Catalytic water dissociation by greigite Fe3S4 surfaces: density functional theory study

The iron sulfide mineral greigite, Fe3S4, has shown promising capability as a hydrogenating catalyst, in particular in the reduction of carbon dioxide to produce small organic molecules under mild conditions. We employed density functional theory calculations to investigate the {001},{011} and {111} surfaces of this iron thiospinel material, as well as the production of hydrogen ad-atoms from the dissociation of water molecules on the surfaces. We systematically analysed the adsorption geometries and the electronic structure of both bare and hydroxylated surfaces. The sulfide surfaces presented a higher flexibility than the isomorphic oxide magnetite, Fe3O4, allowing perpendicular movement of the cations above or below the top atomic sulfur layer. We considered both molecular and dissociative water adsorption processes, and have shown that molecular adsorption is the predominant state on these surfaces from both a thermodynamic and kinetic point of view. We considered a second molecule of water which stabilizes the system mainly by H-bonds, although the dissociation process remains thermodynamically unfavourable. We noted, however, synergistic adsorption effects on the Fe3S4{001} owing to the presence of hydroxyl groups. We concluded that, in contrast to Fe3O4, molecular adsorption of water is clearly preferred on greigite surfaces.

The iron sulfide mineral greigite, Fe 3 S 4 , has shown promising capability as a hydrogenating catalyst, in particular in the reduction of carbon dioxide to produce small organic molecules under mild conditions. We employed density functional theory calculations to investigate the {001}, {011} and {111} surfaces of this iron thiospinel material, as well as the production of hydrogen ad-atoms from the dissociation of water molecules on the surfaces. We systematically analysed the adsorption geometries and the electronic structure of both bare and hydroxylated surfaces. The sulfide surfaces presented a higher flexibility than the isomorphic oxide magnetite, Fe 3 O 4 , allowing perpendicular movement of the cations above or below the top atomic sulfur layer. We considered both molecular and dissociative water adsorption processes, and have shown that molecular adsorption is the predominant state on these surfaces from both a thermodynamic and kinetic point of view. We considered a second molecule of water which stabilizes the system mainly by H-bonds, although the dissociation process remains thermodynamically unfavourable. We noted, however, synergistic adsorption effects on the Fe 3 S 4 {001} owing to the presence of hydroxyl groups. We concluded that, in contrast to Fe 3 O 4 , molecular adsorption of water is clearly preferred on greigite surfaces.

Introduction
The necessity of mitigating climate change has led to policies to regulate and minimize the concentration of (b) Slab model The Fe 3 S 4 surfaces were prepared by cutting the bulk structure and creating slab models using the METADISE code [65]. This code not only considers periodicity in the plane direction, but also provides different atomic layer stacking, resulting in a null dipole moment perpendicular to the surface plane [66]. We considered the three surfaces {001}, {011} and {111}, with respective surface areas of 81.0, 132.3 and 93.5 Å [2], as well as their different terminations. Each slab contains 56 atoms (24 Fe and 32 S) per unit cell, and we added a vacuum width of 12 Å between periodic slabs, which is big enough to avoid interactions between the slab and its images. The slabs are also thick enough to relax the two uppermost Fe 3 S 4 layers until energy convergence, keeping the bottom layer frozen to model the bulk structure. To obtain the properties of an isolated H 2 O molecule, we placed it in the centre of a 15 × 16 × 17 Å [3] simulation cell to avoid lateral interactions, with broken symmetry, and using the same criteria of convergence as for the iron sulfide slabs.

(c) Slab characterization
We describe the atomic charges and derive magnetic moment by means of a Bader analysis [67,68], where the electron (and spin) density associated with each atom is integrated over the Bader volume of the atom in question, as implemented in the Henkelman algorithm [69]. Thus, owing to the changes in the effective atomic radii with the oxidation state of the ion, the Bader volume is not calculated as a sphere of constant radius but is charge density dependent. Even so, the electron delocalization of the DFT method leads to an underestimation of atomic charges, i.e. the DFT-derived charges are smaller than the formal oxidation states. However, they can be used effectively in a direct comparison and to monitor changes in charges, for example as an effect of surface adsorption.
In addition to the steady states of reactants and products, we searched for the saddle point linking both systems. This saddle point is the reaction transition state (TS) and determines the kinetics of the process. We identified the TSs by means of the dimer method [70,71], which searches the TS by giving an initial atomic velocity towards the particular final state (product(s)). From an initial configuration, we generated the initial velocities by making two equal and opposite small finite-difference displacements in the coordinates of the reactant molecule. The method then finds a nearby saddle point by rotation and translation steps implemented with a conjugate-gradient optimizer. We further confirmed the identified saddle point (TS) by a vibrational frequency calculation, in which only one imaginary frequency is obtained corresponding to the reaction coordinate. Afterwards, the dimer images were relaxed to the neighbouring local minima. In a successful search, one of the images will minimize into the initial state, and the other will become the final state.
We calculated the adsorption energies (E ads ) per molecule on the Fe 3 S 4 surfaces via equation (2.1) and via equation (2.2) for the interaction of a second molecule with the surface ( E), where E H 2 O : Fe 3 S 4 is the total energy of a molecule interacting with the Fe 3 S 4 slab (two molecules in the case of 2 · H 2 O : Fe 3 S 4 ), E Fe 3 S 4 is the energy of the naked Fe 3 S 4 slab and E H 2 O is the energy of an isolated molecule in vacuum. When there is more than one molecule in the system, we subtracted the interaction energy between the multiple molecules (E coh ) to isolate its contribution to E ads . We derived the cohesive energy (E coh ) between molecules by equation (2.3) where the energy (E 2·H 2 O ) is the water without the slab, but maintaining the same configuration as in the co-adsorbed situation. We also defined the energy barrier ( E TS ) for the dissociation process as the difference between the initial state (adsorbed molecule) and the TS, equation (2.5), and the reaction energy (E R ) as the total energy difference between the final state (products) and the initial state (reactants), equation (2.6), and

Results and discussion (a) Greigite surfaces
We modelled three low Miller index surfaces by cutting the Fe 3 S 4 bulk crystal to obtain different non-dipolar atomic terminations. The cubic bulk (Fe A (Fe B ) 2 S 4 ) unit cell symmetry in the a-, b-and c-axis makes the (001), (010) and (100) surfaces equivalent as well as the (011), (101) and (110) surfaces. Owing to the presence of non-equivalent Fe ions, each surface has two distinct terminations, depending on the relative Fe A position with respect to the uppermost sulfur layer before atomic relaxation (termination -A or -B). For instance, figure 1 shows a schematic representation of both terminations of the Fe 3 S 4 {001} before relaxation; see the electronic supplementary material, figure S1, for all surfaces studied. The simulation slabs of the {001} and {111} surfaces were symmetrical along the z-axis, but the {011} slab, where top and bottom layers are complementary, is asymmetrical. In this case, the cleavage energy is actually related to the energy to create both top and bottom surfaces of the slab but we still used this average surface energy for both terminations as we were primarily interested in a comparison between pure and hydrated surfaces. Before relaxation, the order of increasing surface energies is  [16].
The spin moments are sensitive to structural changes, showing a spin variation on the two types of Fe, which leads to a different magnetization of saturation per formula unit compared with a bulk analysis (m s (Fe A ) = 2.8 µ B and m s (Fe B ) = 3.0 µ B ), whereas the total magnetization is 3.44 µ B [35]. In the {001} surface, spins on both Fe increase slightly by 0.1 µ B ; in the {011} surface, the Fe remain as in the bulk structure; but in the {111} surface, the Fe spin orientation changes, thereby decreasing M s . These variations are generated because the spins on external atomic layers can be inclined randomly at various angles with respect to the direction of the net moment, thereby modifying the total magnetic moment [75].
Next, we obtained an overview of the surface electronic structure by integrating the local density of states from the Fermi level to a bias by using the Tersoff-Hamann formalism [76], which is expressed as scanning tunnelling microscopy (STM) images implemented in their most basic formulation, approximating the STM tip by an infinitely small point source. STM at constant current mode follows a surface of constant integrated local density of states [50]. Although there are currently no experimental STM measurements in the literature, we have provided STM models in the electronic supplementary material, figure S2, which resemble those for Fe 3 O 4 [72], and the surfaces shown by high-resolution transition electron microscopy obtained from pure greigite nanoparticles [16]. On the Fe 3 S 4 {001} STM, one can see the parallel thick lines corresponding to the sulfur (bright areas) and the Fe A row at lower density. We found a similar arrangement on the Fe 3 S 4 {011}. Finally, the simulated STM of the Fe 3 S 4 {111} shows the maximum current intensity above the Fe B , embedded in lower-density S atoms, where the darker areas correspond to Fe A sites. We also derived the Wulff morphology from the relative surface stabilities [77] [72] and FeNi 2 S 4 [21].        site  The formation of this new bond is mostly owing to the electronic contribution from Fe B and the molecule (red clouds). Note also the S-polarization towards the H atoms (distance S. . . H is 2.748 Å), as well as the electron rearrangement in nearby Fe A , which modifies its magnetic moment to 0.1 µ B .
Once the molecule was adsorbed on the Fe 3 S 4 {001}, we stretched an H towards a polarized surface S, leading to both thiol (-SH) and hydroxy (-OH) groups on the surface, but this configuration is 0.46 eV higher in energy than H 2 O in the gas phase, indicating that molecular water adsorption is preferred over dissociation on the Fe 3 S 4 {001}. Upon dissociation, the Fe-O distance shrinks by 0.46 Å, whereas the S from the -SH group rises in the surface by almost 0.08 Å. The O-H scission takes place through a late TS with an energy barrier of 0.89 eV, making the process both thermodynamically and kinetically unfavourable. Despite the oxidizing character of the -OH groups (q(OH)= −0.7 e − ), the metal does not get oxidized, the electrons come mostly from the Fe-S where the H is located. The charge density rearrangement is shown in figure 4c,d, which indicates the charge density of the dissociated H building a bond of covalent character with S, and re-allocation of the density along the Fe-O bond. This distortion of the electronic structure leads to a synergistic effect upon co-adsorption of a second molecule on neighbouring sites [21]. We have summarized the dissociative adsorption characteristics in table 3.  Table 3. Reaction energies (E R ) with respect to isolated systems, distances (d) and OH charge (q(OH)) on the (001), (011) and (111) Fe 3 S 4 surfaces. Figure 3 shows the schematic of reactants, TSs and products.
site  1.31 eV). The dissociation process from the adsorbed molecule on Fe A has an energetic barrier of 0.72 eV. The adsorption energy of the [OH + H] is 0.71 eV below the gas phase molecule, showing it to be thermodynamically plausible. However, it is still above the molecular adsorption energy by 0.33 eV, making the dissociation unlikely either on Fe A or on Fe B (E R = 0.34 eV). The electron density distribution, in figure 5c,d, shows the formation of an S-H covalent bond, with a 0.5 e − transfer coming mostly from the sulfur and 0.1 e − from the transferred H. It also shows a charge transfer of 0.8 e − to the OH group mostly from Fe A . One can also distinguish the electron lone pair localization at both sides on the oxygen atoms and the density rearrangement on the metallic centres nearby. For the dissociative adsorption process, we placed H on the S site between Fe B and Fe A where the H from H 2 O pointed in the molecular adsorption structure. Upon optimization, the Fe B -OH distance is 0.35 Å shorter than for the H 2 O molecule, which causes the Fe B and the S site to move outwards with a surface destabilization of 0.54 eV. The dissociative adsorption is an unlikely process as it is 0.11 eV higher in energy than the isolated system, despite an increment in the long-range interaction of 0.10 eV. The dissociative process is accompanied by a charge transfer to the OH of 0.7 e − and to the H ad-atom of 0.5 e − , besides a strong repositioning of the charge density (figure 6b). This electron rearrangement modifies the Fe A charge and spin density by 0.2 e − and 0.3 µ B , respectively. The dissociation mechanism has an energy barrier of 0.94 eV above the pre-adsorbed molecule that also makes the process kinetically unlikely.       , providing stabilization to the system. Considering the dissociation as a process that takes place on the surface and not owing to the adsorption itself, the activation energy is 0.1 eV higher than for a single molecule. This change in the energy barrier may be related to the loss of degrees of freedom owing to the second molecule binding to the surface. Fe 3 S 4 {011}. On this surface, a second H 2 O molecule adsorbs at a low-coordinated metallic centre: Fe B or Fe A . As a result, the two adsorbed molecules are 5 Å apart (measured between oxygens), and the interaction energy between them is negligible, E coh = 0.02 eV, although the long-range contribution to the whole system's stability increases by 0.16 eV. The binding energy per molecule decreased by 0.15 eV, in agreement with an H 2 O-Fe distance of approximately 2.1 Å, leaving the S-H at 2.034 Å. We analysed the changes in the electronic structure and found that, as for the single molecule adsorption, there is no charge transfer to the molecules and only slight variations in the spin density of 0.1 µ B . The charge density relocation is depicted in figure 8b, which shows the polarization of the surface S towards the second molecule's H, whereas the structure around the pre-adsorbed H 2 O * remains unaltered.

(c) Two H 2 O on Fe 3 S 4 surfaces
The presence of a second H 2 O molecule, nevertheless, enhances the dissociative adsorption process by 0.04 eV compared with an isolated molecule, although the process is still less favourable than the molecular adsorption. Upon dissociation, the HO-Fe B distance is 1.857 Å,  which is 0.13 Å shorter than in a single dissociated molecule. Note that this is the opposite behaviour to that seen on the {001}, because both molecules adsorb strongly on the surface. The OH group remains tilted towards the H ad-atom at 1.632 Å, and there is no change in the main electronic charge. The second water molecule remains on the Fe A at 2.161 Å, which is 0.04 Å closer than an isolated H 2 O on Fe A . As shown in the schematic representation of figure 7, the second molecule rotates approximately 120 • on its own axis but it does not generate any change in the electronic structure or in the surface. The activation energy for the molecule's dissociation is approximately 0.1 eV lower than for the first molecule, thus becoming kinetically as well as thermodynamically less restricted.  [41]. The hovering H 2 O also stabilizes the system, E coh = 0.06 eV, with a total van der Waals contribution of 0.2 eV stronger than for the single H 2  as for a single molecule adsorption. From the flux diagram in figure 8c, the increased strength of the Fe-O * bond is shown by the increase of charge density, whereas the polarization of the H 2 O molecules causes the H 2 O lone pairs to interact with HO * -H δ+ , which results in stronger polarization of the sulfur close to the second physisorbed molecule. Furthermore, figure 8c shows a hexagonal pattern of the charge density reallocation around the second nearest neighbours of Fe B , without charge or spin density transfer.
We also analysed the effect of the second water on a previously dissociated H 2 O and found that the system is 0.54 eV less stable than for molecular adsorption. Furthermore, the dissociation of the pre-adsorbed molecule has a higher energy barrier, E A = 1.41 eV, which makes the process unlikely to occur. The hydroxy group remains on the Fe B at 1.796 Å and perpendicular to the surface, binding the hovering water via an H bond (d O...HO * = 3.022 Å) and receiving 0.2 e − from the Fe B (0.14 e − ) and surrounding metals through the Fe-S bond, compared with the molecular adsorbed species. Furthermore, the adsorption centre also changes its spin density in the same way as it was modified by the OH from a single molecule interaction, 0.3 µ B higher than in the naked surface. The second molecule also interacts with the thiol's hydrogen at a distance of 1.854 Å. The strong interaction and the short distance to the H on the S site may lead to desorption of a hydronium cation, e.g. in solution (H 3 O + ), and HO-Fe B on the surface.

(d) Trends and discussion
We analysed the trends in any changes in the geometry and electronic structure upon adsorption or dissociation of one and two molecules of water on the greigite surfaces. These are slightly weaker than on pyrite [78,79] but quite similar to its isomorphic oxide (E ads = −0.4 to −1.0 eV) [39][40][41] and to FeNi 2 S 4 surfaces [21].
The H 2 O adsorption on the surface leads to a small rearrangement of the spin densities, although with negligible charge transfer to the molecule, whereby nearby sulfur atoms polarize their electronic clouds towards both hydrogen atoms of the water molecule. Electronic structure analysis showed electron accumulation between the surface and the water molecule, indicating a chemical bond between the species. The O-H bond of the molecule may become stretched towards the polarized sulfur on the surface until its dissociation, leading to both hydroxy and thiol groups. However, the dissociation process on the different surfaces has energy barriers of approximately 0.9 eV. These energies are almost twice the main activation energies on reported Fe 3 O 4 (E A < 0.5 eV) [39][40][41]. The energy profile in figure 9 summarizes the thermodynamic unviability of the dissociation process on these surfaces. If, however, the molecule were to be dissociated, the -OH group subtracts approximately 0.7 e − from nearby metal centres and an −SH bond is formed with a covalent character, deduced from both Bader analysis of the charges and charge density flux diagrams; similar charge-transfer characteristics have been reported for water on the pyrite {100} surface, but with water gaining a charge of only 0.03 e − , reflecting the greater stability of pyrite and its inability to be further oxidized [78]. For dissociative adsorption, the electron density is concentrated on the oxygen atom of the OH group.
We calculated the interaction energies of both molecules with the surface to be −0.48, −0.89 and −0.75 eV for the {001}, {011} and {111}, respectively. These energies are higher than the H 2 O dimer (−0.22 eV) [80] and would lead to preferential adsorption on the surface, rather than remaining as a gas phase species. We have represented in figure 10 the activation energy as a function of the reaction energy and found a linear trend which is typical of a Brønsted-Evans-Polanyi relationship [81].
As is found for metallic or  fairly easily (0.23 eV). Nevertheless, the combination of OH and H leading to H 2 O is both thermodynamically and kinetically favourable on the three surfaces explored.

Conclusion
We studied the iron thio-spinel Fe 3 S 4 surfaces of the same Miller indices as the most common surfaces present in its oxide analogue magnetite, i.e. {001}, {011} and {111}. All the calculations were performed by density functional theory with the Hubbard approximation (DFT+U), including the long-range dispersion forces as derived from the atomic polarizability. The most stable surface is the {001}, followed by {111} and {011}, in agreement with crystals from solvothermal synthesis [16]. Before relaxation, the Fe 3 S 4 {001} and {111} showed protruding Fe A (and a Fe B in the {111}), but these surfaces showed a greater flexibility than their oxide counterparts. The sulfide allows movements perpendicularly to the surface, causing the Fe originally above the surface plane to penetrate beneath the top atomic layer, thereby decreasing the surface energy. Similarly to corundum-structured materials [17], on the greigite surfaces the cations relaxed inwards, moving just beneath the anionic layer. However, their position is restored by water adsorption, because the binding of the molecule decreases the dangling bonds of the surface cation, thereby removing the electrostatic driving force for relaxation.
We considered both molecular and dissociative adsorption, as well as the dissociation of the water molecule once adsorbed on the surface. We have concluded that the water dissociation is thermodynamically unfavourable. In contrast, H 2 O formation has a TS at less than 0.5 eV, indicating a fast recombination. We have also provided insights into the synergistic adsorption of the second H 2 O molecule on a nearby HO-Fe group on the Fe 3 S 4 {001} owing to the electronic structure relocation. Similar synergistic adsorption has been observed on violarite [21], as well as in the adsorption of an ethanol and an ethanol-water dimer to Rh(111) [16,83,84]. Greigite does not show the same affinity towards dissociation of water as does Fe 3 O 4 [36], and molecular adsorption is the most favourable mode on the sulfide. This difference is due to the more acidic character of the -SH group compared with the -OH of the oxide. Therefore, to dissociate water and adsorb H ad-atoms on Fe 3 S 4 surfaces for the reduction processes, a source of potential is required such as a natural chemiosmotic or external applied potential.
Data accessibility. The datasets supporting this article have been uploaded as part of the supplementary material.
Electronic supplementary material contains details of all surface terminations, such as interatomic distances, local and per unit formula magnetization, work function and surface energy. It also provides simulated STM and Wulff construction figures. All data created during this research are openly available from the University of Cardiff Research Portal at http://dx.doi.org/10.17035/d.2016.0008383220.