Interaction of SO 2 with the Platinum (001), (011), and (111) Surfaces: A DFT Study

: Given the importance of SO 2 as a pollutant species in the environment and its role in the hybrid sulphur (HyS) cycle for hydrogen production, we carried out a density functional theory study of its interaction with the Pt (001), (011), and (111) surfaces. First, we investigated the adsorption of a single SO 2 molecule on the three Pt surfaces. On both the (001) and (111) surfaces, the SO 2 had a S,O-bonded geometry, while on the (011) surface, it had a co-pyramidal and bridge geometry. The largest adsorption energy was obtained on the (001) surface ( E ads = − 2.47 eV), followed by the (011) surface ( E ads = − 2.39 and − 2.28 eV for co-pyramidal and bridge geometries, respectively) and the (111) surface ( E ads = − 1.85 eV). When the surface coverage was increased up to a monolayer, we noted an increase of E ads / SO 2 for all the surfaces, but the (001) surface remained the most favourable overall for SO 2 adsorption. On the (111) surface, we found that when the surface coverage was θ > 0.78, two neighbouring SO 2 molecules reacted to form SO and SO 3 . Considering the experimental conditions, we observed that the highest coverage in terms of the number of SO 2 molecules per metal surface area was (111) > (001) > (011). As expected, when the temperature increased, the surface coverage decreased on all the surfaces, and gradual desorption of SO 2 would occur above 500 K. Total desorption occurred at temperatures higher than 700 K for the (011) and (111) surfaces. It was seen that at 0 and 800 K, only the (001) and (111) surfaces were expressed in the morphology, but at 298 and 400 K, the (011) surface was present as well. Taking into account these data and those from a previous paper on water adsorption on Pt, it was evident that at temperatures between 400 and 450 K, where the HyS cycle operates, most of the water would desorb from the surface, thereby increasing the SO 2 concentration, which in turn may lead to sulphur poisoning of the catalyst.


Introduction
The current global energy demand is met primarily by fossil fuels, including natural gas and coal.However, with increased legislation imposed for environmental and sustainability reasons, as well as continuing depletion of the world's fossil fuel resources, the focus is shifting towards energy production that is clean and renewable.Among other possible energy systems, hydrogen (H 2 ) as an energy carrier is considered a potentially viable solution to address sustainable energy production, when coupled with renewable sources and adequate technology [1][2][3][4].H 2 gas is an ideal energy carrier for a number of applications [5][6][7]; it can be produced using a range of technologies [8][9][10][11], and of those, the non-carbon based hybrid sulphur (HyS) cycle is a potential large-scale H 2 production process [12,13].In this cycle, sulphuric acid (H 2 SO 4 ) is thermally (>800 • C) decomposed into water (H 2 O), oxygen (O 2 ), and sulphur dioxide (SO 2 ).In the second step, SO 2 reacts with H 2 O to form H 2 SO 4 and H 2 at temperatures between 80 and 120 • C. The net reaction of this cycle as a whole, without detrimental by-products, is the splitting of H 2 O into O 2 and H 2 .
The current catalyst of choice in the HyS cycle is platinum (Pt), a very expensive and rare noble metal.While various other metals have been investigated [13], Pt is still the best performing catalyst in terms of activity and stability [14 -16].In previous optimisation experiments [17], it was found that an ideal catalyst should (i) not favour the reduction of SO 2 to elemental sulphur, to prevent poisoning of the catalyst, and (ii) be able to activate H 2 O.It is therefore essential to understand the behaviour of SO 2 on the Pt surface in order to suggest less costly alternatives.Insights into the binding and reactivity of SO 2 on various transition metal surfaces, including Cu [18][19][20][21], Ni [22][23][24], Ag [25,26], Rh [27,28], Pd [20,[28][29][30][31][32], and Pt [20,27,[33][34][35][36], have accumulated through experimental and theoretical work over the past two decades.However, major difficulties have been experienced in experiments, in part due to the existence of various co-adsorbed surface sulphur species, even when pure sulphur oxides, such as SO 2 , are introduced from the gas phase onto the metal catalytic surfaces.Moreover, very little work has been performed on evaluating the energetics or thermodynamics of the adsorption of sulphur oxides or their surface reactions.Most experimental and theoretical work has considered the active Pt (111) surface, but it was shown in a water environment and with increasing temperatures that the Pt (001) and (011) surfaces were also important [37].In a previous paper, we showed that in the presence of H 2 O under various temperatures and pressures, the (001), (011), and (111) surfaces were expressed to varying degrees in the particle morphology [38].Thus, it is important for the sake of completeness and comparison that the effects of SO 2 adsorption, concentration, and environmental temperature be considered for all three Pt surfaces.
In this paper, we used density functional theory (DFT) calculations to predict the behaviour of SO 2 on the Pt (001), (011), and (111) surfaces.We examined the electronic properties of the system, i.e., the work function and charge densities.Surface phase diagrams are also generated by taking into consideration the surface free energies and the chemical potential of SO 2 , to determine the effects of temperature and pressure on the surface coverage and the morphology of nanoparticles.In general, it was our aim to develop a comprehensive understanding of SO 2 surface chemistry, including the most stable adsorption sites, adsorption modes, and possible desorption of species that may occur on the major electro-catalytic surfaces of Pt.

SO 2 Adsorption
To calculate the adsorption behaviour of SO 2 on a Pt surface, the most common and widely used surfaces Pt (001), (011), and (111) were investigated, shown in Figure 1 as top and side views.All three surfaces were planar, bulk-terminated structures, with four atomic layers and 15 Å vacuum space in the simulation cell.Pt (001) was a flat surface, while Pt (011) was atomically rough owing to the channels on the surface, whereas Pt (111) was again flat with a face-centred cubic arrangement.In a previous study [38], we used different long-range dispersion approximations, including the DFT-D3 method with Becke-Johnson damping [39], and calculated the lattice parameter of 3.926 Å, which correlated with the experimental value of 3.925 Å [40,41].With regard to the surface energy, the most favourable was Pt (111) with the lowest surface energy at 2.046 J/m 2 , followed by the (001) and (011) surfaces at 2.462 and 2.615 J/m 2 , respectively, which correlated with experimental [42] and modelled values [43].For benchmarking, we also investigated the effect of increasing the number of layers in the Pt slab to six and eight, again keeping the bottom two layers fixed and relaxing the four and six remaining layers, respectively.The data from the thicker slabs correlated well with the four layer Pt surfaces, showing a difference in surface energies of less than 0.1 eV, which fell within the margin of error.The calculated work functions were 5.89, 5.49, and 5.64 eV, which correlated with the literature values [44] of 5.66, 5.26, and 5.69 eV for Pt (001), (011), and (111), respectively.Figure 1 shows the Pt surfaces with possible adsorption sites for each surface.To distinguish between the top layer and subsequent layer atoms, the colour of the second layer atoms in each of the surfaces was changed to lighter gold.The adsorption sites indicated in Figure 1 for the Pt (001) and (011) surfaces are atop (A), bridge (B), and four-fold hollow (4F), while the Pt (111) surface has atop (A), bridge (B), face-cubic centred (fcc), and hexagonal close packed (hcp) sites.
Five modes of SO 2 adsorption on a metallic surface have been suggested [45], parallel, co-planar, bridging, O-bonded, and S,O-bonded.All five modes were investigated in the various adsorption sites shown in Figure 1.The most stable structures found for the adsorption of SO 2 onto the Pt surface are shown in Figure 2. The bond distances and angles of the adsorbed SO 2 with respect to the Pt surfaces are shown in Table 1   SO 2 adsorption on the (001) surface had a S,O-bonded geometry in the 4F binding site, where one S-O bond was in the plane of the surface and the other oxygen was directed away from the surface.The two S-O bond lengths in this case were different due to the position of nearby Pt atoms, i.e., for the upright oxygen (O up ), it was 1.451 Å, and for the oxygen nearer the surface (O plane ), it was elongated to 1.619 Å.Similarly, in an experimental study [29] of SO 2 adsorption on the Pd (100) surface, SO 2 had a S,O-bonded geometry with S-O and S-Pd bond lengths of 1.48 and 2.24 Å, respectively.For the Pt (001) surface, S-O-Pt 1 was 105.62 • , which was smaller than the experimental value of the free molecule of 120 • , and thus was an indication that the molecule was chemisorbed.This stable adsorption mode was also obtained on the six and eight layer (001) Pt surface slabs, with corresponding adsorption energies of −2.40 and −2.47 eV, respectively.
Two stable adsorption configurations were observed on the (011) surface.The first one was a co-pyramidal configuration, where SO 2 was parallel to the Pt surface with the two oxygens bound to two Pt atoms on the (011) ridge, forming an O-O-bridge with Pt.The second was a bridge configuration, where the sulphur formed a bridge between two Pt atoms on the ridge of the surface, with the oxygens directed away from the surface.In the (011) co−pyramidal configuration, the O-S-O bond angle was smaller than 120 • , possibly due to the shorter bond lengths between S, O, and Pt, whereas in the (011) bridge configuration, the O-S-O angle was ~119 • .This stable adsorption mode was also obtained on the six and eight layer (011) Pt surface slabs, with corresponding adsorption energies of −2.55 and −2.55 eV for the co-pyramidal configuration and −2.35 and −2.31 eV for the bridge configuration, respectively.
Similar to the adsorption on Pt (001), SO 2 on the (111) surface had a S,O-bonded geometry on the fcc binding site, where one S-O bond lied in the plane of the surface and the other's oxygen was directed away from the surface.SO 2 can act as both a σ-donor and π-acceptor [49]; when the σ-bonding dominated, the molecule adsorbed with its molecular plane perpendicular to the surface, which could lead to the modes of adsorption seen on the (001), (011) bridge , and (111) surface sites.In contrast, if the π-acceptor aspect dominated, π bonds were formed between the SO 2 and metal, and thus, the molecule lied flat on the surface, which could be the reason for the formation of the (011) co−pyramidal structure.This stable adsorption mode was also obtained on the six and eight layer (111) Pt surfaces, with corresponding adsorption energies of −1.94 and −1.96 eV, respectively.
As part of the benchmarking, the most stable adsorption configurations were also investigated on the (001), ( 011) and (111) surfaces with six and eight layers.The adsorption energies correlated well with the four layer slab, showing a difference of less than 0.11 eV.Therefore, it was decided to use the four layer slab for all remaining calculations of the Pt (001), (011), and (111) surfaces.Overall, the adsorption energy for N SO 2 = 1 was calculated to be most favourable on the (001) surface, followed by the (011) and (111) surfaces, which was the same trend as was found for H 2 O adsorption [38].
Table 1 shows the simulated wavenumbers of the fundamental vibrational modes of the adsorbed SO 2 molecule on the (001), (011), and (111) surfaces, i.e., the asymmetric stretching (ν asym ), symmetric stretching (ν sym ), and bending (δ) vibrational modes.Comparing the vibrational modes of SO 2 on the (001), (011) bridge , and (111) surfaces, the values correlated well with the experimentally observed values [48].However, for (011) co−pyramidal , the values were smaller, due to the constraint in the SO 2 molecule where the O atoms were bound to the Pt ridge atoms.
From the charge analysis in Table 1, the negative values of ∆q indicated charge transfer from the surface to the adsorbate, where the most charge was transferred to the (011) co−pyramidal configuration, followed by (001), (111), and (011) bridge .Figure 3 shows the iso-surfaces of the electron density difference between SO 2 and the Pt surface, which were calculated by subtracting the electron density of a clean Pt surface and that of a single SO 2 molecule from the total electron density of the modelled system.Yellow and teal represent positive (electron gained) and negative (electron depleted) electron densities, respectively.In all four systems, the O atoms gained electron density (∆q = approximately Yellow and teal represent positive (electron gained) and negative (electron depleted) charge density with ±0.0021, ±0.0020, ±0.0016, and ±0.0300 e/Å 3 iso-surfaces, respectively.

SO 2 Surface Coverage
To determine the effect of an increased concentration of SO 2 on the adsorption energy, configuration, work function, and morphology, the number of adsorbed SO 2 molecules (N SO 2 ) was increased on each of the Pt surfaces, until a monolayer was obtained.The lowest energy configurations for single SO 2 adsorptions (Section 3.1) were used as the initial guess geometries for the systematic surface coverage increase.To obtain the lowest energy configurations, shown in Figure 4, more than 30 adsorption configurations were considered for each surface with the different coverages.Similar to the adsorption of H 2 O on all the Pt surfaces [38], it was seen that if the subsequent SO 2 molecules were more than one adsorption site away from each other, the adsorption geometry remained the same as for the single adsorption, suggesting that they behave as isolated adsorbates.
On the (001) surface, as the surface coverage increased up to θ = 1, the mode of adsorption remained the same; no dissociation or recombination occurred during the geometry optimisations.This was also seen on the (011) surface, but when adsorption increased above θ > 0.61, the co-pyramidal adsorption changed to a mixed configuration with bridge adsorptions.The highest surface coverage was θ = 0.67 for both Pt (011) co−pyramidal and Pt (011) bridge adsorption modes.In the Pt (011) bridge coverage of θ = 0.67, two SO 2 molecules reacted to form SO and SO 3 .On the Pt (111) surface, again, the adsorption mode remained the same with increasing coverage up to θ = 0.67.Similar to Pt (011) bridge , on the Pt (111) at the highest coverage of θ = 0.78, two neighbouring SO 2 molecules reacted to form SO and SO 3 .
Figure 5a shows the computed average adsorption energies as a function of the surface coverage of SO 2 , which were calculated by dividing the maximum number of binding sites, e.g., nine for the (001) surface, by the Pt surface area (1.387 nm 2 ).Overall, it can be seen for all three surfaces that the adsorption energy decreased monotonically as the surface coverage of SO 2 increased.On the (001) surface, however, increasing the coverage from θ = 0.11 (0.72 SO 2 /nm 2 Pt) to 0.22 (1.44 SO 2 /nm 2 Pt) increased E ads , thus creating a more stable system.Overall, the (001) surface was most favourable for SO 2 adsorption, and in most cases, it would have at least a coverage of θ = 0.22 (1.44 SO 2 /nm 2 Pt).The maximum coverage where θ = 1 was obtained for 6.49 SO 2 /nm 2 Pt.The (011) surface had a maximum of 18 SO 2 adsorption sites per 1.962 nm 2 Pt.It can be seen that up to θ = 0.33 (3.06 SO 2 /nm 2 Pt), the co-pyramidal configuration was the more stable adsorption, with a gradual decrease in E ads as the surface coverage increased.However, beyond this coverage, the bridge configuration became more stable, due to the surface area required for each SO 2 on the surface.For example, in the co-pyramidal configuration, both O atoms were bound to a Pt atom, whereas in the bridge configuration, only the S atom was bound to a Pt atom, and the two O atoms were directed away from the surface.In fact, at the highest coverage, the dominant configuration of (011) co−pyramidal changed to a mixture of co-pyramidal and bridge adsorptions to allow the increased number of adsorbed SO 2 molecules.A higher coverage than θ = 67 (6.12 SO 2 /nm 2 Pt) could not be achieved as a secondary SO 2 layer began to form.Similarly, the highest coverage for (011) bridge was also θ = 67 (6.12 SO 2 /nm 2 Pt), but here, it was seen that two neighbouring SO 2 molecules reacted to form SO and SO 3 .
The (111) surface was the least favourable of the three surfaces in terms of SO 2 adsorption.Similar to the (001) surface, a maximum of nine binding sites were available on a Pt surface area of 1.068 nm 2 .
E ads changed very little between θ = 0.11 (0.94 SO 2 /nm 2 Pt) and 0.44 (3.75 SO 2 /nm 2 Pt) as the adsorption geometry of the SO 2 molecules did not change.From θ > 0.44 onwards, the surface became "crowded", causing the geometries to change, with one of the SO 2 molecules in a bridging adsorption mode in a bridge adsorption site.At θ = 0.78 (6.56 SO 2 /nm 2 Pt), two neighbouring SO 2 molecules changed geometries in such a way that one had a co-planar adsorption mode in an atop adsorption site, and the second still had its S,O-bonded geometry, but reacted to form SO and SO 3 .When θ > 0.78, two SO 2 molecules still reacted, but a second layer of SO 2 also started to form.
In Figure 5b, we also plot the energies obtained by increasing sequentially the number of SO 2 molecules per Pt surface area until full coverage of the surface was obtained.The trend for SO 2 coverage in terms of the N SO 2 nm −2 Pt was (011) < (001) < (111) at 6.12, 6.49, and 6.56 molecules nm −2 Pt, respectively.On the (001) surface, it can be seen that the absolute value of E ads increased with the addition of two SO 2 molecules, after which E ads decreased sequentially.As for the average E ads (Figure 5a), up to θ = 0.33 (3.06 SO 2 /nm 2 Pt), the co-pyramidal configuration was the more stable adsorption, with a gradual decrease in E ads as the surface coverage increased.However, beyond this coverage, the bridge configuration became more stable, but only up to θ = 0.56 (5.10 SO 2 /nm 2 Pt).Both the co-pyramidal and bridge geometries showed a sharp E ads decrease at θ = 0.61 (5.61 SO 2 /nm 2 Pt) due to crowding on the surface.It was at this point that two neighbouring SO 2 molecules reacted to form SO and SO 3 , which then resulted in lowering the E ads at θ = 0.67 (6.12 SO 2 /nm 2 Pt) to −1.79 and −0.91 eV for co-pyramidal and bridge geometries, respectively.A similar trend can be observed on the (111) surface, where E ads decreased slightly as SO 2 was adsorbed sequentially up to θ = 0.44 (3.75 SO 2 /nm 2 Pt), beyond which E ads reached a minimum value of −0.28 eV at θ = 0.67 (5.62 SO 2 /nm 2 Pt) to increase to −0.5 eV at the highest coverage of θ = 0.78 (6.56 SO 2 /nm 2 Pt) after the formation of SO and SO 3 .
We calculated the reaction energy of 2SO 2 → SO + SO 3 in a vacuum as +1.61 eV, but for the formation of these species on the surfaces as −3.55, −1.47, and −1.39 eV on the Pt (001), (011), and (111) surfaces, respectively.Although it was seen that the reaction energy of SO and SO 3 in theory was more favourable on the (001) surface, only (011) and (111) showed spontaneous reactions.As the mechanistic study of SO 2 reactions was beyond the scope of this work, it will need further investigation to identify the conditions that will favour the formation of SO and SO 3 in both thermodynamic and kinetic terms.
Figure 6 shows the effect of SO 2 coverage on the surface work function, which increased as the SO 2 concentration increased.As more SO 2 was adsorbed, more electrons were transferred from the surface to the adsorbate, leading to a lesser ability of the surface to release electrons into the vacuum.This finding was similar to previous work on SO 2 coverage on Cu (111) [50] and Cu (110) [51], where the work function increased as the coverage increased.A high SO 2 coverage led to an increased work function, which in turn would hinder the adsorption of additional SO 2 molecules.This negative feedback effect was favourable as an increased adsorption rate led to the formation of the secondary products SO and SO 3 , which in turn caused sulphur poisoning of the surface.Figure 7 shows the effects of pressure and temperature on the surface coverage of SO 2 , from which surface phase diagrams could be constructed.These phase diagrams could be used to predict likely processes during, for example the HyS cycle, which was operated at 1 atm (1.103 bar) and 350 to 400 K. Overall, it can be seen that, compared to pressure, temperature had a bigger effect on surface coverage with SO 2 .On the (001) surface, full surface coverage occurred in the experimental region, and gradual desorption of SO 2 would occur at temperatures over 500 K.
At low temperatures, the (011) surface had a coverage of θ = 0.67, which gradually decreased as the temperature increased.In the experimental region, coverage for both the co-pyramidal and bridge geometries would be θ = 0.56.In contrast to the other surfaces, the (111) surface showed decreasing surface coverage from temperatures as low as 200 K. Similar to the (011) surface, coverage in the experimental region for the (111) surface was θ = 0.56, with complete SO 2 desorption occurring at around 1 atm and 700 K.
Since the 1950s, multiple authors [52-56] have reported sulphur poisoning of the catalyst during these types of reactions.Further study is therefore needed to investigate the effect of the by-products of SO 2 on the Pt surfaces.During the investigation of H 2 O adsorption on the Pt surface [38], it was found that if the temperature during an experiment increased above 450 K for (011) and (111) and 800 K for (001), all the H 2 O molecules would desorb from the surface.This could cause an increase in the SO 2 concentration and may lead to the formation of more by-products of SO 2 , which in turn would impact the efficiency of the HyS cycle.Next, we used the surface energies to calculate nanoparticle morphologies using the Wulff construction scheme [57], taking both the temperature and pressure of the adsorbed SO 2 into account.Four temperatures (0, 298, 400, and 800 K) at p SO2 = 1 atm were chosen to explore the effect of temperature on the changes in the Pt morphology, visualised in Figure 8.The morphology at 0 K showed eight truncated triangular (111) faces and six square (001) faces.As the temperature was increased, 12 square faces of the (011) surface became expressed as well, which truncated the six square (001) faces.However, at 800 K, the (011) surfaces disappeared again to present a similar morphology as at 0 K, except that the (001) had a larger relative surface area.
Similar morphologies have been reported by Shi and Sun [58] during the adsorption of hydrogen on Pt at 0 K, where the nanoparticle expressed 14% and 86% of the (110) and (111) surface, respectively.They also showed that the Pt morphology changed with an increase in temperature, resulting in the expression of the (011) surface in the nanoparticle at both 475 and 600 K.

Calculation Methods
Similar to the method used for H 2 O adsorption [38], the Vienna Ab Initio Simulation Package (VASP) [59][60][61][62] Version 5.4.1 was used to simulate the Pt surfaces and their interaction with SO 2 .To describe the interaction between the valence and core electrons, the projector augmented wave (PAW) [63,64] pseudopotential was used.The core electrons of the Pt, S, and O atoms were defined up to and including the 5p, 3p, and 1s orbitals, respectively.The Perdew-Burke-Ernzerhof (PBE) [65] functional within the generalised gradient approximation (GGA) was employed for the exchange-correlation approximation.The long-range dispersion interactions [66][67][68][69] were considered with the D3-BJ method by Grimme with Becke-Johnson damping [70].Plane-waves were included to a cut-off of 400 eV.To ensure an electronic entropy of less than 1 meV•atom −1 , a smearing of 0.05 eV with the Methfessel-Paxton scheme order 1 [71] was used to determine the partial occupancies during geometry optimisation.Furthermore, the tetrahedron method with Blöchl corrections [72] was used in the final static simulations to obtain accurate total energies, charges, and densities of states.The electronic and ionic optimisation criteria were set at 10 −5 eV and 10 −2 eV•Å −1 , respectively.The conjugate gradient technique was adopted for all geometry optimisations.
Our calculated fcc Pt lattice constant was 3.926 Å, in excellent agreement with the experimental value of 3.924 Å [40,41].The Pt (001), (011), and (111) surfaces were constructed with the Minimum Energy Technique Applied to Dislocation, Interface and Surface Energies (METADISE) code [75], using the same method as in a previous study on H 2 O adsorption [38], creating periodic p(3 × 3), p(3 × 3) and p(4 × 4) supercells, respectively, constructed of four layers each.A Γ-centred 7 × 7 × 1 Monkhorst-Pack k-point grid was used for sampling the Brillouin zone in all the surfaces.The atoms in the two bottom layers of the supercells were fixed in the calculated bulk locations, and the atoms in the remaining two layers were allowed to relax.To ensure negligible interactions between neighbouring cells, a vacuum space of 15 Å was added perpendicularly to the surface.The surface areas of each of the super cells were 138.17, 196.18, and 106.79 Å 2 , respectively, for the (001), (011), and (111) surfaces.
To obtain the atomic charges, the Bader analysis [76][77][78][79] was used, where space was partitioned into non-spherical atomic regions enclosed by local minima in the charge density.
For the calculations of the adsorption energies and comparison of geometrical properties, the isolated SO 2 molecule was modelled in a periodic box of 12 × 13 × 14 Å to ensure negligible interaction with neighbouring cells.The Gaussian smearing scheme [71] was used during geometry optimisation and energy calculations with a smearing of 0.05 eV.A Γ-centred 1 × 1 × 1 Monkhorst-Pack [74] k-point mesh was used, and the SO 2 molecule was computed without symmetry constraints, but with added dipole corrections in all directions.
For the adsorption of SO 2 on the Pt surfaces, the optimised isolated SO 2 molecule was added to the surface in various configurations.A Γ-centred 7 × 7 × 1 Monkhorst-Pack k-point grid was used to sample the Brillouin zone in all the surfaces.The Gaussian smearing scheme [71] was used during geometry optimisation with a smearing of 0.05 eV, and the tetrahedron method with Blöchl corrections [72] was used in the final static simulations to obtain accurate total energies, charges, and densities of states.Perpendicular dipole corrections were added to account for the polarisation caused by the adsorption of the SO 2 molecules onto the Pt surfaces.

Coverage-Dependent Surface Energies
To calculate the average adsorption energy (E ads ) per SO 2 molecule adsorbed onto the Pt surface, the following Equation (1) was used [80]: where N SO To determine the effect of the thermodynamics on different SO 2 coverages of the Pt (001), (011), and (111) surfaces, the surface energies (σ) were compared at different temperatures (T) and the SO 2 chemical potential (µ SO2 ) [81].The resulting change in surface energy from the SO 2 adsorption was calculated as follows: The chemical potential of SO 2 in the gas phase can also be expressed as: where E SO2 is the DFT energy of the SO 2 molecule and ∆G SO2 (T, p 0 ) is the Gibbs free energy difference per SO 2 molecule between 0 K and T, at p 0 = 1 bar, which was extracted from the thermodynamic tables [82].The last term (k B Tln p p 0 ) denotes the free energy change of SO 2 gas at constant temperature (T) when the partial pressure changes from p 0 to p.To determine the chemical potential, independent of the calculated quantities, Equation (3) was added to Equation (2) without the energy of SO 2 (E SO2 ).
In this work, we defined surface coverage (θ) as the number of adsorbed SO 2 molecules (N SO 2 ) divided by the number or adsorption sites (N), as denoted by: If no adsorption took place, θ = 0, whereas for full coverage, i.e., when a monolayer formed on the surface, θ = 1.
The work function was defined as the minimum energy needed to remove an electron from the metal bulk structure through the surface to a point outside the solid.The work function (Φ) can be written as: where E vacuum is the vacuum potential energy, which is a product of the electron charge and the electrostatic potential in the vacuum near the surface, and E F is the Fermi level (electrochemical potential of electrons) inside the surface.In our slab-supercell model, both the vacuum potential and the Fermi energy could be derived from the same calculation.
Wulff morphologies [57] were constructed using the GDIS program [83] to determine the effect of SO 2 adsorption on the Pt (001), (011), and (111) surfaces on the shape of nanoparticles.The equilibrium Wulff crystal was constructed assuming that the distance of the crystal face (d 001 , d 011 , d 111 ) to the centre of the nanoparticle was proportional to their surface free energies as:

Conclusions
We employed density functional theory calculations to gain detailed insight into the behaviour of SO 2 single molecules and higher coverages on the Pt (001), (011), and (111) surfaces.When an isolated SO 2 molecule was adsorbed, the molecule -preferred to adsorb in a S,O-bonded geometry on the (001) and (111) surfaces, whereas on the (011) surface, it formed co-pyramidal and bridge geometries.From the charge density analysis, we showed that between 0.2 and 0.35 e − was transferred from the surface to the molecule.
Surface coverage was increased until a monolayer was obtained, where E ads /SO 2 increased with coverage for all the surfaces.Under the conditions where the HyS reaction took place, the highest coverage was obtained on the (001) surface, followed by (011) and (111).On the (111) surface, it was found that, when the surface coverage was θ > 0.78, two neighbouring SO 2 molecules reacted to form SO and SO 3 , which needs to be investigated mechanistically in future work.The most stable SO 2 adsorption was on the (001) surface, but the most reactive was on the (111) surface.An increase of the temperature changed the percentage of the expressed faces in the morphology of Pt, where at 0 and 800 K, only the (001) and (111) faces were present, while at 298 and 400 K, all three faces ((001), (011), and (111)) were expressed.
Future work will include the consideration of mixing of SO 2 and H 2 O on the various Pt surfaces, as well as the effect of the by-products of SO 2 oxidation on the Pt surfaces.

Figure 1 .
Figure 1.Top and side views of the Pt (001), (011), and (111) surfaces, with the four-fold hollow (4F), bridge (B), atop (A), face-cubic centred (fcc), and hexagonal close packed (hcp) adsorption sites.The gold colour is used to depict Pt throughout the manuscript, with the second layer in a lighter colour to distinguish between the top layer and subsequent layer atoms.
Figure1shows the Pt surfaces with possible adsorption sites for each surface.To distinguish between the top layer and subsequent layer atoms, the colour of the second layer atoms in each of the surfaces was changed to lighter gold.The adsorption sites indicated in Figure1for the Pt (001) and (011) surfaces are atop (A), bridge (B), and four-fold hollow (4F), while the Pt (111) surface has atop (A), bridge (B), face-cubic centred (fcc), and hexagonal close packed (hcp) sites.Five modes of SO 2 adsorption on a metallic surface have been suggested[45], parallel, co-planar, bridging, O-bonded, and S,O-bonded.All five modes were investigated in the various adsorption sites shown in Figure1.The most stable structures found for the adsorption of SO 2 onto the Pt surface are shown in Figure2.The bond distances and angles of the adsorbed SO 2 with respect to the Pt surfaces are shown in Table1.
2 is the number of adsorbed SO 2 molecules, E Pt is the energy of the clean Pt surface, and E SO 2 is the energy of the isolated SO 2 molecule after relaxation.