A non-metal doped VTe₂ monolayer: theoretical insights into the enhanced mechanism for the hydrogen evolution reaction

Abstract

Two-dimensional transition metal dichalcogenides (TMDCs), such as vanadium ditelluride (VTe₂), have emerged as promising catalysts for the hydrogen evolution reaction (HER) due to their unique layered structures and remarkable electronic properties. However, the catalytic performance of pristine VTe₂ remains inferior to that of noble metals. In this study, density functional theory (DFT) calculations were employed to systematically investigate the influence of fourteen different non-metal dopants on the HER activity of VTe₂. Our results disclose that N–VTe₂, P–VTe₂ and As–VTe₂ possess exceptional catalytic properties for the HER with the Gibbs free energy of hydrogen adsorption (ΔG_H*) values of 0.031, −0.032 and 0.024 eV, respectively. Furthermore, analyses of the geometric and electronic structures reveal that non-metal doping induces localized geometric distortions and charge redistribution, thereby altering the electronic environment of active sites and enhancing catalytic performance. More importantly, a composite descriptor φ, integrating the bond length between doped non-metal atoms and neighboring V atoms (L_NM–M) and the pz band center (ε_pz) of the doped atoms, demonstrates a strong correlation with ΔG_H* and may serve as an effective predictor of HER activity. These findings shed light on non-metal doping as an effective strategy for developing efficient, non-noble metal HER catalysts based on TMDCs.

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1. Introduction

Given the environmental issues caused by fossil fuel consumption, such as air pollution and greenhouse effect, there is an urgent need to adopt clean and sustainable renewable energy alternatives.^1–3 Green hydrogen (H₂) produced via water electrolysis is a key focus in renewable energy and environmental science because of its high energy density and clean combustion.^4,5 Electrochemical water splitting offers an efficient and environmentally friendly method for H₂ production,^6–8 but the development of cost-effective and high-performance catalysts remains a significant challenge.^9–11 Currently, platinum (Pt)-based catalysts are the most advanced for the cathodic hydrogen evolution reaction (HER), but their high cost and scarcity hinder their large-scale application in water splitting.^12–14 Therefore, developing efficient and affordable HER catalysts using earth-abundant elements is essential for replacing Pt-based materials.

Since the discovery of graphene in 2004,¹⁵ two-dimensional (2D) transition metal dichalcogenides (TMDCs) have attracted considerable attention due to their unique layered structures, expansive surface areas, and versatile electronic properties,^16,17 making them promising candidates for energy conversion. Substantial efforts have been devoted to advancing TMDC-based catalysts for the HER, capitalizing their abundant active sites and exceptional charge transfer properties.^18–21 For example, doping TMDCs with non-metal elements such as B,²² N,²³ O,²⁴ S,²⁵ P,^26,27 Se²⁸ and Te²⁹ has become a widely studied method for improving their catalytic performance in the HER. Impressively, non-metal doping in MoS₂, WS₂, and VSe₂ has been demonstrated to effectively modulate the electronic structure, optimize the hydrogen adsorption free energy, and enhance catalytic activity by improving charge transfer and increasing active site exposure.^30–32 Thus, this cost-effective and durable approach enhances the catalytic activity of TMDCs-based materials by optimizing their electronic structures and active sites, establishing non-metal doping as an effective strategy for advancing HER performance.

VTe₂, a newly synthesized material in the TMDC family, has garnered significant attention in recent years for its exceptional properties and promising potential in advanced applications.^33–38 Different from most traditional TMDCs, VTe₂ is notable for its diverse phase variants, metallic conductivity and magnetic properties.³⁹ It is worth noting that VTe₂ exhibits superior thermodynamic stability in the 1T (octahedral) phase.^40,41 Moreover, 1T-VTe₂ shows exceptional durability and reliable stability during electrocatalysis in aqueous solution.⁴² Recently, Fan et al. emphasized the suitability of VTe₂ monolayers as effective substrates for doping systems, demonstrating that the coordination of transition metals such as Cr and Fe significantly enhances their thermodynamic stability and electrocatalytic efficiency for the HER.⁴³ However, the catalytic activity of VTe₂-based materials remains limited, and the mechanisms underlying the enhancement of HER performance through non-metal doping are not yet fully understood.

In this work, density functional theory (DFT) calculations were systematically conducted to investigate the influence of fourteen different non-metal dopants on the HER activity of 1T-VTe₂ (namely, NM–VTe₂, where NM = B, C, N, O, F, Si, P, S, Cl, As, Se, Br, Te, and I). The calculations revealed that N–VTe₂, P–VTe₂ and As–VTe₂ exhibit considerable potential as HER catalysts. The enhanced catalytic activity of NM–VTe₂ was investigated through a detailed analysis of its geometric and electronic structures. As a key highlight, a descriptor was developed that correlates the bond length between the doped non-metal atom and the adjacent V atom, as well as the pz band center of the non-metal atom, to evaluate the ΔG_H* of NM–VTe₂. This work offers valuable insights into VTe₂-based atomic catalysts and provides a theoretical foundation for the rational design of efficient HER catalysts based on non-metal doped TMDCs.

2. Computational methods

Spin-polarized calculations based on DFT were performed using the Vienna Ab initio Simulation Package (VASP).⁴⁴ The exchange–correlation interactions were treated with the Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA).⁴⁵ The projector augmented wave (PAW) method was used to represent interactions between ionic cores and valence electrons.⁴⁶ The calculations employed a plane-wave basis set with a kinetic energy cutoff of 400 eV. The convergence criteria for the total energy and the maximum force were defined as 10⁻⁵ eV per atom and 0.03 eV Å⁻¹, respectively. To prevent interactions between periodic images, a vacuum layer of 15 Å was added along the z-direction. A 3 × 3 supercell of VTe₂ was constructed and optimized with Brillouin zone sampling performed using a Γ-centered 3 × 3× 1 k-point mesh. The convergence of the k-point was tested (see Fig. S1, ESI†). For electronic structure calculations, a denser k-point mesh of 6 × 6 × 2 was used to enhance accuracy. van der Waals interactions were accounted for using the DFT-D3 correction method proposed by Grimme.⁴⁷ The HER mechanism was analyzed using the climbing image nudged elastic band (CI-NEB) method,⁴⁸ with the same computational parameters as the structural optimizations. The initial and final states were fully optimized to ensure accuracy.

The binding energy (E_b) of the doped VTe₂ systems was calculated using:

E_b = E_NM–VTe2 − E_VTe2 – μ_NM + μ_Te

where E_VTe2–NM and E_VTe2 are the total energies of the doped and pristine VTe₂ systems, respectively. μ_NM and μ_Te represent the chemical potentials of the dopant nonmetal atom and the Te atom, respectively. The chemical potentials were derived from the most stable phases of the elements under standard conditions.

The hydrogen adsorption Gibbs free energy (ΔG_H*) was calculated using the computational hydrogen electrode (CHE) model:^49,50

ΔG_H* = ΔE_H* + ΔE_ZPE − TΔS_H

Here, ΔG_H* is the hydrogen adsorption energy, defined as:

ΔE_H* = E_substrate+H − E_substrate − 0.5E_H2

where E_substrate+H and E_substrate+H denote the total energies of the system with and without hydrogen adsorption, respectively, and E_H2 represents the total energy of a hydrogen molecule in the gas phase. The zero-point energy correction (ΔE_ZPE) and the entropy change (ΔS_H) were obtained from vibrational frequency calculations at the Gamma point. The zero-point energy of the adsorbed hydrogen was calculated directly, while the entropy of hydrogen in the gas phase was referenced from standard thermodynamic tables. These calculations provided the zero-point energy differences and entropy contributions required for determining the free energy. The temperature (T) was set to 298.15 K for all calculations. The CHE model simplifies the calculation of ΔG_H* by equating the chemical potential of a proton-electron pair (H⁺ + e⁻) to half the chemical potential of hydrogen gas under standard conditions.

The exchange current density (i₀) is a critical parameter for describing the kinetics of electrocatalytic interface reactions. It can be determined using the following relation:⁵¹

where k₀ is the rate constant, k_b is the Boltzmann constant, and T is the temperature. In this model, the effect of ΔG_H* is the primary factor, while other influences such as energy barriers and proton transfer are considered secondary.

The p-band center is a crucial concept for understanding the electronic structure and catalytic performance of materials.^52,53 It primarily characterizes the energy distribution of p-electrons on material surfaces and is particularly useful in explaining the catalytic behavior of elements and compounds involving non-metallic elements such as oxygen, nitrogen, and carbon.^54,55 Mathematically, the p-band center is defined as:

where ε represents the energy and n_p(ε) is the density of states (DOS) of p-electrons. This equation defines the center of the p-electron energy distribution as a weighted average of the p-orbital electronic DOS.

3. Results and discussion

3.1. Structure and stability

VTe₂ has a typical layered crystal structure with a central vanadium (V) layer sandwiched between two tellurium (Te) layers. To explore the incorporation of non-metal atoms into VTe₂, a single Te atom was substituted at a surface site within a 3 × 3 supercell of VTe₂, as depicted in Fig. 1a. This substitution corresponds to a doping concentration of 5.56%, representing a realistic low-level doping scenario that is commonly achievable under experimental conditions.^56,57 Fourteen non-metal elements, as shown in Fig. 1b, were selected for doping, encompassing a diverse range of elements that could significantly influence the electronic and catalytic properties of VTe₂.

Fig. 1 Schematic diagram of nonmetal-doped VTe₂, dopant atoms, and binding energy. (a) Top and side views of the VTe₂ structures with non-metal doping; (b) dopant atoms substituted in VTe₂; (c) binding energy between the nonmetal atoms and VTe₂.

Evaluating the stability of doped structures is critical for their practical applications, as it directly affects their performance and durability under operational conditions.⁵⁸ In this study, the stability of the non-metal-doped VTe₂ (NM–VTe₂) structures was evaluated by calculating their binding energy (E_b), as illustrated in Fig. 1c. Binding energy is a key parameter for determining thermodynamic stability, with lower E_b values indicating a more favorable doping process. It is worth noting that E_b values can vary depending on growth conditions and specific experimental parameters. The calculated results reveal that most non-metal dopants, except for Si and Cl, exhibit negative E_b values, suggesting their thermodynamic favorability for integration into the VTe₂ lattice. Particularly, O atom stands out with the most negative binding energy of −4.301 eV, indicating that O–VTe₂ is the most thermodynamically stable dopant and the easiest to incorporate under standard growth conditions. To evaluate the stability of this configuration, which is vital for catalytic performance, we performed ab initio molecular dynamics (AIMD) simulations for 5000 fs at 300 K. As shown in Fig. 2, no significant geometric deformation or bond breaking is observed, and the total energy and temperature of the VTe₂, N–VTe₂, P–VTe₂ and As–VTe₂ remain stable, fluctuating around equilibrium values, which confirms their dynamic stability at room temperature.

Fig. 2 Temperature and energy evolution profiles for (a) VTe₂, (b) N–VTe₂, (c) P–VTe₂ and (d) As–VTe₂ at 500 K, as obtained from AIMD simulations.

3.2. Hydrogen evolution activity

Based on the positions of the doped non-metal atoms, the hydrogen adsorption sites on the NM–VTe₂ surface can be categorized into two distinct types. As illustrated in Fig. S2 (ESI†), site 1 corresponds to the location of the non-metal atom, marked by the green dashed line, while site 2 refers to the nearest Te atom adjacent to the non-metal atom, indicated by the purple dashed box. To assess the HER catalytic activity of NM–VTe₂, the ΔG_H* was calculated for both site 1 and site 2, with the results shown in Fig. 3a. In general, to achieve optimal HER performance, it is widely accepted that catalysts should satisfy the condition |ΔG_H*| ≤ 0.20 eV, which is represented by the blue dashed line.^59,60 The results reveal that at site 2, the ΔG_H* value for NM–VTe₂ remains similar to that of pristine VTe₂ (0.413 eV), indicating a relatively limited impact of site 2 on hydrogen adsorption. In contrast, at site 1, the ΔG_H* values span a much broader range, from −0.532 eV to 1.906 eV. This variability suggests that site 1 is more tunable and, therefore, more likely to facilitate effective hydrogen adsorption. Consequently, the following discussion will focus on site 1. It was found that doping with non-metallic atoms such as O, F, S, Cl, Se, Br, and I generally weakened hydrogen adsorption at site 1, leading to modified ΔG_H* values. Among these, non-metallic dopants, particularly F, Cl, Br, and I, exert a more significant negative effect on catalytic activity. Notably, doping with B, C, N, P, and As resulted in ΔG_H* values that fall within the ideal range for high-performing HER catalysts.

Fig. 3 Evaluation of hydrogen evolution activity for NM–VTe₂ systems. (a) Calculated ΔG_H* values at the site 1 and site 2 positions; (b) volcano plot of the exchange current density log(i₀) as a function of ΔG_H*.

To further evaluate the HER performance of different NM–VTe₂ systems, a volcano curve was constructed by plotting the exchange current density (i₀) as a function of ΔG_H* (Fig. 3b). The relationship between i₀ and ΔG_H* provides a quantitative means to assess the HER catalytic performance of the materials. Catalysts with positive (negative) ΔG_H* values appear on the right (left) side of the volcano curve, while those with ΔG_H* values approaching the optimal range are located at the peak of the curve. According to Sabatier's principle, catalysts such as Si–VTe₂, B–VTe₂, C–VTe₂, and P–VTe₂, which exhibit negative ΔG_H* values (see Fig. 3a), demonstrate strong interactions with adsorbed hydrogen atoms (H*), positioning them at the lower left of the volcano curve, where they show minimal i₀. On the other hand, NM–VTe₂ catalysts (NM = As, N, O, S, Se, F, I, Br, and Cl) with positive ΔG_H* values suggest that hydrogen adsorption is less favorable, placing them at the bottom right of the volcano curve with similarly low i₀ values. Impressively, N–VTe₂ (0.031 eV), P–VTe₂ (−0.032 eV), and As–VTe₂ (0.024 eV) exhibit ΔG_H* values close to the ideal value of 0 eV, corresponding to the highest exchange current densities and positioning them at the top of the volcano curve. The complete HER process starts with hydrogen adsorption (Volmer reaction), followed by either the Heyrovsky (H* + H₃O⁺ + e⁻ → H₂ + H₂O) or Tafel (H* + H* → H₂) reaction. Both the Heyrovsky and Tafel reactions occur concurrently in the second step. The Tafel slope is used experimentally to determine the rate-limiting step of the system.⁶¹ Additionally, when the calculated ΔG_H* approaches zero, the Tafel mechanism predominates in the HER process. To better gain a deeper insight into the HER reaction mechanism for N–VTe₂, P–VTe₂, and As–VTe₂, Tafel reactions were evaluated. For comparison, VTe₂ was also calculated. As illustrated in Fig. 4, the calculated activation barriers for N–VTe₂, P–VTe₂, and As–VTe₂ are 1.193, 0.933, and 0.736 eV, all of which are lower than the 3.931 eV barrier for VTe₂. This indicates that non-metal doping can significantly improve the HER catalytic activity of VTe₂.

Fig. 4 Free energy profiles illustrating the underlying reaction mechanisms of the Tafel step for the HER on (a) VTe₂, (b) N–VTe₂, (c) P–VTe₂ and (d) As–VTe₂. The right panel depicts the reaction pathway, highlighting the initial state (IS), transition state (TS), and final state (FS).

3.3. Electronic structure analysis

The tunability of catalytic activity in NM–VTe₂, which is facilitated by non-metallic dopants from various periods, is critical for optimizing HER performance.^62,63 To better understand this, the connection between ΔG_H* and the dopant's valence electron count was analyzed, as illustrated in Fig. 5. The results show a clear trend in which ΔG_H* increases with the number of valence electrons across different periods. This suggests that dopants with a higher valence electron count result in weaker hydrogen adsorption. This observation highlights the crucial role of the dopant's electronic configuration in modulating HER activity, emphasizing the importance of considering the dopant's electronic properties when designing efficient catalysts.

Fig. 5 Electron density difference of NM–VTe₂ structures before and after doping with a nonmetal atom. The isosurface value is set to 0.005 eV Å⁻³. Regions of electron accumulation and depletion are shown in yellow and cyan, respectively. The inset shows the variation of ΔG_H* with the number of valence electrons in the nonmetal dopant.

To gain deeper insight into the impact of dopants on the electronic structure, further analyses were conducted using charge density difference and Bader charge calculations. As depicted in Fig. 5, electron accumulation between the non-metal dopants and V atoms, represented by the yellow regions, initially increases and then decreases as the atomic number of the dopants increases within each period. This non-monotonic behavior suggests a complex variation in the interaction strength between the dopant and V atoms. Moreover, the net electron gain (Q_NM) by the dopants, presented in Table S1 (ESI†), follows a similar non-monotonic trend, reinforcing the significance of charge redistribution in modulating HER activity. Based on these observations, it can be concluded that the electronic properties of the dopants, particularly the charge transfer between the dopant and V atoms, are critical factors influencing the catalytic performance of NM–VTe₂ systems.

The catalytic performance of materials is closely linked to both structural and electronic modifications, with local structural perturbations playing a crucial role in modulating catalytic activity.⁶⁴Fig. 6a illustrates the variation in bond length (L_NM–M) between the doped non-metal atom and its nearest V atom as a function of the dopant's valence electron count. Initially, the bond length decreases and then increases as the number of valence electrons rises, suggesting that the dopant's electronic properties significantly influence the local structure. Similarly, Fig. 6b demonstrates that the Q_NM for the doped non-metal atom follows an initial increase followed by a decrease with rising valence electron count. The correlation between Q_NM and L_NM–M, shown in Fig. S3 (ESI†), further emphasizes the interplay between structural modifications and charge redistribution. These results underline that doping not only alters the local structure but also modifies the electronic environment, which in turn impacts the HER activity of NM–VTe₂ systems.

Fig. 6 Relationships among bond length, electronic charge, and hydrogen adsorption energy in NM–VTe₂ structures. (a) Dependence of the bond length (L_NM−M) between the doped nonmetal atom and neighboring metal atoms on the number of valence electrons of the dopant; (b) variation of the charge gained by the doped nonmetal atom (Q_NM) with respect to the number of valence electrons of the dopant; (c) correlation between ΔG_H* and L_NM−M; (d) relationship between ΔG_H* and Q_NM.

Despite the structural and electronic variations observed, scatter plots of ΔG_H* against Q_NM and L_NM–M (Fig. 6c, d) reveal no simple correlation between these parameters and ΔG_H*. This suggests that the ΔG_H* values of NM–VTe₂ systems cannot be attributed to any single structural or electronic factor. Instead, the HER activity appears to be governed by a complex interplay of multiple factors, reflecting the inherently intricate nature of its catalytic behavior. This highlights the importance of adopting a comprehensive approach that takes into account both structural and electronic contributions to better understand the catalytic performance of NM–VTe₂ systems.

Further analysis of the orbital hybridization between Te atoms in pristine VTe₂ and hydrogen atoms was performed to elucidate the bonding interactions between the non-metal atoms and hydrogen. As shown in the DOS plots (Fig. 7a and b), the px and py orbitals of the Te atom exhibit negligible changes before and after hydrogen adsorption. In contrast, the pz orbitals show significant hybridization with the hydrogen 1s orbital, resulting in prominent hybridization peaks. This hybridization plays a crucial role in the HER process by inducing orbital splitting between the surface Te atoms and the adsorbed hydrogen into bonding (σ) and antibonding (σ*) orbitals, as schematically illustrated in Fig. 7c. The corresponding splitting significantly influences the strength of hydrogen adsorption, as the reduced occupancy of the antibonding σ* orbital stabilizes hydrogen adsorption, thereby enhancing the catalytic activity of VTe₂. This mechanism mirrors the sp-hybridization observed in oxygen–hydrogen interactions in other catalytic systems, highlighting the importance of orbital interactions in facilitating efficient hydrogen adsorption.^65,66 By analyzing the role of Te p orbitals in hydrogen adsorption, the relationship between ΔG_H* and the pz band center (ε_pz) in the NM–VTe₂ system was explored, as shown in Fig. 7d. The results indicate that while the ε_pz captures the general trend of ΔG_H* across different periods, as shown in Fig. S4 (ESI†), it is inadequate as a standalone descriptor for accurately predicting the ΔG_H* values of NV–VTe₂ systems. Given the complex interplay between the electronic structure and catalytic performance, a multi-parameter approach is essential for effectively predicting and optimizing catalytic behavior.

Fig. 7 Density of states (DOS) and orbital hybridization analysis for VTe₂ before and after hydrogen adsorption, along with the relationship between hydrogen adsorption performance and the pz band center in NM–VTe₂ systems. (a) The p-orbital of Te atom in VTe₂ before hydrogen adsorption; (b) the p-orbital of Te atoms in VTe₂ after hydrogen adsorption, alongside the s-orbital of the adsorbed hydrogen atom; (c) orbital hybridization between Te atom in VTe₂ and the adsorbed hydrogen; (d) relationship between ΔG_H* and the pz band center (ε_pz) in NM–VTe₂ systems.

3.4. Development of predictive descriptors

Previous studies have shown that a single descriptor falls short in accurately predicting catalytic activity, as complex factors such as geometric structure and electronic properties significantly influence performance. To overcome this limitation, a variety of composite descriptors have been developed.^59,67 For example, in the case of transition metal-doped transition metal carbides and nitrides (MXenes), Wang et al. employed symbolic regression to develop a composite descriptor composed of the Fermi level, bond length, and atomic radius to accurately describe HER activity across different sites.⁶⁸ To capture the intricate structure–property relationships of NM–VTe₂ systems, it is essential to combine multiple parameters into composite descriptors.

In this study, we used the sure independence screening and sparsifying operator (SISSO) method to develop a more interpretable composite descriptor,⁶⁹ denoted as φ. The SISSO method constructs descriptors by performing algebraic operations (+, −, ×, /) on primary features, enabling the identification of meaningful combinations that are strongly correlated with the target property. The descriptor φ is defined as follows:

φ = L_NM–M² × ε_pz

where L_NM–M represents the bond length between the doped non-metal atom and the adjacent V atom, while ε_pz denotes the pz band center of the non-metal atom. This combination effectively captures both the local structural distortions introduced by doping and the electronic properties of the active sites. As shown in Fig. 8a, a strong correlation exists between φ and ΔG_H*, with a coefficient of determination (R²) of 0.93, significantly higher than that of the previously discussed individual descriptors.

Fig. 8 Correlation between ΔG_H* and the descriptor φ across two different systems. (a) NM–VTe₂ system. (b) NM–VSe₂ system.

Expanding this study to other doping systems further validates the robustness and generalizability of φ. As illustrated in Fig. 8b, when applied to NM–VSe₂, φ demonstrates a strong predictive capacity with an R² of 0.89, affirming its utility across different doped TMDCs. This finding underscores the descriptor's capability to generalize across chemically similar materials, suggesting that φ could serve as a universal descriptor for evaluating HER activity in TMDCs doped with non-metals. These findings provide valuable insights into the HER mechanism of non-metal-doped TMDCs, particularly within the NM–VTe₂ systems. It underscores the need for advanced composite descriptors that can capture the multifaceted nature of catalytic systems. Such descriptors not only enhance our understanding of catalytic mechanisms but also provide valuable insights for the rational design of high-performance catalysts, paving the way for future advancements in catalyst optimization and discovery.

4. Conclusions

This study systematically examined the effects of non-metal atom doping on the HER activity of VTe₂ using density functional theory calculations. The results indicate that introducing dopants such as N, P, and As significantly enhances HER performance by modulating the electronic structure, which in turn optimizes the ΔG_H*. The doping process induces localized geometric distortions and charge redistribution, thereby altering the electronic environment of the active sites. The enhanced HER activity is strongly correlated with changes in the bond length between the doped non-metal atoms and neighboring V atoms (L_NM–M) and the pz band center (ε_pz) of the dopants. To accurately predict the HER activity, an effective composite descriptor φ was developed using the SISSO method. This descriptor correlates strongly with ΔG_H*, accounting for both structural and electronic factors influenced by doping and achieving an R² = 0.93. These findings provide valuable insights into the design of non-noble metal HER catalysts based on TMDCs.

Data availability

The data supporting this article have been included as part of the ESI.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Fund from the Research Foundation for Advanced Talents of Xuzhou College of Industrial Technology (Grant XGY2023ZXJB01), the Natural Science Foundation of Jiangsu Higher Education Institutions of China (No. 24KJB150031), and the National Natural Science Foundation of China (NSFC Grant number 12404086 and 52370057).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5cp00670h

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