# First-principles investigation of electrified monolayered MoS2/water interface

Fabien Mortier, Di Zhao, Minoru Otani, Samuel Bernard, Yun Wang, Assil Bouzid

► To cite this version:

Fabien Mortier, Di Zhao, Minoru Otani, Samuel Bernard, Yun Wang, et al., First-principles investigation of electrified monolayered MoS2/water interface. Surface Science: A Journal Devoted to the Physics and Chemistry of Interfaces, 2025, 764, pp.122870. 10.1016/j.susc.2025.122870. hal-05338110

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# First-principles investigation of electrified monolayered MoS₂/water interface

Fabien Mortier<sup>a</sup>, Di Zhao<sup>b</sup>, Minoru Otani<sup>c,d</sup>, Samuel Bernard<sup>a</sup>, Yun Wang<sup>b,†</sup>,*, Assil Bouzid<sup>a,‡</sup>

## ARTICLE INFO

### Keywords:

MoS₂

Water

Interface

Modeling

DFT

## ABSTRACT

We investigate electrochemical properties of electrified MoS₂/water interface under applied bias potential. We show that water molecules rearrange depending on whether the surface is positively or negatively charged. A positive charge pulls water's oxygen atoms closer to the surface, while extra electrons make water flip so that hydrogen atoms get nearer the surface. Abrupt changes are observed in the double layer charge and in the capacitance evolution as a function of bias potential and are explained by semiconductor nature of the MoS₂ material. Overall, our findings confirm earlier results on the water dynamics at electrified metal-water interfaces and highlight that using explicit and hybrid modeling approaches helps to capture the fine details of electrochemical processes at solid/liquid interfaces.

## 1. Introduction

Electrochemical processes occurring at the interfaces between metal and water are of great interest in many industrial fields such as energy conversion and storage technologies. For example, the proper functioning of fuel cells, solar cells or electrolyzers relies on interface processes [1,2] and the improvement of these devices requires an accurate understanding of interfacial electrochemical processes and their impact on the overall material properties. While such a task can be achieved experimentally by performing in-situ experiments in ultra-high vacuum chambers, its application to real cases remain highly problematic [1].

Alternatively, atomic scale modeling of electrode/water interfaces is a viable way to access the intimate details of interface electrochemical processes of interest [3]. In the case of the water electrolysis, the involved processes are either the oxygen and/or the hydrogen evolution reactions [4], or the structure and evolution of the electrical double layer (EDL) during the cycling [2]. However, the high computational cost of such simulations, usually implying the need of running long molecular dynamics calculations on sufficiently large systems, remains an obstacle to the massive adoption of such techniques [5]. Another layer of complexity is added when dealing with charged surfaces and interfaces. In order to simplify the electrode/water systems, several

simulation schemes have been proposed. A common approach to reduce the computational cost, consists in considering the water as an implicit dielectric medium [6,7]. Although this method suffers from an inherently limited accuracy, it was found useful to investigate neutral interfaces [6,8]. However, this approach runs short when dealing with charged surfaces as the explicit description of the water molecules becomes highly important to describe a correct water dynamics at the interface, which in turn, has a sizable impact on the interface properties [9].

When considering electrified interfaces, several approaches were developed to mimic the applied bias potential and simulate the charged metal/water interface. For example, the behavior of water on a charged Pd(111) surface [10] was simulated by inserting an excess amount of electrons at the metal surface together with a uniform compensating background charge that ensures the charge neutrality of the supercell. On the contrary, in the work of Skúlasson's et al. no background charge was necessary as the surface potential is induced through the insertion of H atoms in the water layer at the interface with platinum. Consequently, a H⁺ ion is formed and an electron is transferred to the metal [4]. Buraschi et al. used the hairy probes formalism to introduce electronic open-boundaries into DFT calculations, thereby allowing the simulation of electrified interfaces [11]. Otani et al.

<footnote><sup>a</sup> Institut de Recherche sur les Céramiques (IRCER), UMR CNRS 7315-Université de Limoges, Centre Européen de la Céramique, 12 rue Atlantis, 87068, Limoges, France</footnote>

<footnote><sup>b</sup> Centre for Catalysis and Clean Energy, School of Environment and Science, Griffith University, Gold Coast, QLD 4222, Australia</footnote>

<footnote><sup>c</sup> Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki, 305-8577, Japan</footnote>

<footnote><sup>d</sup> Department of Materials Science and Tsukuba Research Center for Energy Materials Science, Institute of Pure and Applied Sciences and R&D Center for Zero CO₂ Emission with Functional, Tsukuba, Ibaraki, 305-8573, Japan</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: yun.wang@griffith.edu.au (Y. Wang), assil.bouzid@cnrs.fr (A. Bouzid).</footnote>
proposed another scheme where the periodicity of the cell is broken in the normal direction of the slab and the screening effects are considered through a semi-infinite continuum with an infinite dielectric constant. The bias potential is then monitored by inserting excess electrons in the solvent [12,13]. An interesting and easy to implement method was developed by Bonnet et al. [14] to perform molecular dynamics simulations at a predefined constant Fermi level. In this scheme, the system is able to exchange electrons with an external reservoir at fixed potential in order to maintain its Fermi level constant during the dynamics. Consequently, the system evolves in the grand canonical ensemble. In practice, the electronic charge is considered as a dynamical variable with an associated fictitious Newton-like equations of motion. In addition, a separate thermostat can be employed on the electron reservoir in order to get a better control over the potential fluctuations. This approach has been extended by Bouzid et al. to investigate the re-organization of the electrical double layer at several bias potentials [2] and to explore the oxygen evolution reaction mechanisms at a Pt(111) interface [15]. Recently, a cost effective method was developed to model the EDL and its related properties of the Pt(111)/water interface by exploiting a hybrid explicit/implicit solvation model [16]. Within this innovative approach, a mere two layers of explicit water molecules are placed at the electrode interface, while a continuous dielectric medium mimics the rest of the water solvent. The bias potential is simulated through controlled charge variations, while allowing the structural relaxation of the system. The potential is aligned to the SHE by referencing the Fermi level to the electrostatic potential located at the center of the electrolyte, and then further aligning the electrostatic potential originating from the implicit solvent to the SHE potential. This method was further validated an applied to several metal/water interfaces, including Ag, Au, Ni, Pt, Pd, and Cu, yielding robust agreement with experiments [17].

While these computational setups are valuable in accessing the interfaces properties, they are currently largely limited to the study of charged metal/water interfaces. In this work, we extend the application of the study of the charged interfaces to the investigation of the interface between water and a two-dimensional (2D) material. The interest in 2D materials has increased in the last years thanks to the progress made in both advanced synthesis processes and the understanding of their characteristics highlighting very interesting electrical and optical properties [18,19]. Graphene is the most famous 2D material but many others exist. One class of material of specific interest for nanoelectronics and nanophotonics applications is the transition metal dichalcogenides (TMDC). The chemical formula of TMDC has a MX₂ shape where M is a transition metal such as Mo, W or Ti and X is a chalcogen like S or Se [18]. The molybdenum disulfide (MoS₂) is the prototypical material of TMDC. In a nanoparticle form it has proven to have a good catalytic activity for the hydrogen evolution reaction (HER) of the water electrolysis [20,21]. Indeed, the quasi-neutral adsorption energy of hydrogen on Mo-edge sites [22] make them very suitable for such catalysis applications according to the Sabatier principle.

In this work, we focus on monolayered MoS₂ as it offers a large specific area that exposes a large number of catalytic active sites. In addition, while bulk MoS₂ possesses an indirect band gap, the monolayered material features a direct band semiconductor behavior [23] with positions of the valence and conduction bands aligning well with the oxidation and reduction potentials of the water splitting reaction [24]. As such, 2D MoS₂ appears to be a major candidate for electrocatalytic water splitting reaction. At this level, the study of the electrochemical processes and the structure of the 2D MoS₂/water interface becomes crucial for achieving a fundamental understanding of these processes and to improve the catalytic properties of the overall material [25].

In this paper, we resort to first-principles molecular dynamics simulations (FPMD) to investigate the MoS₂/water interface under several bias potentials with a particular focus on the evolution and the organization of the water molecules in the electrical double layer. We consider

a monolayer of MoS₂ and explicit water molecules to describe the solvent and model the effects of bias potential though controlled excess charge. Our calculations illustrate the change in organization of the EDL depending on the applied bias potential. Indeed, while the oxygen atoms point to the MoS₂ slab when the interface is positively charged, the orientations of the water molecules change when the applied potential becomes negative. In this case the hydrogen atoms moves towards the MoS₂ layer. We observed that this tendency increases with the applied potential. Finally, we resort to the hybrid solvation model to investigate the electrochemical properties of the interface.

This paper is organized as follows. The computational details of the calculations are presented in Section 2. Section 3 presents first, the results of the structural evolution as a function of bias potential, and second, the evolution of the electrochemical properties. The conclusions of our work are drawn in Section 4.

## 2. Computational details

In this work we resort to two complementary approaches to investigate the electrified MoS₂/water interface: (i) fixed charges ab initio molecular dynamics of MoS₂ interfaced with explicit liquid water and (ii) fixed charge geometry optimization of MoS₂ interfaced with a hybrid solvation model. Together, these approaches provide a thorough details about the evolution of the structural and electrochemical properties of the electrified interface under bias potential.

### 2.1. First-principles molecular dynamics

Electronic structure is described using the density functional theory (DFT) framework as implemented in the CP2K code [26]. Within this scheme, an atom-centered Gaussian basis set are used to describe the orbitals, whereas the plane-wave functions are used to expand the electron density. In particular, we use the triple-ζ polarized MOLOPT basis sets [27] for molybdenum atoms and triple-ζ cc-TZ [28] basis sets for sulfur, oxygen and hydrogen atoms and employ a 800 Ry energy cutoff for the expansion of the plane wave functions. Goedecker–Teter–Hutter (GTH) pseudopotentials are used to describe core–valence interactions [29] along with the Perdew–Burke–Emzerhof (PBE) exchange and correlation functional [30]. The van der Waals interactions are described using the rVV10 functional [31,32] where the *b* parameter is set to the value optimized for liquid water *b* = 9.3 [33].

First-principles molecular dynamics are carried out within the Born–Oppenheimer scheme as implemented in CP2K [26]. Specifically, we adopt the NVT ensemble at a constant temperature of T = 350 K thanks to a Nose–Hoover thermostat [34–36] for a total duration of 20 ps with a time step of 0.48 fs. The choice of T = 350 K allows to overcome the limitations of semi-local exchange and correlation functionals in achieving a liquid-like water at lower temperatures [37,38].

The structure of the MoS₂ model consists of a 4 × 4 unit cell where a molybdenum layer is stacked around two layers of sulfur atoms. Fig. 1 shows a cross-section and a top view of a MoS₂ single layer. The interface between water and 2D MoS₂ is modeled through an MoS₂ monolayer and 64 water molecules inside an orthorhombic simulation box (a=b=12.66 Å and c=21.07 Å) with periodic boundary conditions. The length of the periodic simulation cell in the normal direction to the MoS₂ slab (z-axis) is calibrated to achieve a water density around 1 g/cm³ in the region far from the interface (see. Figure S1). Fig. 2 displays a configuration of the neutral water/MoS₂ interface.

In addition to the neutral interface, we have carried out calculations on six charged systems in which the charge at the interface is fixed and monitored through the manipulation of the number of electrons in the system. The overall charge neutrality is ensured through a uniform compensating background. Specifically, following Ref. [2], we consider systems with a charge Q of −10, -8, -6, -4, −2 and +2 electrons. This wide range of charge allows us to induce and track
<figure><img src="image_3.png" /><figcaption>Fig. 1. Top and cross section views of a MoS₂ monolayer.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 2. Snapshot of the simulation box for a neutral water/MoS₂ interface.</figcaption></figure>

significant water reorganization as a function of various potentials within simulations at the ps time-scale. The double layer charge is estimated as $Q_{dl} = \frac{1}{2} \frac{L_{water}}{L_z} Q$, where we consider that the charge is equally shared between the two interfaces, $L_{water}$ and $L_z$ are the lengths of the water slab and the cell dimension in the z direction [2]. This definition accounts for the fact that part of the charge is compensated by the uniform background within the electrode. Thereby the actual charge that contributes to the establishment of the interfacial properties is therefore reduced. Hence, the applied double layer charges are: -46,17, -36,93, -27,70, -18.46, -9.23 and 9.23 µC/cm². These values are within typical values used in previous investigation based on classical force fields [39].

## 2.2. Hybrid-solvation of electrified interfaces

The DFT calculations were performed with the Vienna ab initio Simulation package (VASP) and part of the postprocessing with the VASPKIT package [40–42]. The kinetic energy cutoff value was set to 600 eV. Structural optimizations were performed by allowing all atoms to relax until Hellmann–Feynman forces fell below $5 \times 10^{-2}$ eV/Å. The electronic self-consistent loop employed an energy convergence threshold of $1 \times 10^{-5}$ eV. The optPBE exchange–correlation (XC) functional was selected for this work due to its proven accuracy in modeling solid-state systems and aqueous environments, as documented in prior studies [16,17,43]. This functional enhances the XC energy description by incorporating nonlocal correlation effects, enabling improved treatment of non-spherical electron density distributions and weak

<figure><img src="image_5.png" /><figcaption>Fig. 3. Illustration of the double reference method for calculating the applied bias potential in terms of the SHE potential from the Fermi level of the system (purple: molybdenum, yellow: sulfur, red: O, and pink: H).</figcaption></figure>

intermolecular interactions [43,44]. To model both explicit and implicit solvation effects, the MoS₂ slab was positioned between two layers of explicit water molecules. The implicit solvation component was simulated using the VASPSol package, which incorporates a dielectric constant of 78.40 and a Debye length of 3.40 Å [45,46].

To simulate an applied bias potential (U), the charge of the double-layer in the system was adjusted [47]. Subsequently, the structures underwent geometry optimization. The applied bias potential was calculated from the Fermi energy of the interface systems ($E_{Fermi}$) relative to the standard hydrogen electrode (SHE) potential, employing a dual-reference method depicted in Fig. 3. In this methodology, the Fermi level is initially aligned with the electrostatic potential at the core of the electrolyte, which is methodically adjusted to zero ($E_{Fermi}$) in accordance with the Poisson–Boltzmann equation. Following this, the electrostatic potential of the implicit solvent is aligned to the SHE potential using an additional empirical adjustment of 4.6 V, derived from the discrepancy between experimental and computed potential of zero charge (PZC) values through the implicit solvation method [46]. Therefore, the applied bias potential relative to the SHE (U(V) vs SHE) is determined as follows:

$$U(V) \text{ vs SHE} = \frac{-(E_{Fermi} + E_{shift})}{|e|} - 4.6 \quad (1)$$

# 3. Results

## 3.1. Model validation and water structure under bias potential

A common approach to validate atomistic models issued from molecular dynamics simulations of water relies on the comparison of the oxygen–oxygen pair distribution function (PDF) of the models to experimental results. Indeed, the O–O partial PDF ($g_{OO}(r)$) gives a direct access to the structure of the liquid and is sensitive to the intermolecular forces and the dynamical motion [48]. For all the studied systems, we compute the $g_{OO}(r)$ over 2000 configurations equally distributed over the 20 ps trajectory and compare to experimental PDF of liquid water from Ref. [48] (see Fig. 4). We note that the $g_{OO}(r)$ of O belonging to liquid water were computed accounting for the broken periodicity along the z direction as outlined in Ref. [49].

Focusing on the neutral interface, the computed $g_{OO}(r)$ shows a good agreement with the experimental one with the peak positions and intensities closely matching the measured ones. These results are in agreement with previous modeling efforts [2,15,33] and indicate that far from the interface the water bloc bears a liquid-like structure, thereby validating our atomistic model. When the system is positively charged (+2e), we observe a strong increase of the first and second peak
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** $g_{OO}(r)$ pair distribution functions computed on our models of neutral and various charged interfaces and compared to experimental [48] results on bulk liquid water.</figcaption></figure>

intensities as well as the first-minimum depth. This behavior is induced by the structuring of the water molecules when subject to an electric field. As negative charges are inserted in the system, the opposite trend happens reflecting strong changes in the water organization at the $MoS_2$/water interface.

## 3.2. Structure of the EDL under bias potential

We now delve into the study of the EDL structure under bias potential by focusing on the evolution of the distance between the water molecules and the $MoS_2$ interface as well as the orientation of these molecules when varying the applied potential on the electrode. Fig. 5 shows the distribution of the distances between the 2D electrode surface and the atoms of the water molecules along the direction perpendicular to the charged $MoS_2$ slab and reflects the change in the positions and orientations of water molecules as a function of the bias potential.

This distribution shows that the water molecules exhibit a particular organization within the first 5 Å at the vicinity of the interface. Above this threshold, we observe typical fluctuations of liquid-like water region. At neutral conditions, the distribution shows a broad peak located at 3.6 Å with a tail in the region down to 2 Å. As shown in Fig. 5, the main peak can be ascribed to both the contributions from of O and H atoms, while the tail is mainly due to H atoms. This reflects a mixed orientation of the water molecules, where they exhibit at the same time O-down and H-down configurations. When positively charged, we observe that the tail due to the H-down configurations is suppressed while the central main peak gets closer to the interface which reflects a reorientation of the water molecules to favor an O-down configuration that satisfies the electrostatics of the interface. When negatively charged, one observes a peak at around 2.5 Å that corresponds to the presence of H atoms near the $MoS_2$ with an intensity that grows positively when more negative charge is injected into the system. Furthermore, the position of this peak shift towards the small distances as increasing the negative charge. Such trend indicates a high preference for the negatively charged interface to attract water molecules in H-down configurations. Similarly, the main peak exhibits a shift from 3.8 Å to 3.5 Å when going from -2e to -10e indicating a general tendency of the water molecules to be attracted to the negatively charged surface.

Fig. 6 displays snapshots of three different charged interfaces where one can identify the various O-down and H-down molecules. A global

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** (a) Distribution of the oxygen and hydrogen (b) hydrogen and (c) oxygen atoms positions along the normal direction to the $MoS_2$ monolayer for various charged interface. These distributions correspond to averages over 2000 configurations regularly spaced in the whole trajectory files. The labels in the legend box indicates the amount of charges in the system going from -10 to +2e.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Orientation of the water molecules for three different charged interfaces at the end of molecular dynamics simulations.</figcaption></figure>

description of the water molecules positions and orientations as a function of the bias potential is obtained by following the evolution of the water molecule dipole against the normal direction of the $MoS_2$ slab as displayed on Fig. 7. A negative value means that the dipole points to the slab that is to say that the hydrogen atoms
<figure><img src="image_9.png" /><figcaption>Fig. 7. Orientation of the dipole of the water molecules in comparison to the z-axis for different electrode potentials.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 8. Side views and planar average electrostatic potential with the Fermi level set to zero of the electrified MoS₂-water interface using (a) an implicit-only solvation model; (b) with a single explicit water layer.</figcaption></figure>

are closer to the slab than the oxygen atoms of the water molecules (H-down configuration). On the contrary, a positive value indicates that the water molecules is oriented in the opposite direction to the slab meaning that the oxygen atom is closer to the monolayer than the hydrogen atoms for this specific molecule (O-down configuration). When we look at Fig. 7 we notice that the orientation of the water molecules changes depending on the sign of the charges. When the interface is negatively charged, the molecules point to the monolayer. Conversely, for a positive potential the water molecules are oriented in the opposite direction. These results prove the observations made on the snapshots of Fig. 6 and are also in good accordance with the Figs. 5b and 5c. They can be explained by the fact that when the interface is positively charged, the negative part (oxygen atom) of the water dipole is attracted to the slab surface and on the other way around the positive part (hydrogen atoms) of the water dipole goes closer to the monolayer when the surface is negatively charged. Thus, it forces the water molecules to adopt a specific orientation: O-down for a positively charged interface and H-down for a negatively charged one. According to Fig. 7 this phenomenon is stronger when the absolute value of the applied potential rises. It means that the more the potential at the water/MoS₂ interface is high, the more the water molecules of the EDL will adopt a specific orientation.

<figure><img src="image_11.png" /><figcaption>Fig. 9. (a) Variation of double layer charge with applied bias potential (b) Variation of double layer capacitance with applied bias potential.</figcaption></figure>

### 3.3. Interface electrochemical properties through hybrid-solvation model

Fig. 8a illustrates the computed electrostatic potential distribution over the MoS₂ model, determined using a sole implicit solvation model. A PZC value of 1.13 V vs SHE is obtained. Following the procedure described in Ref. [16], a “sandwich” model is employed to construct the hybrid implicit/explicit model by mirroring the water layer along a perpendicular plane to the MoS₂ surface. As such, a symmetric setup that accelerates the convergence of the electrostatic potential within the implicit water region is achieved (see Fig. 8b). The potential of zero charge calculated for the sandwich model is 0.98 V vs SHE, a notably smaller value than that obtained without the explicit water layers. We note that adding more explicit water layers does not change the PZC value indicating that the two explicit water layers ensure a sufficient screening effect. Similar values of PZC were obtained in the case of semiconductor Rhombohedral boron monosulfide (r-BS) using the ESM-RSIM method [50].

Starting from the neutral model, the net charge in the cell was varied from -0.5 |*e*| to -0.5 |*e*| and the potential values calculated as shown in Fig. 9a. In addition, Fig. 9b shows the evolution of the calculated double-layer capacitance as a function of the applied potential. The double layer capacitance is obtained as the derivative of *Q*<sub>dl</sub> with respect to U and is numerically evaluated through centered finite differences derivation. Interestingly, two distinct linear regimes can be noticed in the evolution of the interfacial charge and the applied electrode potential (Fig. 9a). Initially, as the potential increases from -1.2 V to approximately -0.8 V, there is a gradual transition from a high negative charge of -3 µC/cm² to nearly zero charge. Above 1.0 V, there is a linear increase in the charge starting from a near zero value. This behavior can be ascribed to the semiconductor nature of the electrode. Typically, in a semiconductor/electrolyte interface, changing the electrode potential moves the semiconductor's energy bands relative
to the solution's Fermi level which leads to a smooth variation of the interfacial charge thanks to mobile ions that can continuously screen or neutralize the charge. However, when simulating a semiconductor/water interface in the absence of counter ions, the excess charge at the interface can only be balanced by the water dipoles. As a result, the charge in the semiconductor must be compensated almost exclusively by changes in band bending and occupancy of surface states, which can lead to the observed sudden shifts in total interfacial charge once the potential crosses particular energy levels. In an n-type material, applying an increasingly negative potential drives electrons to accumulate at the surface (accumulation regime) until the conduction band edge aligns with the Fermi level. Crossing this alignment point, commonly called the flat-band potential, triggers a rapid reconfiguration of charge, producing the observed jump around zero charge. Beyond this point, as the potential becomes more positive relative to the flat-band, a depletion region forms where the semiconductor surface is depleted of majority carriers, and the total interfacial charge again varies linearly. This behavior is also reflected on the capacitance values where we find a near constant plateau around 8.5 µF/cm² at negative potentials followed by a substantial decrease and a plateau of zero capacitance before increasing linearly for positive potentials. These results are in an overall agreement with the findings of Chen et al. where a declining trend in capacitance is also observed within the potential range of -0.3 V to 0.4 V [51].

The Bader charge analysis revealed a net electron transfer of 0.06 electrons per MoS₂ unit from interfacial water molecules to the MoS₂ substrate at the MoS₂/water interface.

## 4. Conclusion

We investigate the evolution of the double layer structure and its electrochemical properties at the interface with a MoS₂ monolayer under several bias potentials. We find that the structure of the electric double layer depends on the sign and the intensity of the applied bias potential. Indeed, a positively charged interface tends to attract the oxygen atoms of the water molecules while an excess of electrons in the system entails a modification of the orientation of the water molecules with hydrogen atoms coming closer to the MoS₂ slab. These results are in agreement with reported double layer structure at charged metal/water interfaces [2,52–54]. As for the double layer charge and capacitance, we find the semiconductor nature of the electrode entails a more complex band alignment, leading to abrupt jumps in surface charge and capacitance. These results demonstrate the usefulness of the hybrid implicit/explicit to achieve a fine understanding of electrochemical processes occurring at electrified interfaces.

### CRediT authorship contribution statement

**Fabien Mortier:** Writing – original draft Investigation, Formal analysis, Data curation. **Di Zhao:** Writing – original draft, Investigation, Formal analysis, Data curation. **Minoru Otani:** Writing – review & editing, Validation, Methodology. **Samuel Bernard:** Supervision. **Yun Wang:** Writing – review & editing, Validation, Supervision, Investigation, Funding acquisition, Conceptualization. **Assil Bouzid:** Writing – review & editing, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

The authors acknowledge financial support from the Australian Research Council Discovery Project (Grant No. DP210103266, DP210104010). This research was conducted on the supercomputers in National Computational Infrastructure (NCI) in Canberra, Australia, which is supported by the Australian Commonwealth Government, and Pawsey Supercomputing Centre in Perth with the funding from the Australian government and the Government of Western Australia, Australia. Calculations were performed by using resources from Grand Equipement National de Calcul Intensif (GENCI, grant no. A0120913426). Computational resources provided by the computing facilities Mésocentre de Calcul Intensif Aquitain (MCIA) of the Université de Bordeaux and of the Université de Pau et des Pays de l'Adour. We acknowledge funding from CNRS Institute of Chemistry through the "International Emerging Actions 2022" mobility grant (2DH2 project) and from Agence national de recherche under the RECIFE ANR-DFG project (Grant Number ANR-21-CE08-0036-01).

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.susc.2025.122870.

### Data availability

Data will be made available on request.

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