CO 2 and H 2 O Coadsorption and Reaction on the Low-Index Surfaces of Tantalum Nitride: A First-Principles DFT-D3 Investigation

: A comprehensive mechanistic insight into the photocatalytic reduction of CO 2 by H 2 O is indispensable for the development of highly e ﬃ cient and robust photocatalysts for artiﬁcial photosynthesis. This work presents ﬁrst-principles mechanistic insights into the adsorption and activation of CO 2 in the absence and presence of H 2 O on the (001), (010), and (110) surfaces of tantalum nitride (Ta 3 N 5 ), a photocatalysts of signiﬁcant technological interest. The stability of the di ﬀ erent Ta 3 N surfaces is shown to dictate the strength of adsorption and the extent of activation of CO 2 and H 2 O species, which bind strongest to the least stable Ta 3 N 5 (001) surface and weakest to the most stable Ta 3 N 5 (110) surface. The adsorption of the CO 2 on the Ta 3 N 5 (001), (010), and (110) surfaces is demonstrated to be characterized by charge transfer from surface species to the CO 2 molecule, resulting in its activation (i.e., forming negatively charged bent CO 2 − δ species, with elongated C–O bonds conﬁrmed via vibrational frequency analyses). Compared to direct CO 2 dissociation, H 2 O dissociates spontaneously on the Ta 3 N 5 surfaces, providing the necessary hydrogen source for CO 2 reduction reactions. The coadsorption reactions of CO 2 and H 2 O are demonstrated to exhibit the strongest attractive interactions on the (010) surface, giving rise to proton transfer to the CO 2 molecule, which causes its spontaneous dissociation to form CO and 2OH − species. These results demonstrate that Ta 3 N 5 , a narrow bandgap photocatalyst able to absorb visible light, can e ﬃ ciently activate the CO 2 molecule and photocatalytically reduce it with water to produce value-added fuels.

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Recently, many active visible light absorbers with narrow bandgaps, in particular Ta-based materials, such as tantalum nitrides (Ta 3 N 5 ) and tantalum oxynitrides (TaON), have attracted a lot of attention owing to their unique catalytic properties [27].Various forms of nanostructured Ta 3 N 5 including nanorod, nanoparticle, hollow sphere, and thin films have been considered as photocatalysts with reported enhanced photocatalytic activities [28][29][30][31][32]. Ta 3 N 5 and TaON have narrow band gap energies of 2.1 and 2.4 eV, respectively, which make them suitable to absorb visible light to initiate photocatalysis [33].Due to its narrow bandgap energy, Ta 3 N 5 could generate a sufficient number of electrons and holes even under visible light, which could directly reduce CO 2 into a radical anion (CO 2 −δ ) and reduce H 2 O to protons (H + ).Several studies have been conducted on the application of Ta 3 N 5 for water splitting and photocatalytic degradation of organic pollutants [15,16,34,35].The obtained results indicated that the T 3 N 5 is a promising candidate as a visible light-driven photocatalysis.Recently, the photocatalytic reduction of CO 2 to CO over Ta 3 N 5 has been reported [36,37].However, detailed mechanistic understanding of the interaction between CO 2 and Ta 3 N 5 photocatalyst is still limited.
The adsorption and activation of CO 2 are the foremost and fundamental steps in the photocatalytic reduction of CO 2 on the surface of a photocatalyst [38][39][40][41].Compared to the linear gas-phase molecule, chemisorbed CO 2 (mainly carbonate or CO 2 −δ anion) is characterized by a bent geometry with a decreased lowest unoccupied molecular orbital (LUMO), which favours charge transfer from the photoexcited semiconductors to the surface-adsorbed CO 2 molecules [41].Generally, exposed surfaces with a smaller work function provide greater activation for CO 2 as they favour electron transfers [42].In this work, a comparative first-principles density functional theory (DFT) study of the adsorption and activation of CO 2 in the absence and presence of H 2 O on Ta 3 N 5 (001), (010), and (110) surfaces is presented.First, the structures and relative stabilities of the low-index (001), (010), and (110) surfaces were systematically characterized and the equilibrium crystal morphology of the Ta 3 N 5 crystal was constructed based on calculated surface energies.Secondly, the fundamental adsorption and coadsorption geometries of CO 2 and H 2 O, including the energetics and electronic properties are discussed.The stabilities of the coadsorbed CO 2 -H 2 O species on the various surfaces were also evaluated to determine the pathways for the surface reactions involving these species, and to characterize the stability of the different reduced forms of CO 2 , in particular the formate and bicarbonate species that were identified experimentally [37].[43].The structure of Ta 3 N 5 is composed of octahedra of N atoms centred by Ta atoms.Since the N atoms are both three and four coordinated, the octahedra are irregular.The conventional unit cell consists of 32 atoms, where each Ta atom is bonded to six N atoms, while N atoms are bonded to three or four Ta atoms.The Ta-N distances in Ta 3 N 5 range from 1.96 to 2.24 Å.From full relaxation (ions + cell shape + volume) until the required accuracy was reached, the lattice parameters of Ta 3 N 5 were predicted at a = 3.921 Å, b = 10.317Å, and c = 10.323Å, in close agreement with experimental data [43] and earlier theoretical predictions [44][45][46][47].The Ta-N distances for the N atoms coordinated to three Ta atoms were calculated at 2.000, 2.083, and 2.048 Å, whereas those for the N atoms coordinated to four Ta atoms are 2.117(×2) and 2.241(×2) Å. Figure 1c shows the partial density of states of Ta 3 N 5 , from which the band gap is estimated at 2.11 eV, which is in good agreement with ultraviolet-visible (UV-vis) spectroscopy measurements of Ta 3 N 5 powders and thin films which estimate an optical gap of approximately 2.1 eV [48,49].Previous theoretical studies based on GGA+U [45] and HSE06 [50,51] functionals predicted the bandgap in the range of 2.1-2.21eV.It is evident from Figure 1c that the top of the valence band is mainly composed of N-2p orbitals, while the bottom of the conduction band is mainly composed of Ta-5d orbitals, indicating that transitions near the absorption edge occur between N-2p and Ta-5d orbitals, which is in agreement with earlier theoretical works [45,50,51].Figure 2 shows the optimized structures of the most stable terminations of the Ta 3 N 5 (001), (010), and (110) surfaces, which have calculated surface energies of 2.33, 2.04, and 1.58, Jm −2 , respectively.All surfaces are terminated by N atoms and exhibit step-like surface topologies.Using the calculated surfaces energies, the equilibrium Wulff shape of Ta 3 N 5 nanocrystal was constructed, as shown in Figure 3.The Ta 3 N 5 nanocrystal is found to exhibit an elongated shaped, with the (110) and (010) facets expressed in the rectangular crystal edges and the (001) facet enclosing the hexagonal edge.The predicted morphology is consistent with the elongated polyhedral crystal shape observed in experiments [30,52].The differences in the structure, composition and stabilities of the (001), (010), and (110) surfaces are expected to dictate their reactivity towards CO 2 and H 2 O molecules, which is investigated in detail and discussed in the following sections.Considering that the initial step for CO 2 reduction is its activation [53], the lowest-energy adsorption configurations of CO 2 on the Low-Miller index (001), (010), and (110) Ta 3 N 5 surfaces were first investigated in order characterize the strength of interaction and the extent of the C−O bond activation.Shown in Figure 4 are the lowest-energy adsorption geometries of CO 2 on the different Ta 3 N 5 (001), (010), and (110) surfaces, with the calculated adsorption energy and structural parameters summarized in Table 1.The less stable CO 2 adsorption geometries predicted on the different Ta 3 N 5 surface are displayed in Supplementary Information Figures S1-S3.At the (001) surface, the CO 2 molecule interacts through all three atoms, as shown in Figure 4a

Bulk and Surface Properties
where ρ CO 2 +sur f ace , ρ sur f ace and ρ CO 2 are the electron density of the total CO 2 -Ta 3 N 5 system, the bare Ta 3 N 5 surface, and the isolated CO 2 molecule as in the relaxed adsorbed configuration.The differential charge density iso-surface contours inserts in Figure 4d Shown in Figure 5 are the most stable coadsorption geometry of CO + O pair from CO 2 dissociation (CO 2 →CO + O) reaction on the (001), (010), and (110) Ta 3 N 5 surfaces.At the Ta 3 N 5 (001) surface, the oxygen atom binds at Ta site, whereas the carbon of the CO moiety bridges two N atoms, as shown in Figure 5a, releasing a coadsorption energy of −1.64 eV.At the Ta 3 N 5 (010) surface, the oxygen atom binds at bridge Ta sites, whereas the carbon of the CO moiety binds at the N site, as shown in Figure 5b, releasing a coadsorption energy of −2.99 eV.At the Ta 3 N 5 (110) surface, as shown in Figure 5c, the oxygen atom and the carbon of the CO moiety bind at Ta and N sites, respectively, releasing a coadsorption energy of −0.68 eV.The results show that the coadsorption of (CO + O) pairs is more favourable on the Ta 3 N 5 (010), followed by Ta 3 N 5 (001), and then the Ta 3 N 5 (110) surface.The geometrical parameters and calculated coadsorption (E coads ), reaction (E rxn ), and the activation energy barriers (E act ) of CO 2 dissociation are shown in Table 2.The Ta 3 N 5 (010) surface exhibits the lowest CO 2 /Ta 3 N 5 (010)→(CO + O)/Ta 3 N 5 (010) reaction energy-exothermic by −1.09 eV.The CO 2 →CO + O reaction is, however, endothermic by 1.04 and 0.52 eV on the Ta 3 N 5 (001) and Ta 3 N 5 (110) surfaces, respectively.The activation energy barrier (E act ) for the dissociation of CO 2 on the (001), (010), and (110) Ta 3 N 5 surfaces are calculated at 1.34, 1.15 and 1.56 eV, respectively.The higher E act and the endothermic E rxn for the dissociation of CO 2 predicted on the (001) and (110) surfaces suggest that direct dissociation may be hindered at room temperature and without surface promoters such as H 2 O and H species. Direct CO 2 dissociation may, however, occur at room temperature on the Ta 3 N 5 (010) surface owing to its calculated exothermic E rxn and the lower E act .

CO 2 and H 2 O Coadsorption and Reactions
Water is a suitable source of hydrogen for CO 2 conversion via its hydrogenation to valued-added chemicals [54].As such, investigations of H 2 O and CO 2 coadsorption and the possible reactions between them are indisputable.Prior to investigating the coadsorption structures of CO 2 and H 2 O, the most stable adsorption geometries of isolated H 2 O on the (001), (010), and (110) Ta 3 N 5 surfaces were systematically characterized.The calculated energetics and structural parameters for molecular and dissociative water adsorption on the three Ta 3 N 5 surfaces are presented in Table 3 and Figure 6.The most stable adsorption of water is predicted at the Ta sites via its O atoms.The adsorption energy of molecular water at the (001), (010), and (110) Ta 3 N 5 surfaces is calculated to be −1.42,−1.07, and −1.08 eV, respectively, indicating that the interaction is strongest at the (001) surface and weakest on the (110) surface, similar to the trend predicted for CO 2 adsorption.The most stable dissociative water adsorption configurations (OH + H pair) provided in the rightmost panel of Figure 6 show that when dissociated, the OH species preferentially bind to the Ta sites through the O atom, whereas the H atoms bind at the N sites.From Table 3, it is worth noting that the dissociative adsorption of water on three surfaces is thermodynamically more favourable than molecular adsorption as reflected is the larger coadsorption energies released by the OH + H pairs.The H 2 O→OH + O reaction energies on the (001), (010), and (110) surfaces can be calculated at −1.15, −0.28, and −1.03 eV, respectively, all of which are exothermic and thus indicate favourable dissociation of water.The interacting Ta−OH distances are calculated at 1.987, 2.297, and 1.978 Å, whereas the N−H distances were converged at 1.031, 1.056, and 1.022 Å on the (001), (010), and (110) surfaces, respectively.The transition states structures were determined (central panels, Figure 6) in order to estimate the activation energy barriers for the dissociation of water, which were predicted at 0.18, 0.34, and 0.27 eV at the (001), (010), and (110) surfaces, respectively.In a previous study the energy barriers for the dissociation of water was calculated at to be as low as 0.05 eV on the Ta 3 N 5 (110) surface [55].Compared to direct CO 2 dissociation, the predicted low activation energy barriers and the exothermic reaction energies suggest that spontaneous water dissociation will occur on the (001), (010), and (110) surfaces.The lowest-energy coadsorption structures of CO 2 + H 2 O on the (001), (010), and (110) surfaces of have been characterized, as shown in Figure 7.The coadsorption energy of CO 2 + H 2 O on the different surfaces is calculated as follows: where E (CO  Hydrogen-bonded interactions between the CO 2 and H 2 O species are observed at the Ta 3 N 5 (010) surface, evident by the close interaction of the electron density of the two species.This may favour proton transfer to the CO 2 molecule, which has been investigated and found to results in spontaneous dissociation of the surface-bound C−O bond to form CO and 2OH − species (Figure 9a).Relative to the initial coadsorbed CO 2 + H 2 O system, the reaction energy for the formation of the CO + 2OH − species on the Ta 3 N 5 (010) surface is calculated to be highly exothermic by 1.11 eV.When the proton is transferred to unbound O of CO 2 , a stable carboxyl COOH species (Figure 9b) is formed with a reaction energy of −0.67 eV.No stable formate HCOO species is formed as the attached proton to the C atom detaches during energy minimisation to the surface N site, as shown in Figure 9c, with the reaction energy calculated to be −0.19 eV.These results suggest that the Ta 3 N 5 (010) surface favours the dissociation CO 2 in the presence of H 2 O, and the resulting CO species could be further hydrogenated to form CH 2 O and CH 3 OH.Compared to the Ta 3 N 5 (010) surface, the reaction energy for the proton transfer from H 2 O to CO 2 to form COOH and HCOO species is found to be highly endothermic on the Ta 3 N 5 (001) and Ta 3 N 5 (110) surfaces, as shown in Figure 10.The less endothermic reaction energies predicted for the COOH species than for the HCOO species, however, suggest that further hydrogenation reactions to products will proceed via the carboxyl COOH route.

Summary and Conclusions
This work presents comprehensive first-principles density functional theory analyses of the adsorption and activation of CO 2 in the absence and presence of H 2 O on the (001), (010), and (110) surfaces of Ta 3 N 5 , a photocatalyst able to absorb visible light to initiate photocatalysis.The strength of adsorption and extent of CO 2 activation is found to be influenced by the stability of the different Ta 3 N surfaces, where it adsorbs most strongly onto the least stable Ta 3 N 5 (001) surface and most weakly onto the most stable Ta 3 N 5 (110) surface.Direct dissociation of CO 2 is suggested to occur on the Ta 3 N 5 (010) surface owing to the calculated exothermic reaction energy and lower activation energy barrier.In contrast, direct CO 2 dissociation would be hindered on the Ta 3 N 5 (001) and Ta 3 N 5 (110) surfaces without surface promoters such as H 2 O and H species. Spontaneous water dissociation is predicted occur on the (001), (010), and (110) surfaces, providing the necessary hydrogen source for CO 2 reduction reactions.The strongest attractive interaction between coadsorbed CO 2 and H 2 O is predicted on the Ta 3 N 5 (010) surface, which gave rise to proton transfer to the CO 2 molecule, causing its spontaneous dissociation to form CO and 2OH − species with an exothermic reaction energy of −1.11 eV.The formation of COOH* and HCOO* intermediates is found to be highly endothermic on the Ta 3 N 5 (001) and Ta 3 N 5 (110) surfaces, although the COOH* species are less endothermic, indicating that further hydrogenation reactions will proceed via the carboxyl COOH* route.A further hydrogenation of the OH end of the COOH* intermediate may lead to CO + H 2 O formation, where the formed CO species could be further hydrogenated towards methane of methanol formation.This is consistent with the findings of Lu et al. [37], who, based on their detected intermediates, suggested that the possible reaction pathway for CO 2 reduction over the Ta 3 N 5 catalysts is CO 2 →COOH*→CO→CH * x →CH 4 .The present results demonstrate that Ta 3 N 5 can efficiently activate the CO 2 molecule and photocatalytically reduce it with water to produce value-added fuels.Future investigations of the Eley-Rideal type of mechanism will be important to draw a direct comparison with the Langmuir-Hinshelwood mechanism unravelled in the present study.Further investigations of the effects of transition metal doping on the electronic structure and CO 2 conversion reactions over Ta 3 N 5 catalyst under visible light will also be important.

Computational Details
The density functional theory (DFT) calculations were performed within the VASP package [55][56][57][58].The projected augmented wave (PAW) method [59] was employed to describe the interactions between the valence electrons and the ionic core.Geometry optimisations were carried out using the Perdew−Burke−Enzerhof (PBE) generalized gradient approximation (GGA) functional [60], while the Hubbard U correction (PBE+U) was employed for accurate determination of the electronic structures [61][62][63][64].From an analysis of how the electronic band gap increases with increasing strength of the on-site Coulomb repulsion, it was found that an effective U of 6.5 eV gives an accurate description of the structural parameters and the electronic properties of Ta 3 N 5 [65].Dispersion forces were accounted for through the Grimme DFT-D3 scheme [66].The kinetic energy cut off was set to 600 eV, which ensured convergence of the total energy of the Ta 3 N 5 to within 10 −6 eV and the residual Hellman−Feynman forces to within 10 −3 eV Å −1 .A 7 × 3 × 3 mesh of Monkhorst−Pack [67] k-points was used to sample the Brillouin zone of Ta 3 N 5 .For accurate determination of the electronic structure of Ta 3 N 5 , a higher mesh of 9 × 5 × 5 was used.
The (001), (010), and (110) surfaces, which are commonly observed in Ta 3 N 5 nanoparticles, were created from the optimized bulk material using the METADISE code [68,69], which ensures the creation of surfaces with zero dipole moment perpendicular to the surface plane.In each simulation cell (slab thickness of at least 15 Å), a vacuum region of 20 Å was added in the z direction to avoid interactions between periodic slabs.The relative stabilities of the (001), (010), and (110) Ta 3 N 5 surfaces were determined according to their relaxed surface energy (γ r ), calculated as: where E relaxed slab is the energy of the relaxed slab, nE bulk is the energy of an equal number (n) of the bulk Ta 3 N 5 atoms, and A is the area of the slab surface.The adsorption energy (E ads ) of CO 2 and H 2 O species is determined as follows: where E M+surface is the total energy of the relaxed M+Ta 3 N 5 systems (M = CO 2 and H 2 O), E surface the total energy of the naked Ta 3 N 5 surfaces alone, and E M the total energy of the isolated adsorbates (CO 2 and H 2 O).Because of the adsorption of reactant molecules at only one side of the surface, Makov-Payne dipole correction was applied perpendicular to each surface [70].In order to determine the preferred adsorption sites and lowest energy adsorption modes of CO 2 and H 2 O molecules on the Ta 3 N 5 surfaces, different initial orientations of the molecules were optimized without any symmetry constraints.Charge transfer between the surfaces and adsorbates is quantified via Bader charge analysis [71].Transition states (TS) along reaction pathways were determined using the climbing-image nudged elastic band (CI-NEB) method [72], wherein six images were generated between the states of reactants (IS) and products (FS) in each elementary process.Located TS were characterized by only one imaginary frequency, corresponding to the reaction coordinate.The reaction activation energy barrier (E A ) is determined by E A = TS -IS, whereas the reaction energy (E R ) is determined by E R = FS -IS.
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− 2 Figure 1 .
Figure 1.The orthorhombic crystal structure of Ta 3 N 5 in terms of TaN 6 octahedra viewed in the (a) c-b and (b) b-a planes.(c) The electronic density of state of Ta 3 N 5 showing the total and projection on the Ta d states and N p states.(Colour scheme: Ta = pale olive and N = blue.) extent of the C−O bond −2.73 eV.The interacting Ta−O

2. 2 .
CO 2 Adsorption on (001), (010), and (110) Ta 3 N 5 Surfaces , with the C atom bound to N sites and the O atoms bound to Ta sites, releasing an adsorption energy of −2.73 eV.The interacting Ta−O and the N−C bonds were calculated at 2.176 and 1.361 Å, respectively.The strong adsorption induced structural transformation in the CO 2 molecules with the C−O bonds elongated from 1.176 Å in the gas phase to 1.301 Å in the adsorbed state and the ∠O a CO b angle reduced to 130.0 • , indicating activation of the CO 2 molecule.Compared to the (001), the CO 2 molecule interacts with the (010) surface via the carbon and one oxygen atom, as shown in Figure 4b, releasing an adsorption energy of −1.89 eV.The C−O bonds are significantly elongated, in particular the surface-bound one (1.422Å) compared to the unbound one (1.202Å) and the ∠O a CO b angle is reduced to 123.9 • .Similar to the (001) surface, CO 2 adsorption on the (110) surface involves all three atoms, as shown in Figure 4c, with the C atom binding at the N site and the O atoms bound to Ta sites, releasing an adsorption energy of −1.20 eV.Consistent with the weaker adsorption, longer Ta−O and the N−C bonds than on the (001) were calculated at 2.217 and 1.400 Å, respectively.The average C−O bond and ∠O a CO b angle are calculated at 1.292 Å and 125.5 • , respectively.and the N−C bonds were calculated at 2.176 molecules with the C−O bonds elongated from 1.176 ∠ −1.89 eV.The C−O bonds are significantly elongated, in particular the surface ∠ − Ta−O and the N−C bonds than on , respectively.The average C−O bond and∠

Figure 4 .
Figure 4. Lowest-energy CO 2 adsorption structures on (a) (001), (b) (010), and (c) (110) Ta 3 N 5 surfaces.The DOS projected on the surface Ta d states and N p states interacting with the C and O p states of CO 2 (d-f) and the corresponding isosurface contours of the differential charge density are shown as inserts in (d-f), where green contours denote electron density increase and the red contours denote electron density decrease by 0.02 e/Å 3 , respectively.(Atomic colour scheme: Ta = pale olive, N = blue, C = green, and O = red.)Partial density of states (PDOS) and differential charge density isosurface contours analyses provided further atomic-level insights into the mixing atomic orbitals and redistribution of electron density within the CO 2 -Ta 3 N 5 systems.The adsorption of CO 2 on Ta 3 N 5 surface is characterized by a strong mixing of interacting surface (Ta-d and N-p) and CO 2 (C-p and O-p) orbitals, as shown in Figure 4d-f.Consistent with chemisorption, electron density redistributions within the CO 2 -Ta 3 N 5 systems is observed, which was analysed through differential charge density isosurface contours, obtained as:

Figure 9 .
Figure 9. Optimized structures of the reaction products of proton transfer from H 2 O to CO 2 on Ta 3 N 5 (010) surface.(a) Proton transfer to surface-bound O atom, (b) proton transfer to unbound O atom and (c) proton transfer to the C atom.(Atomic colour scheme: Ta = pale olive, N = blue, C = green, and O = red.)

Figure 10 .
Figure 10.Optimized structures of the reaction products of proton transfer from H 2 O to CO 2 to COOH and HCOO species on (a,b) Ta 3 N 5 (001) and (c,d) Ta 3 N 5 (110) surfaces.(Atomic colour scheme: Ta = pale olive, N = blue, C = green, and O = red.)

Table 1 .
-f reveal a charge transfer from the bound surface ions into the π-antibonding orbital of the CO 2 molecule via the newly formed Ta−O and the N−C bonds.The CO 2 molecule gained a net charge of 0.40, 0.35 and 0.28 from the (001), (010), and (110) surfaces, resulting in the formation of negatively charged bent species (CO 2 δ− ) with elongated C−O bonds, confirmed by vibrational frequencies analyses, as shown in Table1.Adsorption energies, geometrical parameters, charges, and vibrational frequencies of molecular CO 2 on Ta 3 N 5 (001), (010), and (110) surfaces.

5 (001) Ta 3 N 5 (010) Ta 3 N 5 (110)
2 +H 2 O)/sur f ace , E CO 2 , E H 2 O and E sur f ace are the total energy of the coadsorbed (CO 2 +H 2 O) surface system, the free CO 2 , the free H 2 O, and the bare Ta 3 N 5 surfaces, respectively.The calculated CO 2 + H 2 O coadsorption energies and the geometrical parameters are presented in Table4.The coadsorption energy for the CO 2 + H 2 O pair on the (001), (010), and (110) Ta 3 N 5 surfaces were calculated at −3.94, −3.68, and −2.43 eV, respectively.Consistent with attractive interactions, the coadsorption energies are more exothermic than the sum of the separate CO 2 and H 2 O adsorption energies.
Funding: This research was funded by the UK's Engineering and Physical Sciences Research Council (EPSRC), grant number EP/S001395/1.