through the “Programa de Estancias de Investigación en la UNAM (PREI)”. In addition, this work

47



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has been funded by the “Proyecto Nacional de Ciencias Básicas” code P223LH001079 “Absorción de moléculas organosulfuradas en superficies metálicas”. Finally, the authors thank Fernando Aguilar-Galindo and Sergio Díaz-Tendero for fruitful discussions.

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Kolb, D.; Schneider, J. Surface Reconstruction in Electrochemistry: Au (100-

(5× 20), Au (111)-(1× 23) and Au (110)-(1× 2). Electrochim. Acta 1986, 31, 929-936.

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Tunnelling Microscopy. J. Microsc. 1988, 152, 449-457.

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N‐Octadecane Thiol Monolayers Self‐Assembled on Au (001) Studied by Synchrotron X‐Ray and Helium Atom Diffraction. J. Chem. Phys. 1995, 102, 5012-5028. 48


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Figure 1. Schematic representation of the sulfur adsorption in island and vacancy on the (1×1)-Au(100) surface. T1-T2 and T3-T4 models are represented in (2√2×8√2) and (2√2×10√2) supercells, respectively. The island, terrace, vacancy and bulk layers of Au(100) are identified as dark gray, gray, light gray and white balls, respectively and the sulfur atoms in red. All the models consider that six sulfur atoms were adsorbed on the island and four on the vacancy forming the sulfur (√2×√2) structure.



Figure 2. Representation of the (6√2×12√2) and (6√2×14√2) supercells corresponding H1 model and H2 model. The terrace size after the sulfur adsorption is depicted to the left of each model. The identifier colors of the island, terrace, vacancy, bulk layers of Au(100) and sulfur atoms coincide with Figure 1. It is also depicted the island and the vacancy with sulfur atoms adsorbed on it forming the (√2×√2) structure. The black dot indicates the center of terrace. The dash line points out at zero value (DTcenter = 0). The positive and negative distances respect to dash line are also represented in the models. In the charts, the Au-Au bond lengths above 2.940 Å are represented in orange dots, instead those between 2.930-2.940 Å and below 2.929 Å are depicted in blue and dark yellow dots, respectively. 159x108mm (300 x 300 DPI)


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Figure 3. Unfiltered STM images of the reconstruction lifting of the modified surface Au(100) by sulfur adsorption. (a) 50 nm × 50 nm. (b) 20 nm × 20 nm. (c) 14 nm × 14 nm. Zooming in at the squared area showing the sulfur structures on the four regions of the (1×1)-Au(100) surface. The black arrow highlights a bright region where non-periodicity was observed after the adsorption of sulfur on the surface Au(100). The height profile along the line I and schematic of the proposed model for the arrangement of sulfur structures are drawn (red balls (√2×√2), yellow balls hexamer). 82x80mm (300 x 300 DPI)



Figure 4. Filtered high resolution images of the sulfur (√2×√2) structures and hexamer on the (1×1)Au(100) surface. (1) island 3.6 nm × 3.2 nm. (2) terrace 3.5 nm × 3.6 nm. (3) vacancy 3.3 nm × 3.0 nm. (4) deep 3.5 nm × 3.4 nm. Height profiles along the lines corresponded to directions A and B. 82x145mm (300 x 300 DPI)


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Figure 5. Representation of the sulfur dimers arrangement into hexamer structures after full optimization of T2/S and T4/S models. Top view (Left) and side view (Right). Sulfur atoms on islands and vacancies (red balls), sulfur dimers on terraces (yellow balls) and gold surface domains are represented: island (dark gray balls), terrace (gray balls), vacancy (light gray balls) and Au(100) bulk layers (white balls). The dimers along the [010] direction are labeled as A and B while dimers C correspond to the ones along the [001] direction. The sulfur atoms of dimers A,B are denoted as 2 and 1, respectively.



Figure 6. Comparison between simulated and experimental STM images of the hexamer structure. Experimental images size: (Top) 2.5 × 2.7 nm2 (Bottom) 2.6 × 1.7 nm2. The hexamer model (yellow balls) along with the sulfur atoms (red balls) of the (√2×√2) structure are inserted in the STM images. 60x52mm (300 x 300 DPI)


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Figure 7. (a) Comparison between the total d-PDOS of flat surface (dark green color) and of the terrace in T2, T4 and H2b models (black color). The d-band center energy for T2, T4 and H2b models is depicted in the top-right corner of the graphics. (b) The deconvolution of the d states according to their orientation on the Au(100) surface is represented for T2, T4 and H2b models. A schematic representation of the orientation of the atomic d orbitals wavefunctions along the different crystallographic directions is also included. 140x186mm (300 x 300 DPI)



Figure 8. PDOS of Au(5d,6s,6p) states of terrace and the S(3s,3p) states of the hexamer. The Au(5d,6s,6p) projections of the clean terrace are shown in shadow gray and in solid line after the formation of the hexamer. The Au(5d║) and Au(5d┴) notations represent the 5dz2, 5dxz, 5dyz and 5dx2-dy2, 5dxy states, respectively. Zooming from -17 to -10 eV are inset in the graphics using a scaling factor for the intensity, which is indicated in the graphics. 82x103mm (300 x 300 DPI)


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Figure 9. PDOS of hexamer S(3s) projection of T2 and T4 models: in vacuum and after the formation on the terrace. The different σS-S states from the combination of sulfur dimers A+B and C are also represented inside the vacuum and after the adsorption. 82x93mm (300 x 300 DPI)



Figure 10. PDOS of the S(3p) projection decomposed in the px, py and pz states for the combination of sulfur dimers: A+B and C. In soft line are represented the projections inside the vacuum and the ones after the adsorption in bold line. 159x95mm (300 x 300 DPI)


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Surface: A Combined Density Functional Theory and Scan

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