Carbon dioxide and water co-adsorption on the low-index surfaces of TiC, VC, ZrC and NbC: a DFT study

Abstract

We present a theoretical DFT study into the activation of CO₂ by TiC, VC, ZrC and NbC. Particular focus is given to the study of CO₂/H₂O co-adsorption and interaction on four carbide low-index surfaces: {001}, {011}, carbon-terminated {111} and metal-terminated {111}. The adsorption and activation of CO₂ is shown to be most exothermic and indeed barrierless on the metal-terminated {111} surfaces, whilst adsorption on the {001} and {011} planes occurs via a small activation energy barrier. In contrast, the carbon-terminated {111} surface proves to be unstable in the presence of the adsorbates. Both water and carbon dioxide adsorb most strongly on TiC and most weakly on NbC, with the strongest co-adsorption interactions being seen in conformations that maximise hydrogen-bonding.

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Introduction

As atmospheric carbon dioxide (CO₂) concentrations continue to rise, policy makers and the general public are becoming increasingly aware of its unfolding negative consequences for climate change and ocean acidification.^1,2 To slow the rate of this increase and realise the ambitious targets set out in the Paris Agreement,³ three main options appear viable: (i) reducing emissions through higher energy efficiency,⁴ (ii) developing sustainable resources in order to reduce reliance on fossil fuels⁵ and (iii) chemically trapping waste CO₂ thereby reducing the volume of atmospheric emissions via an integrated carbon capture and storage (CCS) protocol.⁶ Carbon capture, utilisation and storage has become a major area of research^7–9 with progress being made using both heterogeneous^10–12 and homogeneous^13–15 catalysts. However, the high stability of CO₂ means that, for many catalysts, there is a high barrier for chemical interaction. This problem, combined with the need for a high enough adsorption energy for the material to retain the adsorbate, limits the number potential catalysts. Candidate materials must efficiently bind CO₂ in the presence of many other compounds dispersed in, for example flue gas.^16,17 Water in the form of steam is also of particular importance.¹⁸ There have been several previous theoretical studies that have confirmed the important role of H₂O in both reducing the barrier and directing the pathways for CO₂ reduction to methanol on solid state materials.^19,20 Fortunately, carbon dioxide possesses a considerable quadrupole moment, which in the presence of the right catalyst can result in a relatively small barrier for chemical adsorption,²¹ due to the strong interaction between the quadrupole moment of carbon dioxide and specific binding sites on the catalyst. Thus, an increased strength of charge–charge, hydrogen-bonding and many other interactions decrease the relative activation barriers by increasing the exothermicity of chemisorbed species, when compared to non-quadrupolar adsorbates.^22,23 Additionally, since this chemical adsorbed state requires electron transfer from the catalyst to produce an activated anionic CO₂^δ− species,^24,25 there is potential for the development of chemical processes that further reduce CO₂ by sustainably produced hydrogen.^26–29 The search for the ideal catalyst to perform this reaction has been frustrated by low activity,³⁰ or because of the need for expensive and scarce metals.^31,32 However, it has become clear in the years following the seminal work of Levy and Boudart in 1973³³ that transition metal carbides (TMCs) have platinum-like activity and can catalyse a diverse array of reactions, including hydrogenation,³⁴ water–gas shift,^35,36 CO oxidation^37,38 and importantly the hydrogenation of CO₂.^39–42 Recently, combined experimental and computational studies have confirmed that TMCs catalyse CO₂ reduction to CO, as the first step in hydrogenation.^43,44 Our previous work has used periodic Density Functional Theory (DFT) calculations to study a large range of bulk and surface properties of TMCs, which indicated that the low-index surfaces of TiC, VC, ZrC and NbC could be highly active in catalysing CO₂ reduction.⁴⁵ This work focuses on carbides with 1 : 1 stoichiometries and rock-salt structures, which are only consistently found with carbides that include metal from group 3–5 metals.^46,47 Therefore, in this paper we present a detailed computational study of CO₂ and H₂O binding and activation on these surfaces.

Methodology

All calculations were undertaken with the standard Perdew–Burke–Ernzerhof functional,⁴⁸ as implemented in the Vienna Ab initio Simulation (VASP) package.^49–51 This method has been benchmarked previously for the systems reported here, using periodic density functional calculation.⁴⁵ The Perdew–Burke–Ernzerhof⁴⁸ exchange functional (PBE) in combination with plane-wave basis sets were applied to the valence electrons, whilst the core electrons were described via the projected augmented wave method (PAW).⁵² Long range interactions were included using the D3 Grimme dispersion method.^53,54 Bulk structures for TiC,⁵⁵ VC,⁵⁵ ZrC,⁵⁶ and NbC⁵⁷ were taken from the Inorganic Structure Database (ICSD).⁵⁸ The lattice parameters and the internal coordinates of these bulk structures were then fully optimized and cut along the {001}, {011} and {111} planes using the METADISE code.⁵⁹ Since there are alternating layers of metal and carbon along the {111} direction of TMCs,^60–62 two surfaces were prepared that describe either the metal or carbon termination. Our previous work⁴⁵ benchmarked these pristine surfaces with those that were reconstructed by migration of surface atoms and confirmed that the unreconstructed models were valid, which is also in agreement with experiment.^63–65 Finally, each unit cell was replicated 2 × 2 × 3 to give slabs with six atomic layers and 96 atoms.⁴⁵ The low-index surfaces were modelled using Monkhorst–Pack grids of k-points of 5 × 5 × 1. All energies were converged to within a cut-off of 520 eV and the threshold for ionic relaxation was set to 0.01 eV Å⁻¹. The electronic threshold for the self-consistency cycles (SCF) was set at 10⁻⁵ eV and the convergence was determined via the Blöchl smearing method.⁶⁶ All structures were fully optimised, with only the bottom two atomic layers of each slab constrained at their bulk-optimised positions to replicate the bulk. No other internal coordinate or symmetry constraints were added and spin polarization was enabled in all systems. Adsorption energies for H₂O and CO₂ are defined as:

E_ads = E(slab/molec) − [E(slab) + E(molec)], (1)

whereby, the sum of the energies of the pristine slab and gas phase adsorbate(s) are subtracted from the total energy of the chemically adsorbed minimum energy structure. Transition state (TS) structures were located using the nudge elastic band (NEB) technique and eight climbing images. All adsorption minima and TS structures were subsequently characterized via frequency analysis. These calculations confirmed the absence of negative frequencies for all of the minima and a single imaginary frequency in every transition state, along the reaction coordinate.

Results

Carbon dioxide activation

The adsorption of CO₂ onto each surface was studied by initially conducting full geometry optimisations with the CO₂ placed high in the vacuum, which led, in most cases, to an initial physisorbed state, whereby the adsorbate retained an O–C–O bond angle of 180° and oriented in such a way as to lie parallel to the surface (see Fig. 1). The adsorbate position was then systematically scanned towards the surface, to locate both the chemisorbed global minimum and approximate transition state. During these scans, all internal coordinates except for that associated with the Z-position of the carbon atom of CO₂ were allowed to relax fully (see ESI† Tables S1–S4). Additionally, chemically adsorbed structures were fully optimised and transition states located via NEB calculations.

Fig. 1 One electron reduction of CO₂. The physisorbed (left) transition state (middle) and chemisorbed (right) structure, obtained with CO₂ adsorbed on the NbC{001} surface.

An illustration of the physisorbed, transition state and activated structures of the CO₂ chemisorption process on the {001} surface of NbC is given in Fig. 1, although, it is important to note that this is only one of the two possible chemisorption pathways, which are discussed in detail below. Energies for each minimum and transition state are shown in Table 1. Recently, Illas et al.,²¹ studied chemically adsorbed CO₂ on the {001} surface of the same series of TMCs and, whilst no other surfaces or states were considered, the available results are in excellent agreement with ours (see 2I^theo, column in Table 1). This agreement also helps to validate our approach of using geometry scans to locate global minima, since our results closely mirror their lowest energy species. The O–C–O bond angle of the adsorbate is transformed from 180° in the physically adsorbed structures, via a transition state bond angle of ∼150°, to <130° in the bent structure. These two forms of chemisorbed CO₂ correspond to an increase of ∼1 to 2 electrons in the CO₂ group according to the Bader charges (β) analysis, of atomic charges (see Table 2).

Table 1 Binding energies of the physically (1I) and chemically (2I) adsorbed states, relative to isolated components, as well as the activation barrier (1TS_CO2), of CO₂ absorbed on the low-index surfaces of TMCs. Previous theoretical CO₂ absorption energies on {001} surfaces are also included (2I^theo) [ref. 21]. All energies are given in eV

	1I	TSCO2	iFreq	2I	2I^theo
Imaginary frequencies (iFreq) are given in cm^−1.
TiC{001}	−0.26	0.25	219.37	−0.86	−0.81
TiC{011}	−0.45	0.00	203.43	−3.45
TiC{111}M	—	—		−3.05
VC{001}	−0.32	0.17	439.18	−0.33	−0.19
VC{011}	−0.22	0.05	171.27	−0.21
VC{111}M	—	—		−1.93
ZrC{001}	−0.27	−0.15	186.51	−1.62	−1.60
ZrC{011}	−0.23	−0.19	117.59	−1.03
ZrC{111}M	—	—		−3.32
NbC{001}	−0.20	0.06	320.54	−0.76	−0.87
NbC{011}	−0.29	−0.12	208.17	−0.39
NbC{111}C	−0.21	0.61		−0.43
NbC{111}M	—	—		−1.98

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Table 2 Changes in workfunction (φ), the grouped adsorbate Bader charge (β) and geometric data for CO₂ adsorption. The naked surfaces with four layers relaxed are indicated with subscript r and the physically and chemically adsorbed states are indicated by subscript phys and chem, respectively. In the chemically adsorbed structures, the distance between the surface and adsorbate (r_surf-C), the O–C–O(OCO) bond angle and the average CO (r_CO,ave) bond length are also given

	Φ r	Φ phys	Φ chem	β phys	β chem	R surf-C	OCO	r CO,ave
TiC{001}	3.93	3.73	4.58	0.06	0.92	1.47	128.1	1.29
TiC{011}	3.39	—	3.55	—	1.27	1.26	146.4	1.50
TiC{111}C	5.25	4.01	—	0.02	—	—	—	—
TiC{111}M	5.33	—	5.18	0.06	1.79	1.85	138.5	1.21
VC{001}	3.90	3.42	4.27	0.05	0.76	1.48	127.6	1.29
VC{011}	3.98	3.64	4.37	0.06	0.67	1.46	125.0	1.37
VC{111}C	5.51	5.13	—	0.02	—	—	—	—
VC{111}M	5.20	—	5.26	—	1.12	2.07	103.2	1.42
ZrC{001}	3.97	3.64	4.00	0.08	1.01	1.49	130.9	1.28
ZrC{011}	3.00	2.90	3.37	0.12	0.96	1.26	147.3	1.49
ZrC{111}C	5.10	4.62	—	0.03	—	—	—	—
ZrC{111}M	5.08	—	5.27	—	1.84	1.76	140.1	1.20
NbC{001}	3.21	2.75	3.58	0.07	0.93	1.47	124.5	1.30
NbC{011}	3.16	3.18	3.78	0.07	0.71	1.21	143.0	1.50
NbC{111}C	5.75	5.21	—	0.07	—	—	—	—
NbC{111}M	5.37	—	5.45	—	1.19	2.43	107.2	1.60

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Results highlighted in Table 2 show that the workfunction (φ) of all carbide surfaces increases with the chemisorption of CO₂, which is the result of a deeper d-band caused by electron transfer. The workfunction is calculated by subtracting the energy of the Fermi level from the vacuum energy, and is an important component linking the redox potential at the ground state to the valence bond curves (see Fig. 3). Unfortunately, except for the workfunction of the carbide surfaces, it is impossible to calculate the energetics of the other components of the excited wavefunction (ϕ*) and therefore this figure is intended as a powerful schematic representation of the valence bond diagrams for the two main reaction profiles. As mentioned above, the CO₂ reduction was confirmed by the Bader charge analysis, which indicates that the adsorbate's valence electrons increased by at least ∼1 electron. We also observe that the variation in this charge transfer correlates very well with the exothermicity of the chemisorbed species (see Fig. 2). This clear correlation links a more exothermic adsorption energy with an increase in charge transfer, indicating that the more CO₂ is reduced the greater the exothermicity of the adsorption. We note that, as there is no stable chemically adsorbed species on the {111}C surfaces, there is also a lack of electronic and structural data, for these states.

Fig. 2 Negative correlation between chemical adsorption energy and amount of CO₂ reduction, upon chemisorption.

When the CO bond length in the activated adsorbate is plotted against adsorption energy, we observe two distinct trends, which also strongly correlate with the number of electrons transferred to the chemisorbed species (see Fig. 4). The first series has surface geometries of adsorption that promote activation of a double bond, with CO bond lengths that are between >1.20 Å and <1.45 Å. Additionally, adsorption on a surface of the second series promotes an activated single bond greater than 1.5 Å. Importantly, the latter also correlates to a two-electron reduction of the adsorbate, and represents the reaction pathway (b) in Fig. 3. These different trends are mostly caused by the different binding geometries, which are promoted by each surface. Variations in surface area and surface morphology change the most stable adsorption geometry for the carbon dioxide molecule. This adsorption geometry either leads to a stable P₁ single electron transfer intermediate (a) or can promote a barrier-less pathway to a second electron transfer (P₂), which in turn is the result of an elongated C–O bond length in the adsorbate of P₁.

Fig. 3 Schematic valence bond crossing diagrams for CO₂ reduction on carbide surfaces. (a) Single electron reduction of CO₂ leading to intermediate P₁. (b) Two electron reduction of CO₂ leading to intermediate P₂.

It has previously been reported that changes in the value of transition state imaginary frequencies are often closely linked to changes in reactivity,^67,68 which seems also to apply to the current results, where the smallest imaginary frequency (186.51 cm⁻¹) is associated with the most reactant-like transition state (i.e. occurring at the greatest distance from the surface). Importantly, the largest frequency was found for CO₂ adsorption onto VC{001}, which was also described as the most product-like transition and indeed leads to the most exothermic adsorption, whilst CO₂ adsorption on ZrC{001} was least exothermic. However, when the magnitude of the imaginary frequencies from each transition state was plotted against the adsorption energy of the chemically adsorbed state, a relatively poor correlation was observed (see Fig. S5 ESI†). It has frequently been reported that when different species catalyse the same redox process, there is often a correlation between the stability of the product ground state and the position along the potential energy surface at which the transition state occurs.^69–71 This correlation is due to the position of the avoidance crossing (kinetic barrier) when plotted on a valence bond (VB) diagram (see Fig. 3). Transition states that happen earlier occur higher in the vacuum and have imaginary frequencies with smaller wavenumbers, and it should therefore be possible to directly correlate the imaginary frequencies of a transition state to the reaction thermodynamics. Fig. 3 graphically illustrates two distinct chemical adsorption pathways and helps to explain the lack of correlation, shown in Fig. S5, in the ESI.† The surfaces responsible for these two pathways will be discussed in more depth below. However, it is clear from the valence bond analysis that only the first adsorption type (a) will lead to a stable one electron absorbed intermediate (P₁) that can be connected directly to a single conical intersection, since in the second reaction pathway (b) the adsorption geometry of the CO₂, in P₁, increases the electron affinity enough to overcome the surface workfunction and lower the ϕ_P1 below . In other words, the geometry of P₁ promotes a barrier-less second electron transfer and the adsorption energy of the subsequent P₂ intermediate can no-longer be directly linked to the avoidance crossing of the wavefunction linking the ground state product and the excited state reactant with the wavefunction linking the excited state reactant and the ground state product.

Fig. 4 shows, that of the two surfaces where transition states are observed, only CO₂ adsorption on the {001} surfaces exclusively follow reaction pathway a, whereby a single electron transfer is coupled to limited C–O bond elongation. We therefore decided to evaluate the correlation between the position of the transition states and the sum of the energy of surface workfunctions and the chemical adsorption energies (see Fig. 5), which in practice means a subtraction of the energy gained by chemical adsorption (right hand side of VB curve) from the energy lost through the reduction of the carbide d-band (left hand side of VB curve). In this case, the lower the energy the earlier the transition state, which is to be expected since the energies are positive and therefore the higher the energy the later the transition state (conical intersection). This correlation is important, because it helps to confirm the similarities and trends of all potential energy surfaces and means that the heights of the respective barriers are comparable.

Fig. 4 Correlation between chemical adsorption energy and the CO bond length of CO₂ reduction transition state. (red) activated double bonds. (green) activate single bonds.

Fig. 5 Negative correlation between the sum of the φ and chemical adsorption energy and the imaginary frequency for the CO₂ reduction transition state.

The {011} surface of transition metal carbides are also of significance, as previous work⁴⁵ has shown that they are the second lowest energy surface in all the carbides reported here. Therefore, a Wulff construction⁷² of any TMC nanoparticles would probably indicate that the {011} surface would be the second most dominant, in conditions of thermodynamic equilibrium and in the absence of stabilizers and surfactants. Such a prediction has been supported by many studies that have used DFT-derived surface energies to predict such morphologies.^73,74 Owing to the importance of these surfaces, a detailed study of their reactivity was also undertaken, which showed that chemical adsorption proceeded via small barriers. It is notable that for all carbides, the {011} surfaces greatly increase C–O bond activation above that of the comparative {001} surfaces (see Fig. 4). It is also noteworthy that carbides with parent metals of the fourth group appear to adsorb CO₂ much more strongly than those of the fifth. Indeed, this is a general trend across all surfaces and is accompanied with generally stronger adsorption of period four metal carbides.

Unlike the behaviour on the {001} and {011} surfaces, no physically adsorbed structures were found on any of the metal terminated {111} surfaces, which instead catalysed direct chemical adsorption pathways. Despite an optimized adsorbate being placed high in the vacuum, the initial geometry optimisations lead inevitably and without an energy barrier to the formation of a carbide-bound, activated and bent carboxylate (CO₂^δ−) species.⁷⁵ Attempts were made to locate any shallow physically adsorbed intermediate by scanning the adsorbates up into the vacuum and running stepwise optimisation with the only fixed degree of freedom associated position of the CO₂ in the Z-direction. However, in all cases the results indicated a barrierless chemical adsorption process without stable physically adsorbed states (see ESI† Tables S1 and S2). It has previously been argued that the {111}M surfaces of early TMCs represent a polar metastable phase that can eventually reconstruct to produce open stepped and defect surfaces.^76,77 However, there is no evidence of such a reconstruction and it appears that these pristine surfaces are stable.^63–65 These surfaces are therefore considered to be important and their activity indicates that they represent examples of a small and privileged class of solid surfaces that are able to activate CO₂ without any activation energy.^78,79

Geometries and relevant bond lengths for these chemically adsorbed states are shown in Fig. 6. It is very noticeable that despite binding motifs that appear to position the bent CO₂ molecule with the oxygen atoms pointing up into the vacuum, in all cases, the bond distances between the surface metals and all three adsorbate atoms are very similar, which is to be expected since all the structures reported represent the lowest energy binding configurations. These binding motifs are explained by the central carbon atom filling the hollow sites between metal atoms, on the {111}M surfaces, thereby allowing maximum overlap between the dangling orbitals of the surface atoms and atoms of the adsorbate. Very similar binding motifs are seen on the {001} and {011} surfaces, where the C_ontop position enables the maximum number of interactions between two adjacent metal atoms. As stated above, there are also two very pronounced trends between the CO₂ adsorption energies and C–O bond lengths. For both activated modes, the two carbides with the most elongated C–O bonds (TiC and ZrC) were also the materials causing the greatest adsorption energies (see Fig. 4). It is also important to note that such elongated C–O bond lengths would imply lower barriers for further reduction,^44,80 which in turn would suggest that surfaces from the elongated single bond series could be expected to have lower CO₂ dissociation barriers, even if their adsorption is less exothermic than that seen in a comparable surface from the double bond elongation series.

Fig. 6 Chemically adsorbed CO₂ on the {111}M carbide surfaces. Structural images and important bond distances are given for: TiC (top left), VC (top right), ZrC (bottom left) and NbC (bottom right). All distances are given in angstroms.

In contrast to the metal-terminated {111} surfaces, those terminated with carbon proved to be very unstable in all cases except NbC. Although the NbC{111}C surface did remain stable during the chemical adsorption of CO₂, the barrier for this reaction (at >0.8 eV) was comparatively high. This result is in excellent agreement with our previous computational work that predicted that the metal-terminated {111} surfaces would become progressively less favoured over the carbon-terminated {111} surfaces as the parent metal moves across the groups and down the periods.⁴⁵ Other work focused on the hydrogenation of these same carbon-terminated {111} surface also found these termination to be unstable.⁸¹ Furthermore, these results are also in good agreement with experimental observations, which report that the {111} surface of TiC is exclusively terminated by titanium.^60,82 However, since all these studies showed that a carbon-terminated {111} surface might be important for NbC, we have still included these surfaces for the sake of completeness.

Water activation

As already mentioned, H₂O is an important component in flue gas that has the ability to direct the hydrogenation of CO₂, as catalysed by solid materials.^19,20 The H₂O molecule prior to adsorption was initially placed high in the vacuum and sequentially scanned towards the surfaces, in a manner similar to that discussed in the previous section for CO₂. Also as seen for the CO₂ adsorption, this protocol led to lowest binding energy conformation and indeed it was not possible to locate more exothermic energies using alternative techniques. This protocol produced two clearly favoured binding configurations as shown in Fig. 7. In the two surfaces that maintained the surface stoichiometry of the bulk, namely the {001} and {011} surfaces, the lowest energy binding configuration was the on-top (OTS) metal site. The carbon-terminated {111} surface were all unstable in the presence of water, in a manner that is not only observed in the presence of CO₂, but also seen on the hydrogenated surfaces, where in the presence of molecular hydrogen only the {111}C surface of NbC was stable.⁸¹ In contrast to the carbon terminated surface, which were only stable in the absence of an adsorbate, the metal terminated {111} surfaces were both stable and strongly adsorbed H₂O in the hollow site (HS) configuration (see Fig. 7).

Fig. 7 Depiction of the two lowest energy water binding configurations. The hollow site configuration (HS) is the most exothermic adsorption motif on the {111}M surface, whilst the metal on-top configuration (OTS) is most stable on the {001} and {011} surfaces.

A strong trend in the binding energies is seen in the remaining three low-index surfaces, as shown in Fig. 8. In all cases the binding energy of H₂O on the {111}M is far higher than that found for the {011} and {001} surfaces, which both show very comparable adsorption energies. The one exception to this observation is that the {011} surface of TiC binds water more exothermically than the TiC{111}M surface, which can be explained by the fact that the TiC{011} surface adsorbs H₂O dissociatively. Geometry and Bader charge analysis confirms that adsorption on this surface produces bound hydrogen and hydroxyl groups, and this values is therefore not so much a measure of the binding energy of H₂O as of the formation energy of hydroxyl and hydrogen species on the TiC{011} surface. Multiple attempts were made to locate a chemisorbed local minima that included an intact H₂O, with all cases leading to either dissociative or physisorbed states upon full optimisation.

Fig. 8 Binding energies of water on three low-index surfaces of TiC, VC, ZrC and NbC. The orange diamond bar (left) represent the {001} surfaces; whilst, the brown square bar (middle) and the blue diagonally stripped bar (right) represent the {011} and {111}M surfaces respectively. Water adsorption is an exothermic process on the NbC{011} surface, so the physically adsorbed energy has been included instead and marked with an asterisk (*).

In contrast to the adsorption of CO₂, there appears to be no correlation between average O–H bond lengths and chemical adsorption energies of H₂O (see ESI† Fig. S7). However, charge transfer is also extremely small in all but the three most exothermic cases. These three surfaces, namely ZrC{111}M, TiC{111}M and TiC{011}, see charge transfer to H₂O of 0.11, 0.16 and 0.67 electrons respectively (see ESI,† Table S6). In every case, this additional electron density is transferred to the oxygen of the adsorbate. Once this centre is fully reduced a subsequent heterogeneous O–H cleavage will lead to the formation of a surface hydroxyl group and hydrogen atom. Importantly, ZrC{111}M and TiC{111}M are the surfaces that promote the second and third longest O–H bond lengths during chemical adsorption, with the longest O–H bond lengths reserved for the TiC{011} surface that promotes complete cleavage of this bond and consequently promotes the most electron transfer.

H₂O decomposition on the {001} carbide surfaces

The occurrence of any adsorbate co-binding configuration depends strongly on whether the final product is more stable than the sum of CO₂ and the water dissociation products. Therefore, we accessed the dissociative adsorption energies of H₂O on the {001} surfaces of all the carbides studied. To achieve this, the distance between the hydrogen and hydroxyl groups were sequentially elongated before full geometry optimisations of the minima of the scans. The resulting bond distances, Bader charges and dissociative adsorption energies are shown in Fig. 9. Interestingly, although no chemical adsorption of water was observed on the {001} surface of NbC, dissociative adsorption is an exothermic process. Also of note is the finding that the changes in electronic structures of the dissociative adsorption states are almost identical, i.e. instead of protons we observe adsorbed hydrogen atoms that all retain one valence electron, which result is in excellent agreement with our work on molecular hydrogen adsorption.⁸¹ It appears that the surface d-bands donate approximately half of this electron density with the other half coming from the hydroxyl group.

Fig. 9 Bader charges, adsorption energies and important bond distances resulting from dissociative adsorption of H₂O on the {001} surfaces of TIC (top left), VC (top right), ZrC (bottom left) and NbC (bottom right). The metal–oxygen (r_XO) and hydrogen–hydroxyl (r_H,OH) distances are included alongside the dissociative adsorption energy (ΔE_dis). The total bader charges for the hydroxyl (β_OH) and hydrogen (β_H), as well as the total change in grouped bader charge (β_OH). All distances are given in Å, whilst energy values are in eV.

From the results shown in Fig. 9, it is clear that on the {001} surface of group four carbides, dissociative absorption of H₂O is either energetically the same or less favourable than the alternative chemically adsorbed state. In practice, this result means that chemically adsorbed water would probably remain intact on the {001} surface of TiC and VC, where they could form strong hydrogen bonding networks with CO₂. In contrast, dissociation of water on the {001} surfaces of NbC and ZrC is indeed an exothermic process. Indeed, as mentioned previously, dissociative adsorption is the only exothermic type of chemically adsorbed H₂O on the {001} surface of NbC. However, this process would require a concerted surface binding and O–H bond breaking transition state that would probably make this binding motif a rare event. On the {001} surface of ZrC, dissociative adsorption is 0.31 eV more exothermic than the intact chemical adsorption of H₂O, which could indicate that the dissociative adsorption of water could be important on this specific surface. Therefore, it is possible that chemical adsorption of molecular water could form a relatively stable intermediate state preceding the formation of surface-bound hydrogen and hydroxyl groups via a HO–H bond stretch. Such a process is expected to be heavily dependent on the presence of other adsorbate molecules in the local environment and the potential hydrogen-bonding network such species would initiate. In order to assess the importance of such interactions, a detailed study of the co-adsorption of both CO₂ and H₂O on the {001} surfaces of all four carbides is hence presented below.

CO₂ and H₂O co-adsorption on the {001} carbide surfaces

Competitive binding of water and carbon dioxide was assessed to examine the surface interactions between the two adsorbates. Of particular interest is the possibility of surface-mediated bicarbonate (HCO₃⁻) formation via a carbonic acid (H₂CO₃) intermediate, which was examined on the lowest energy {001} surface only, since that is the dominant surface where these co-binding effects are believed to be most prevalent, as described previously.¹² Sequestering carbon dioxide in the form of carbonic acid is becoming an increasingly important research area in the field of green chemistry.^83–85 It has been hypothesised that surface mediated carbonic acid formation on a suitable catalyst would sequester CO₂ at higher concentrations and at much faster rates than in the absence of such a material.⁸⁶ Such a process has obvious application in CCS technologies and could also form an intermediate compound in the formation of calcium bicarbonate, whereby the natural process of rock weathering is replicated and accelerated, leading to affordable and long-term carbon sequestration.⁸⁷

To improve the probability of locating the global minimum for the co-binding of the adsorbates, a water molecule was placed high in the vacuum and sequentially scanned onto surfaces preloaded with CO₂, see ESI† Tables S8 and S9. In all cases, this approach led to a co-bound configuration that includes a single OCO–H–OH hydrogen-bond. Transitions states were located using the same climbing NEB protocol mentioned previously and the resulting two-dimensional potential energy landscapes are shown in Fig. 10. All physisorption energies (1I_X) are extremely similar, whilst there is much more divergence observed for the reaction barriers (1TS) and exothermicities (2I_X). VC{001} showed both the smallest barriers as well as the most exothermic co-adsorption; whilst the reverse was true for TiC{001}. Importantly, none of the surfaces studied reported a co-adsorption barrier above 0.65 eV and all reported exothermic processes. Interestingly, whilst it was shown in the previous section that water decomposition is a likely occurrence on the {001} surfaces of ZrC and NbC, the energies of such processes are both remarkably similar to the co-binding energies of intact H₂O on these surfaces, preloaded with CO₂.

Fig. 10 Potential energy surface for the co-adsorption of H₂O on the CO₂ loaded {001} surfaces of TiC, VC NbC and ZrC. All values are given in eV relative to one molecule of H₂O and the CO₂ loaded surfaces.

To assess the strength of the CO₂ and H₂O interactions on the different surfaces studied for the reaction outlined in eqn (2), the interaction energy (E_inter) was calculated using eqn (3).⁸⁸

E_inter = [E(slab) + E(slab + CO₂ + H₂O)] − E(slab + CO₂) − E(slab + H₂O) (3)

where, the energies of the CO₂ and H₂O bound surfaces are subtracted from the sum of the clean and co-bound surface. Note, that the addition of the non-bound surface energy is needed to balance the left-hand side of the equation. E_inter values proved to be very carbide dependent with the preferred co-binding sites for the group four carbides showing very weak interaction energies of −0.01 eV and −0.05 eV, for TiC and ZrC respectively. Much more exothermic values were found for VC (−0.43 eV) and NbC (−0.65 eV). However, water absorption is not an exothermic process on the NbC{001} surface, so this value is related to the lowest energy physically adsorbed species.

Also, none of these binding conformations would be expected to promote efficient carbonic acid formation. Therefore, to locate the optimal binding confirmation to promote H₂CO₃ formation, it was decided to study the reverse reaction (from carbonic acid to separate adsorbates).

To investigate the possibility of the carbide-mediated formation of H₂CO₃, carbonic acid was adsorbed onto the {001} surfaces of each carbide, before following the reaction pathway that included both a hydrogen atom transfer and a C–O bond formation step. Fig. 11 shows the potential energy surface for the carbide-mediated formation of carbonic acid, on the {001} surfaces of TiC, VC, NbC and ZrC. Although the results were obtained in the reverse direction, the figure shows the potential energy surface along the reaction path, whereby, the co-bound adsorbates (2I*_X) transform into the carbonic acid products (3I_X) via a carbon–carbon bond cleavage transition state (2TS_X), where (X = TiC/VC/NbC/ZrC). Very high barriers of between 0.76 eV and 1.20 eV are observed for the concerted hydrogen transfer and C–O bond formation step from the 2I*_X intermediates. However, none of these intermediate states represents the lowest energy co-binding confirmations (2I_X). These are the same binding confirmations shown in Fig. 10, whereby the dominant (low energy) binding geometries are very far from optimal for carbonic acid formation. Therefore, the surface mediated formation of carbonic acid is probably a rare event and would have to proceed via an activation barrier of >1 eV, with the end products being endothermic. Optimised structures of carbonic acid adsorbed on TiC{001} and VC{001} surfaces are shown in Fig. 12. Although the adsorption geometries of both species are very similar, there is a slightly longer average metal–oxygen distance for carbonic acid adsorbed on VC, which is caused by the absence of one formal V–C bond and helps to explain why adsorption on the {001} surface of TiC is more exothermic. This is shown clearly in Fig. 12, where the distal bond of the hydroxyl group of carbonic acid on VC{001} points up into the vacuum.

Fig. 11 Potential energy surface for the surface mediated formation of carbonic acid, on the {001} surfaces of TiC, VC, NbC and ZrC. All values are given in eV relative to separate surface and adsorbate energies.

Fig. 12 Side and top adsorption geometries of carbonic acid on the {001} surfaces of TIC (left) and VC (right). The average metal–oxygen (r_XO,ave) and carbon–oxygen (r_CO,ave) distances are given alongside the length of the carbon–carbon bond (r_CC), formed between the adsorbate and the surface. All values are given in Å.

Summary and conclusions

We have used a DFT methodology to model the catalytic activity of the low-index surfaces of TiC, VC, ZrC and NbC towards water and carbon dioxide. Our results indicate that the metal terminated {111} surfaces of all the carbides will be the most reactive and that in general reactivity is greater in period four metal carbides. We also report two distinct CO₂ bonding modes that correspond to differing amounts of electron transfer and C–O bond elongation. Water adsorption is mostly a very exothermic process, even though it results in very modest amounts of charge transfer. On NbC{001} and TiC{011} surfaces only dissociative H₂O adsorption is found to be exothermic. This work predicts the formation of hydrogen bonds when the two adsorbates are co-adsorbed. These strongly hydrogen bonded species are formed via relatively accessible energy barriers on all the {001} surfaces studied. However, surface-mediated carbonic acid formation is unlikely to proceed due to relatively high activation energy barrier and endothermic reaction energies, that could be outcompeted by alternative pathways that are initiated by water dissociation on the {001} surfaces of ZrC and NbC.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was funded as part of an EPSRC low carbon fuels grant (EP/N009533/1). Computing facilities for this work were provided by ARCCA at Cardiff University, HPC Wales, and through our membership of the UK's Materials Chemistry Consortium (MCC). The MCC is funded by EPSRC (EP/F067496). All data created as part of this study are openly available at DOI: 10.17035/d.2019.0070602444.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9cp00924h

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