Reduction of NO_x on metal-free hydrogenated hexagonal boron nitride

Abstract

Sustainable catalysts are essential for critical industrial and environmental processes. 2D materials have exceptional surface area and unique thermal and electronic properties, making them excellent candidates for catalytic applications. Moreover, 2D materials can be functionalised to create metal-free active sites, which provide sustainable alternatives to transition and precious metals. Among the pollutants emitted by combustion engines, NO_x stands out as one of the most detrimental gases, contributing to environmental pollution and posing risks to human health. We demonstrate that functionalised defects in hexagonal boron nitride (hBN) provide a thermodynamically viable route to removing NO_x by reaction with a hydrogenated boron vacancy (3HV_B). The decomposition of NO₂ proceeds by initially overcoming an activation energy barrier of 1.12 eV to transfer a hydrogen atom from the surface, forming a NO₂H species, followed by the elimination of a water molecule. A thermodynamically favourable product consisting of a surface-bound hydroxyl adjacent to a nitrogen antisite defect (where a nitrogen atom occupies a site typically occupied by a boron atom) forms after overcoming an energy barrier of 1.28 eV. NO can further decompose by overcoming an activation energy barrier of 2.23 eV to form a surface HNO species. A rearrangement of the HNO species takes place with an activation energy of 1.96 eV, followed by the elimination of water. The overall reactions reduce NO_x into defective hBN and H₂O.

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1 Introduction

The high temperatures and pressures experienced during fuel combustion enable the fixation of N₂ and O₂, resulting in NO and NO₂ emissions (referred to as NO_x).¹ NO_x is known to cause ailments such as impaired lung function and irritation of the eyes and throat.^2,3 The environment is adversely affected by NO_x dissolving in rainwater, forming nitric acid (HNO₃), and creating acid rain.⁴ Acid rain has many detrimental effects, including hindering plant growth above and below ground and damaging plant leaves, with food-producing plants most severely affected.^5,6 NO_x pollution can contaminate soils and water bodies, leading to eutrophication and acidification.⁷ Furthermore, NO₂ is the starting point for the photochemical formation of ground-level ozone,^8,9 leading to further detrimental effects on ecosystems and thousands of premature deaths.^10–12 The World Health Organisation Global Air Quality Guidelines specify a NO₂ limit of 10 g m⁻³ as an annual average; however, this limit is often exceeded in major cities such as New York, London, Paris, Delhi and Beijing.¹³

The main emitters of NO_x are vehicles (with diesel engines being exceptionally high emitters),¹⁴ power plants, agricultural and industrial processes.^15,16 Despite technological advances in engine manufacturing and the rapid increase of electric vehicles, fossil fuels still make up a large proportion of the energy market to meet demand.¹⁷ Hence, much research has focused on eliminating the toxic and polluting gases emitted by fossil fuel combustion.¹⁸

Using metal-based heterogeneous catalysts for emission control is widely accepted as an effective way of reducing pollution from NO_x and gas exhaust emissions, with many vehicles equipped with selective catalytic reduction (SCR) systems.^19,20 SCR reduces NO_x into environmentally benign N₂ and H₂O by utilising a catalyst and reducing agent.²¹ Reducing agents include NH₃ and H₂ in NH₃-SCR and H₂-SCR. NH₃-SCR has shown to be an attractive choice for low-temperature reduction; however, challenges include N₂O formation and the need for an additional system to supply and store ammonia in applications.^21,22 Safe storage and distribution of H₂ remain technological challenges which delay the widespread employment of hydrogen use as a fuel.²³ However, recently, there has been significant interest in producing H₂ “on-demand” via water-gas shift reaction post-combustion (CO + H₂O → CO₂ + H₂),²⁴ thus providing a source of H₂ for H₂-SCR. Presently, automotive catalysts dominate the global demand for platinum group metals,²⁵ with platinum and palladium commonly employed for H₂-SCR.²¹ However, platinum and palladium catalysts often exhibit peak activity at temperatures around 200 °C,²¹ whereas catalytic converters in vehicles frequently surpass this threshold with passenger vehicles operating over a wide range of temperatures (280–650 °C).²⁶ Therefore, there is potential to find alternative catalysts that are active at higher temperatures. Perovskites have recently been of interest as a greener alternative for NO_x removal but still rely (although quantitatively less) on metal atoms in their structure.^27,28 Metal-free NH₃-SCR has been investigated using ketone-terminated graphene nanoribbon edges,^29,30 yet metal-free H₂-SCR remains underexplored within a critically significant field.

Hexagonal boron nitride (hBN) consists of sp² hybridised boron and nitrogen atoms forming single-atom thick nanosheets.³¹ These so-called ‘2D’ nanosheets are held together by van der Waals forces and stacked in an ABAB pattern.³² Due to the B–N bond's ionic character, charge localisation³³ hBN is an insulator with a large band gap of 6 eV. Potential applications of hBN include electrical,³⁴ optoelectronic³⁵ and spintronic³⁶ devices. Due to its outstanding antiwear and antifriction properties, hBN is also employed in the automotive industry as a lubricant.³⁷ hBN can be grown by various methods. Bottom-up approaches include chemical vapour deposition (CVD), which uses boron and nitrogen-containing precursors, such as borazine or ammonia borane, to grow epitaxial, single layers of hBN on a metal substrate.³⁸ Alternatively, hBN can be formed by reacting molecules containing boron and nitrogen, such as boric oxide and urea.³⁹ In each case, a single layer of hBN can be produced by subsequent physical or chemical exfoliation.⁴⁰

hBN has high thermal stability,^31,41 a low coefficient of thermal expansion,⁴² and a high specific surface area;⁴³ these properties make hBN ideally suited for industrial catalysis. Through high-resolution transmission electron microscopy, hBN has been found to contain various vacancy defects, including boron (V_B) and nitrogen (V_N) single-atom vacancies.^44,45 Ball milling has been established as an effective method for creating additional defect sites on hBN.^46,47 Using V_N as an active site to remove NO₂ has already been the subject of previous density functional theory (DFT) studies.^48,49 In these earlier studies, the V_N defect was repaired, and molecular oxygen was produced. Pd and Ni-doped hBN have also been considered to catalyse NO reduction by CO to form N₂ and CO₂.⁵⁰ Other dopants such as carbon,⁵¹ silicon,⁵² and rhodium⁵³ doped hBN have also been investigated for the fabrication of sensors for NO₂.

Research on hBN defects has shown the hydrogenated V_B (HV_B) to be significantly more stable than the hydrogenated V_N defect and the non-hydrogenated counterpart V_B supported by X-ray absorption and luminescence measurements.^54,55 We have previously reported that HV_B vacancies can be effectively produced by exposing boron–nitrogen divacancies to ammonia.⁵⁶ Furthermore, as hydrogen atoms are ordinarily contained in hBN precursors, HV_B defects are likely to be generated during hBN processing, such as during the growth of hBN nanowalls.⁵⁷

Previous work by Nash et al.⁵⁸ investigated HV_B defects as active sites for the hydrogenation of alkenes on metal-free hBN. The authors reported a reactor based on a pebble mill to introduce HV_B defects by mechanical force. The hydrogenation reaction was achieved with high yields of 97–100% for several alkenes. The work was supported by DFT calculations, which determined a barrier for the hydrogenation of propane to propane of 1.53 eV. Given the activity of HV_B defects in the hydrogenation of alkenes, other similar reactions may be possible.

A deep understanding of the molecular level mechanisms is required to develop more efficient and greener NO_x catalysts. This study investigates the reactivity of the HV_B with NO and NO₂ molecules. Our computational study shows that HV_B defects in hBN can provide an excellent metal-free site for removing NO_x by providing a stable source of hydrogen for reduction.

2 Computational methodology

First-principles electronic structure calculations were carried out using CASTEP.⁵⁹ The PBE functional⁶⁰ was used to treat exchange and correlation in combination with the Tkatchenko–Scheffler dispersion correction method.⁶¹ The plane wave basis set was expanded to a cut-off energy of 400 eV. All calculations used Vanderbilt ultrasoft pseudopotentials⁶² and a Monkhorst–Pack k-point sampling of the first Brillouin zone⁶³ with a uniform grid of (10 × 10 × 1) or (4 × 4 × 1) for modelling of (1 × 1) and (5 × 5) unit cells, respectively. The surface structures were optimised until the maximum force on each atom was less than 0.025 eV Å⁻¹ and a self-consistent field energy tolerance of 1 × 10⁻⁶ eV. During relaxation, the lattice parameters remained fixed to those of a pristine hBN unit cell. The transition states along the reaction pathways were identified with the linear and quadratic synchronous transit (LST/QST) algorithm,⁶⁴ with a force tolerance of 0.1 eV Å⁻¹. A (5 × 5) unit cell was employed for all defect calculations, with a vacuum region of at least 20 Å to separate the periodically repeated images and avoid spurious interactions. Molecular diagrams were produced using VESTA.⁶⁵

Adsorption energies E_Ads were calculated using the standard formula:

E_Ads = E_AB − E_A − E_B (1)

where E_AB is the energy of the adsorbed species, E_A and E_B are the energy of the dissociated species.

Formation energies E_f were calculated using the formula:

where E_V is the energy of a vacancy or system, E_hBN is the energy of the pristine hBN sheet, n_N and n_B are the number of nitrogen and boron atoms removed to create a vacancy, respectively. E_N2 is the energy of an isolated N₂ molecule, E_B is the reference energy of a boron atom in its α-rhombohedral phase,⁶⁶n_H is the number of hydrogen atoms added to hydrogenated vacancies and E_H2 is the energy of an isolated H₂ molecule.

Reaction rate coefficients (K_TST) for the surface reactions were calculated according to the transition state theory:

where k_b is the Boltzmann constant, T is the temperature, h is the Plank constant, q^‡ and q are the partition functions for the transition state and initial state, respectively, and ΔE_a is the activation energy. The adsorption rate coefficients k_ads were calculated using Hertz–Knudsen kinetics:⁶⁷where P is the partial pressure of the molecule, A is the surface area of the surface site, m is the mass of the particle k_b is the Boltzmann constant and T is the temperature.

3 Results and discussion

Each of the vacancy models can be seen in Fig. 1. The structure and properties of V_B and V_N vacancies have been discussed in detail in previous work and are shown in b and c.⁵⁶ V_N is more stable than V_B with E_f of 8.63 eV and 9.75 eV, respectively. V_B has C_2v symmetry, whereas V_N has D_3h symmetry due to Jahn–Teller distortion.^68–71Fig. 1d shows an HV_B with all three nitrogen dangling bonds saturated by hydrogen atoms (3HV_B); it is by far the most stable configuration investigated, with a low E_f of 1.98 eV. The geometry of 3HV_B can be rationalised through a combination of electronic and steric factors. Comparing the N–H–N angle (θ) variation between vacancies, we can rationalise the increase in in-plane steric hindrance as a function of the increasing number of adsorbed hydrogens. In 3HV_B, only one of the three hydrogen atoms points into the hBN plane with a θ of 180° and Hirshfeld charge of +0.07 e. The remaining two hydrogens point above and below the hBN plane where θ is 130° with a Hirshfeld charge of +0.11 e. This difference in angle can be explained by the need to prevent steric clashes of hydrogen atoms and minimise partial positive charges yet maintain sp² hybridisation of the hBN as much as possible. The H–H distance is 2.49 Å between the outer hydrogens and 1.58 Å between the in-plane hydrogen and each external hydrogen, with an average H–H distance of 1.88 Å. The in-plane nitrogen has a 0.08 e higher N–H bond population than the average N–H bond, reflecting a greater extent of sp² hybridisation and stronger bonding. The minor change in bond population results in the N–H in-plane bond being shorter by 0.008 Å (0.8%) than the out-of-plane N–H bonds. This minor change in bond length is unlikely to affect the reactivity of 3HV_B significantly.

Fig. 1 (a) Pristine hBN sheet, (b) V_B (E_f = 9.75 eV, spin = 1 μ_B) (c) V_N (E_f = 8.63 eV, spin = 1 μ_B), (d) 3HV_B (E_f = 1.98 eV, spin = 0 μ_B), (e) 2HV_B (E_f = 4.22 eV, spin = 1 μ_B), (f) 1HV_B (E_f = 6.82 eV, spin = 0 μ_B), (g) 3HV_N (E_f = 5.29 eV, spin = 0 μ_B), (h) 2HV_N (E_f = 6.86 eV, spin = 1 μ_B), (i) 1HV_N (E_f = 6.93 eV, spin = 0 μ_B). Boron atoms are shown in green, and nitrogen atoms are shown in grey.

Removing a hydrogen atom to create a 2HV_B increases E_f to 4.22 eV. In 2HV_B, the hydrogen atoms are further coplanar with hBN, with an average θ of 155°, and have an H–H distance of 1.83 Å. The loss of a hydrogen atom allows the remaining hydrogens to be orientated more in the plane as there is now less steric hindrance inside the vacancy, allowing for θ values closer to 180°. In 2HV_B, the N–H distances are 2.01 Å and 2.16 Å; therefore, one hydrogen atom is slightly closer to the nitrogen atom in this structure. The hydrogens interact with the lone pair on the nitrogen dangling bond asymmetrically, thus reducing the N–H distance for the interacting H. 2HV_B has a magnetic moment of 1 μ_B due to an unpaired electron on the nitrogen dangling bond. These changes in the geometry of 2HV_B are not enough to compensate for creating a dangling bond, decreasing the stability of this defect relative to that of 3HV_B.

The 1HV_B has a higher E_f of 6.82 eV due to the creation of an additional nitrogen-dangling bond. Here, only one hydrogen atom remains on the vacancy; the reduced steric clashes allow for an θ of 157°. It follows that the remaining hydrogen is positioned only slightly above the hBN plane with H–N distances of 1.98 Å and 2.02 Å. Removal of the final hydrogen will form a V_B with an E_f of 9.75 eV. It is clear that the stability of HV_B increases with an increasing number of hydrogen atoms; hence, 3HV_B is the most likely to form and will be the subject of our investigation for the hydrogenation of NO₂.

In addition to 1–3HV_B, we also investigated the structure and geometry of hydrogenated V_N vacancies (1–3HV_N) for comparison and are shown in Fig. 1(g–i). The configurations obtained by DFT are in good agreement with the work presented in Surya et al.⁷² with a detailed comparison provided in the ESI.† Of these vacancies, 3HV_N has the lowest E_f of 5.29 eV, significantly higher than that of 3HV_B (E_f 1.98 eV). The greater decrease in formation energy of boron vacancies compared to nitrogen vacancies upon the addition of hydrogen atoms can be rationalised by considering the electronegativity and geometry of the atoms around the vacancy. As N is more electronegative than B, the N–H bonding is stronger than that of B–H, with average bond lengths of 1.10 Å and 1.19 Å for 3HV_B and 3HV_N. Furthermore, longer B–H bonds lead to an increased steric clash of hydrogen atoms, requiring greater deformation of the vacancy site. Therefore, 3HV_B vacancies maintain stronger N–B bonding than 3HV_N with average B–N bond lengths of H-connected atoms of 1.42 Å and 1.44 Å, respectively. Given the stability observed in the 3HV_B vacancy and the likelihood of the formation of hydrogenated V_B vacancies compared to hydrogenated V_N, we have elected to focus our investigation primarily on this site.

3.1 NO₂ decomposition

The adsorption of NO₂ on pristine hBN was initially considered. A range of sites and orientations were investigated (as described in the ESI†), with the most stable adsorption site pictured in Fig. 2. Here, NO₂ is adsorbed with the nitrogen atom at a height of 3.32 Å above hBN with the O–N–O plane almost parallel to the hBN plane. In this position, NO₂ has an E_Ads of −0.202 eV, indicative of physisorption. Previous works have also investigated the adsorption of NO₂ on hBN and have found the orientation with oxygen atoms pointing upwards, away from the surface, to be the preferred orientation,⁵² with one study providing an E_Ads of −0.09 eV.⁴⁹ However, these studies used generalised gradient approximation exchange–correlation functionals without dispersion corrections, thus underestimating dispersion forces and the adsorption energy of physisorption. In our study, initiating geometry optimisation with the oxygen atoms pointing away from the surface leads to a rotation of the NO₂ molecule, resulting in a parallel orientation. The particular stability of NO₂ parallel to the plane can be rationalised by considering that the dispersion interaction between the hBN and NO₂ is maximised by increasing the contact area between the adsorbate and the substrate. The boron atoms of hBN and NO₂ oxygen atoms have average Hirshfeld charges of 0.21 e and −0.07 e, respectively; these charges attract stabilising the adsorbed NO₂.

Fig. 2 Adsorption site and orientation of NO₂ on hBN. The oxygen atoms are angled slightly towards the hBN plane at a height of 3.219 Å. The nitrogen is situated at a height of 3.324 Å. This adsorption position maximises attractive dispersion forces between hBN and NO₂ with an E_Ads of −0.202 eV.

The step-wise mechanism for the reaction of NO₂ with 3HV_B was then considered by exploring multiple possible reaction pathways to ensure the minimum energy path was found (as described in the ESI†). The reaction mechanism, starting from the adsorption of NO₂ above 3HV_B and ending with the creation of a nitrogen antisite defect (N_B) and H₂O, can be seen in Fig. 3 with the overall equation NO₂ + 3HV_B ⇌ N_B + H₂O + OH. This reaction pathway, TS1–9, consists of nine elementary steps that connect reactants, intermediates, and products through transition states. Fig. S5 of the ESI† displays each structure along the reaction path from both perpendicular and parallel orientations. The highest transition state barrier in TS1–9 is 1.28 eV (TS7), and the ΔE of the reaction is −0.99 eV, indicating that this reaction is possible at moderate temperatures and is thermodynamically favourable. We will examine each of these steps in turn.

Fig. 3 The reaction pathway of NO₂ with a 3HV_B to N_B and H₂O. The product of the reaction, a nitrogen antisite adjacent to a boron site with a hydroxyl group, is used as the reference energy. Transition states are identified by ‡ and labelled TS1–9. The highest energy barrier, TS7, reflects the movement of a hydrogen atom through the hBN plane in preparation for making an N_B site. Other steps occur with energy barriers between 0.04 and 1.09 eV. The reaction is thermodynamically favourable with a ΔE of −0.99 eV.

Firstly, a range of NO₂ adsorption sites on 3HV_B and orientations were examined (Fig. S2 of the ESI†). The adsorption energy minimum can be seen in Fig. 4a with an E_Ads of −0.247 eV, compared to −0.202 eV for physisorption on pristine hBN. Here, NO₂ is oriented to bring one of the oxygen atoms close to the surface at a height of 2.93 Å (Fig. 4a). Hydrogen bonding between the oxygen lone pair and the hydrogen pointing above the hBN plane stabilises this orientation with an O–H distance of 2.28 Å, reducing its adsorption energy relative to pristine hBN. Prior to the reaction, the adsorbed NO₂ diffuses to a position where an oxygen atom is directly above a hydrogen atom of 3HV_B after overcoming a low energy barrier of 0.11 eV (TS1).

Fig. 4 (a) Adsorption geometry of NO₂ over a 3HV_B with an E_Ads of −0.25 eV. (b) NO₂ adsorbed over a 3HV_B prior to reaction with an E_Ads of −0.16 eV. NO₂ can migrate from (a) to (b) by overcoming a low energy barrier of 0.11 eV. (c) NO₂H adsorbed over 2HV_B with an E_Ads of −0.38 eV. The barrier to transferring a hydrogen atom from (b) to (c) is 1.12 eV.

Next, hydrogen transfer from 3HV_B to NO₂ was considered to create a NO₂H species in a NO₂ + 3HV_B ⇌ NO₂H reaction step. A range of orientations was assessed to find the most stable NO₂H conformation. The most stable position of NO₂H is close to the vacancy, with an O–H bond directly above the nitrogen dangling bond and with the second oxygen atom above a surface boron atom. Structural relaxations of other geometries either resulted in the formation of 3HV_B or produced a higher energy NO₂H orientation. As with NO₂ adsorption on pristine hBN, the NO₂H is stabilised by van der Waals interactions between the oxygen lone pair and surface boron (Fig. 4b). The N–H bond-breaking step requires an activation energy of 1.02 eV (TS2). The products of this step are a 2HV_B and a NO₂H species. Hydrogen bonding between the NO₂H hydrogen moiety and the uncoordinated surface nitrogen gives NO₂H an E_Ads of −0.28 eV.

The NO₂H species can easily rotate parallel to the hBN plane. The NO₂H rotation proceeds via an initial step with a low activation barrier of only 0.15 eV to bring the oxygen atoms parallel to the plane (TS3), as shown in Fig. 5b. This barrier reflects the breaking of van der Waals forces between the surface and NO₂H. A second rotation occurs with a more significant energy barrier of 0.72 eV (TS4). This higher barrier reflects the need to overcome the repulsive forces of the nitrogen lone pairs and form an N–N bond between NO₂H and the surface nitrogen dangling bond. NO₂H is now chemisorbed onto the surface, as shown in Fig. 5c. Here, the surface nitrogen is puckered 0.5 Å above the plane, and the N–N bonded nitrogen atoms have sp³ hybridised character. Subsequently, after forming a NO₂H species, the hydroxyl can accept another hydrogen atom to produce water (TS5, NO₂H + H ⇌ NO + H₂O) after overcoming an energy barrier of 0.96 eV. The produced water molecule is hydrogen bonded to the surface. Adsorbed water could remain on the surface and contribute to stabilising further structures and transition states through hydrogen bonding; therefore, it continues to feature in our simulations.

Fig. 5 (a) Adsorption site of NO₂H over 2HV_B with an E_Ads of −0.38 eV. (b) NO₂H adsorbed over 2HV_B before reaction to form a chemisorbed NO₂H species (c). The rotation barrier from (a) to (b) is 0.15 eV. The transition from (b) to (c) has a barrier of 0.72 eV. Charge accumulation is shown in blue, and charge depletion in red with respect to an isolated NO₂H (isosurface cut-off in (a) and (b) is 0.01 e Å⁻³). (a) Shows a much greater change in charge densities due to the stronger van der Waals interactions with the surface. NO₂H decomposes to produce H₂O after overcoming a reaction barrier of 0.96 eV to change from (c) to (d).

Following the formation of a water molecule (TS5), the surface structure now contains an O=N–N moiety, a nitrogen dangling bond in the vacancy, and an N–H group. Bonding of the O=N nitrogen to the nitrogen dangling bond can substantially lower the total energy of the surface. This step occurs after overcoming a low barrier of 0.04 eV (TS6) and forms a nitrogen antisite defect (N_B), where the nitrogen atom occupies the site usually occupied by boron in hBN. The N_B nitrogen atom is bound to both the nitrogen atoms of the vacancy and the oxygen atom above, as seen in Fig. 6a. Further surface rearrangement takes place to bring the sub-layer hydrogen through the vacancy before positioning itself above the plane 1.87 Å away from the surface oxygen. This rearrangement occurs with an energy barrier of 1.28 eV (TS7) due to steric hindrance destabilising the transition state as the hydrogen needs to pass through an in-plane position (Fig. 6b), and the subsequent geometry has moved the N–O bond into a sp³-like orientation. These steric factors cause TS7 to proceed with the highest barrier in the decomposition of NO₂.

Fig. 6 (a) N_B with additional oxygen and hydrogen atoms positioned above and below the hBN plane, respectively (b) transition state to bring the hydrogen atom from below to an above plane position with a barrier of 1.28 eV (TS7). (c) N_B with additional oxygen and hydrogen atoms both positioned above the plane.

Surface hydrogen and oxygen atoms can now form a surface hydroxyl group bound to the antisite nitrogen (N_B) after overcoming an energy barrier of 0.82 eV, as shown in TS8, reflecting the breaking of an N–H bond and the forming of an H–O bond (RN–H + N_BO ⇌ RN + N_BO–H). Given the electron density accumulation provided by the four nitrogen atoms and the oxygen around the N_B, it is thermodynamically favourable for the hydroxyl species to migrate to an adjacent boron atom as it has a lower electron density, as shown in Fig. 7. The migration through TS9 (with an energy barrier of 0.33 eV) minimises the electron repulsion and satisfies the remaining nitrogen dangling bond, reducing the overall energy of the product.

Fig. 7 Electron density slice contour map from 0 to 3 e Å⁻³ of (a) N_B with attached hydroxyl functional group and (b) N_B adjacent to a surface boron site with a hydroxyl group attached. The barrier to transition from (a) to (b) is 0.33 eV (TS9) in an exothermic process with a reaction enthalpy of −2.73 eV. Note: the water molecule is in the plane of the slice in (b) but not in (a). In (b), the electron density surrounding the N_B site repels that of the adsorbed oxygen. Therefore, the hydroxyl migrates to an adjacent boron site (a), lowering electron–electron repulsion and producing a more thermodynamically stable product.

The overall reaction forms a water molecule and a surface-bound hydroxyl adjacent to a nitrogen antisite defect (NO₂ + 3HV_B ⇌ N_B + H₂O + OH). This reaction is thermodynamically favourable to form with a ΔE of −0.98 eV. The highest energy barrier for a single step in the overall NO₂ reduction mechanism is 1.28 eV. The barrier for the reaction of NO₂ with HV_B is comparable to that of NO₂ with V_N as explored in work by Feng et al.⁴⁹ where NO₂ decomposes to form O₂ and the ‘healing’ of V_N to form a pristine hBN sheet with a barrier of 1.17 eV. We note that this paper did not include dispersion correction in the DFT calculations, therefore likely underestimating the energy of adsorption. Given the low formation energy of the initial 3HV_B defect, the relatively low energy barrier of the rate-determining step and the production of a thermodynamically favourable product, the catalytic reduction of NO₂ over hydrogenated hBN defects appears to be a promising way of controlling NO₂ emissions from combustion engines.

If an additional hydrogen atom is added, further steps could be taken to produce a second water molecule, as shown in Fig. 8. The hydroxyl group can then be hydrogenated to form a second water molecule (OH + ½H₂ ⇌ H₂O) after overcoming an energy barrier of 0.36 eV (TS10). This step is exothermic with an overall ΔE of −1.30 eV. The thermodynamic stability is due to the creation of a second water molecule, the return to sp² binding of the surface boron atom and the original water molecule being able to adsorb strongly on top of the N_B site. An isolated N_B has an E_f of 5.45 eV, higher than that of a 2HV_B vacancy with an E_f of 4.22 eV. The overall product of the reaction NO₂ + 3HV_B + H ⇌ N_B + 2H₂O between NO₂ and a 3HV_B, in the presence of hydrogen atoms, is an N_B and two water molecules. Once exhausted, new vacancy defects need to be introduced to regenerate active sites. The difference in E_f between N_B and 3HV_B is 3.47 eV, thus requiring an input of energy to regenerate the active site. The introduction of such sites can be achieved by mechanical methods such as ball milling,^46,47 and has been achieved in work by Nash et al.⁵⁸ to complete a catalytic cycle.

Fig. 8 Reaction step of the hydroxyl group on a surface-born atom adjacent to a N_B site with an adsorbed hydrogen atom. Transition states are identified by ‡ labelled TS10. An energy barrier of 0.36 eV facilitates the hydrogenation of the hydroxyl group to create a water molecule as the product. This step is thermodynamically favourable with a ΔE of −1.30 eV.

The overall reaction of NO₂ to N_B and two water molecules is thermodynamically feasible, yet many activated steps are involved. Therefore, a microkinetic model consisting of 10 elementary steps was constructed to evaluate the reaction's kinetic viability. The consumption of NO₂ and production of H₂O at different temperatures, and a pressure of 10 bar was chosen to align with the optimal conditions for the water-gas shift reaction²⁴ (further details of the microkinetic model are reported in the ESI†). The rate of NO₂ consumption compared to the rate of H₂O formation was calculated with results shown in Fig. 9. Below 800 K, the rate of NO₂ consumption remains very low (<1.10 × 10⁻⁶ s⁻¹); increasing the temperature, the rate of H₂O production rises to a maximum of 7.48 × 10⁻⁵ s⁻¹ at 990 K, accompanied by a NO₂ consumption rate of 3.68 × 10⁻⁵ s⁻¹. As temperatures rise, the energy of the molecules increases, allowing multiple reaction barriers to be overcome. Beyond the optimal temperature, the reactants cease to adsorb onto the surface and persist in the gas phase. Our results show that NO₂ decomposition can occur at 3HV_B defect sites in hBN via a Langmuir–Hinshelwood mechanism.

Fig. 9 Microkinetic simulations for the reaction of NO₂ and 3HV_B displaying the consumption of NO₂ compared to the production of H₂O as a function of temperature.

3.2 NO decomposition

NO pollution shares many of the same detrimental effects as NO₂ pollution leading to acid rain; hence, these two species and their effects are often combined in NO_x. Moreover, NO oxidised to NO₂ by reacting with sources of O.⁷³ We included the reaction of NO in the scope of our work to explore any possible reactions with 3HV_B. Adsorption of NO was first considered above pristine hBN. The most favourable adsorption site is pictured in Fig. 10 and adsorbs with an E_Ads of −0.17 eV, similar to NO₂.

Fig. 10 Adsorption site and orientation of NO on hBN. The nitrogen atom is angled slightly towards the hBN plane at a height of 3.07 Å. The oxygen atom is situated in the centre of a hBN ring. This adsorption position maximises attractive dispersion forces between hBN and NO₂ with an E_Ads of −0.17 eV.

NO adsorption on 3HV_B was considered by starting with the most stable orientation pictured in Fig. 11 with an E_Ads of −0.240 eV at a height of 3.041 Å, similar to NO₂. Multiple reaction routes were then analysed; here, the reaction begins with the direct reaction of NO with 3HV_B to form a chemisorbed HNO species after overcoming a high energy barrier of 2.23 eV (TS11, NO + 3HV_B ⇌ HNO + 2HV_B). The size of this barrier reflects the breaking of the N–H bond and stretching of the N–O bond to accommodate the additional coordination of the nitrogen atom, partially stabilised by the nitrogen lone pair orientated towards the surface hydrogen. This step has the highest barrier for the reaction of NO with 3HV_B. Hydrogen transfer to produce a hydroxyl group occurs with another high energy barrier of 1.96 eV (TS12). Following the creation of a hydroxyl group, the NOH intermediate can accept an N–H hydrogen atom in TS13 (ΔE of 1.63 eV) to form a chemisorbed HNOH species and a dangling bond over the nitrogen atom. The reaction's final step (TS14) involves the migration of the nitrogen atom to bind with the nitrogen dangling bond of the vacancy to create an N_B site with a remaining hydrogen attached (HN_B). Simultaneously, the hydroxyl group accepts a hydrogen atom to form a water molecule. The overall reaction NO + 3HV_B ⇌ H₂O + HN_B is slightly exothermic with a ΔE of −0.09 eV. The surface product of the reaction (HN_B) has an E_f of 5.42 eV.

Fig. 11 The reaction pathway of NO with a 3HV_B to N_B and H₂O. The product of the reaction, a molecule of water and an N_B site with the final surface hydrogen remaining, is used as a reference energy. Transition states are identified by ‡ and labelled TS11–14. The highest energy barrier at TS1 (2.23 eV) reflects the energy to break an N–H bond and lengthen the N–O bond simultaneously. The reaction is thermodynamically favourable with a ΔE of −0.09 eV.

The reaction pathway of NO with 3HV_B significantly differs from that of NO₂. For NO reduction, the hydrogen transfer to create a chemisorbed HNO_x species occurs with a much higher energy barrier than NO₂, with activation energies of 2.23 eV and 1.28 eV, respectively, for this step. The weaker N–O bonds in NO₂ with O=N–O and O–N=O resonance structures result in greater electron density on the oxygen atoms, making an O=N–O–H species possible. Thus, NO₂ can accept a hydrogen atom from 3HV_B to form a physisorbed NO₂H species before chemisorption. In contrast, NO has a stronger N–O bond with less electron density available to accept a hydrogen atom on the O or N atoms. Therefore, hydrogen transfers and chemisorption occur in a single step with a higher energy barrier, with O–H and N–N bonds forming simultaneously. The barriers relating to NO decomposition on 3HV_B are significantly higher than those revealed in work by Xiao et al.⁴⁸ where the reaction of NO with a V_N results in the formation of a B–O–N epoxy structure. The reaction of 3HV_B with NO is less exothermic with a ΔE of −0.09 compared to NO₂ with a ΔE of −0.98 eV. Here, the product of the reaction is an N_B site with an additional N–H bond pointing hydrogen below the hBN monolayer.

Our results show that NO₂ decomposition is energetically facile at 3HV_B defect sites in hBN with a barrier of 1.28 eV and achieves optimum NO₂ consumption at 990 K. The decomposition product is H₂O, an N_B site adjacent to a surface hydroxyl species. This hydroxyl species can then be hydrogenated to yield a second water molecule. Similarly, NO can be decomposed by NO with a limiting step of 2.23 eV to create an N_B and a vacancy hydrogen.

4 Conclusions

In conclusion, we have investigated the reaction of NO_x with a 3HV_B site in a “free-standing” hBN mono-layer using DFT calculations. NO₂ decomposition proceeds via Langmuir–Hinshelwood hydrogenation of NO₂ to form a NO₂H species before the chemisorption of this intermediate on the hBN vacancy. The reaction follows several further steps that end with eliminating a molecule of water, forming an N_B site adjacent to a surface-bound hydroxyl. An additional hydrogen atom diffusing from other sites can react with the hydroxyl and yield a second water molecule. The atomistic details of the NO₂ reduction mechanism, encompassing ten elementary steps, have been described in section 3, focusing on linking reaction energy and barriers to steric and electronic effects. Our calculations prove that the decomposition of NO₂ over hydrogenated hBN vacancies is a feasible approach to removing NO₂. The rate-determining step has an energy barrier of 1.28 eV. Using micro-kinetics to evaluate the reaction path as a whole, we have calculated an optimum temperature of 990 K under a pressure of 10 bar with a very low rate of reaction below 800 K. The NO decomposition proceeds via the formation of a surface HNO species before rearrangement and elimination of a water molecule before forming an N_B. The NO reaction mechanism progresses through four steps (discussed in section 3.2). The decomposition of NO to N_B + H₂ has an energy barrier of 2.32 eV and is slightly exothermic (0.09 eV). Therefore, higher temperatures are required to achieve NO reduction. These reactions transform harmful and polluting NO₂ into benign H₂O using a selective and metal-free catalyst. This paper has thoroughly investigated the complete removal of NO_x 3HV_B defects in hBN, demonstrating its potential to be developed as an effective metal-free catalyst for deNO_x applications.

Data availability

The datasets generated and/or analysed during the current study are available in the University of Surry research repository: https://doi.org/10.15126/surreydata.901080.

Author contributions

A. P. conceived the presented idea, performed the DFT simulations, and wrote the manuscript under M. S.' guidance. N. X. provided expertise in simulations and kinetic calculations.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

A. P. acknowledges the University of Surrey for access to the Eureka High Performance Computing facility and funding in the form of a PhD studentship. MS acknowledge the Royal Society for personal funding through a Royal Society University Research Fellowship URF\R\191029. This work used ARCHER2, the UK's national high-performance computing service, via the UK's HPC Materials Chemistry Consortium, which is funded by EPSRC (EP/R029431 and EP/X035859).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4cy00206g

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