CO₂ and H₂O Coadsorption and Reaction on the Low-Index Surfaces of Tantalum Nitride: A First-Principles DFT-D3 Investigation

Abstract

A comprehensive mechanistic insight into the photocatalytic reduction of CO₂ by H₂O is indispensable for the development of highly efficient and robust photocatalysts for artificial photosynthesis. This work presents first-principles mechanistic insights into the adsorption and activation of CO₂ in the absence and presence of H₂O on the (001), (010), and (110) surfaces of tantalum nitride (Ta₃N₅), a photocatalysts of significant technological interest. The stability of the different Ta₃N surfaces is shown to dictate the strength of adsorption and the extent of activation of CO₂ and H₂O species, which bind strongest to the least stable Ta₃N₅(001) surface and weakest to the most stable Ta₃N₅(110) surface. The adsorption of the CO₂ on the Ta₃N₅(001), (010), and (110) surfaces is demonstrated to be characterized by charge transfer from surface species to the CO₂ molecule, resulting in its activation (i.e., forming negatively charged bent CO₂^−δ species, with elongated C–O bonds confirmed via vibrational frequency analyses). Compared to direct CO₂ dissociation, H₂O dissociates spontaneously on the Ta₃N₅ surfaces, providing the necessary hydrogen source for CO₂ reduction reactions. The coadsorption reactions of CO₂ and H₂O are demonstrated to exhibit the strongest attractive interactions on the (010) surface, giving rise to proton transfer to the CO₂ molecule, which causes its spontaneous dissociation to form CO and 2OH⁻ species. These results demonstrate that Ta₃N₅, a narrow bandgap photocatalyst able to absorb visible light, can efficiently activate the CO₂ molecule and photocatalytically reduce it with water to produce value-added fuels.

1. Introduction

Photocatalytic reduction of carbon dioxide (CO₂) with water (H₂O) to produce value-added fuels such as such as CO, HCOOH, CH₃OH, and CH₄ is a promising route to reduce CO₂ emissions and address the global energy crisis [1,2,3,4,5]. The activation and reduction of CO₂ is, however, an energetically demanding process that involves multiple electron transfer reactions [6,7,8,9,10], hence highly efficient and robust photocatalysts are critical. Several photocatalysts, such as TiO₂ [11,12,13], In₂O₃ [14,15], Ga₂O₃ [16,17], Al₂O₃ [18,19], ZnO [20,21], CeO₂ [22,23], ZnGe₂O₄ [24], and BiVO₄ [25,26], have been investigated for their performance in catalysing CO₂ reduction. However, because of their large bandgaps and high charge-carrier recombination rates, most of these semiconductor materials have low CO₂ conversion efficiencies. Therefore, there is continuous active research to find novel photocatalytic materials that are active under visible/solar light.

Recently, many active visible light absorbers with narrow bandgaps, in particular Ta-based materials, such as tantalum nitrides (Ta₃N₅) and tantalum oxynitrides (TaON), have attracted a lot of attention owing to their unique catalytic properties [27]. Various forms of nanostructured Ta₃N₅ including nanorod, nanoparticle, hollow sphere, and thin films have been considered as photocatalysts with reported enhanced photocatalytic activities [28,29,30,31,32]. Ta₃N₅ 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, Ta₃N₅ could generate a sufficient number of electrons and holes even under visible light, which could directly reduce CO₂ into a radical anion (CO₂^−δ) and reduce H₂O to protons (H⁺). Several studies have been conducted on the application of Ta₃N₅ for water splitting and photocatalytic degradation of organic pollutants [15,16,34,35]. The obtained results indicated that the T₃N₅ is a promising candidate as a visible light-driven photocatalysis. Recently, the photocatalytic reduction of CO₂ to CO over Ta₃N₅ has been reported [36,37]. However, detailed mechanistic understanding of the interaction between CO₂ and Ta₃N₅ photocatalyst is still limited.

The adsorption and activation of CO₂ are the foremost and fundamental steps in the photocatalytic reduction of CO₂ on the surface of a photocatalyst [38,39,40,41]. Compared to the linear gas-phase molecule, chemisorbed CO₂ (mainly carbonate or CO₂^−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 CO₂ molecules [41]. Generally, exposed surfaces with a smaller work function provide greater activation for CO₂ as they favour electron transfers [42]. In this work, a comparative first-principles density functional theory (DFT) study of the adsorption and activation of CO₂ in the absence and presence of H₂O on Ta₃N₅(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 Ta₃N₅ crystal was constructed based on calculated surface energies. Secondly, the fundamental adsorption and coadsorption geometries of CO₂ and H₂O, including the energetics and electronic properties are discussed. The stabilities of the coadsorbed CO₂–H₂O 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 CO₂, in particular the formate and bicarbonate species that were identified experimentally [37].

2. Results and Discussion

2.1. Bulk and Surface Properties

Ta₃N₅ crystalizes in the orthorhombic structure, as shown in Figure 1a,b, with space group Cmcm (No. 63). The neutron diffraction-derived lattice parameters are a = 3.886 Å, b = 10.212 Å, c = 10.262 Å, and α = β = γ = 90° [43]. The structure of Ta₃N₅ 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 Ta₃N₅ 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 Ta₃N₅ were predicted at a = 3.921 Å, b = 10.317 Å, and c = 10.323 Å, 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 Ta₃N₅, from which the band gap is estimated at 2.11 eV, which is in good agreement with ultraviolet–visible (UV–vis) spectroscopy measurements of Ta₃N₅ 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 2.1–2.21 eV. 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 Ta₃N₅(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 Ta₃N₅ nanocrystal was constructed, as shown in Figure 3. The Ta₃N₅ 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 CO₂ and H₂O molecules, which is investigated in detail and discussed in the following sections.

2.2. CO₂ Adsorption on (001), (010), and (110) Ta₃N₅ Surfaces

Considering that the initial step for CO₂ reduction is its activation [53], the lowest-energy adsorption configurations of CO₂ on the Low-Miller index (001), (010), and (110) Ta₃N₅ 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 CO₂ on the different Ta₃N₅(001), (010), and (110) surfaces, with the calculated adsorption energy and structural parameters summarized in

Table 1. Adsorption energies, geometrical parameters, charges, and vibrational frequencies of molecular CO₂ on Ta₃N₅(001), (010), and (110) surfaces.

Parameter	Free CO2	Ta3N5(001)	Ta3N5(010)	Ta3N5(110)
Eads (eV)	-	−2.73	−1.89	−1.20
Δq(CO2) (|e|)	0.0	0.40	0.34	0.31
d(C−Oa) (Å)	1.176	1.302	1.422	1.293
d(C−Ob) (Å)	1.176	1.301	1.202	1.290
$\angle$OaCOb (o)	180.0	130.0	123.9	125.5
d(C−N) (Å)	-	1.361	1.396	1.400
d(Oa−Ta) (Å)	-	2.176	2.012	2.217
d(Ob−Ta) (Å)	-	2.180	-	2.230
υas (cm−1)	2373	1465	1804	1718
υs (cm−1)	1323	1265	911	881
υb (cm−1)	631	819	737	691

. The less stable CO₂ adsorption geometries predicted on the different Ta₃N₅ surface are displayed in Supplementary Information Figures S1–S3. At the (001) surface, the CO₂ molecule interacts through all three atoms, as shown in Figure 4a, 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 CO₂ 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 $\angle$O_aCO_b angle reduced to 130.0°, indicating activation of the CO₂ molecule. Compared to the (001), the CO₂ 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 (1.422 Å) compared to the unbound one (1.202 Å) and the $\angle$O_aCO_b angle is reduced to 123.9°. Similar to the (001) surface, CO₂ 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 $\angle$O_aCO_b angle are calculated at 1.292 Å and 125.5°, respectively.

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 CO₂-Ta₃N₅ systems. The adsorption of CO₂ on Ta₃N₅ surface is characterized by a strong mixing of interacting surface (Ta-d and N-p) and CO₂ (C-p and O-p) orbitals, as shown in Figure 4d–f. Consistent with chemisorption, electron density redistributions within the CO₂-Ta₃N₅ systems is observed, which was analysed through differential charge density isosurface contours, obtained as:

$$\mathsf{\Delta }\rho ={\rho }_{C{O}_2+surface}-({\rho }_{surface}+{\rho }_{C{O}_2})$$

(1)

where ${\rho }_{C{O}_2+surface}$, ${\rho }_{surface}$ and ${\rho }_{C{O}_2}$ are the electron density of the total CO₂-Ta₃N₅ system, the bare Ta₃N₅ surface, and the isolated CO₂ molecule as in the relaxed adsorbed configuration. The differential charge density iso-surface contours inserts in Figure 4d–f reveal a charge transfer from the bound surface ions into the π-antibonding orbital of the CO₂ molecule via the newly formed Ta−O and the N−C bonds. The CO₂ 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 (CO₂^δ−) with elongated C−O bonds, confirmed by vibrational frequencies analyses, as shown in Table 1.

2.3. CO₂ Dissociation on (001), (010), and (110) Ta₃N₅ Surfaces

Shown in Figure 5 are the most stable coadsorption geometry of CO + O pair from CO₂ dissociation (CO₂→CO + O) reaction on the (001), (010), and (110) Ta₃N₅ surfaces. At the Ta₃N₅(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 Ta₃N₅(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 Ta₃N₅(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 Ta₃N₅(010), followed by Ta₃N₅(001), and then the Ta₃N₅(110) surface. The geometrical parameters and calculated coadsorption (E_coads), reaction (E_rxn), and the activation energy barriers (E_act) of CO₂ dissociation are shown in

Table 2. Coadsorption (E_coads), reaction (E_rxn), activation (E_act) energies and geometrical parameters of (CO + O) pairs on Ta₃N₅(001), (010), and (110) surfaces.

Parameter	Ta3N5(001)	Ta3N5(010)	Ta3N5(110)
Ecoads (eV)	−1.69	−2.99	−0.68
Erxn (eV)	1.04	−1.09	0.52
Eact (eV)	1.34	1.15	1.56
d(C−N) (Å)	1.467/1.388	1.237	1.242
d(Oa−Ta) (Å)	1.788	2.126/1.979	1.788
d(C−Ob) (Å)	1.227	1.173	1.170

. The Ta₃N₅(010) surface exhibits the lowest CO₂/Ta₃N₅(010)→(CO + O)/Ta₃N₅(010) reaction energy—exothermic by −1.09 eV. The CO₂→CO + O reaction is, however, endothermic by 1.04 and 0.52 eV on the Ta₃N₅(001) and Ta₃N₅(110) surfaces, respectively. The activation energy barrier (E_act) for the dissociation of CO₂ on the (001), (010), and (110) Ta₃N₅ 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 CO₂ predicted on the (001) and (110) surfaces suggest that direct dissociation may be hindered at room temperature and without surface promoters such as H₂O and H species. Direct CO₂ dissociation may, however, occur at room temperature on the Ta₃N₅(010) surface owing to its calculated exothermic E_rxn and the lower E_act.

2.4. CO₂ and H₂O Coadsorption and Reactions

Water is a suitable source of hydrogen for CO₂ conversion via its hydrogenation to valued-added chemicals [54]. As such, investigations of H₂O and CO₂ coadsorption and the possible reactions between them are indisputable. Prior to investigating the coadsorption structures of CO₂ and H₂O, the most stable adsorption geometries of isolated H₂O on the (001), (010), and (110) Ta₃N₅ surfaces were systematically characterized. The calculated energetics and structural parameters for molecular and dissociative water adsorption on the three Ta₃N₅ surfaces are presented in

Table 3. Coadsorption (E_coads), reaction (E_rxn), activation (E_act) energies and geometrical parameters of (OH + H) pairs on Ta₃N₅(001), (010), and (110) surfaces.

Parameter	Ta3N5(001)		Ta3N5(010)		Ta3N5(110)
State	Molecular	Dissociative	Molecular	Dissociative	Molecular	Dissociative
Eads (eV)	−1.42	−2.16	−1.07	−1.35	−1.08	−2.12
Erxn (eV)	-	−0.74	-	−0.28	-	−1.04
Eact (eV)	0.18	-	0.34	-	0.27	-
d(O−Ta) (Å)	2.307	1.987	2.395	2.297	2.295	1.978
d(H−N) (Å)	-	1.031	-	1.056	-	1.022
d(O−H) (Å)	0.977/0.977	0.969	0.980/0.979	0.976	0.986/1.006	0.970

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) Ta₃N₅ 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 CO₂ 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 H₂O→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 Ta₃N₅(110) surface [55]. Compared to direct CO₂ 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 CO₂ + H₂O on the (001), (010), and (110) surfaces of have been characterized, as shown in Figure 7. The coadsorption energy of CO₂ + H₂O on the different surfaces is calculated as follows:

$$E_{coads}=E_{(C{O}_2+H_{2}O)/surface}-(E_{surface}+E_{C{O}_2}+E_{H_{2}O})$$

(2)

where $E_{(C{O}_2+H_{2}O)/surface}$, $E_{C{O}_2}$, $E_{H_{2}O}$ and $E_{surface}$ are the total energy of the coadsorbed (CO₂+H₂O) surface system, the free CO₂, the free H₂O, and the bare Ta₃N₅ surfaces, respectively. The calculated CO₂ + H₂O coadsorption energies and the geometrical parameters are presented in

Table 4. Coadsorption energies and structural parameters for CO₂ + H₂O on Ta₃N₅(001), (010), and (110) surfaces.

Parameter	Ta3N5(001)	Ta3N5(010)	Ta3N5(110)
Ecoads (eV)	−3.94	−3.68	−2.34
Δq(CO2+H2O) (|e|)	0.40	0.35	0.31
Δq(H2O) (|e|)	0.03	0.03	0.02
d(C−Oa) (Å)	1.305	1.460	1.292
d(C−Ob) (Å)	1.307	1.202	1.292
$\angle$OaCOb (o)	125.6	122.1	125.5
d(C−N) (Å)	1.354	1.378	1.399
d(Oa−Ta) (Å)	2.187	2.045	2.231
d(Ob−Ta) (Å)	2.188	-	2.244
d(Ow−H) (Å)	0.981	1.022	0.978
d(Ow−Ta) (Å)	2.299	2.226	2.315
d( O–H) (Å)	3.619	1.606	3.454

. The coadsorption energy for the CO₂ + H₂O pair on the (001), (010), and (110) Ta₃N₅ 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 CO₂ and H₂O adsorption energies.

Analysis of the differential charge density isosurface contours (Figure 8) shows accumulation of electron density within the C–N and O–Ta bonding regions, indicating chemisorption.

Hydrogen-bonded interactions between the CO₂ and H₂O species are observed at the Ta₃N₅(010) surface, evident by the close interaction of the electron density of the two species. This may favour proton transfer to the CO₂ 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 CO₂ + H₂O system, the reaction energy for the formation of the CO + 2OH⁻ species on the Ta₃N₅(010) surface is calculated to be highly exothermic by 1.11 eV. When the proton is transferred to the unbound O of CO₂, 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 Ta₃N₅(010) surface favours the dissociation CO₂ in the presence of H₂O, and the resulting CO species could be further hydrogenated to form CH₂O and CH₃OH.

Compared to the Ta₃N₅(010) surface, the reaction energy for the proton transfer from H₂O to CO₂ to form COOH and HCOO species is found to be highly endothermic on the Ta₃N₅(001) and Ta₃N₅(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.

3. Summary and Conclusions

This work presents comprehensive first-principles density functional theory analyses of the adsorption and activation of CO₂ in the absence and presence of H₂O on the (001), (010), and (110) surfaces of Ta₃N₅, a photocatalyst able to absorb visible light to initiate photocatalysis. The strength of adsorption and extent of CO₂ activation is found to be influenced by the stability of the different Ta₃N surfaces, where it adsorbs most strongly onto the least stable Ta₃N₅(001) surface and most weakly onto the most stable Ta₃N₅(110) surface. Direct dissociation of CO₂ is suggested to occur on the Ta₃N₅(010) surface owing to the calculated exothermic reaction energy and lower activation energy barrier. In contrast, direct CO₂ dissociation would be hindered on the Ta₃N₅(001) and Ta₃N₅(110) surfaces without surface promoters such as H₂O and H species. Spontaneous water dissociation is predicted occur on the (001), (010), and (110) surfaces, providing the necessary hydrogen source for CO₂ reduction reactions. The strongest attractive interaction between coadsorbed CO₂ and H₂O is predicted on the Ta₃N₅(010) surface, which gave rise to proton transfer to the CO₂ 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 Ta₃N₅(001) and Ta₃N₅(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 + H₂O 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 CO₂ reduction over the Ta₃N₅ catalysts is CO₂→COOH*→CO→CH^*_x→CH₄. The present results demonstrate that Ta₃N₅ can efficiently activate the CO₂ 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 CO₂ conversion reactions over Ta₃N₅ catalyst under visible light will also be important.

4. 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 Ta₃N₅ [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 Ta₃N₅ 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 Ta₃N₅. For accurate determination of the electronic structure of Ta₃N₅, a higher mesh of 9 × 5 × 5 was used.

The (001), (010), and (110) surfaces, which are commonly observed in Ta₃N₅ 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) Ta₃N₅ surfaces were determined according to their relaxed surface energy (${\gamma }_r$), calculated as:

$${\gamma }_r=\frac{E_{slab}^{relaxed}-n{E}_{bulk}}{2A}$$

(3)

where $E_{slab}^{relaxed}$ is the energy of the relaxed slab, $n{E}_{bulk}$ is the energy of an equal number (n) of the bulk Ta₃N₅ atoms, and A is the area of the slab surface. The adsorption energy (E_ads) of CO₂ and H₂O species is determined as follows:

E_ads (M) = E_M+surface – (E_surface + E_M)

(4)

where E_M+surface is the total energy of the relaxed M+Ta₃N₅ systems (M = CO₂ and H₂O), E_surface the total energy of the naked Ta₃N₅ surfaces alone, and E_M the total energy of the isolated adsorbates (CO₂ and H₂O). 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 CO₂ and H₂O molecules on the Ta₃N₅ 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.