# Effect of the water coverage on the interaction of O_2 and H_2 with the Na-LTA zeolite by first-principles simulations

Joharimanitra Randrianandraina, Michael Badawi, Christophe Ramseyer, Bruno Cardey, Jean-Emmanuel Groetz, Noah Perreau, Freddy Torrealba-Anzola, Caroline Chambelland, Didier Ducret, Manuel Grivet

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Joharimanitra Randrianandraina, Michael Badawi, Christophe Ramseyer, Bruno Cardey, Jean-Emmanuel Groetz, et al.. Effect of the water coverage on the interaction of O_2 and H_2 with the Na-LTA zeolite by first-principles simulations. Inorganic Chemistry Frontiers, 2023, 10 (2), pp.383-395. 10.1039/d2qi01280d. hal-04226791

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Cite this: Inorg. Chem. Front., 2023, **10**, 383

# Effect of the water coverage on the interaction of O₂ and H₂ with the Na-LTA zeolite by first-principles simulations

Joharimanitra Randrianandraina, <sup>id a</sup> Michael Badawi, <sup>id *b</sup> Christophe Ramseyer, <sup>id a</sup> Bruno Cardey, <sup>id a</sup> Jean-Emmanuel Groetz, <sup>a</sup> Noah Perreau, <sup>a</sup> Freddy Torrealba-Anzola, <sup>a</sup> Caroline Chambelland, <sup>c</sup> Didier Ducret <sup>c</sup> and Manuel Grivet <sup>id *a</sup>

The very wide applications of LTA zeolites, e.g. tritiated water storage, imply that a precise atomic-scale description of the adsorption processes taking place in their structure is crucial. The zeolite structure seems to have a catalytic effect on the O₂/H₂ recombination during the storage process after water radiolysis. To look closely at the conditions that could bring O₂ and H₂ to this particular point, we have conducted investigations using static DFT and systematic *ab initio* molecular dynamics calculations. We have investigated the interaction of these two molecules with the sodium cations, on which the adsorption capacity of the Na-LTA zeolite depends. The O₂ and H₂ molecules' behaviour inside the cavities is linked to the Na⁺ position and availability. The latter is regulated by the presence of H₂O which interacts with Na⁺ in a stronger way than O₂ and H₂. Thus, the adsorption studies of different mixtures (O₂/H₂O, H₂/H₂O and H₂/O₂) have been carried out to characterise the competition between water and other guest molecules. The absence of an obvious interaction between the adsorbates strongly suggests a potential reaction path involving the catalytic effect of the zeolite. Since we have been able to show that the behaviour of O₂ and H₂ molecules is directly affected by the water coverage rate, the reaction path is very likely to be affected too. These results mark a step towards the description of a recombination mechanism between O₂ and H₂ in a zeolite structure, a crucial issue for such systems involving tritiated water adsorbed in nanoporous materials.

Received 16th June 2022,
Accepted 2nd November 2022

DOI: 10.1039/d2qi01280d

rsc.li/frontiers-inorganic

## 1. Introduction

With the development of projects requiring the use of tritium such as ITER, the treatment of tritiated waste will be a major environmental issue in the future. This waste can be found in the form of tritiated water adsorbed in nanoporous materials such as zeolites, during which a water radiolysis phenomenon occurs where oxygen and hydrogen are the main gas products. Experimental studies carried out by L. Frances *et al.*¹,² showed a progressive decrease of these products from the resulting gaseous formation through time until their total disappearance. Although the water radiolysis reaction is enhanced by the catalytic effect of the zeolite into which it is contained,

L. Frances *et al.* presumed that the aluminosilicate structure also contributes to the recombination of O₂ and H₂ back to H₂O, with which is associated the gaseous quantity decrease. The period in which these decays occur depends on the loading rate of water present in the zeolite: the higher the loading rate, the later they start. The strong affinity between the water molecules and the Na⁺ cations of the Na-LTA zeolite, as observed in our previous study,³ leads us to link this time lag to the hindrance to the access of O₂ and H₂ molecules to the cationic sites by H₂O. Therefore, the zeolite contributes to the catalysis of the recombination reaction of the two molecules through the Na⁺ cations. This implies that the dihydrogen and dioxygen molecules must interact with the zeolite, i.e., the cations, for the recombination reaction to start.

The role of the adsorbent surface as a catalyst has already been studied on other surfaces than zeolites, mostly metallic.⁴⁻⁸ G. J. K. Acres⁹ observed the inhibitory effect (as a decrease of the reaction rate) of water on H₂/O₂ recombination on a platinum surface. As the surface catalyses the dissociation of dihydrogen and dioxygen molecules, its coating by water prevents both from interacting with the surface. Acres thus

<figure><img src="image_5.png" /></figure>

<footnote><sup>a</sup>Laboratoire Chrono-Environnement, UMR 6249, Université de Bourgogne
Franche-Comté, F-25000, Besançon, France. E-mail: manuel.grivet@univ-fcomte.fr;
Tel: +33 3 81 66 65 16</footnote>

<footnote><sup>b</sup>Laboratoire de Physique et Chimie Théoriques, UMR 7019, CNRS, Université de Lorraine, F-54000 Nancy, France. E-mail: michael.badawi@univ-lorraine.fr;
Tel: +33 3 72 74 98 67</footnote>

<footnote><sup>c</sup>CEA, Centre d'études de Valduc, F-21120 Is-sur-Tille, France</footnote>
<figure><img src="image_6.png" /></figure>

showed the necessity for the molecules to be in contact with the adsorbing surface in order to be activated, in good agreement with the observations from the experimental works by L. Frances et al.¹ concerning the delaying effect of water on the decrease of the amounts of O₂ and H₂ molecules in zeolites. L. Morales,¹⁰ who studied the recombination on a plutonium dioxide surface, emphasizes the important role of a catalyst that the surface plays in the reaction and minimizes that of the radicals formed during radiolysis. Lloyd and Eller¹¹ define this catalytic role of the surface as being a platform on which the O₂ and H₂ molecules dissociate before recombining. Like Acres,⁹ Morales also noted that the presence of water on the surface reduces the rate of the reaction because its strong affinity limits the access of O₂ to the surface. The adsorption studies of H₂O, O₂ and H₂ in zeolites showed that the order of the adsorption affinity of the molecules in zeolites is as follows: H₂O ≫ O₂ > H₂¹²⁻¹⁸ as represented in Fig. 1. The affinity of O₂ for zeolites is thus more important than that of H₂. In addition to the presence of H₂O, this difference also affects the rate of the reaction between O₂ and H₂ as shown by G. J. K. Acres,⁹ who observed a faster rate of reaction when O₂ is the case of H₂. A strong interaction of the molecule, whether O₂ or H₂, with the surface thus accelerates its activation to dissociation followed by recombination. Numerous studies of O₂ and H₂ molecules' dissociation in zeolites¹⁹⁻²¹ highlighted the contribution of cations on their activation. These play a significant part in the catalysis by zeolites, especially by controlling the interaction between adsorbates and adsorbents. These observations lead us to assume that a possible path to recombination between the two adsorbed molecules is through their dissociation via the adsorbent surface, where water plays a disruptive role.

To our knowledge, no study has yet been carried out to describe the O₂/H₂ competition, let alone their recombination

mechanism in zeolites with Na⁺ cations, neither numerically nor experimentally. Yet, the different works cited above show the interest of understanding such competition governed by H₂O in an accessible and no less efficient porous material such as a zeolite. Given the stronger interaction of O₂ molecules with zeolites compared to that of H₂, we have described the O₂···Na⁺ and H₂···Na⁺ interactions and looked carefully at the influence of the occupancy rate of Na⁺ sites by H₂O since there is probably a competition between the stable products of radiolysis and the water molecules. The recombination mechanism of the two molecules will not be described in this paper since our study on this topic is still in progress, but we will focus here on the path that leads to this phenomenon through the O₂ and H₂ molecules' adsorption on dehydrated and hydrated Na-LTA zeolites. In particular, we demonstrate the important role played by the Na⁺ cation in the activation of O₂ and H₂ and assess how the water loading rate in the zeolite affects its catalytic efficiency. For this purpose, numerical methods like static and dynamic DFT have been used to provide a detailed description of the behavior of these molecules on the adsorption sites of the studied zeolites.

## 2. Materials and methods

### 2.1.Z4A and ZK4 models

Two zeolites from the LTA framework have been used for this work. Since the Z4A unit cell (672 atoms) cannot be reduced due to Lowenstein's rule,²²,²³ the smaller elementary lattice of the ZK4 zeolite was used as a substitute for *ab initio* molecular dynamics (AIMD) calculations.

The optimised unit cell of the dehydrated Z4A framework has the chemical formula Na₉₆Si₉₆Al₉₆O₃₈₄²⁴ with a Si/Al ratio of 1 and the following lattice parameters: *a* = 24.47 Å, *b* = 24.65 Å, *c* = 24.82 Å, *α* = 90.7°, *β* = 89.8° and *γ* = 90.1°. These are very similar to the initial values given by J. J. Pluth *et al*.²⁵ The ZK4 unit cell was created from the optimised Z4A by extracting 1/8th of its lattice, i.e., one sodalite cage. Si and Al distributions have been rearranged to avoid the Al-O-Al sequence according to the model used by Yoshida *et al.*,²⁶ who already used the ZK4 structure to substitute the Z4A unit cell for AIMD calculations. The ZK4 unit cell has the formula Na₉Si₁₅Al₉O₄₈ with a Si/Al ratio of 1.66 and the lattice parameters *a* = 12.35 Å, *b* = 12.28 Å, *c* = 12.19 Å, *α* = 90.3°, *β* = 90.4°, and *γ* = 89.7° after DFT geometry optimisation.

Both Z4A and ZK4 structures have three types of windows (4R, 8R and 8R) that allow the communication between the different cavities (Fig. 2). The 4R window is a pathway allowing access from the *α* and *β* cages to a rectangular prism. The 6R window is a passage between the *α* and *β* cages and the 8R window gives access between two *α* cages.

The Na⁺ cations are located on three cationic sites, denoted I, II and III, respectively (Fig. 3). In the Z4A unit cell, they are distributed as follows: 64 Na⁺ on site I on the 6R windows, denoted Na(I), 24 on site II inside the 8R windows, denoted Na(II), and 8 on site III, in front of the 4R windows, denoted

<figure><img src="image_7.png" /><figcaption>**Fig. 1** Adsorption energy level calculated from our simulations for each molecule, H₂O (blue), O₂ (red) and H₂ (yellow), inside the Na-LTA zeolite according to the adsorption site where they are located: between two cationic sites (II–III, I–III, and I–II), on the 8R window (8R), and inside the *β* cage or near Na(I) (I).</figcaption></figure>
Ab initio molecular dynamics simulations (AIMD) were performed with the electronic parameters set for static DFT relaxations over a minimum total simulation time of 110 ps including a 15 ps of equilibration period. Systems containing hydrogen atoms require the use of a time step smaller than 1 fs (ref. 34 and 35) to avoid fictitious molecular splitting. Another method, that we did not apply in this work, consists of increasing the mass of the hydrogen atom to 3, which corresponds to the atomic mass of tritium. Thus, the time step of 1 fs would be suitable for reaction studies.36,37 The energy criterion for electronic convergence was set to $10^{-4}$ eV. The temperature was set to a mean of 298 K using the Andersen thermostat.38 The adsorption energies for static simulations (or binding energies, depending on the community) were calculated using the following expression:

$$E_{\text{ads}} = \frac{E_{\text{system}} - N_{\text{W}} \times E_{\text{W}} - E_{\text{Z}}}{N_{\text{W}}} \quad (1)$$

where $E_{\text{system}}$ is the total energy of the system, $E_{\text{W}}$ is the mean energy of H₂O molecules, $E_{\text{Z}}$ is the total energy without H₂O molecules, and $N_{\text{W}}$ is the number of H₂O molecules.

All of the illustration figures of the system and the RDF graphs have been generated with the VMD (visual molecular dynamics) program.† 39

Because of the large size of the system with the Z4A unit cell (672 atoms), several optimisation steps were taken to ensure a smooth and accurate energy minimization of the structure. A first classical geometry optimisation was necessary using the general utility lattice program40 in order to preoptimise the structure, thus saving the computation time for the following DFT calculations as performed in our previous study.3

<figure><img src="image_8.png" /><figcaption>Fig. 2 Different cavities constituting an unit cell of the LTA type zeolite – the α cage (green) is the largest one, surrounded by the β cages (orange), connected to each other through the rectangular prisms (purple).</figcaption></figure>

Na(III). Thus, all 6R and 8R windows are occupied by one cation, in agreement with the description made by J. J. Pluth et al.25 To ensure the presence of local atomic configurations that can be found in both ZK4 and Z4A structures, the Na⁺ cations inside the ZK4 unit cell were distributed as follows: 6 on site I, 2 on site II and 1 on site III (Fig. 3).

## 2.2. Computational methods

To perform geometry optimisation and energy determination, density functional theory calculations were carried out using the Vienna Ab initio Simulation Package (VASP 5.4) code27 with the generalized gradient approximation and the Perdew-Burke-Ernzerhof exchange correlation functional.28,29 Pseudopotentials were described by using the projector-augmented wave method,30,31 and the D2 dispersion correction of Grimme32,33 was applied for the description of van der Waals forces. The plane wave cut-off energy was set to 520 eV. The Brillouin zone and the reciprocal space were sampled through the Γ-point sampling. The convergence criterion for ionic relaxation was set to 0.01 eV Å⁻¹ for static DFT calculations.

<figure><img src="image_9.png" /><figcaption>Fig. 3 Cationic sites (blue) of the Na-LTA structures.</figcaption></figure>

# 3. Results and discussion

## 3.1. O₂ adsorption

To clarify how the O₂ molecule interacts with the zeolite, we studied its adsorption in three types of structures (Fig. 4): purely silicated (Pur-Si), with one Al and one Na (1Al-1Na), and with two Al and two Na (2Al-2Na). Table 1 summarizes the calculated adsorption energies for these three systems.

These results show the important effect of Na⁺ cations on the adsorption of the O₂ molecule inside the zeolite. It is the most stable when the molecule is interacting with two cations where the adsorption energies are ~158% and ~38% stronger than those for the silicated and 1Al-1Na systems, respectively.

The cationic sites of the LTA zeolite are distributed in its α and β cages. Although the probability for the O₂ molecule to be present in the β cage is very weak, as shown in experimental adsorption studies, inside the dehydrated zeolites,16 water radiolysis leading to the production of oxygen occurs in both cavities. In this context, the β cage can therefore be occupied

<figure><img src="image_10.png" /></figure>

<footnote>† https://www.ks.uiuc.edu/Research/vmd/.</footnote>
<figure><img src="image_11.png" /><figcaption>Fig. 4 Optimised positions of O₂ in the α cage of three different structures: purely silicated without the Na⁺ cation (a), with one Na⁺ cation (b) and two Na⁺ cations (c) – the position of the O₂ molecule before the addition of a supplementary cation is represented in transparent, interatomic distances are given in Å.</figcaption></figure>

<table><caption>**Table 1** Calculated adsorption energy ($E_{ad}$) of the O₂ molecule on each of these three structures: without the Na⁺ cation (Pur-Si), with one Al atom and one Na⁺ cation (1Al-1Na), and with two Al atoms and two Na⁺ cations (2Al-2Na)</caption><thead><tr><th>System</th><th><i>E</i><sub>ad</sub> (eV)</th><th>O<sub>2</sub>···Na(Å)</th><th>O–O (Å)</th></tr></thead><tbody><tr><td>Pur-Si</td><td>-0.114</td><td>—</td><td>1.23</td></tr><tr><td>1Al-1Na</td><td>-0.213</td><td>2.55</td><td>1.23</td></tr><tr><td>2Al-2Na</td><td>-0.294</td><td>2.66 and 2.69</td><td>1.23</td></tr></tbody></table>

by the O₂ molecule and the α cage. Thus, we have studied its adsorption inside both these parts of the Na-LTA zeolites.

Inside the β cage, the optimised position of the O₂ molecule lies unsurprisingly between two Na⁺ cations, with an adsorption energy of -0.290 eV. This stability is justified by the distribution of the electronic density around the oxygen atoms of O₂ obtained from an electron localization function (ELF) study, as shown in Fig. 5, which illustrates the optimised position of the molecule inside the β cage. The electrons are distributed around the oxygen atoms of the molecule on a perpendicular plane to the O–O axis, which limits the configuration possibilities of the molecule with respect to the cation. In this represented configuration, each oxygen atom of O₂ is interacting with one Na⁺ cation, with O(O₂)···Na⁺ distances of 2.68 and 2.75 Å and a O–O bond length of 1.24 Å.

The dynamics (AIMD) calculations show that another possible configuration of O₂ inside the β cage is when only one of

its two O atoms interacts with two Na⁺ cations, as shown in Fig. 7 (config. 1). The mobility of the O₂ molecule inside the β cage is then mainly oscillating between its four surrounding Na⁺ cations by alternating these configurations and gives the adsorbed molecule a very strong stability on its adsorption site.

A comparison between both the configurations will be discussed in the adsorption studies inside the α cage part, where both of them can be encountered as well.

Since the interaction of the O₂ molecule with the zeolite framework is mainly through the Na⁺ cation, its location inside the α cage should follow the distribution of the cationic sites (I, II and III). The radial function distribution (RDF) calculation of the Na···Na distance (Fig. 6) indicates that the shortest distance is located around 4 Å (first peak), mainly associated with those between Na(I) and Na(III) (~3.90 Å) but also between Na(I) and Na(II) (~4.4 Å), while the majority of Na⁺ cations are separated from each other by around 4.8 Å (second peak), which is associated with the distance between Na(I) cations. The shortest distance between the Na(II) and Na(III) cations is located around ~5.2 Å. Therefore, taking into account the O₂···Na distances calculated previously (2.6–2.7 Å), it is highly likely for the O₂ molecule to be located between two cations. Hence, we have chosen the initial positions of the molecule before optimisation using static DFT calculations with reference to this observation.

<figure><img src="image_12.png" /><figcaption>Fig. 5 Optimised position of the O₂ molecule inside the β cage after static DFT calculations – the calculated electron localisation function (ELF), around O(O₂) atoms, is represented with an isovalue of 0.78, interatomic distances are given in Å.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 6 Radial distribution function (RDF) of the distances between the Na⁺ cations.</figcaption></figure>

<figure><img src="image_14.png" /></figure>
The mobility of the cations of the Na-LTA zeolite depends on the sites on which they are located. The cations of sites II and III are more mobile than those located on site I.⁴¹⁻⁴⁴ This is due to the coordination of Na⁺ with the oxygen atoms of the window where the site is located. This mobility of the cations has an influence on the stability of the adsorbed molecules, in particular, that of O₂. For the static studies inside the α cage, we placed the O₂ molecule on the two cationic sites of the Na-LTA zeolite between two cations: Na(I)-Na(II) and Na(I)-Na(III). For each position, the two configurations described above have been applied (Fig. 7):

* config. 1: one oxygen atom interacting with two cations,

* config. 2: each of the oxygen atoms of the molecule interacting with a cation.

The calculation of the adsorption energies shows that the affinity of the adsorbed O₂ molecule with the zeolite structure varies according to its stabilized position. This affinity seems stronger when the guest molecule is located between Na(I) and Na(III), and preferably positioned according to the configuration config. 2 (Table 2). This can be explained by the higher mobility of the Na(III) cation compared with those belonging to the other sites.²⁵,⁴¹,⁴⁵ The Na⁺ cation and the O₂ molecule thus approach each other mutually. Moreover, the O-O bond seems to stretch in this particular position (1.25 Å).

Whether or not this elongation (+0.02 Å compared with the bond length in the gaseous phase) is significant enough to be considered as a preparation of the molecule for dissociation remains to be discussed. When O₂ is located between Na(I) and Na(II), its bond length is shortened by 0.01 Å from config. 1 to config. 2 (Table 2). However, this configuration seems to be more favorable energetically speaking and referring to the relationship between the bond order and the bond length made by T. Chen and T. A. Manz,⁴⁶,⁴⁷ a variation of the bond length means a variation of the bond order. In our case, we observe a decrease of the O-O bond order, i.e. a weakening of the bond.

From a dynamics perspective, both configurations can be encountered during the evolution of the O₂ molecule in the α cage (Fig. 8). In a time interval of 120 ps, the molecule has moved from its initial cationic site to a neighbouring site with a residence time of about 30 ps at each site, whereas the molecule remains 1 to 2 ps in one configuration before changing to another.

Therefore, the cations slow down the diffusion of the O₂ molecule inside the α cage by moving it from one cationic site to another – at least in the case of a fully dehydrated zeolite where all Na⁺ sites are available to the molecule.

<figure><img src="image_15.png" /><figcaption>**Fig. 7** Possible configurations of the O₂ molecule when interacting with two Na⁺ cations.</figcaption></figure>

<table><caption>**Table 2** Comparison, after static DFT calculations, between the two configurations (config. 1 and config. 2) of the O₂ molecule positioned between two Na⁺ cations located on sites I and II (Na(I)/Na(II)) and on sites I and III (Na(I)/Na(III)) in the α cage – the adsorption energy (Ead) is expressed in eV and the other values are distances expressed in Å where: Na(X)···Na(Y) is the distance between two cations, O(O₂)···Na(X) is the distance between the oxygen atom of the molecule and one Na⁺ cation, (X and Y = I, II or III), and diff is the difference between the calculated values in config. 1 and config. 2</caption><thead><tr><th>Position</th><th>Values</th><th>Config. 1</th><th>Config. 2</th><th>Diff</th></tr></thead><tbody><tr><td rowspan="4">Inside the β cage</td><td>E<sub>ad</sub></td><td>—</td><td>-0.290</td><td>—</td></tr><tr><td>Na(I)···Na(I)</td><td>—</td><td>4.47</td><td>—</td></tr><tr><td>O(O₂)···Na(I)</td><td>—</td><td>2.68 and 2.75</td><td>—</td></tr><tr><td>O₂ bond length</td><td>—</td><td>1.24</td><td>—</td></tr><tr><td rowspan="5">Na(I)/Na(II)</td><td>E<sub>ad</sub></td><td>-0.200</td><td>-0.233</td><td>0.033</td></tr><tr><td>Na(I)···Na(II)</td><td>4.38</td><td>4.45</td><td>0.07</td></tr><tr><td>O(O₂)···Na(I)</td><td>2.90</td><td>2.68</td><td>0.22</td></tr><tr><td>O(O₂)···Na(II)</td><td>2.75</td><td>2.63</td><td>0.12</td></tr><tr><td>O₂ bond length</td><td>1.24</td><td>1.23</td><td>0.01</td></tr><tr><td rowspan="5">Na(I)/Na(III)</td><td>E<sub>ad</sub></td><td>-0.309</td><td>-0.332</td><td>0.023</td></tr><tr><td>Na(I)···Na(III)</td><td>3.85</td><td>3.92</td><td>0.07</td></tr><tr><td>O(O₂)···Na(I)</td><td>2.65</td><td>2.63</td><td>0.02</td></tr><tr><td>O(O₂)···Na(III)</td><td>2.57</td><td>2.50</td><td>0.07</td></tr><tr><td>O₂ bond length</td><td>1.24</td><td>1.25</td><td>0.01</td></tr></tbody></table>

<figure><img src="image_16.png" /><figcaption>**Fig. 8** Transition from one cationic site to another of the O₂ molecule during the AIMD calculations (duration: 139 ps) – each figure represents a snapshot of the position of the molecule at moment t.</figcaption></figure>

Actually, given the stronger interaction of water with the Na⁺ cation compared with that of O₂,¹⁶,¹⁸,⁴⁸,⁴⁹ the latter has only access to the cationic sites that are still unoccupied by the H₂O molecules. Indeed, static DFT calculations of the co-adsorption of the two molecules have shown that the presence of O₂ near the H₂O adsorption site is not sufficient to remove the watermolecule from it, either in the β or α cage.
**3.1.1. O₂/H₂O mixture studies.** To perform the adsorption of O₂ in the hydrated zeolite, O₂ was introduced near the H₂O molecule, whose position was previously optimised. The studies were performed in the vicinity of four H₂O adsorption sites located in our previous work (Fig. 9) where the H₂O molecule is: (a) inside the β cage, (b) on the 8R window, considered as a very stable site in the α cage, (c) between two cations Na(I) and Na(III) and (d) between two cations Na(II) and Na(III).

The first observation is that, in most configurations, the water molecule remains on its adsorption site (Fig. 9a-c) where its equilibrium position has already been well optimised. Even the fact that both O₂ and H₂O molecules interact with the same Na(III) cation (Fig. 9c) is not sufficient to release the water molecule from its adsorption site. Instead, it reorientates itself while remaining in interaction with the two cations Na(I) and Na(III). However, when the H₂O molecule is placed between Na(II) and Na(III) (Fig. 9d), the water molecule is only in a pseudostable position considering the distance of Na(II) ... Na(III) (~5.2 Å), which is longer than those of Na(I) ... Na(III) and Na(I) ... Na(II) as we have seen earlier on the description of the intercationic distances (Fig. 6). The perturbation brought by the addition of the O₂ molecule naturally leads the water molecule to reconfigure its equilibrium position for a more stable site nearby, i.e., the 8R window. One of the atoms of O₂ is then interacting with two cations Na(II) and Na(III), which are separated by a Na(II) ... Na(III) distance of 4.79 Å, with Na ... O₂ distances of 2.60 and 2.52 Å, respectively, while the other oxygen atom is interacting with one Na(I) at a distance of 2.71 Å. The observations made on these systems do not show a clear interaction between H₂O and O₂, both molecules tend to favor interactions with the Na⁺ cations. There is thus a competition between O₂ and H₂O molecules to occupy the cationic sites. More precisely, since both molecules interact preferably with the Na⁺ cations, the occupation of the site by the O₂ molecule depends on its availability, and thus its occupancy rate by H₂O molecules. This was confirmed by our AIMD calculations where the evolution of two O₂ molecules inside the α cage has been studied as a function of the number of water molecules in the cage (N). As N increases, the dioxygen molecules have

<figure><img src="image_17.png" /><figcaption>**Fig. 9** Optimised positions of the O₂/H₂O mixture for different configurations inside the β (a) and α (b, c, and d) cages – the positions of the adsorbates before the optimisation are represented in transparent.</figcaption></figure>

less and less access to the cationic sites, as shown by the radial distribution function of the O₂...Na distance (Fig. 10) where the intensity of the first peak (located at ~2.75 Å), representing the distance between O₂ and the nearest Na⁺ cation, decreases as the water loading increases until N = 15. Then its intensity becomes lower than that of the other peaks located at other distances.

This correlates with the experimental observation by Izumi and Suzuki⁵⁰ where a clear decrease of the O₂ adsorption capacity of the Na-LTA zeolite is noted from a water loading rate of 15% (approximately ~15 H₂O in the α cage), which supports the role of Na⁺ cations in the adsorption of the O₂ molecule. At this particular point of the water filling of the α cage, it is relevant to state that the majority of the cations are occupied at least by one water molecule.³ Accordingly, the interaction of the O₂ molecules with the cationic sites is more and more restricted by the presence of water until there is no (or very little) access to cations, as shown in Fig. 10 at N = 20, corresponding to the number of H₂O molecules in the α cage near the saturation of the zeolite which is around 25 H₂O per α cage.⁴¹,⁴⁹,⁵¹,⁵² At this stage of water filling, the O₂ molecules are mostly distributed around 6 Å from the nearest Na⁺ cation, the majority peak is shifted by +3.25 Å with respect to the positions of the other water quantities, even if the O₂ molecules occasionally interact with the cations at a distance of 2.75 Å (Fig. 10, N = 20). However, an increase in the number of water molecules does not promote the formation of hydrogen bonds between O₂ and H₂O molecules, which remain mostly at a distance of 3.75 Å from each other, as shown by the radial distribution function of the distance O(O₂)...H₂W between the oxygen atom of O₂ and the hydrogen atom of H₂O (Fig. 11). Again, at N = 10, the reciprocal behavior of O₂ and H₂O is different from those associated with other water quantities. The results obtained from Fig. 10 and 11 allow us to say that the mobility of the O₂ molecule in the α cage is particularly

<figure><img src="image_18.png" /><figcaption>**Fig. 10** RDF of the O₂...Na⁺ distance depending on the number of H₂O molecules (N) inside the α cage from AIMD calculations – each system is constituted of N H₂O and 2 O₂.</figcaption></figure>

<figure><img src="image_19.png" /></figure>
<figure><img src="image_20.png" /><figcaption>**Fig. 11** RDF of the distance between the oxygen atom of O₂ and the hydrogen atom of H₂O (O₂···Hw) as a function of the number of H₂O molecules (N) inside the α cage obtained from AIMD calculations.</figcaption></figure>

important when 15 water molecules are present since as we said previously, all the cations are occupied by at least one H₂O molecule. This step represents the saturation of the cationic sites of the α cage and the accentuation of the growth in the number of hydrogen bonds between the water molecules⁵³ (Fig. 12).

Therefore, the amount of water in the cavity not only affects the interaction of the O₂ molecules with the zeolite but also their mobility. On the one hand because of the competition between the two molecules (O₂ and H₂O) for the occupation of the cationic sites, on the other hand because of the congestion created by the water molecules forming rings between them via hydrogen bonds and Na⁺ cations. One of the direct consequences of this phenomenon was observed experimentally by L Frances et al.¹ on the consumption of the gaseous phase composed, among other elements, of O₂ that has been released

<figure><img src="image_21.png" /><figcaption>**Fig. 12** Number of H bonds during water filling of the α cage of the Na-LTA zeolite – O<sub>w</sub>···H<sub>w</sub> is the H-bond formed between the water molecules and O<sub>z</sub>···H<sub>w</sub> is the H-bond formed between the water molecule and the zeolite structure.⁵³ O···H distances less than 2.1 Å have been taken into account as the H bond.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Fig. 13** Released quantity of O₂ from the NaA zeolite at different water loading rates – framed periods indicate the gas decrease and the quantity of reacting O₂. Reprinted with permission from L. Frances et al.¹ Copyright 2015 Amercian Chemical Society.</figcaption></figure>

following the radiolysis of water in the Na-A zeolite (Fig. 13). The delay between each decrease in the O₂ component is closely related to the amount of water present in the structure, i.e., the water loading rate that is indicated in mass % in the results. It is interesting to note that this decay does not occur when the zeolite is saturated, i.e., when the O₂ molecules in the zeolite do not have access to the Na⁺ sites because of their total occupation by water molecules. One of the hypothesis to explain this decrease in the quantity of O₂ is its recombination with H₂, which is also a product of water radiolysis, to form back water. This implies that the recombination reaction requires the contact of the reactants O₂ and most likely H₂ with the cations, which underlines the catalytic role of the zeolite.

Hence, as for the O₂ molecule, we have studied the interaction of H₂ with the Na-LTA zeolite and the other adsorbates (H₂O and O₂).

## 3.2. H₂ adsorption

First, to describe the interaction of the H₂ molecule with the zeolite framework, its adsorption was studied through the static DFT method inside two types of LTA structures: purely silicated (no cation) and with one Na⁺ cation (Fig. 14).

The adsorption energy calculations yielded a more stable configuration when the molecule is adsorbed on a cation at the H₂···Na distances of 2.34 and 2.41 Å (Table 3). When adsorbed inside the structure composed of one Na⁺ cation, the distance of 2.64 Å between the H₂ molecule and one oxygen atom of the zeolite framework indicates the formation of a weak hydrogen bond between the adsorbate and the adsorbed. Therefore, the H₂ molecule also interacts with the oxygen of the zeolite in addition to Na⁺, although the latter remains the main actor in the interaction of H₂ with the zeolite. The most stable configuration for the molecule seems to be when its two hydrogen atoms are in interaction with the same Na⁺ cation, which is described as the most stable equilibrium geometry for the Na⁺H₂ complex.⁵⁴⁻⁵⁶

The way H₂ interacts with the oxygen atoms of the zeolite depends on its environment and the proximity of the oxygen
<figure><img src="image_23.png" /><figcaption>**Fig. 14** Optimised positions of the H₂ molecule (white) in the α cage of two LTA structures: with and without the Na⁺ cation – the position of the molecule before the addition of the Na⁺ cation is represented in transparent.</figcaption></figure>

<table><caption>**Table 3** Calculated adsorption energy ($E_{ads}$) of the H₂ molecule in each of the two structures: without the Na⁺ cation (Pur-Si) and with one Na⁺ cation and one Al atom (1Al–1Na)</caption><thead><tr><th>System</th><th><i>E</i><sub>ad</sub> (eV)</th><th>H<sub>2</sub>···Na<sup>+</sup> (Å)</th><th>H<sub>2</sub>···O<sub>2</sub> (Å)</th><th>H–H (Å)</th></tr></thead><tbody><tr><td>Pur-Si</td><td>−0.049</td><td>—</td><td>3.24</td><td>0.75</td></tr><tr><td>1Al–1Na</td><td>−0.182</td><td>2.34 and 2.41</td><td>2.64</td><td>0.75</td></tr></tbody></table>

atoms. For example, inside the β cage, the proximity between the oxygen atoms of the wall provided by the confinement of the cage gives H₂ the possibility to interact with two oxygen atoms from the zeolite wall, which results in an asymmetry in the distribution of the electronic isodensity around the molecule (Fig. 15) and an adsorption energy of −0.077 eV.

Elsewhere, inside the α cage, H₂ adopts the same configuration as in the β cage, i.e., the two hydrogen atoms are interacting with the same Na⁺ cation, while a hydrogen bond is formed between the adsorbate and the adsorbent, with an adsorption energy of −0.151 eV. These interactions between the H₂ molecule and the zeolite remain short-range, the molecule very weakly perceives the effect of the adsorbent surface when it is placed close to the middle of the α cage, ~4.5 Å from the nearest Na⁺ cation (adsorption energy of −0.027 eV). It is interesting to note that this value represents a weaker

<figure><img src="image_24.png" /><figcaption>**Fig. 15** Optimised position of the H₂ molecule (white) in the β cage by two oxygen atoms (red) and one Na⁺ cation (blue) – the calculated electron localisation function is represented at an isovalue of 0.986.</figcaption></figure>

<table><caption>**Table 4** Calculated adsorption energy ($E_{ads}$) of the H₂ molecule in the α cage</caption><thead><tr><th>Location</th><th><i>E</i><sub>ad</sub> (eV)</th><th>H<sub>2</sub>···Na (Å)</th><th>H<sub>2</sub>···O<sub>2</sub> (Å)</th></tr></thead><tbody><tr><td>Inside β</td><td>−0.077</td><td>2.72 and 2.79</td><td>2.65 and 2.67</td></tr><tr><td>Close to the α center</td><td>−0.027</td><td>4.57</td><td>5.38</td></tr><tr><td>Near the Na<sup>+</sup> cation in the α cage</td><td>−0.151</td><td>2.43 and 2.37</td><td>2.59</td></tr></tbody></table>

adsorption of the H₂ molecule compared to that in the purely silicated structure (−0.049 eV, Table 3). This can be explained by the position of the molecule which is closer to the walls of the zeolite in this latter case, the influence of the adsorbing surface through its oxygen atoms is therefore more important with respect to the case where the H₂ molecule is at least at 4.75 Å from the closest Na⁺ cation and 5.38 Å from the nearest oxygen atom of the cage (Table 4). The values in Table 4 are given to compare the interactions of the H₂ molecule with the zeolite according to its localisation and configuration inside the α cage. In each case, the bond length of the molecule remained equal to 0.75 Å. The adsorption of the H₂ molecule does not seem to affect its geometry, except for one particular configuration where it is located on a 8R window (Fig. 16).

When adsorbed on the 8R window, the two hydrogen atoms of the H₂ molecule interact with the same Na(II) cation at H₂···Na⁺ distances of 2.31 and 2.36 Å, each of them also form hydrogen bonds with the oxygen atoms of the window where the shortest H₂···O₂ distances are at 2.84 and 2.56 Å. This configuration gives the H₂ molecule a bond length of 0.76 Å (0.01 Å longer than for the other configurations). However, the most peculiar value is that of the adsorption energy of −0.280 eV, which is unusually strong for the H₂ molecule, because this implies a stronger adsorption than for some O₂ sites as seen in Fig. 1.

This “abnormally” high value of the adsorption energy of the H₂ molecule is also noticed by Areán *et al.*⁵⁷ for the same configuration, in their adsorption studies of the molecule in a CaA zeolite (of the LTA structure with Ca²⁺ cations). They attribute this strong stability of the molecule to its particularly

<figure><img src="image_25.png" /><figcaption>**Fig. 16** Particular configuration of the H₂ molecule (white) on the 8R window – in addition to the Na(II) cation (blue), each hydrogen atom of the molecule interacts with two oxygen atoms of the window, respectively, interatomic distances are given in Å.</figcaption></figure>

<figure><img src="image_26.png" /></figure>
favorable configuration with a strong electrostatic interaction with the oxygen atoms of the zeolite, in addition to its interaction with the cation. This configuration thus seems very stable for H₂. It turns out that the 8R window is also among the most stable adsorption site for the H₂O molecule inside the α cage.³ Further investigations are obviously needed on this particular adsorption site since it amplifies the catalytic effect of the zeolite on H₂O and H₂ molecules. *Ab initio* molecular dynamics calculations inside the α cage have confirmed the H₂ molecule preference to interact with the Na⁺ cation instead of the oxygen atom of the zeolite, as shown by the radial distribution functions where the distances between the H₂ molecule and the Na⁺ cations (H₂···Na⁺) are mostly distributed around 2.45 Å (Fig. 17a). This result is consistent with the potential energy studies of the Na⁺-H₂ interaction,⁵⁴,⁵⁸ albeit longer (~+0.1 Å) than the value that we have obtained from static calculations. The distribution for those between the adsorbed molecule and the oxygen atoms of the structure (H₂···O₂) is wider (Fig. 17b), showing a small contribution of O₂ atoms to the displacement of H₂.

The residence time of the H₂ molecule on the cationic sites is less than 1 ps (~0.22 ps), which is a much shorter duration than for the O₂ molecule (~30 ps). The mobility of the H₂ molecule in the α cage is therefore more important than that of O₂ although both evolve from a cationic site to another, which is in accordance with the results of Kahn *et al*.⁵⁹ who describe the movement of the H₂ molecule in the zeolite as a succession of jumps from one site to another.

**3.2.1. H₂/H₂O mixture studies.** Regarding the co-adsorption of H₂ and H₂O, the observation is the same as for the O₂/H₂O mixture, the interaction of the dihydrogen molecule with the cations is not sufficient to remove the H₂O molecule from its adsorption site whether in the α or β cage. The only disturb-

ance the H₂ molecule can bring to H₂O is a reorientation of the latter when the optimised position of the H₂O molecule is on a pseudostable configuration, which makes it switch to a more stable adsorption site, e.g., the 8R window, as already seen in the H₂O/O₂ co-adsorption case (Fig. 9d), or when the two molecules interact with the same Na(III) cation (Fig. 18).

In this configuration, the two atoms of H₂ interact with the same Na(III) cation, at H₂···Na(III) distances of 2.42 and 2.43 Å, while one of them is forming in parallel a hydrogen bond with the oxygen atom of the zeolite (H₂···O₂ distance of 2.36 Å). The H-H bond length is at 0.76 Å (+0.01 Å compared with the gas phase). However, the oxygen atom of the H₂O molecule interacts with one Na(I) cation and the Na(III) cation, with which it shares the interaction with H₂, it also forms an hydrogen bond with the oxygen of the structure, at a H₂O···O₂ distance of 1.71 Å, which is shorter than the one formed between H₂ and the cage, i.e., the hydrogen bond between the water molecule and the zeolite is stronger than between the dihydrogen molecule and the adsorbant. At the same time, there seems to be no significant interaction between the guest molecules H₂ and H₂O, and the interaction with the zeolite being favored by both of them.

### 3.3. O₂/H₂ mixture studies

The absence of an obvious interaction is true between H₂ (or O₂) and the water molecule, but also between the H₂ and O₂ molecules. Static studies of the simultaneous adsorption of the two molecules inside the Na-LTA zeolite showed that the introduction of a H₂ molecule near the optimised position of the O₂ molecule can disturb its configuration, especially when H₂ is directly placed on the Na⁺ cation with which the O₂ molecule is already interacting (Fig. 19).

In this particular configuration, the presence of H₂ causes O₂ to interact with only one Na⁺ located on site II, while both atoms of H₂ interact with the same Na(I) with which O₂ has previously interacted. The reasons for this reconfiguration of the O₂ position are, on the one hand, the weakening of the O₂···Na(I) interaction due to the positioning of H₂ on the same cation, and on the other hand, the distance imposed by the repulsion between O₂ and H₂ that the dynamic calculations

<figure><img src="image_27.png" /><figcaption>**Fig. 17** Radial distribution function of the H₂···Na⁺ (a) and H₂···O₂ (b) distances obtained from AIMD calculations – the interaction of H₂ with the Na⁺ cation is preponderant.</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>**Fig. 18** Optimised position of the H₂/H₂O mixture inside the α cage after static DFT calculations – the positions of the adsorbed molecules before the optimisation are represented in transparent.</figcaption></figure>

<figure><img src="image_29.png" /></figure>
<figure><img src="image_30.png" /><figcaption>**Fig. 19** Optimised position of the H₂/O₂ mixture inside the α cage of the Na-LTA structure after static DFT calculations – the positions of the adsorbed molecules before the optimisation are represented in transparent.</figcaption></figure>

have estimated mainly around 3.85 Å for the co-adsorption of the two molecules inside the α cage (Fig. 20). Even increasing the probability of meeting between the two molecules by increasing their number in the alpha cage is not enough to sufficiently reduce the O₂···H₂ distance (which is decreased to 3.35 Å) to form a hydrogen bond.

This value of 3.35 Å is too important to consider the formation of a hydrogen bond between the two molecules even if the probability for this to occur is not zero if we take into account the O₂···H₂ distances between 2 and 3 Å regarded as weak hydrogen bonds (Fig. 20, 1 O₂ and 1 H₂). Therefore, as for the O₂ molecule, water is the main regulator of the H₂ molecules access to the cationic sites. Thus, even if the H₂···Na⁺ interaction is weaker than that of O₂···Na⁺, the impact of the occultation of these cationic sites by water on the H₂ interaction with the zeolite and its mobility should be as consequential as for O₂. The experimental observation of the consumption of gaseous hydrogen formation, released during water radiolysis in the NaA zeolite,¹ is in line with our numerical calculations. As for O₂ (Fig. 13), the time at which H₂ decays start depends on the water loading rate in the

<figure><img src="image_31.png" /><figcaption>**Fig. 20** Comparison of the RDF of the O₂···H₂ distance in the α cage for two systems constituted of different numbers of adsorbates (1O₂ + 1H₂ and 5O₂ + 10H₂) obtained from AIMD calculations.</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>**Fig. 21** Released quantity of H₂ from the NaA zeolite at different water loading rates – framed periods indicate the gas decrease and the quantity of reacting H₂. Reprinted with permission from L. Frances et al.¹ Copyright 2015 Amercian Chemical Society.</figcaption></figure>

zeolite (Fig. 21): the higher the coverage of the Na⁺ sites by H₂O, the later the disappearance of H₂ from the gaseous phase. Also, no decrease was observed when the Na-LTA zeolite is saturated with water, i.e., when no cationic site is available or to interact with H₂. This behaviour should be observed from the point where all the cationic sites are occupied by H₂O (at a loading rate of around 13–15%) and eventually O₂, since the latter has priority over H₂ in their occupation given a stronger O₂ interaction with the cations.

The behaviour of both H₂ and O₂ molecules within the zeolite structure depends on the availability of the cationic sites, which is directly linked to their occupancy by water molecules. Experimental observations of the production and consumption of the two gases¹ highlight this dependence (Fig. 13 and 21). Since a decrease in the quantity was observed for both O₂ and H₂ molecules, the hypothesis of recombination where the zeolite and the water would play a role in the catalyst and inhibitor, respectively, is put forward, considering the application of the Na⁺ cations in their adsorption as shown in this work. However, since no direct interaction leading to a reaction between H₂ and O₂ molecules has been noted inside the Na-LTA zeolite, the path to the recombination through the activation of the two molecules via the adsorbent surface, as described by L. Benco et al.¹⁹ and L. Chen et al.,²⁰ is still under study.

## 4. Conclusions

The O₂ molecule exhibits a higher affinity for the Na-LTA zeolite than H₂ despite the fact that both interact with the Na⁺ cations. Therefore, as expected, the mobility of the H₂ molecule in the structure is higher compared to that of O₂, as shown by our *ab initio* molecular dynamics (AIMD) studies. As a result, both molecules evolve from one cationic site to another in the α cage, but the residence time of the O₂ molecule is significantly longer than that of H₂. This behaviour around the Na⁺ cations leads us to consider that the ‘vectorization’ of the displacement of H₂ increases its probability to meet O₂ while the latter is slowed down on its cationic site,
<figure><img src="image_33.png" /></figure>

especially since the studies of the co-adsorption of both molecules have shown that the interaction with the cations is favored rather than with the co-adsorbate. However, inside the hydrated zeolite structure, the cationic sites are mostly occupied by H₂O molecules and their interaction with the cations is much stronger than those of O₂ and H₂ molecules. Thus, since the water molecule can hardly be removed by H₂ and O₂ from its adsorption site, only the remaining available sites will be occupied by O₂ as shown previously by the RDF calculations (see Fig. 10). An increase of the water loading significantly reduces the possibility of O₂ (and even more for H₂) to access the Na⁺ sites which affect, on the one hand, its mobility and, on the other hand, its activation for the recombination reaction, as described by Acres⁹ on the reduction of the reaction rate due to the presence of water on the adsorbant surface. Then, with a high water loading rate, O₂ and H₂ molecules have less interaction with Na⁺ cations and higher mobility, thus reducing the probability of encounter between the two via a cation-guided trajectory. Experimental studies by L. Frances et al.² have shown the important role that the amount of water adsorbed in the zeolite has in the production and consumption of O₂ and H₂ (Fig. 13 and 21). Through a simulation study, we have established a link between these experimental observations and the occupancy rate of the cationic sites which states that once all the cationic sites are hydrated, i.e., saturation of the Na⁺ sites, the consumption of O₂ and H₂ stops, leading to a continuous production of both gases as can be seen at a water loading rate of ~18% in Fig. 13 and 21. The synchronized disappearance of both O₂ and H₂ being associated with the recombination phenomenon, these combined experimental and simulation results imply that the main actor in the catalytic role of the Na-LTA zeolite for H₂/O₂ recombination is the Na⁺ cation. The availability of cationic sites and the nature of the cation itself are therefore important factors to consider for an efficient catalytic effect of the zeolite.

## Conflicts of interest

There are no conflicts to declare.

## Acknowledgements

The computations in this work were performed on the supercomputer facilities of the Mésocentre de calcul de Franche-Comté and on the TGCC (Très Grand Centre de Calcul du CEA). We were granted access to the HPC resources of TGCC under the allocations 2019-A0060910785 and 2020-A0080910785 provided by GENCI.

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