Hydrogen adsorption and dissociation on transition metal anchored B₁₂N₁₂ nanocages: insights from density functional theory

Abstract

The growing worldwide transition to carbon-neutral energy systems requires the development of novel, efficient, and sustainable catalysts for key reactions, including hydrogen dissociation. As hydrogen is increasingly recognised as a clean and scalable energy carrier, the design of cost-effective, noble metal-free single-atom catalysts (SACs) has become a pressing priority. In this study, we employ density functional theory (DFT) to systematically explore a new class of SACs based on transition metal-anchored boron nitride nanocages (M@B₁₂N₁₂) for the hydrogen dissociation reaction (HDR). To better reflect real reaction environments, H₂ dissociation was studied in water using an implicit solvation model. Interaction energy (E_int) analyses confirm the thermodynamic stability of all designed complexes, while Co@B₁₂N₁₂, Ni@B₁₂N₁₂, Fe@B₁₂N₁₂, and Cr@B₁₂N₁₂ have been found to possess very low activation energy (E_a) barriers, 0.14 eV, 0.16 eV, 0.19 eV, and 0.21 eV for H₂ activation, respectively, showing the best catalytic performance. To get insights into the intrinsic activation process, we perform detailed natural bond orbital (NBO), electron density difference (EDD), and quantum theory of atoms in molecules (QTAIM) analyses. Furthermore, reduced density gradient (RDG) and non-covalent interaction (NCI) analyses reveal the presence of both weak van der Waals forces and directional covalent interactions that collectively stabilise transition states and promote efficient H–H bond cleavage. Following the multi-dimensional analysis of the electronic structure, the synergistic mechanism of charge transfer and orbital hybridization observed demonstrates that the Co@B₁₂N₁₂ complex exhibited high efficiency as a SAC with a minimum E_a value of 0.14 eV for hydrogen dissociation. The insights provide useful design guidelines for the next-generation hydrogenation catalysts, which directly leads to the establishment of hydrogen technologies that are scalable in providing clean energy solutions to the world.

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Introduction

The swift increase in the global population has driven an unprecedented rise in energy demand. However, this surge contrasts sharply with the rapid depletion of traditional fossil fuel resources.¹ Moreover, the persistent reliance on fossil fuels continues to exacerbate environmental degradation, primarily through the emission of greenhouse gases and other pollutants.² In light of these dual challenges, energy scarcity and environmental deterioration, there is a pressing need to shift towards cleaner and more sustainable energy solutions. Among the various alternatives, hydrogen emerges as a particularly attractive candidate.³ It offers high energy density and can be synthesized from renewable resources, and its use results in water as the sole byproduct, thereby minimizing environmental harm.⁴ Furthermore, hydrogen demonstrates remarkable energy conversion efficiency, making it especially promising for transportation sectors.⁵ Collectively, these attributes establish hydrogen as a critical player in the transition towards a sustainable and environmentally responsible energy future.⁶ Hydrogen dissociation involves the cleavage of molecular hydrogen (H₂) into reactive atomic hydrogen species, which can then be adsorbed onto or diffused into the catalyst.⁷ This mechanism facilitates the storage of substantial quantities of hydrogen under relatively mild conditions of pressure and temperature.⁸ The kinetics of hydrogen dissociation in metal–hydrogen systems are strongly influenced by thermodynamic parameters, particularly temperature and pressure.^9,10 The capability of metals to dissociate hydrogen varies according to their electronic structure and surface properties.¹¹ Importantly, in hydrogenation reactions, the dissociation of H₂ is regarded as one of the rate-limiting steps, thus highlighting the importance of understanding the nature and behavior of active sites on catalytic surfaces.¹² This has led to extensive research into optimizing metal-based catalysts for improved dissociation performance. Furthermore, catalytic adsorption and activation of molecular hydrogen are fundamental steps in large-scale hydrogenation and dehydrogenation processes.¹³ Typically, hydrogen is first physisorbed or chemisorbed onto the catalyst surface, followed by its dissociation into reactive hydrogen atoms.¹⁴ Therefore, a detailed understanding of the elementary mechanisms involved in hydrogen dissociation is vital for the rational design of high-efficiency catalysts. One of the persistent challenges in advancing the hydrogen economy remains the development of materials capable of storing hydrogen in a safe and energy-efficient manner.

Catalysts play a pivotal role in advancing hydrogen dissociation reactions (HDRs), which are essential for hydrogen storage and energy conversion technologies. While noble metals like platinum,¹⁵ palladium,¹⁶ rhodium,¹⁷ ruthenium,¹⁸ and gold¹⁹ demonstrate superior catalytic performance for the HDR, their limited availability and high cost hinder large-scale application. To address these limitations, research is increasingly focused on developing cost-effective alternatives that do not compromise efficiency. Single-atom catalysts (SACs) have emerged as a highly promising class of materials for the HDR due to their exceptional atom utilization and catalytic activity.²⁰ In SACs, individual metal atoms are uniformly anchored on suitable supports, offering highly active and accessible sites for hydrogen molecule adsorption and dissociation.²¹ Although SACs show great potential in the HDR, deeper insights into their mechanistic behavior and long-term stability are still needed to optimize their practical performance.

Traditional materials such as graphene oxide,²² activated carbon,²³ carbon nanotubes,²⁴ and fullerenes^25–28 have been extensively studied for hydrogen storage applications. Yet, their pristine forms often exhibit weak interactions with hydrogen molecules, limiting their storage capacities. To overcome these limitations, various modification strategies have been employed, including doping with alkali,^29–31 alkaline earth,^32–34 and transition metals,^35–42 as well as heteroatom substitution with elements like boron (B)^43–46 and nitrogen (N).^47,48

Among the diverse materials explored, boron nitride (BN) nanostructures have garnered considerable attention due to their exceptional thermal stability, chemical inertness, and unique electronic properties.^49–51 Notably, the B₁₂N₁₂ nanocage, a highly symmetrical and stable structure, has emerged as a promising candidate for hydrogen storage applications. However, pristine B₁₂N₁₂ exhibits limited hydrogen adsorption capabilities, primarily due to its inert surface and lack of active sites. To enhance its hydrogen storage performance, recent studies have investigated the doping of B₁₂N₁₂ with various transition metals.^52,53 Weng et al. developed porous BN materials with tailored textures and chemical features to study hydrogen adsorption.⁵⁴ Co and Pt-functionalized, carbon-doped h-BN structures achieved remarkable hydrogen storage up to 24.9 wt%.⁵⁵ Hu et al. employed DFT to explore Si₂BN monolayers, reporting H₂ adsorption energies between 0.187 and 0.214 eV.⁵⁶ Banerjee et al. found that Li atoms on BN nanosheets resist clustering, supporting stable hydrogen storage.⁵⁷ Bhattacharya et al. showed that Ti doping in graphene, BN, and BC₄N prevents metal clustering, enhancing hydrogen uptake.⁵⁸ Chen et al. synthesized BN nanotubes on a large scale, while carbon-doped BN structures dispersed with Sc stored up to six H₂ molecules.^59,60 Bis-BN cyclohexane exhibited high kinetic stability and fast hydrogen release under catalytic conditions. Similarly, Rakrai et al. explored the hydrogen storage and sensing capabilities of group 8B transition metal-doped B₁₂N₁₂ nanocages. Their DFT calculations demonstrated that doping with metals like Os and Ir not only strengthens the interaction between hydrogen molecules and the nanocage but also reduces the energy gap, thereby improving the material's hydrogen adsorption capacity.⁶¹ Ni-doped B₁₂N₁₂ clusters have been investigated for their hydrogen adsorption properties, revealing that the presence of Ni atoms facilitates the dissociation of hydrogen molecules and alters the electronic structure of the nanocage, thereby improving storage performance.⁶²

Despite these advancements, a comprehensive understanding of the hydrogen adsorption and dissociation mechanisms of first-row transition metal-anchored B₁₂N₁₂ nanocages remains limited. In the present study, a novel B₁₂N₁₂ nanocage structure has been designed and systematically explored for hydrogen adsorption and dissociation using DFT. The proposed nanoring framework is composed of eight six-membered (hexagonal) and six four-membered (tetragonal) B–N rings. To the best of our knowledge, this specific B₁₂N₁₂ nanoring architecture is reported for hydrogen splitting applications for the first time. The hydrogen activation and storage capabilities of first-row transition metal (Sc–Zn) decorated B₁₂N₁₂ nanocages have been investigated, a study not previously addressed in the literature. Transition metal atoms are exohedrally anchored onto the nanocage surface, and the stability and efficiency of these complexes are evaluated through key computational descriptors including interaction energies, hydrogen adsorption energies, hydrogen activation barriers, Natural Bond Orbital (NBO) analysis, Electron Density Difference (EDD) mapping, Noncovalent Interaction (NCI) analysis, Quantum Theory of Atoms in Molecules (QTAIM) analysis, and electronic Density of States (DOS) profiles.

Computational methodology

All density functional theory (DFT) simulations in this study for the aqueous phase were performed using the Gaussian 09 software suite.⁶³ Geometry optimizations for all molecular systems were carried out at the ωB97X-D/def2-TZVP level of theory.^64,65 The ωB97X-D functional, a range-separated hybrid functional with empirical dispersion corrections, has been widely recognized for its accuracy in describing noncovalent interactions, electronic structures, and reaction energy profiles.^66,67 This level of theory has been particularly effective in modeling the properties and reactivities of B₁₂N₁₂-based nanostructures, making it suitable for SAC applications.^68,69 As such, ωB97X-D was consistently employed throughout this work for optimizing molecular geometries and evaluating reaction mechanisms.

To characterize the nature of the stationary points on the potential energy surface (PES), vibrational frequency calculations were performed at the same theoretical level. Reactants and products were confirmed as local minima based on the complete absence of imaginary frequencies, while transition states were identified by the presence of a single imaginary frequency. These transition states were further validated through eigenvector analysis, ensuring that the imaginary mode corresponded to the reaction coordinate, thereby confirming the transition state nature. The solvent effect on the dissociation pathway was assessed by applying the PCM (polarizable continuum model)^70–72 with water as the solvent by using the same level of theory.

Optimized geometries and structural analyses were performed using GaussView 5.0⁷³ and Chemcraft,⁷⁴ while additional visualization and trajectory inspections were conducted using Visual Molecular Dynamics (VMD)⁷⁵ where applicable. These tools enabled comprehensive examination of spatial arrangements and electronic interactions within the anchored nanostructures.

To investigate catalytic behavior toward the HDR, first-row transition metals, specifically from Sc to Zn, were exohedrally anchored onto the B₁₂N₁₂ nanocage. Multiple adsorption sites were explored for each metal to determine the most stable binding configuration. Owing to the electronic diversity and open-shell nature of TMs, spin multiplicities significantly affect the stability and reactivity of the anchored systems. Therefore, for each metal-anchored complex, the first four lowest spin multiplicities, ranging up to the septet or octet states, were optimized to identify the ground-state configuration with the minimum Gibbs free energy.

Following spin-state optimization, the most thermodynamically favorable configurations were subjected to further analysis. Interaction energy calculations and mechanistic evaluations of the hydrogen dissociation process were conducted on these selected spin states. The interaction energy (E_int) between the metal atom and the B₁₂N₁₂ nanocage was computed using the standard supermolecular approach, expressed as:

Here, refers to the total energy of the optimized metal-anchored complex, E_B12N12 denotes the energy of the isolated B₁₂N₁₂ nanocage, and E_M represents the energy of the isolated transition metal atom in its most stable spin multiplicity. This method provides a quantitative measure of the binding strength and thermodynamic stability of the metal-anchored complexes.

To evaluate the binding strength between the hydrogen molecule and the designed transition metal-anchored B₁₂N₁₂, the adsorption energy (ΔE_ads) was calculated using the following equation:

In this equation, represents the total energy of the hydrogen-adsorbed M@B₁₂N₁₂ complex, E_H2 denotes the energy of an isolated hydrogen molecule, and corresponds to the energy of the optimized M@B₁₂N₁₂.

In this study, the reaction energy (ΔE) and activation energy barrier (E_a) for hydrogen dissociation on M@B₁₂N₁₂ complexes were computed using the following equations:

ΔE = E_P − E_R (3)

E_a = E_TS − E_R (4)

where E_R, E_TS, and E_P represent the energies of the reactants, transition state, and products, respectively. These calculations provide insights into the thermodynamic feasibility and kinetic barriers of the HDR on the M@B₁₂N₁₂ complexes. To further investigate the interaction between the donor (hydrogen molecule) and the acceptor (transition metal-anchored B₁₂N₁₂) species during the hydrogen dissociation process, EDD analysis was performed. This analysis highlights the redistribution of electron density upon adsorption, indicating the nature of the interaction between the hydrogen molecule and the catalyst surface. Additionally, NBO analysis was conducted at the ωB97X-D/def2-TZVP level to examine the orbital interactions and charge transfer between the hydrogen molecule and the transition metal sites. This analysis aids in understanding the bonding characteristics and electronic perturbations upon hydrogen adsorption. Furthermore, QTAIM analysis was performed using the Multiwfn 3.8 program⁷⁶ to evaluate the nature of interatomic interactions, providing a topological perspective on the bonding interactions within the M@B₁₂N₁₂ complexes. Collectively, these computational analyses offer a comprehensive understanding of the reaction mechanisms, electronic interactions, and catalytic properties of the M@B₁₂N₁₂ complexes in HDRs.

MD simulation

The GROMACS package was used to perform MD simulations for this study.^77,78 The ACPYPE tool generated topology files and force field parameters for nanocage complexes.^79,80 The LINCS algorithm⁸¹ enforced constraints on all hydrogen atom bonds. The particle mesh Ewald method⁸² handled electrostatic interactions at a 1.2 nm cutoff distance while van der Waals interactions received the same 1.2 nm cutoff distance. The Berendsen thermostat was used to control the temperature at 300 K before starting 100 ns production simulations to assess the stability and dynamic behavior of the nanocage system.

Results and discussion

Optimized geometrical configurations and adsorption energetics

M@B₁₂N₁₂ catalysts were subjected to full geometric optimization to determine their most energetically favorable configurations before hydrogen adsorption. All optimizations were carried out using the hybrid DFT approach, specifically at the ωB97X-D/def2-TZVP level of theory. The pristine B₁₂N₁₂ nanocage exhibits a quasi-spherical structure comprising eight six-membered (hexagonal) and six four-membered (tetragonal) B–N rings, characterized by two distinct B–N bond lengths.^83,84 The bond length between two hexagonal rings (hh) is approximately 1.43 Å, while the bond length between a hexagonal and a tetragonal ring (ht) is about 1.47 Å. Our computed structural parameters are in strong agreement with the literature data,⁵² thereby validating the reliability of the current computational methodology. The optimized structure of the pristine B₁₂N₁₂ cage is illustrated in Fig. 1.

Fig. 1 Optimized molecular geometry of the isolated B₁₂N₁₂ nanocage. Boron atoms are depicted in yellow, while nitrogen atoms are shown in blue.

To investigate the interaction between M and the B₁₂N₁₂ framework, various exohedral and endohedral anchoring configurations were explored. Specifically, the exohedral anchoring sites included adsorption on top of tetragonal and hexagonal rings (referred to as position 64), as well as atop the bond connecting two adjacent hexagonal rings (position 66).

Additionally, endohedral encapsulation of the TM atom within the cage was also considered. Among these configurations, the exohedral anchoring at position 64, where the M atom establishes direct bonding interactions with both tetragonal and hexagonal rings, was consistently found to be the most energetically stable across all M@B₁₂N₁₂ complexes.

Spin-polarized DFT calculations were employed to identify the ground-state spin multiplicity for each complex. For each M@B₁₂N₁₂ system, the four lowest possible spin states were analyzed to determine the most stable electronic configuration.

Owing to their partially filled d-orbitals, metals can exhibit a diverse range of spin states, which originate from distinct electronic arrangements including spin-up and spin-down interactions. These spin states are also significantly modulated by the nature of the metal–ligand coordination environment. The relative energies associated with the different spin states, calculated in kcal mol⁻¹, are tabulated in Table S1 (SI). These values are almost comparable to those reported in the literature.⁸⁵ The most stable spin states identified for each complex are as follows: Sc@B₁₂N₁₂ (doublet), Ti@B₁₂N₁₂ (triplet), V@B₁₂N₁₂ (quartet), Cr@B₁₂N₁₂ (quintet), Mn@B₁₂N₁₂ (sextet), Fe@B₁₂N₁₂ (quintet), Co@B₁₂N₁₂ (quartet), Ni@B₁₂N₁₂ (singlet), Cu@B₁₂N₁₂ (doublet), and Zn@B₁₂N₁₂ (singlet). All computations were carried out assuming neutral charge conditions for the M@B₁₂N₁₂ complexes. The spin state corresponding to the lowest total electronic energy was considered the ground state and was consequently used for all subsequent analyses.

Interaction bond lengths and energies are fundamental parameters for evaluating the thermodynamic feasibility and structural integrity of molecular systems. As shown in Fig. 2, the computed distances between M atoms and the B₁₂N₁₂ nanocage range from 1.84 Å to 2.88 Å for M–N bonds and from 1.96 Å to 2.66 Å for M–B bonds. These values suggest that the interaction is primarily chemisorptive in nature. The Ni@B₁₂N₁₂ complex demonstrates the shortest M–N and M–B bonds at 1.84 Å and 1.96 Å, respectively, which aligns with its most favorable interaction energy of −2.71 eV, indicating enhanced thermodynamic stability. In contrast, the Zn@B₁₂N₁₂ system presents the longest M–N bond (2.88 Å) and M–B separation (2.66 Å).

Fig. 2 Optimized molecular structures of the thermodynamically stable M@B₁₂N₁₂ nanocage complexes, illustrating the metal–boron (M–B) and metal–nitrogen (M–N) bond lengths.

In this study, we modeled neutral transition metals; however, the anchoring process induces noticeable charge transfer from the M atoms to the electron-deficient boron cage. This redistribution of charge endows the B–M bonds with partial ionic character, allowing them to exhibit behaviour similar to that of cationic metal centres within the otherwise neutral framework. The B–M interaction results from a mix of orbital overlap and electrostatic forces. The electron-deficient B atoms of the B₁₂N₁₂ cage act as suitable acceptors, engaging with the valence d-orbitals of the transition metals. As in the case of Ni, partially filled d-orbitals promote both σ-donation and π-back-donation with boron 2p orbitals, strengthening the covalent character and yielding a shorter bond length of 1.96 Å, while Zn possesses a filled d-shell that restricts effective orbital overlap, so its bonding with B is weaker and primarily electrostatic, which explains the longer separation of 2.66 Å. Overall, the differences in bond lengths across the series can be directly linked to variations in orbital interaction, charge transfer, and back-donation between the metal centers and the B₁₂N₁₂ framework.

Interaction energies (ΔE_int) for all M@B₁₂N₁₂ systems were determined using the expression provided in eqn (1), and the numerical results are listed in Table 1. The consistently negative values for all complexes confirm the energetic favorability of M adsorption on the B₁₂N₁₂ surface. Among these, Ni@B₁₂N₁₂ is the most stable, exhibiting the highest interaction energy (−2.71 eV), followed by Cr@B₁₂N₁₂ (−2.46 eV), both suggesting strong metal–cage interactions. This energetic stability corresponds well with the observed trend of decreasing bond lengths. The interaction energies for all systems fall within the range of −0.31 eV to −2.71 eV. Importantly, no noticeable structural deformation of the nanocage is detected after full geometry optimization, indicating the structural resilience of B₁₂N₁₂ upon M anchoring.

Table 1 Computed values of interaction energies (ΔE_int) for M adsorption on the B₁₂N₁₂ nanocage, hydrogen adsorption energies (ΔE_ads) for H₂TM@B₁₂N₁₂ complexes, and activation energy barriers (ΔE_a) associated with the H₂ dissociation process

Complexes	ΔEint (eV)	Complexes	ΔEads (eV)	ΔEa (eV)
Sc@B12N12	−1.01	H2Sc@B12N12	−2.89	1.37
Ti@B12N12	−1.10	H2Ti@B12N12	−2.96	1.20
V@B12N12	−0.31	H2V@B12N12	−1.80	1.41
Cr@B12N12	−2.46	H2Cr@B12N12	−2.49	0.21
Mn@B12N12	−1.17	H2Mn@B12N12	−3.62	1.50
Fe@B12N12	−1.91	H2Fe@B12N12	−3.38	0.19
Co@B12N12	−1.74	H2Co@B12N12	−2.53	0.14
Ni@B12N12	−2.71	H2Ni@B12N12	−3.61	0.16
Cu@B12N12	−0.33	H2Cu@B12N12	−1.02	0.61
Zn@B12N12	−0.82	H2Zn@B12N12	1.38	2.96

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Hydrogen molecule adsorption on M-decorated B₁₂N₁₂ nanocage catalysts

Adsorption energy (E_ads) of an atom or molecule on a surface is quantitatively defined as the energy required to desorb the species from the surface, thereby reflecting the strength of the interaction between the adsorbate and the substrate. Typically, this process is exothermic in nature, releasing energy when a gaseous molecule binds to a surface. In the present investigation, the average E_ads values were calculated for hydrogen adsorption across all M@B₁₂N₁₂ complexes via the PCM model (refer to Fig. 3). The adsorption energies for hydrogen interacting with M-decorated B₁₂N₁₂ nanocages are compiled in Table 1. A more negative value of E_ads indicates stronger and more stable binding of the hydrogen molecule to the catalyst surface, signifying an exothermic and thermodynamically favorable adsorption. In contrast, a positive E_ads denotes a less favorable, endothermic interaction. Accordingly, greater negativity in E_ads corresponds to enhanced stability of the H₂-adsorbed M@B₁₂N₁₂ systems. Out of the ten M@B₁₂N₁₂ complexes investigated, hydrogen adsorption was found to be energetically favorable in all systems except H₂Zn@B₁₂N₁₂, with calculated E_ads values ranging between −3.62 eV and −1.02 eV, implying stable hydrogen interaction without causing structural deformation. However, H₂Zn@B₁₂N₁₂ exhibited positive E_ads values of 1.38 eV, indicating relatively weak or unfavorable adsorption. Among the catalysts studied, H₂Mn@B₁₂N₁₂, Ni@B₁₂N₁₂, and H₂Fe@B₁₂N₁₂ demonstrated particularly strong hydrogen adsorption with E_ads values of −3.62 eV, −3.61 eV, and −3.38 eV, respectively (see Table 1 for details). The negative values of E_ads observed in most complexes underscore the spontaneous nature of H₂ adsorption on these M-modified B₁₂N₁₂ nanocages. Structural parameters further validate the adsorption phenomena. The H–H bond length following adsorption was found to increase relative to the isolated H₂ molecule (0.74 Å), extending to values between 0.76 and 0.93 Å (see Fig. 3). This bond elongation suggests the initiation of H₂ activation on the catalyst surface. Additionally, the computed M–H interaction distances ranged from 1.55 Å to 2.23 Å, supporting the evidence of strong metal–hydrogen interactions. Among all studied systems, H₂Mn@B₁₂N₁₂ exhibited the most negative E_ads (−3.62 eV), highlighting it as the most effective candidate for hydrogen adsorption. On the other hand, H₂Zn@B₁₂N₁₂ displayed the highest positive E_ads (1.38 eV), implying the least favorable adsorption. Overall, the slight elongation in the H–H bond length observed across the M@B₁₂N₁₂ systems indicates the activation of molecular hydrogen, affirming the catalytic potential of these nanostructured materials.

Fig. 3 Geometrically optimized configurations of hydrogen-adsorbed M@B₁₂N₁₂ nanocage systems, highlighting key intermolecular interaction distances.

Hydrogen molecule dissociation on M@B₁₂N₁₂ complexes

The dissociative adsorption of molecular hydrogen (H₂) represents a fundamental step in numerous catalytic processes, particularly on M surfaces. This reaction involves the cleavage of the strong covalent H–H bond and the concurrent formation of new bonds between the resulting hydrogen atoms and the catalyst surface. Due to the energy-intensive nature of this transformation, the catalytic behavior of M@B₁₂N₁₂ toward hydrogen dissociation has been comprehensively investigated in this study. To assess the catalytic efficiency of the M@B₁₂N₁₂ complexes, the homolytic dissociation pathway of the adsorbed hydrogen molecule was analyzed. It involves the symmetrical splitting of H₂ into two neutral hydrogen atoms. The reaction proceeds via a two-step mechanism: initially, the H₂ molecule adsorbs onto the catalyst, forming an intermediate H₂* state; subsequently, the H–H bond breaks, and the resulting hydrogen atoms chemisorb on the same M center. This is evidenced by the significant elongation of the H–H bond from its equilibrium gas-phase value of ∼0.74 Å to values ranging between 2.21 Å and 2.81 Å in the product state, as summarized in Table S2. Computational results indicate that the final state (2H*), where both hydrogen atoms are bound to the catalyst, is thermodynamically favored across all studied M@B₁₂N₁₂ systems, as evidenced by consistently negative reaction energies. Fig. 4 illustrates the potential energy profiles for these dissociation processes, demonstrating that the homolytic pathway is exothermic. These findings underscore the ability of M@B₁₂N₁₂ nanocages to act as efficient catalysts for hydrogen activation and dissociation, an essential step in various hydrogenation and energy conversion reactions.

Fig. 4 Energy profiles for the HDR on M@B₁₂N₁₂. The relative energies of the adsorbed H₂ intermediate (H₂*), transition state, and dissociated H-atoms (2H*) to the reactant are reported in eV.

Among the examined M@B₁₂N₁₂ complexes for homolytic hydrogen dissociation, the Co@B₁₂N₁₂ system exhibits the lowest activation energy, calculated at only 0.14 eV, indicating its superior catalytic efficiency for H–H bond cleavage. In contrast, Zn@B₁₂N₁₂ presents the highest energy barrier of 2.96 eV, signifying limited catalytic performance.

The energy barriers associated with Ni@B₁₂N₁₂ (0.16 eV), Fe@B₁₂N₁₂ (0.19 eV), Cr@B₁₂N₁₂ (0.21 eV), and Cu@B₁₂N₁₂ (0.61 eV) are relatively close in magnitude, suggesting comparable activity profiles among these systems. For the remaining catalysts, the dissociation barriers are calculated as follows: Ti@B₁₂N₁₂ (1.20 eV), Sc@B₁₂N₁₂ (1.37 eV), V@B₁₂N₁₂ (1.41 eV), Mn@B₁₂N₁₂ (1.50 eV), and Zn@B₁₂N₁₂ (2.96 eV). Structural parameters, including selected bond lengths (in Å) and bond angles (in degrees) at key points along the reaction coordinate, namely, the intermediate, transition state, and final product configurations, are detailed in Table S2. Analysis of the H–H bond distances in the transition states reveals that all M@B₁₂N₁₂ complexes follow an early transition state mechanism. In such cases, the transition state geometry closely resembles that of the reactant, typically requiring lower activation energy. A shorter H–H bond length in the transition state is characteristic of this early transition state behavior. The H–H bond distances in the transition state range from 1.14 to 1.35 Å, indicating bond elongation that facilitates the activation and homolytic cleavage of H₂. The ∠H–M–H bond angles are larger in the transition state compared to the intermediate, suggesting angular expansion during dissociation. Additionally, M–H bond lengths are shorter in the transition state, reflecting stronger metal–hydrogen interactions. These geometric variations are depicted in Fig. 5 and Table S2.

Fig. 5 Potential energy profiles illustrating the reaction pathway for hydrogen dissociation over (a) Cr@B₁₂N₁₂, (b) Fe@B₁₂N₁₂, (c) Co@B₁₂N₁₂, (d) Ni@B₁₂N₁₂, and (e) Cu@B₁₂N₁₂ single-atom catalysts.

A noteworthy structural feature observed during the HDR process is the formation of a weak but significant interaction between the dissociated H atom and the adjacent B atom directly linked to the anchored M centre, as shown in Fig. 5. This attraction can be attributed to the enhanced Lewis acidity of the B atom, which arises from the electron-withdrawing nature of the coordinated transition metal and the local electronic polarization within the cage. Such a Lewis-acidic B site can act as a secondary binding centre that stabilizes the dissociated hydrogen, effectively lowering the energy barrier for H–H bond cleavage and promoting the overall reaction kinetics. Such a secondary H–B interaction has been reported in catalytic systems involving B-doped supports and frustrated Lewis pair catalysts.^86–88 These findings highlight the dual role of the TM@B₁₂N₁₂ catalyst, where both the transition metal centre and the boron framework participate synergistically in promoting hydrogen activation.

In this study, Cr@B₁₂N₁₂, Fe@B₁₂N₁₂, Co@B₁₂N₁₂, Ni@B₁₂N₁₂, and Cu@B₁₂N₁₂ catalysts, identified for their superior catalytic performance, are selected as representative models for an in-depth analysis of the hydrogen dissociation process. These efficient complexes are illustrated in Fig. 5, while the energy profiles of the remaining systems are provided in the SI (Fig. S1(a)–(e)). As depicted in Fig. 5(c), the H₂ molecule initially adsorbs on the Co@B₁₂N₁₂ surface, followed by homolytic cleavage into two hydrogen atoms that anchor at the Co site, overcoming a minimal activation energy barrier of 0.14 eV. Structural analysis shows the H–H bond elongates from 0.90 Å (intermediate) to 1.35 Å (transition state), accompanied by an increase in the ∠H–Co–H bond angle from 33° to 46°, indicating molecular activation. The Co–H bond lengths contract from 1.52 Å (intermediate) to 1.49 Å in the transition state. In the final product, the ∠H–Co–H bond angle expands to 69°, signifying stronger metal–hydrogen interactions and confirming bond formation. In the case of H₂Co@B₁₂N₁₂, the H–B distance decreases from 2.02 Å in the transition state to 1.44 Å in the final structure, indicating the formation of a much stronger B–H interaction that further stabilizes the dissociated hydrogen atom. The reaction releases −0.82 eV energy, and the product complex (H₂Co@B₁₂N₁₂) exhibits a lower enthalpy of −1.05 eV, indicating thermodynamic stability relative to the reactant state.

The Ni@B₁₂N₁₂ complex exhibits the second lowest activation barrier for hydrogen dissociation among the studied systems. The corresponding free energy profile and structural representations are shown in Fig. 5(d). During the reaction, the H–H bond length increases from 0.93 Å in the intermediate state to 1.27 Å in the transition state, as indicated in Table S2. Concurrently, the ∠H–Ni–H bond angle widens from 31° to 47°, reflecting a shift toward product-like geometry and effective activation of the H₂ molecule. The calculated energy barrier for this process is 0.16 eV. In the transition state, Ni–H interaction distances decrease to 1.48 Å and 1.44 Å from the intermediate values of 1.58 Å and 1.55 Å. Following dissociation, the hydrogen atoms stably chemisorb at the Ni center, forming Ni–H bonds with lengths of 1.48 Å and 1.51 Å, indicating favorable bonding in the product complex and the ∠H–Ni–H bond angle further expands to 76°. The H–B separation shortens significantly from 1.80 Å in the transition state to 1.41 Å in the final configuration, pointing to the development of a stronger B–H bond that helps stabilize the dissociated hydrogen. The reaction releases −0.15 eV energy, and the product complex (H₂Ni@B₁₂N₁₂) exhibits a lower enthalpy of −1.51 eV.

For Fe@B₁₂N₁₂, the adsorbed hydrogen molecule initially possesses an H–H bond length of 0.86 Å, which undergoes substantial elongation to 1.27 Å in the transition state, indicative of effective bond activation. The energy barrier associated with the dissociation process is computed to be 0.19 eV. In the intermediate stage, the Fe–H bond lengths are found to be 1.61 Å, which decrease to 1.51 Å, as the system transitions toward the dissociation pathway. Concurrently, the ∠H–Fe–H bond angle widens from 30° to 48°, reflecting structural reorganization and progressive cleavage of the H–H bond, as illustrated in Fig. 5(b). Post-dissociation, the two hydrogen atoms independently coordinate with the Fe center, forming stable Fe–H bonds of 1.56 Å and 1.60 Å and the ∠H–Fe–H bond angle expands to 75°. The H–B distance decreases markedly from 2.25 Å in the transition state to 1.52 Å in the final state, indicating the emergence of a stronger interaction that aids in anchoring the hydrogen atom after dissociation. Furthermore, the computed enthalpy of the product complex (H₂Fe@B₁₂N₁₂) is −3.02 eV, confirming that the dissociated state is thermodynamically more favorable than the reactant configuration. This reaction releases −1.74 eV energy.

For the Cr@B₁₂N₁₂ SAC, the hydrogen molecule initially exhibits a bond length of 0.85 Å upon adsorption. This bond undergoes a significant elongation to 1.24 Å in the transition state, indicating progressive activation toward dissociation. The associated activation energy for this process is calculated to be 0.21 eV. During the intermediate stage, the Cr–H bond distance is measured as 1.83 Å, which further decreases to 1.64 Å in the transition state. Concurrently, the ∠H–Cr–H bond angle increases markedly from 24° to 38°, reflecting geometric reorganization associated with H–H cleavage, as depicted in Fig. 5(a). Following dissociation, the individual hydrogen atoms establish stable interactions with the Cr center, yielding a final Cr–H bond length of 1.60 Å, and the ∠H–Cr–H bond angle expands to 85°. The H–B separation remains within the attractive range, shifting slightly from 1.71 Å in the transition state to 1.80 Å in the final state. The reaction releases −1.82 eV energy. Additionally, the computed enthalpy of the product complex (H₂Cr@B₁₂N₁₂) is −1.65 eV, suggesting that the dissociated state is thermodynamically more stable than the initial reactant configuration.

In the case of the Cu@B₁₂N₁₂ catalyst, the initially adsorbed H₂ molecule exhibits an H–H bond distance of 0.84 Å, which extends significantly to 1.14 Å in the transition state, indicating successful activation of the molecular hydrogen. The calculated activation energy required for the dissociation process is 0.61 eV. During the intermediate stage, the Cu–H bond lengths are observed to be 1.67 Å and 1.61 Å; these contract to 1.54 Å in the transition state. Simultaneously, the ∠H–Cu–H bond angle expands from 38° to 67°, suggesting a geometric rearrangement that facilitates bond cleavage, as shown in Fig. 5(e). Following dissociation, the hydrogen atoms anchor separately to the Cu atom, forming a robust Cu–H bond, 1.53 Å in length, and the ∠H–Cu–H bond angle expands to 84°. The H–B distance decreases notably from 2.94 Å in the transition state to 1.80 Å in the final state, indicating the emergence of a stabilizing interaction that becomes more pronounced after hydrogen dissociation. Additionally, the enthalpy of the product complex (H₂Cu@B₁₂N₁₂) is calculated to be −0.30 eV, underscoring the thermodynamic stability of the product relative to the initial reactant complex.

As summarized in Table 1, the computed activation energy barriers for H₂ dissociation across the series of M@B₁₂N₁₂ catalysts span a broad range, from 0.14 eV to 2.96 eV. Notably, the Co@B₁₂N₁₂ complex exhibits the lowest energy requirement (0.14 eV) among all the transition metal-anchored B₁₂N₁₂ systems investigated. This minimal barrier suggests that hydrogen cleavage on the Co-functionalized nanocage can proceed efficiently under mild operational conditions, which aligns well with the fundamental prerequisites for catalytic hydrogenation processes. Therefore, the Co@B₁₂N₁₂ system emerges as the most promising candidate for facilitating H–H bond dissociation among the series, underscoring its superior catalytic performance relative to other investigated counterparts. Here, we focused only on the adsorption and dissociation of a single H₂ molecule, since this approach captures the essential features of the catalytic mechanism at the active site. Investigating multiple H₂ adsorption events, while relevant for storage applications, is beyond the present scope and will be explored in future work.

The computed activation energy for hydrogen dissociation on the Co@B₁₂N₁₂ complex is significantly lower than that reported for conventional noble metal-based catalysts. For instance, the dissociation barriers on Pt(111),⁸⁹ Au(111),⁹⁰ and Ag(111)⁹¹ surfaces have been reported as 0.23 eV, 1.30 eV, and 1.55 eV, respectively. Moreover, Co@B₁₂N₁₂ exhibits superior performance compared to various transition metal-doped nanomaterials, such as Sc@NB (0.13 eV),⁹² Zn@C₂₀ (0.53 eV),²⁵ Ni@C₂N (0.40 eV), and Co@C₂N (0.45 eV).⁹³ Even in comparison with similar alloy-based systems like the Mg₁₅Ni₂Al₁₂ (0.53 eV) and Mg₁₇Al₁₂ (0.82 eV) surfaces,⁹⁴ the Co@B₁₂N₁₂ catalyst demonstrates a markedly lower energy barrier. This comparative analysis, summarized in Table 2, underscores the exceptional catalytic proficiency of Co@B₁₂N₁₂ as a SAC for hydrogen dissociation. Owing to its minimal activation barrier, Co@B₁₂N₁₂ stands out as a highly promising SAC for the efficient facilitation of the HDR.

Table 2 Comparison of hydrogen dissociation barriers for various catalysts

Catalyst	Structure type	Activation barrier (eV)	Ref.
Co@B12N12	SAC on nanocage	0.14	Present study
Pt (111)	Noble metal surface	0.23	89
Au (111)	Noble metal surface	1.30	90
Ag (111)	Noble metal surface	1.55	91
Ag (211)	Noble metal surface	1.33	91
Sc@NB	TM-doped 2D sheet	0.13	92
Ni@C2N	TM-doped graphene analogue	0.40	93
Mn@C24	TM-doped fullerene	0.04	26
Zn@C20	TM-doped fullerene	0.53	25
Mg15Ni2Al12	Alloy surface	0.53	94
Ni@Mg17Al12	Alloy surface	0.82	94
Mg9Rh cluster	Cluster	0.63	95
Sc@C60	TM-doped fullerene	0.13	28
Mg (0001)	Metal surface	1.18	96
Cu (001)	Metal surface	0.59	97

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Topological analysis of electron density using quantum theory of atoms in molecules (QTAIM)

QTAIM was employed to investigate the interatomic interactions between the hydrogen molecule and the M@B₁₂N₁₂ catalytic systems. The topological parameters derived from the QTAIM analysis provide comprehensive insights into the nature of these interactions at the bond critical points (BCPs). These parameters include electron density (ρ), Laplacian of electron density (∇²ρ), kinetic energy density (G_r), potential energy density (V_r), and total energy density (H_r). The electron density at the BCP helps assess bond strength, while the Laplacian of electron density (∇²ρ) characterizes the interaction type. Moreover, the −V/G ratio is used to evaluate the strength and nature of the interactions: a ratio greater than 2 indicates covalent bonding, while a value less than 1 corresponds to weaker interactions. The values for these parameters derived from the QTAIM analysis are provided in Table 3, and the corresponding molecular plots for the hydrogen-adsorbed M@B₁₂N₁₂ complexes are shown in Fig. 6.

Fig. 6 Molecular plots obtained from QTAIM analysis for the hydrogen-adsorbed M@B₁₂N₁₂ complexes.

Table 3 Results of the topological parameters derived from the QTAIM analysis of hydrogen-adsorbed M@B₁₂N₁₂ complexes

Analyte–H2	ρ (a.u)	∇^2ρ (a.u)	G (r) (a.u)	V (r) (a.u)	H (r) (a.u)	−V/G
Sc–H1	0.213	−0.005	0.166	−0.333	−0.167	2.01
Sc–H2	0.205	0.082	0.178	−0.336	−0.158	1.88
Ti–H1	0.047	0.123	0.036	−0.041	−0.005	1.15
Ti–H2	0.079	0.038	0.035	−0.060	−0.025	1.72
V–H1	0.153	0.342	0.187	−0.288	−0.101	1.54
V–H2	0.185	0.278	0.249	−0.429	−0.180	1.72
Cr–H1	0.054	0.186	0.051	−0.056	−0.005	1.09
Cr–H2	0.103	0.003	0.048	−0.094	−0.047	1.98
Mn–H1	0.075	0.237	0.078	−0.096	−0.018	1.24
Mn–H2	0.108	0.101	0.076	−0.127	−0.051	1.67
Fe–H1	0.097	0.391	0.127	−0.157	−0.029	1.23
Fe–H2	0.106	0.151	0.087	−0.136	−0.049	1.56
Co–H1	0.189	0.011	0.150	−0.297	−0.147	1.98
Co–H2	0.183	0.137	0.175	−0.315	−0.140	1.80
Ni–H1	0.182	0.024	0.147	−0.288	−0.141	1.96
Ni–H2	0.179	0.115	0.167	−0.304	−0.138	1.83
Cu–H1	0.175	0.048	0.151	−0.289	−0.13	1.92
Cu–H2	0.173	0.132	0.17	−0.307	−0.137	1.81
Zn–H1	0.169	0.178	0.167	−0.290	−0.123	1.74
Zn–H2	0.166	0.308	0.197	−0.318	−0.121	1.61

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For all the designed catalytic systems, two metal–hydrogen BCPs were observed for each complex, as summarized in Table 3. In these H₂M@B₁₂N₁₂, two metal–hydrogen BCPs are present. The hydrogen molecule dissociates effectively upon adsorption, with both hydrogen atoms exhibiting a strong interaction. Consequently, this hydrogen dissociates over the catalyst, indicating that H₂M@B₁₂N₁₂ effectively facilitates the dissociation of the hydrogen molecule. This property is crucial for the catalyst's ability to enhance catalytic performance, particularly for processes that rely on hydrogen dissociation.

The Laplacian of electron density (∇²ρ) for the BCPs of the hydrogen-adsorbed M@B₁₂N₁₂ systems ranges from −0.005 to 0.391. A value of ∇²ρ greater than zero suggests the presence of closed-shell interactions, which are typically weaker in nature. The H_r, which is the sum of G_r and V_r, is found to be negative for all the designed systems, confirming the presence of covalent interactions. A negative H_r value is indicative of covalent bonding, implying that the interactions between the hydrogen molecule and the catalyst are of a covalent nature.

Additionally, the −V/G ratio ranges from 1.09 to 2.01, further supporting the conclusion that these interactions are covalent. Specifically, the ratios fall within the range that suggests the presence of shared electron density between the hydrogen molecule and the metal centers, thus reinforcing the covalent or shared-shell nature of the interactions.

These QTAIM-derived results provide an in-depth understanding of the interatomic interactions, offering insights that cannot be directly obtained through structural analysis alone. Moreover, the findings are consistent with the computed adsorption energies and reactivity profiles of the complexes, providing further validation of the QTAIM analysis. This consistency demonstrates that the QTAIM results accurately reflect the bonding characteristics and catalytic behavior of the systems. In particular, the ability of Co@B₁₂N₁₂ to support the dissociation of hydrogen after adsorption highlights its role in promoting efficient catalytic processes, thereby enhancing the overall catalytic performance of the system. This reaffirms the significance of QTAIM in characterizing the bonding interactions and their implications for catalytic activity.

Analysis of the electronic structure via natural bond orbitals and electron density difference mapping

EDD and NBO analyses were performed to unravel the mechanism of H₂ activation and dissociation on the M@B₁₂N₁₂ catalysts. NBO calculations (Table 4) quantify electron transfer from the metal 3d orbitals to the adsorbed H₂ molecule: in every H₂* + M@B₁₂N₁₂ complex, the transition-metal center acquires a net positive charge, evidence of its electron-donor role driven by its electropositive character; while both hydrogen atoms bear negative charges in H₂Sc@B₁₂N₁₂, only one hydrogen bears a negative charge in H₂Cr@B₁₂N₁₂, H₂Mn@B₁₂N₁₂, and H₂Zn@B₁₂N₁₂. In all other systems, both hydrogens display a slightly positive value. Among the series, scandium donates the most charge (+1.037e), and nickel the least (+0.329e).

Table 4 Natural bond orbital-derived charge allocations for the H₂-adsorbed M@B₁₂N₁₂ complexes

Complexes	H1 (e)	M (e)	H2 (e)
H2Sc@B12N12	−0.021	1.037	−0.003
H2Ti@B12N12	0.027	0.869	0.012
H2V@B12N12	0.014	0.506	0.014
H2Cr@B12N12	0.061	0.695	−0.008
H2Mn@B12N12	0.056	0.516	−0.026
H2Fe@B12N12	0.069	0.357	0.033
H2Co@B12N12	0.072	0.341	0.030
H2Ni@B12N12	0.035	0.329	0.016
H2Cu@B12N12	0.025	0.527	0.040
H2Zn@B12N12	−0.037	0.702	0.034

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Focusing on the representative Co@B₁₂N₁₂ system, adsorption induces +0.341e charge at Co, with H1 and H2 carrying +0.072e and +0.030e, respectively. EDD maps corroborate this directional charge flow by showing depletion around Co and accumulation at the hydrogen sites, as displayed in Fig. 7. The injected electrons populate the H₂ σ* antibonding orbital, weakening and elongating the H–H bond until cleavage occurs. Together, the NBO and EDD results confirm that metal-to-hydrogen electron transfer into antibonding orbitals is the key driver of efficient H₂ splitting on M@B₁₂N₁₂, underscoring the strong metal–hydrogen binding that enables self-dissociation of the molecule.

Fig. 7 Electron density difference isosurfaces for hydrogen-adsorbed M@B₁₂N₁₂ complexes. Red-orange: electron accumulation; purple-blue: electron depletion.

EDD analysis was performed to validate the NBO-derived charge transfer upon H₂ adsorption. The EDD isosurfaces for all hydrogen-adsorbed M@B₁₂N₁₂ complexes are displayed in Fig. 7, where purple-blue regions denote electron depletion and red-orange regions indicate electron accumulation. In all systems, purple-blue isosurfaces are predominantly localized on the transition-metal center and hydrogen atoms, signifying regions of electron-density depletion. These maps clearly show electron donation from the transition-metal centers to both H1 and H2 upon adsorption, in excellent agreement with the NBO results. This transferred electron density populates the σ* antibonding orbital of the hydrogen molecule, weakening the H–H bond and thereby facilitating its dissociation over the M@B₁₂N₁₂ catalysts.

Collectively, our QTAIM, NBO, and EDD findings establish that transition-metal-anchored B₁₂N₁₂ nanocages serve as highly effective single-atom catalysts for the HDR. In particular, Co@B₁₂N₁₂ exhibits an exceptionally low activation barrier of 0.14 eV, underscoring its promise as a high-performance electrocatalyst. These insights pave the way for the rational design of heteroatom-anchored nanocage SACs tailored to promote facile hydrogen splitting.

Reduced density gradient (RDG) analysis

Reduced density gradient (RDG) analysis was conducted using Multiwfn 3.8⁷⁶ to map regions of low electron-density variation and thus identify any noncovalent (closed-shell) interactions within the H₂M@B₁₂N₁₂ complexes. In this approach, the reduced density gradient is plotted against sign(λ₂)ρ, where λ₂ is the second eigenvalue of the electron-density Hessian and ρ is the electron density enabling discrimination between attractive and repulsive contacts. Conventionally, spikes in the 2D RDG vs. sign(λ₂)ρ plot near sign(λ₂)ρ ≈ 0 (ρ > 0) reflect weak van der Waals interactions, whereas negative sign(λ₂)ρ values (below −0.02 a.u.) are characteristic of strong attractive (covalent-like) interactions.⁹⁸ As shown in Fig. 8, none of the H₂M@B₁₂N₁₂ complexes exhibit the hallmark peaks around sign(λ₂)ρ ≈ 0, confirming the absence of significant hydrogen bond or dispersion contacts. Three-dimensional RDG isosurfaces rendered in VMD⁷⁵ further substantiate this finding: greenish regions, which would indicate weak noncovalent interactions, are absent, while only blue-tinged lobes appear between the TM centers and the hydrogen atoms, signaling strong, attractive (shared-shell) bonding. Red cylindrical projections highlight zones of positive λ₂ρ, corresponding to steric repulsion that may contribute to homolytic H–H bond elongation. These observations confirm that H–M bonding in all H₂M@B₁₂N₁₂ catalysts is dominated by covalent interactions, in agreement with their comparable electronegativities and previous studies on metal-doped B₁₂N₁₂ surfaces^99–101 for hydrogen dissociation. By ruling out competing noncovalent forces, RDG analysis underscores the intrinsic ability of these SACs to facilitate efficient H₂ cleavage via strong orbital overlap and electron-density redistribution.

Fig. 8 Reduced density gradient (RDG) analysis of representative M@B₁₂N₁₂ complexes, featuring three-dimensional RDG isosurfaces to visualize interaction regions and the corresponding two-dimensional RDG versus sign(λ₂)ρ spectra.

Electronic properties of molecular hydrogen adsorbed M@B₁₂N₁₂

To elucidate the electronic interactions between hydrogen molecules and the M@B₁₂N₁₂ catalysts, Density of States (DOS) and Frontier Molecular Orbital (FMO) analyses were conducted following hydrogen adsorption. The calculated energies of the HOMO and the LUMO, along with the corresponding energy gaps (E_gap), are compiled in Table 5. These values provide insights into the electronic properties and potential reactivity of the catalysts. The interaction between the adsorbed H₂ and the M@B₁₂N₁₂ nanocages was further examined through TDOS and PDOS spectra. Fig. S2 illustrates the TDOS and PDOS spectra of M@B₁₂N₁₂ complexes before the adsorption of hydrogen. Fig. S3 illustrates the TDOS and PDOS spectra for the hydrogen-adsorbed M@B₁₂N₁₂ complexes. The changes can be clearly observed by comparing Fig. S2 and S3. Among the studied complexes, the Co@B₁₂N₁₂ complex exhibits the most significant increase in the HOMO–LUMO gap upon hydrogen adsorption, increasing by 0.80 eV (from 7.71 to 8.51 eV), which suggests a significant stabilization of the electronic structure and improved chemical hardness after H₂ activation. Conversely, a reduction in the energy gap is observed for the Sc@B₁₂N₁₂, Fe@B₁₂N₁₂, Cu@B₁₂N₁₂, and Zn@B₁₂N₁₂ complexes. This reduction is corroborated by the appearance of new peaks in their DOS spectra post hydrogen adsorption. For the remaining complexes such as Ti@B₁₂N₁₂, V@B₁₂N₁₂, Cr@B₁₂N₁₂, Mn@B₁₂N₁₂, and Ni@B₁₂N₁₂, an increase in the energy gap is noted. Specifically, the H₂Co@B₁₂N₁₂ complex exhibits an energy gap of 8.51 eV, H₂Mn@B₁₂N₁₂ shows 7.88 eV, H₂Fe@B₁₂N₁₂ has 7.02 eV, H₂Ni@B₁₂N₁₂ presents 7.65 eV, and H₂Cu@B₁₂N₁₂ demonstrates 5.90 eV. These findings suggest enhanced hydrogen dissociation reaction (HDR) activity for these catalysts. The designed SACs anchored on the B₁₂N₁₂ nanocage exhibit superior catalytic performance for the HDR compared to other noble metal-based and metal-doped clusters. Notably, the Co@B₁₂N₁₂ complex emerges as a promising SAC, effectively catalyzing the HDR process.

Table 5 Outcome of the calculated energies of the HOMO and LUMO, as well as the associated HOMO–LUMO energy gaps (ΔE_gap), for M@B₁₂N₁₂ and H₂M@B₁₂N₁₂ complexes (expressed in eV)

M@B12N12	HOMO	LUMO	E gap (ΔE)
Sc@B12N12	−6.43	−0.36	6.07
H2Sc@B12N12	−6.87	−1.00	5.87
Ti@B12N12	−6.73	−0.53	6.20
H2Ti@B12N12	−7.26	−0.83	6.43
V@B12N12	−6.13	−0.06	6.07
H2V@B12N12	−6.66	−0.14	6.53
Cr@B12N12	−7.78	−0.79	6.99
H2Cr@B12N12	−8.26	−0.71	7.55
Mn@B12N12	−8.59	−0.80	7.78
H2Mn@B12N12	−8.67	−0.80	7.88
Fe@B12N12	−7.74	−0.53	7.21
H2Fe@B12N12	−7.93	−0.91	7.02
Co@B12N12	−7.93	−0.22	7.71
H2Co@B12N12	−8.93	−0.42	8.51
Ni@B12N12	−7.91	−0.33	7.58
H2Ni@B12N12	−8.18	−0.54	7.65
Cu@B12N12	−6.67	−0.15	6.52
H2Cu@B12N12	−6.93	−1.03	5.90
Zn@B12N12	−8.51	−0.37	8.14
H2Zn@B12N12	−6.17	−0.19	5.98

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Molecular dynamics simulation

Root mean square deviation (RMSD). The RMSD plot shown in Fig. 9 illustrates the structural behavior of the Co@B₁₂N₁₂ nanocage during a 100 ns molecular dynamics simulation. Throughout the simulation, the system retained a highly stable configuration, with RMSD values confined within a narrow range of 0.03–0.09 Å and an average value of approximately 0.06 Å. The absence of significant drifts or abrupt fluctuations reflects the robustness of the nanocage framework. The Co atom remained securely positioned within the B₁₂N₁₂ cavity for the entire simulation period, indicating strong structural confinement. The minor variations observed in RMSD values are consistent with normal atomic motions that occur under equilibrium conditions. Overall, the simulation confirms that the Co@B₁₂N₁₂ nanocage preserved its integrity and structural consistency throughout the 100 ns trajectory, verifying its dynamic and thermal stability under the applied simulation parameters.

Fig. 9 RMSD of Co@B₁₂N₁₂ during MD simulation of 100 ns.

Conclusion

This DFT-based study presents an in-depth analysis of first-row transition metal-anchored B₁₂N₁₂ nanoclusters (M@B₁₂N₁₂) as SACs for hydrogen dissociation. The anchoring of metals onto the B₁₂N₁₂ framework is thermodynamically favorable, with Ni@B₁₂N₁₂ showing the strongest metal–support interaction. Hydrogen adsorption and dissociation studies reveal that the formation of two adsorbed hydrogen atoms (2H*) is energetically preferred, indicating an exothermic reaction profile. Notably, Co@B₁₂N₁₂ demonstrates the lowest activation barrier (0.14 eV), confirming its superior catalytic performance for H–H bond cleavage. Electronic structure analyses, NBO and EDD, highlight efficient charge transfer from the metal to the H₂ molecule, leading to σ* orbital population and bond weakening. QTAIM and NCI analyses confirm covalent (shared-shell) interactions, while RDG plots further emphasize the role of short-range covalent forces in promoting the HDR. In summary, Co@B₁₂N₁₂ emerges as a highly promising, noble metal-free electrocatalyst. These insights not only deepen our understanding of the SAC-mediated HDR but also guide the rational design of advanced catalysts for hydrogen-related energy applications.

Author contributions

Zainab Fareed: data curation, writing – original draft, writing – review & editing, software and data analysis. Tayyaba Tariq: data curation. Shaaban M. Shaaban: writing – review & editing. Muhammad Yar: project administration, software, and supervision. Muhammad Ali Khan: project administration, resources, supervision, writing – review & editing. Ajaz Hussain: conceptualization. Khurhsid Ayub: writing – review & editing. Sehrish Sarfaraz: software and data analysis. Yasser M. Riyad: funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). The supplementary information includes energies of spin-polarized complexes along with spin-states, Key bond lengths (in Å) and bond angles (in degrees) for the intermediate, transition state, and product structures of H₂M@B₁₂N₁₂ nanocage complexes, potential energy profiles illustrating the reaction pathway for hydrogen dissociation over (a) Sc@B₁₂N₁₂, (b) Ti@B₁₂N₁₂, (c) V@B₁₂N₁₂, (d) Mn@B₁₂N₁₂, and (e) Zn@B₁₂N₁₂ single-atom catalysts and DOS profile of all H₂M@B₁₂N₁₂ complexes after the adsorption of Hydrogen. See DOI: https://doi.org/10.1039/d5dt01548k.

Acknowledgements

The researchers wish to extend their sincere gratitude to the Deanship of Scientific Research at the Islamic University of Madinah for the support provided to the Post-Publishing Program.

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