Yttrium-Modified B₁₂N₁₂ Nanocages for High-Performance H₂ Sensing: Insights from DFT Calculations on Sensitivity, Selectivity, and Recovery

Abstract

Boron nitride (B₁₂N₁₂) nanocages have attracted considerable attention due to their exceptional structural stability and tunable electronic properties, making them promising candidates for gas-sensing applications. In this study, DFT-D3 calculations at the B3LYP/def2-TZVP level, including relativistic effects for yttrium (SARC-ZORA-def2-TZVP), were employed to investigate H₂ adsorption on pristine and Y-modified (doped, decorated, and encapsulated) B₁₂N₁₂ nanocages. The pristine nanocage exhibited weak physisorption (E _ads = −0.04 eV), whereas the Y@b₆₄ configuration demonstrated strong chemisorption (E _ads = −0.96 eV), pronounced electronic sensitivity (ΔE _gap = 74.94%), and a feasible recovery time (τ = 166.8 s). Analyses of electrostatic potential, molecular dynamics (1000 ps), IR, and UV–vis spectra confirmed the structural robustness and optical detectability of H₂. Furthermore, the Y@b₆₄ nanocage showed remarkable selectivity toward H₂ compared to common interfering gases (CH₄, CO, H₂S, and N₂). Overall, Y@b₆₄ combines high adsorption energy, strong sensitivity, and efficient recovery time, underscoring its potential as a selective, stable, and high-performance H₂ gas sensor.

1. Introduction

The development of sensors for odorless, colorless, and toxic gases such as H₂, NH₃, SO₂, O₂, NO₂, H₂S, CO, and CO₂ has generated great interest in the scientific community and industry. − Sensors capable of quickly and accurately identifying these gases play a crucial role in mitigating environmental impacts, such as global warming, and in advancing alternative energy sources. In the case of hydrogen (H₂), efficient sensors are essential to ensure safety and efficiency in industrial processes such as coal mining, nuclear reactors, and semiconductor manufacturing, where rigorous monitoring is required to reduce risks and optimize operations. −

Nanomaterials, including nanosheets, nanotubes, and nanocages, have been widely studied as gas sensors due to their exceptional electronic properties and high surface area. Among them, boron nitride-based structures stand out, such as nanotubes (BNNTs), two-dimensional structures (h-BN), nanoclusters (B₆N₆), and nanocages (BN) _n , combining sensitivity, rapid detection, and short recovery times. Theoretical studies using DFT calculations have demonstrated the efficiency of these systems in the adsorption of various gases. For example: Aasi et al. observed that Pt- and Pd-decorated novel green phosphorene exhibit high reactivity for C₂H₂, H₂, and CH₄; Kalateh et al. showed that B₁₆N₁₆ has superior electronic adsorption properties for H₂ compared to C₃₂ and B₈C₂₄; and Choir et al. found that B₁₂N₁₂ nanocages interact spontaneously and exothermically with CO₂ and H₂ (E _ads = −26.86 and −6.94 kJ/mol, respectively). Nair et al. also demonstrated that B₁₂N₁₂ strongly adsorbs gases such as AsH₃, H₂Se and H₂S, while H₂ and CH₄ present weaker interactions, with relevant modifications in reactivity indices, such as chemical potential and hardness.

Despite the potential of B₁₂N₁₂ for atmospheric gas sensors, some molecules such as H₂, H₂S, CO, COCl₂, and NO do not spontaneously adsorb on the pure cage due to weak interactions, requiring structural modifications to optimize their electronic properties. − The insertion of transition metals is an efficient strategy to increase the affinity of the nanocage for different gases. Experimentally, Oku et al. − synthesized B₁₂N₁₂ and B₃₆N₃₆ cages, pure and modified with transition metals (Fe, Ag, La, and Y), confirming their structures by electron microscopy and mass spectrometry. Yttrium, in particular, proved effective in improving H₂ adsorption, for example: (i) Wang and Tian indicated, via DFT, that each Y atom in a C₄₈B₁₂ cage can bind up to six H₂ molecules with significant binding energies, suggesting chemisorption-type interactions; (ii) Kundu and Chakraborty showed, via DFT, that Y atom attached on Triazine can adsorb seven H₂ molecules with binding energy of 0.33 eV/H₂ leading to 7.3 wt % of H₂; (iii) Srivastava et al. reported experimentally that the chemoresistive gas sensor based on Y-CeO exhibited excellent long-term stability, outstanding sensitivity, fast response and recovery times, and selectivity to H₂ in comparison to other gases. Revealing the exceptional potential of the Y-CeO sensor as a low-trace H₂ gas detector; (iv) Ferlazzo et al. showed experimentally that the novel yttria-doped ZrO₂ exhibited excellent characteristics in terms of sensor response, fast response and recovery time (5 and 10 s, respectively) and good selectivity to H₂.

Therefore, all of these findings motivated us to design a system that efficiently binds the H₂ gas by structural modification of B₁₂N₁₂ nanocage with Y metal and helps in detecting this gas in the environment. The novelty of this work lies in the comprehensive comparative analysis of five distinct yttrium-based configurations, offering a deeper understanding of the electronic and structural factors that govern the interaction between H₂ molecules and the nanocage surface.

This study aims to fill this gap by employing density functional theory (DFT) calculations, including relativistic effects, to elucidate how different yttrium insertion strategies influence the adsorption behavior of H₂. By mapping these effects, we identify key mechanisms that enhance selectivity, sensitivity, and adsorption efficiency, ultimately contributing to the rational design of high-performance hydrogen sensors. In this context, our investigation aims to identify a material with the potential to be applied as a selective sensor, exhibiting high sensitivity and rapid detection of hydrogen gas in the environment.

2. Computational Methodology

Density Functional Theory (DFT) calculations were performed using ORCA 5.0. The isolated and yttrium-modified B₁₂N₁₂ nanocages were optimized with the B3LYP functional and Grimme D3 dispersion correction, , suitable for long-range interactions. The B3LYP-D3 functional was adopted due to its accuracy in geometries and vibrational frequencies, combined with low computational cost. Thus, B3LYP stands out as a stable, economical and reproducible option, as validated in gas adsorption studies. , Different basis sets were used: def2 with relativistic effects SARC-ZORA-def2-TZVP for yttrium and ZORA-def2-TZVP for the other elements. The adopted convergence criteria were: RMS gradient (5 × 10^–6 Hartree), RMS shift (1 × 10^–4 Hartree/Bohr), maximum gradient (2 × 10^–3 Bohr), maximum shift (3 × 10^–4 Hartree/Bohr) and energy (4 × 10^–3 Hartree). Frequency analyses confirmed the global minima of the optimized structures. The structural modification of B₁₂N₁₂ with yttrium gave rise to five distinct structures: ,

• Y-doped (YB₁₁N₁₂), in which one B atom of B₁₂N₁₂ is replaced by a Y atom;

• Y-doped (YB₁₂N₁₁), in which one N atom of B₁₂N₁₂ is replaced by a Y atom;

• Y-decorated (Y@b₆₄), in which a Y atom is externally adsorbed onto the B₁₂N₁₂ nanocage, positioned above one b₆₄ bond that connects a hexagonal and a tetragonal ring;

• Y-decorated (Y@b₆₆), in which a Y atom is externally adsorbed onto the B₁₂N₁₂ nanocage, positioned above one b₆₆ bond that connects two hexagonal rings;

• Y-encapsulated (Y@B₁₂N₁₂), where a Y is located inside the B₁₂N₁₂ nanocage.

The nanocages were optimized in their neutral forms (charge = 0). Preliminary spin-state tests showed that B₁₂N₁₂, YB₁₁N₁₂, and B₁₂N₁₁Y converge to closed-shell singlet states (multiplicity = 1), confirming their diamagnetic character (see Table S1 in Supporting Information). In contrast, the Y-decorated and -encapsulated structures (Y@b₆₄, Y@b₆₆, and Y@B₁₂N₁₂) exhibit open-shell doublet ground states (multiplicity = 2), as evidenced by the distinct α/β orbital energies (Tables and ) and a total spin population of 1.0, indicating the presence of one unpaired electron. After H₂ adsorption, all complexes retain the multiplicity of their corresponding ground states, showing that the magnetic behavior induced by yttrium remains unchanged upon interaction with the adsorbates. The stability of the systems was evaluated by determining the cohesive energy (E _coh) following eq

$$E_{\mathrm{coh}}=\frac{1}{N}(E_{\mathrm{nanocage}}-x{E}_{\mathrm{B}}-y{E}_{\mathrm{N}}-z{E}_{\mathrm{Y}})$$ 1

in this equation, E _nanocage represents the total energy of the nanocage, whether pure or modified with yttrium. E _B, E _N, and E _Y correspond to the energies of the boron, nitrogen, and yttrium atoms. The variables x, y, and z denote the number of B, N, and Y atoms in the structure, while N represents the total number of atoms of the studied nanocages.

1. Calculated Values of Formation Energy (E _form), Cohesive Energy (E _coh), Dipole Moment (DM), NPA Charge on the Y Atom (Q _Metal), Energy Gap (E _gap) and Work Function (Φ) for Isolated Systems.

system	E form (eV)	E coh (eV)	DM (Debye)	Q Metal (|e|)	E gap (eV)	Φ (eV)
B12N12	–3.04	–7.33	0.00		6.80	4.46
YB11N12	–2.96	–7.25	9.75	2.024	3.72	4.70
B12N11Y	–2.91	–6.93	8.89	1.310	2.54	3.83
Y@b64	–2.92	–7.07	5.90	1.134	2.43	3.14
					2.93
Y@b66	–2.91	–6.99	5.64	0.986	2.30	3.72
					1.64
Y@B12N12	–2.58	–6.71	1.79	0.576	2.07	3.41
					2.33

^aSpin up.

^bSpin down.

3. Values of HOMO-LUMO gap (E _gap), Sensitivity (ΔE _gap), Variation of the Work Function (ΔΦ), NPA Charge on the Y Atom (Q _Metal) and NPA Charge on the H Atoms (Q _H2 ), of the Systems, Calculated for the Interaction of H₂ Gas with Pure and Modified B₁₂N₁₂ .

system	E gap (eV)	ΔE gap (%)	ΔΦ (%)	Q Metal (|e|)	Q H2 (|e|)
B12N12–H2	6.62	2.67	0.93	–	0.007
YB11N12–H2	3.85	3.39	0.21	2.006	0.033
B12N11Y–H2	2.60	2.61	2.09	1.606	–0.630
Y@b64–H2	2.57	5.52	36.62	1.782	–1.147
	5.12	74.94
Y@b66–H2	1.46	36.62	26.88	1.350	–0.681
	4.82	193.53
Y@B12N12–H2	3.43	65.47	30.77	1.711	–0.002
	2.60	11.78

^aSpin up.

^bSpin down.

For thermodynamic analysis of the most viable systems to be synthesized and to compare with the cohesion energy data, we also calculated the formation energy of the nanocages, according to eq

$$E_{\mathrm{form}}=\frac{(E_{\mathrm{modified}}-a{\mathit{E̅}}_{\mathrm{B}}-b{\mathit{E̅}}_{\mathrm{N}}-c{\mathit{E̅}}_{\mathrm{Y}})}{N}$$ 2

where the E _modified is the total energy nanocage modified, E̅ _B, E̅ _N and E̅ _Y are the energies for elements in B₂, N₂ and cluster of the Y atom, respectively; a, b, and c are the numbers of B, N, and Y atoms, respectively, and N is the total number of atoms.

The energy gap E _gap is defined as the difference between the energy levels LUMO (E _LUMO) and HOMO (E _HOMO). The electronic sensitivity (ΔE _gap) of the interaction between the H₂/nanocages was determined using eq .

$$\mathrm{\Delta }{E}_{\mathrm{gap}}=\left[\frac{(E_{\mathrm{gap}(\mathrm{nanocage}‐{\mathrm{H}}_2)}-E_{\mathrm{gap}(\mathrm{nanocage})})}{E_{\mathrm{gap}(\mathrm{nanocage})}}\right]\times 100$$ 3

the E _{gap(nanocage‑H2)} represents the energy gap associated with the interaction of H₂ with both pure and modified B₁₂N₁₂ nanocages, while E _{gap(nanocage)} refers to the energy gap of pure or Y-modified B₁₂N₁₂. To better understand the spontaneity of the cage/gas adsorption process, thermodynamic parameters were analyzed. Specifically, the variation in adsorption enthalpy (ΔH _ads) and free energy (ΔG _ads) using eqs and .

$${\mathrm{\Delta }G}_{\mathrm{ads}}=G_{\mathrm{gas}‐\mathrm{nanocage}}-(G_{\mathrm{gas}}+G_{\mathrm{nanocage}})$$ 4

$${\mathrm{\Delta }H}_{\mathrm{ads}}=H_{\mathrm{gas}‐\mathrm{nanocage}}-(H_{\mathrm{gas}}+H_{\mathrm{nanocage}})$$ 5

G _{gas‑nanocage} and H _{gas‑nanocage} represent the free energy and enthalpy of gas-nanocage adsorption. H _gas and G _gas are related to the energies of H₂ gas and G _nanocage and H _nanocage are the energies of the isolated nanocages, respectively. Equation was used to obtain adsorption energy (E _ads) values to study the interaction between B₁₂N₁₂ or yttrium-modified nanocages and H₂ gas.

$$E_{\mathrm{ads}}=E_{(\mathrm{nanocage}‐{\mathrm{H}}_2)}-(E_{(\mathrm{nanocage})}+E_{({\mathrm{H}}_2)})+E_{\mathrm{BSSE}}$$ 6

the system energy E _{(nanocage‑H2)} corresponds to the B₁₂N₁₂ or Y–B₁₂N₁₂ nanocage with H₂, including the zero-point vibrational energy (ZPVE), while E _(nanocage) and E _(H2) refer to the energies of the isolated nanocages and the H₂ molecule. The error correction of the basis set superposition (BSSE) was applied for greater accuracy in the interactions. The recovery time (τ) is given by eq −

$$\tau ={\mathrm{v}}_0^{-1}{\mathrm{e}}^{-E_{\mathrm{ads}}/k_{\mathrm{B}}T}$$ 7

with v₀ = 10¹² s^–1, k _B = 8.62 × 10^–5 eV K^–1 and T is the thermodynamic temperature (K). E _ads values between −0.3 and −1.0 eV result in τ of order of seconds, indicating a sensor potential. The work function (Φ) was calculated from the frontier orbitals, and the variation (ΔΦ) before and after adsorption was the criterion for evaluating the applicability of the nanocages (eqs and ).

$$\mathrm{\Phi }\approx E_{\mathrm{H}}+\frac{1}{2}(E_{\mathrm{L}}-E_{\mathrm{H}})$$ 8

$$\mathrm{\Delta }\mathrm{\Phi }=|\frac{({\mathrm{\Phi }}_{(\mathrm{nanocage}‐{\mathrm{H}}_2)}-{\mathrm{\Phi }}_{(\mathrm{nanocage})})}{{\mathrm{\Phi }}_{(\mathrm{nanocage})}}\times 100|$$ 9

where Φ_{(nanocage–H2)} represents the work function values of the adsorbed systems (B₁₂N₁₂/H₂) and Φ_(nanocage) corresponds to the work function of the pure B₁₂N₁₂ or Y-modified nanocage. The quantum descriptor parameters were obtained based on the values of frontier orbitals (HOMO and LUMO) , by applying eqs –.

$$\mathrm{IP}\approx {-E}_{\mathrm{HOMO}}$$ 10

$$\mathrm{eA}\approx {-E}_{\mathrm{LUMO}}$$ 11

$$\eta \approx \frac{1}{2}(E_{\mathrm{LUMO}}-E_{\mathrm{HOMO}})$$ 12

$$\mu \approx \frac{1}{2}(E_{\mathrm{LUMO}}+E_{\mathrm{HOMO}})$$ 13

$$S\approx \frac{1}{2\eta }$$ 14

$$\omega =\frac{{\mu }^2}{2\eta }$$ 15

The electrostatic potential map (MEP) and density of state spectra (DOS) were obtained using the MultiWfn program, in addition to UV–vis spectra, in order to investigate the electronic and optical properties of the cage/gas interactions, elucidating the electronic distribution, reactivity and sensing potential toward H₂. The stability of the most favorable system after H₂ adsorption was evaluated by quantum molecular dynamics (MD) of 1000 ps, with an integration interval of 2 fs, using the GFN-1 Hamiltonian in the xTB software.

The electrical conductivity (σ) can be employed to investigate the interactions of pure and modified B₁₂N₁₂ nanocages with H₂. Its value was calculated as eq ,

$$\sigma ={\mathit{AT}}^{3/2}{\mathrm{e}}^{(-E_{\mathrm{gap}}/2k_{\mathrm{B}}T)}$$ 16

where A is a constant (electron m^–3 K^–3/2), E _gap is the energy gap, k _B is the Boltzmann constant (8.62 × 10^–5 eV K^–1) and T is the thermodynamic temperature (K). Based on this, the most promising yttrium-doped nanocage for H₂ detection was subjected to interactions with interfering gases (CH₄, CO, H₂S and N₂), with selectivity being analyzed by calculating the sensor response (S) and the selectivity coefficient (κ), according to eqs and . ,

$$S=\frac{|R_{\mathrm{gas}}-R_{\mathrm{pure}}|}{R_{\mathrm{pure}}}=\frac{\left|\frac{1}{{\sigma }_{\mathrm{gas}}}-\frac{1}{{\sigma }_{\mathrm{pure}}}\right|}{\frac{1}{{\sigma }_{\mathrm{pure}}}}=\frac{|{\sigma }_{\mathrm{pure}}-{\sigma }_{\mathrm{gas}}|}{{\sigma }_{\mathrm{gas}}}$$ 17

$${\kappa }_{{\mathrm{H}}_2\mathrm{\text{−}}\mathrm{int}}=\frac{S_{{\mathrm{H}}_2}}{S_{\mathrm{int}}}$$ 18

the σ_gas represents the conductivity of the gas adsorbed, σ_pure is the conductance of the isolated nanocage and R _gas and R _pure represent the electrical resistance of the gas/cage system and pure nanocage, respectively. In eq , S _H2 and S _int indicate sensitivity to H₂ gas and to interferents gases, respectively, and κ_H2–int represents the sensitivity ratio to H₂ against an interfering gas.

3. Results and Discussion

3.1. Structural Analysis

The structure of the B₁₂N₁₂ nanocage was optimized, presenting a configuration with eight hexagonal and six tetragonal rings (Figure ). In this geometry, all B and N vertices are equivalent. Two types of B–N bonds were identified: b₆₄, between hexagonal and tetragonal rings, with a length of 1.435 Å, and b ₆₆, between hexagonal rings, with a length of 1.483 Å. These values are close to those reported by Zhao et al., who studied the structural and electronic properties of B₁₂N₁₂ doped with transition metals. For the tetragonal rings, the B–N–B and N–B–N angles were 80.5° and 98.9°, respectively, in agreement with the literature. −

1.

Optimized structure of B₁₂N₁₂ nanocage with B3LYP functional and ZORA-def2-TZVP basis set.

The optimized structures of the pristine and yttrium-modified B₁₂N₁₂ nanocages (YB₁₁N₁₂, B₁₂N₁₁Y, Y@b₆₄, Y@b₆₆, and Y@B₁₂N₁₂) are shown in Figure . The replacement of B or N atoms by yttrium causes evident structural deformations, attributed to the larger atomic radius of Y compared to B and N. In the decorated structures, Y@b₆₄ and Y@b₆₆, the B–N bond lengths near the metal increased to 2.460 Å and 2.380 Å, respectively, indicating significant local distortions. Similarly, the encapsulation in Y@B₁₂N₁₂ resulted in bond lengths of 2.620 Å (b ₆₆) and 2.360 Å (b ₆₄), greater than those of the pristine structure. These results demonstrate that yttrium modification, whether through doping, decoration, or encapsulation, induces structural changes in the B₁₂N₁₂ nanocage. The expansion of B–N bonds, in turn, directly affects electronic stability and molecular adsorption, aspects detailed in subsequent analyses. However, despite the structural changes, it is clear that all yttrium-modified structures are stable over 1000 ps, as shown by the molecular dynamics results.

2.

Illustration of the optimized structures and molecular dynamics of the B₁₂N₁₂ nanocage and the yttrium metal-modified nanocages: doped (YB₁₁N₁₂ and B₁₂N₁₁Y), decorated (Y@b₆₄ and Y@b₆₆), and encapsulated (Y@B₁₂N₁₂).

In Table , we present the formation energy (E _form), cohesive energy (E _coh), dipole moment (DM), NPA charge on the Y atom (Q _Metal), energy gap (E _gap), and work function (Φ) for the pristine B₁₂N₁₂ and its yttrium-modified nanocages. The α-spin (spin up) and β-spin (spin down) orbital energies are reported for the open-shell systems. The pristine nanocage exhibited zero DM, while YB₁₁N₁₂ presented the highest value (9.75 D), and Y@B₁₂N₁₂ the lowest (1.79 D), reflecting a lower charge partitioning in the encapsulation. , These results are corroborated by the lower charges on the yttrium atom. The E _coh analysis indicates that the doped, decorated or encapsulated structures are less stable than the pristine B₁₂N₁₂, although YB₁₁N₁₂ stands out as the most stable among them (E _coh = −7.25 eV). In addition, the negative formation energy for all the nanocages confirms their thermodynamic stability. ,

In this study, it was employed to investigate the interaction between the transition metal yttrium (Y) and the B₁₂N₁₂ nanocage, as presented in Table . The natural charges (NPA) indicate that Y acts as an electron donor, transferring electron density to the nanocage due to its lower electronegativity. Among the evaluated structures, the YB₁₁N₁₂-doped nanocage exhibited the highest charge transfer, demonstrating that substituting a boron atom with Y enhances electronic redistribution and directly influences the electronic and chemical properties of the nanocage. The work function (Φ) values, calculated by eq , were reduced after the modification with yttrium, except in YB₁₁N₁₂ (Φ = 4.70 eV), which maintained the highest value. The decorated system Y@b₆₄ presented the lowest (Φ = 3.14 eV), evidencing the impact of the decoration on the electronic response.

3.2. Adsorption Analysis

Figure shows the structures resulting from H₂ adsorption on the nanocages. Before locating the minimum-energy complexes, we explored different initial adsorption orientations. For the B₁₂N₁₂ and Y@B₁₂N₁₂ systems, we tested positions over B and N atoms. In the doped and decorated nanocages, H₂ was initially placed near the metal, allowing full geometric relaxation to reach the most stable configuration. Only a single initial position of H₂ was required for each system, as hydrogen is a small molecule that adjusts spontaneously during optimization. In the doped B₁₂N₁₁Y–H₂ and decorated Y@b₆₆–H₂ systems, H–H bond rupture and formation of new H–B and H–Y bonds were observed. In the Y@b₆₄–H₂ system, the H₂ molecule dissociated and bonded to the yttrium atom, giving rise to the H–Y–H configuration. This behavior was also reported by Ahangari and Mashhadzadeh, verifying H–H bond rupture and formation of new bonds with the cage atoms. For the encapsulated system Y@B₁₂N₁₂–H₂, structural deformation occurred, with displacement of the yttrium atom from the center to the outside of the cage. The thermodynamic properties ΔG _ads and ΔH _ads (298.15 K), adsorption energy (E _ads), and dipole moment (DM) are listed in Table . The B₁₂N₁₂–H₂ system showed positive ΔG _ads (+0.25 eV), characterizing nonspontaneous adsorption. After modification, all systems presented negative ΔG _ads, evidencing spontaneous adsorption. The ΔH _ads values were predominantly negative, indicating exothermic processes associated with intermolecular interactions, which reduce the energy and increase the stability of the system.

3.

Optimized structures of hydrogen gas (H₂) adsorption on the surfaces of pure and Y-modified B₁₂N₁₂ nanocages.

2. Values of Gibbs Energy (ΔG _ads), Enthalpy of Adsorption (ΔH _ads), Adsorption Energy (E _ads), Dipole Moment (DM) and Stretching Frequencies H–H (v _H2 ) of Pure and Modified B₁₂N₁₂ after Adsorption with H₂ Gas.

system	ΔG ads (eV)	ΔH ads (eV)	E ads (eV)	DM (Debye)	v H2 (cm–1)
B12N12–H2	+0.25	0.00	–0.04	0.16	4374.21
YB11N12–H2	–0.16	–0.08	–0.15	10.53	4327.23
B12N11Y–H2	–1.23	–1.61	–2.04	5.94
Y@b64–H2	–0.40	–0.76	–0.96	0.83
Y@b66–H2	–0.24	–1.85	–2.17	2.54
Y@B12N12–H2	–7.86	–8.03	–13.24	8.21	4371.54

The adsorption energy (E _ads), obtained by eq , indicated physical adsorption for the B₁₂N₁₂–H₂ system (−0.04 eV). The nanocages modified with yttrium presented more negative values. However, the E _ads values of the B₁₂N₁₁Y–H₂, Y@b₆₆–H₂ and Y@B₁₂N₁₂–H₂ systems were higher (more negative) than −1.0 eV, thus limiting their application as sensors, as it makes the chemisorption process irreversible. , On the other hand, the decorated Y@b₆₄–H₂ system presented an adsorption energy value between – 0.3 eV < E _ads < −1.0 eV, , showing that the interaction between Y@b₆₄ and H₂ gas was a moderate chemisorption and suitable for application in H₂ detection. Regarding the H–H stretching frequency, a decrease was observed for systems without dissociation compared to the isolated H₂ molecule (v _H2 = 4412.76 cm^–1), which also exhibit the lowest charges on the hydrogen atoms, as will be discussed later.

3.3. Electronic Analysis

In Table , it is observed that the energies of the HOMO and LUMO orbitals of B₁₂N₁₂ underwent changes after the interaction with H₂, resulting in a direct variation of the energy gap (E _gap). The B₁₂N₁₂ gap presented a slight reduction, from 6.8 to 6.62 eV, corresponding to a variation of 2.67%, indicating low sensitivity and weak interaction with H₂. These results are corroborated by the low adsorption energy of the system (E _ads = −0.04 eV), characterizing a physisorption (E _ads > −0.3 eV) with van der Waals-type interaction. The variation of the work function (ΔΦ), calculated by eq and presented in Table , also indicates low sensitivity for the B₁₂N₁₂–H₂ system (ΔΦ = 0.93%). In the yttrium-modified systems, the lowest value was observed in YB₁₁N₁₂–H₂ (ΔΦ = 0.21%), while the highest occurred in Y@b₆₄–H₂ (ΔΦ = 36.62%), standing out as the most sensitive and promising system for work function-based sensor applications. These data confirm the high sensitivity between the Y@b₆₄ nanocage and the H₂ molecule.

The sensitivity of a system is evaluated by the variation of the band gap (ΔE _gap) before and after gas adsorption (eq ), being influenced by the modification of the nanocage with yttrium. Pure B₁₂N₁₂ showed low sensitivity to H₂ (ΔE _gap = 2.67%; ΔΦ = 0.93%; E _ads = −0.04 eV), characterizing physisorption. In the modified systems, the doped B₁₂N₁₁Y–H₂ was not very sensitive (ΔE _gap = 2.61%; ΔΦ = 0.21%), while Y@b₆₆–H₂ (β-spin down), Y@b₆₄–H₂ (β-spin down) and Y@B₁₂N₁₂–H₂ (α-spin up) showed significant responses (ΔE _gap = 193.53%, 74.94% and 65.47%; ΔΦ = 36.62% for Y@b₆₄). Considering E _ads and recovery time, Y@b₆₆–H₂ and Y@B₁₂N₁₂–H₂ (E _ads = −2.17 and −13.24 eV) are suitable for H₂ storage, as recently demonstrated by Sergio and Sousa for the Y@b₆₄ nanocage, while Y@b₆₄–H₂ (E _ads = −0.96 eV) combines high sensitivity and moderate adsorption energy, being promising as a sensor. Furthermore, analysis of the NPA charges revealed that part of the charge transfers to the hydrogen atoms (with or without H₂ dissociation) originates from the nanocage. For example, in the YB₁₁N₁₂–H₂ system (undissociated H₂), the charge variation on the Y atom was −0.018 and that on H₂ was +0.033, whereas in the Y@b₆₄–H₂ system (dissociated H₂), the charge variation on the Y atom was +0.648 and that on H₂ was −1.147. This indicates a contribution from the nanocage to the overall charge-transfer process.

The results presented in Table S1 demonstrate that the magnetism induced by yttrium modification significantly affects H₂ activation, although it is not a necessary condition for molecular adsorption and dissociation. In the Y@b₆₄ and Y@b₆₆ decorated systems, the nanocage exhibits open-shell behavior prior to adsorption, with multiplicity 2, ⟨S ²⟩ ≈ 0.75, μ_ef in the range of 1.733–1.744 μ_B, and substantial spin populations on Y (0.939 and 0.840, respectively). After H₂ adsorption on the Y@b₆₄ nanocage, for example, a pronounced decrease in the metal spin population (0.939 → 0.282) is observed, accompanied by spin redistribution to the nanocage atoms and to the hydrogen atoms, which preferentially adsorb on yttrium (see Figure ). This electronic reorganization is associated with the stronger adsorption energies observed for the decorated systems (−0.96 and −2.17 eV), reflecting the direct participation of partially occupied Y d orbitals in H₂ activation through σ­(H–H) donation and back-donation into σ*­(H–H).

On the other hand, H₂ dissociation does not depend exclusively on magnetism. The B₁₂N₁₁Y nanocage, although diamagnetic (μ_ef = 0, ⟨S ²⟩ = 0), also promotes H–H bond cleavage, as evidenced by the significant negative NPA charges on hydrogen (−0.53 and – 0.09) and by the decrease in the Y electron population (37.7 → 37.4 e^–). In this case, the process is predominantly governed by charge transfer and electrostatic stabilization, independently of open-shell states. The encapsulated Y@B₁₂N₁₂ system exhibits an intermediate behavior: before adsorption, the spin population on Y is nearly negligible (0.008) with μ_ef = 2.645 μ_B, but upon interaction with H₂, local magnetism is induced, increasing the spin on the metal to 0.17 and on the hydrogen atoms to 0.98, consistent with the absence of H₂ dissociation on the Y@B₁₂N₁₂ surface. Overall, these results indicate that magnetism plays a central role in the adsorption process, either enhancing the H₂-nanocage interaction or being induced by adsorption itself, depending on the doping topology and the initial electronic distribution.

To elucidate the electronic interactions associated with H₂ adsorption on the surfaces of the pristine and Y-modified B₁₂N₁₂ nanocages, charge density difference (CDD) calculations were performed for the nanocage-H₂ systems and the corresponding results are shown in Figure . It was observed that the interactions between the B₁₂N₁₁Y, Y@b₆₄, and Y@b₆₆ nanocages and the H₂ molecule were more effective, as confirmed by the substantial NPA charge transfers occurring upon adsorption. In these cases, H₂ dissociation on the nanocage surfaces was identified; however, the most pronounced charge transfer was found in the Y@b₆₄–H₂ system, primarily because the two hydrogen atoms remained bonded to the yttrium atom, in contrast to what was observed in the B₁₂N₁₁Y–H₂ and Y@b₆₆–H₂ systems (see Figure ). The FMO analysis in Figure highlights the electronic distribution and supports the interpretation of gas-nanocage interactions for Y@b₆₄ nanocages with H₂ gas.

4.

Charge density difference (CDD) of hydrogen gas adsorption on the surfaces of pure and Y-modified B₁₂N₁₂ nanocages with isosurface of 0.001 e·Å^–3. Red and blue colors represent charge accumulation and depletion, respectively. The arrows indicate the magnitude and direction of the electronic charge transfer.

5.

HOMO and LUMO of pure B₁₂N₁₂ and Y@b₆₄ nanocages before and after H₂ adsorption.

The HOMO presents electron density uniformly distributed over the B and N cage, while the LUMO is slightly concentrated in the peripheral regions of the B₁₂N₁₂ nanocage. This distribution indicates weak electronic polarization and limited interaction with H₂, consistent with the observed low adsorption energy (E _ads = −0.04 eV), small band gap variation (ΔE _gap = 2.67%), and low work function variation (ΔΦ = 0.93%). In the Y@b₆₄ nanocage, the HOMO shows accumulation of electron density near the yttrium atom, suggesting that yttrium acts as an active center for interaction with gases. The LUMO is concentrated in regions close to yttrium and the nanocage, favoring partial charge transfer with H₂. This explains the higher observed sensitivity (ΔE _gap = 74.94%) and the moderate adsorption energy (E _ads = −0.96 eV). After H₂ adsorption, the HOMO and LUMO orbitals overlap between H₂ and the doped nanocage, indicating a more significant chemical interaction than in the pure system. The electronic redistribution demonstrates the system’s responsiveness to the presence of H₂, corroborating the high work function variation (ΔΦ = 36.62%) and the adequate adsorption energy for sensing.

The DOS analysis of both pristine and Y-modified B₁₂N₁₂ nanocages after hydrogen gas adsorption is presented in Figure S1 in Supporting Information. The DOS plots reveal that upon interaction with H₂, the B₁₂N₁₂ nanocage experiences slight HOMO destabilization and LUMO stabilization, leading to a reduction in its energy gap from 6.80 to 6.62 eV. Additionally, all yttrium-modified nanocages exhibited an increase in E _gap values after H₂ adsorption compared to the values of the pure nanocages. These findings further support the conclusion that the modified systems are more reactive than the pristine B₁₂N₁₂ nanocage, as evidenced by the previously discussed parameters.

3.4. Quantum Descriptors and Stability

The values of chemical potential (μ), chemical hardness (η), softness (S), ionization potential (IP), electron affinity (eA), and electrophilicity (ω) for the isolated systems were calculated by applying eqs – and are listed in Table , as well as for the modified nanocages after gas adsorption. Initially, it is highlighted that the value of the chemical potential is negative in all conditions, implying the stability of the structures and the spontaneity of all processes. The results show that the pure B₁₂N₁₂ has the highest hardness (η = 3.38 eV) and the lowest softness (S = 0.15 eV^–1) and electrophilicity (ω = 2.94 eV). These results agree with values published in previous studies. − It also shows a higher ionization potential compared to the doped structures, whereas the electron affinity increases upon modification, revealing an enhanced electron-accepting capability. Chemical hardness (η) is associated with a system’s resistance to changes in its electronic distribution; therefore, larger HOMO–LUMO gaps correspond to more rigid and less reactive systems. Conversely, softness (S) characterizes the tendency to accept electronic charge and is inversely related to hardness. Consequently, systems with smaller HOMO–LUMO gaps become more polarizable and reactive, as observed for Y@B₁₂N₁₂, whose behavior is consistent with its higher adsorption energy in the Y@B₁₂N₁₂–H₂ complex. Among the investigated systems, B₁₂N₁₂–H₂ showed the lowest softness (S = 0.15 eV^–1), whereas Y@b₆₆–H₂ exhibited the highest value (S = 0.68 eV^–1). In terms of hardness, Y@b₆₆–H₂ displayed the lowest value (η = 0.73 eV), while B₁₂N₁₂–H₂ retained the highest hardness (η = 3.31 eV). The Y@b₆₄–H₂ system presented intermediate values of chemical potential (μ = −4.29 eV), softness (S = 0.20 eV^–1), and electrophilicity (ω = 3.60 eV).

4. Quantum Descriptors: Chemical Hardness (η), Softness (S), Ionization Potential (IP), Electron Affinity (eA), Chemical Potential (μ), Electrophilicity (ω).

system	IP (eV)	eA (eV)	η (eV)	μ (eV)	S (eV–1)	ω (eV)
B12N12	7.84	1.07	3.38	–4.46	0.15	2.94
B12N12–H2	7.82	1.19	3.31	–4.50	0.15	3.06
YB11N12	6.73	2.67	2.03	–4.70	0.25	5.44
YB11N12–H2	6.63	2.78	1.92	–4.71	0.26	5.76
B12N11Y	5.10	2.56	1.27	–3.83	0.39	5.79
B12N11Y–H2	5.05	2.45	1.30	–3.75	0.38	5.42
Y@b64	4.35	1.92	1.22	–3.14	0.41	4.04
Y@b64–H2	6.85	1.73	2.56	–4.29	0.20	3.60
Y@b66	4.40	1.97	1.22	–3.18	0.41	4.16
Y@b66–H2	3.45	1.99	0.73	–2.72	0.68	5.07
Y@B12N12	4.41	2.40	1.01	–3.41	0.50	5.77
Y@B12N12–H2	6.18	2.75	1.71	–4.46	0.29	5.81

3.5. Electrostatic Potential Analysis

In Figure presents the Molecular Electrostatic Potential (MEP) for the optimized Y@b₆₄ and Y@b₆₄–H₂ structures. This analysis demonstrates the variations in the electronic density of the nanocage after modification with Y and adsorption of hydrogen gas, revealing charge distributions as well as the electrophilic and nucleophilic regions of the molecules.

6.

Molecular electrostatic potential (MEP) map of the Y@b₆₄ nanocage and the Y@b₆₄–H₂ adsorption system.

The MEP is directly associated with physicochemical properties, such as partial charges, dipole moment, and chemical reactivity. In the analyzed systems, the MEP maps show distinct regions: red and yellow indicate negative charges, corresponding to nucleophilic sites; blue represents positive charges, characterizing electrophilic sites; and light green corresponds to neutral areas. , According to Janjua, in the pristine B₁₂N₁₂ nanocage, the boron atoms exhibit a positive electrostatic potential (blue regions), whereas the nitrogen atoms display a negative potential (yellow regions). The B₁₂N₁₂ structure is highly symmetrical and presents a homogeneous charge distribution, which explains its zero dipole moment. Moreover, it was found that H₂ adsorption on B₁₂N₁₂ does not induce significant charge redistribution, indicating a weak interaction between the gas and the nanocage.

In this study, the Y@b₆₄ decorated structure shows a clear modification in the charge distribution pattern, with the region associated with the yttrium atom exhibiting a nucleophilic character (red regions). After H₂ adsorption, electrophilic regions emerge along the Y–H bonds, as well as intermediate neutral areas, revealing a stronger interaction between the gas and the modified surface, compared to the interaction of B₁₂N₁₂ with H₂.

3.6. Thermodynamic Stability Study

Molecular dynamics (MD) analysis was performed in the 0–1000 ps time range, a methodology similar to that employed by De Sousa Sousa et al. It is noteworthy that this time interval is sufficient to observe possible configurational changes. The stability of the Y@b₆₄ nanocage was evaluated before and after the interaction with H₂, as shown in Figure . Previous results by Kundu and Chakraborty demonstrated that yttrium-doped triazine structures maintain their integrity at high temperatures (420 K), allowing the stable adsorption of up to seven H₂ molecules per Y atom at 300 K. Similarly, the results obtained for Y@b₆₄–H₂ show that the gas remains adsorbed on the cage surface, presenting only small energetic variations, attributed to geometric adjustments and H₂ rotations. This stability throughout the simulation confirms the potential of the Y@b₆₄ nanocage as a gas sensor, corroborating the chemical interaction data (E _ads = −0.96 eV) and electronic sensitivity (ΔE _gap = 74.94%).

7.

Quantum molecular dynamics trajectory for the Y@b₆₄ nanocage before and after interaction with H₂ gas.

3.7. Optical Analysis

The absence of negative frequencies in the spectra confirms the stability of the analyzed geometries (for a more detailed analysis, all frequency values before and after interaction with the H₂ molecule are presented in Table S2, and the corresponding IR spectra before and after H₂ adsorption are shown in Figures S2 and S3). The vibrational modes located at approximately 706 and 1632 cm^–1 correspond to the B–N stretching and B–N bending modes, respectively. After the adsorption of the H₂ molecule on the surface of the Y@b₆₄ nanocage, the appearance of a peak at 1619 cm^–1 is observed, which is characteristic of the Y–H interaction.

UV–vis spectroscopy is widely used to monitor adsorption processes. Nair et al., for example, applied this technique to monitor the adsorption of 5FU on PLGA. In Figure shows that the Y@b₆₄ nanocage exhibits three absorption peaks. The first occurs at 235.8 nm, associated with an excitation energy of E = 5.2, with a predominant electronic contribution from the H­(α) → L­(α) transition (49%). The second peak is observed at 314.6 nm, corresponding to E = 3.8, resulting from the HOMO → LUMO transitions [H­(α) → L­(α) (27%) and H–1­(α) → L+1­(α) (25%)]. The third peak appears at 453.7 nm, associated with E = 2.5, with a greater contribution from the H­(α) → L­(α) transition (72%). After adsorption of the H₂ molecule, the Y@b₆₄–H₂ system presented a maximum absorbance peak at λ_max = 219.2 nm, corresponding to an excitation energy of E = 5.6, with contributions from the transitions [H­(β) → L­(β) (26%) and H–1­(β) → L+1­(β) (20%)]. Furthermore, a peak was identified at λ_min = 339.0 nm, associated with E = 3.5, with electronic transition [H­(α) → L­(α) (83%)]. Wavelengths (λ_max), oscillator intensities (f), energies (E), and main electronic transitions associated with the absorption peaks of the Y@b₆₄ and Y@b₆₄-H₂ systems are presented in Table S3. The spectral shift thus provides a promising experimental signature for in situ validation of gas adsorption via UV–vis.

8.

UV–vis spectrum of the Y@b₆₄ nanocage before and after H₂ gas adsorption.

The changes in the UV–vis spectrum of the Y@b₆₄–H₂ system occur due to the absorption of the H₂ molecule by the Y atom. The results indicate that the yttrium-decorated nanocage Y@b₆₄ exhibits optical sensitivity to H₂ gas, suggesting that this material possesses characteristics suitable for application in optical hydrogen gas detection.

3.8. Study of Adsorption of Interfering Gases

The selectivity of the Y@b₆₄ nanocage for H₂ was evaluated relative to some interfering gases commonly used in previous experimental studies reported in the literature (CH₄, CO, H₂S, and N₂) ,,, (see Figure ). The adsorption distances showed that H₂ interacts more strongly (d = 1.98 Å) than the interfering gases, which presented larger distances (2.39 to 3.56 Å) and weak interactions. The NPA charge analysis of the interfering gases showed that the charge variation on the Y atom was 1.782, whereas for the H₂ molecule it was −1.147, indicating a significantly greater charge transfer from the Y@b₆₄ nanocage to H₂ compared with the gases CO, CH₄, H₂S, and N₂. H₂ adsorption (E _ads = −0.96 eV) characterizes chemisorption, with an adequate recovery time (τ = 166.8 s), while the interferents present very short recovery times. These results confirm the high selectivity and efficiency of Y@b₆₄ in the detection of hydrogen gas. However, as pointed out by Kaewmaraya et al., we need to treat the calculated binding energy with caution because this value is based on the single molecule adsorption which does not take into, for example, the factor of gas concentration feeding to the sensor.

9.

Optimized structures of the adsorption of Y@b₆₄ nanocage with interfering gases CO, CH₄, H₂S, and N₂.

The ΔE _gap results show that the Y@b₆₄ nanocage presents greater sensitivity to hydrogen gas compared to the other gases evaluated (ΔE _gap = 74.94%), indicating that the system preferentially detects H₂ (data presented in Table ). The variation in the free energy of adsorption (ΔG _ads) confirms that the adsorption processes are spontaneous for all gases studied, except for methane (ΔG _ads = +0.32 eV), characterized as nonspontaneous. Selectivity was analyzed by calculating the sensor response (S) and the selectivity coefficient (κ), according to eqs and , parameters that express the efficiency of the system in the selective detection of H₂ compared to the tested atmospheric gases. Greater selectivity was observed for the H₂/CH₄ pair, reinforcing the lower detection of methane and confirming the high sensitivity of Y@b₆₄ to hydrogen gas.

5. Values of Gap HOMO-LUMO (E _gap), Cage/Gas Distance (d), NPA Charge on the Y Atom (Q _Metal) and NPA Charges on the Atoms of Interfering Gases (Q _gas), Adsorption Energy (E _ads), Electronic Sensitivity (ΔE _gap), Free Energy of Adsorption (ΔG _ads), Recovery Time (τ), the Sensitivity (S) and Selectivity Coefficient (κ) Calculated for the Interaction of CO, CH₄, H₂S, and N₂ Gases with the Y@b₆₄ Cage.

system	E gap (eV)	d (Å)	Q Metal (|e|)	Q gas (|e|)	E ads (eV)	ΔE gap (%)	ΔG ads (eV)	τ	S	κ
Y@b64–H2	5.12	1.98	1.782	–1.147	–0.96	74.94	–0.40	166.80 s	3.19 × 1018
Y@b64–CO	1.77	2.39	1.413	0.002	–0.62	27.12	–0.03	299.87 μs	6.33 × 109	5.04 × 108
Y@b64–CH4	3.01	3.56	1.170	–0.295	–0.06	2.76	+0.32	103.25 fs	3.74	8.53 × 1017
Y@b64–H2S	2.32	2.83	1.110	0.052	–0.65	4.65	–0.04	963.55 μs	1.43 × 105	2.23 × 1013
Y@b64–N2	1.75	2.39	1.258	–0.177	–0.33	28.00	–0.07	3.77 ns	9.33 × 109	3.42 × 108

Table shows the performance of different nanomaterials in H₂ detection reported in the literature, ,− whose adsorption energies range from −0.072 to −1.830 eV. Values in the range −0.3 eV < E _ads < −1.0 eV are considered ideal for sensor applications. ,, Pure B₁₂N₁₂ presented E _ads = −0.072 eV, characterizing physisorption, a behavior similar to other nanomaterials, such as AlP-doped graphene (E _ads = −0.218 eV), NiN₄S-doped SWCNT (E _ads = −0.082 eV), and C₁₆Mg₈O₈ nanocage (E _ads = −0.170/–0.114 eV). It is noteworthy that the rGO-ZnO–Ag-Pd film and Al₁₂C₁₂ nanocage systems, despite presenting adequate adsorption energies and recovery times, as well as the Y@b₆₄–H₂ system (E _ads = −0.96 eV and τ = 166.8 s), proposed in this work. The Y@b₆₄ nanocage, in comparison to the systems presented in Table , presented the highest electronic sensitivity to H₂ (ΔE _gap = 74.94%), in addition to being selective to CH₄, CO, H₂S and N₂ gases, positioning the Y@b₆₄ nanocage as a promising material for application in selective H₂ gas sensors.

6. Comparison of Sensing Materials for the Detection of Hydrogen Gas (H₂).

sensor	functional	E ads (eV)	ΔE gap (%)	τ (s)	other gases	refs
B12N12 nanocage	B3LYP-D4	–0.072	5 × 10–3		CO2	Choir et al.
C16Mg8O8 nanocage	M06-D3	–0.170	0.54		N2	Ghamsari et al.
	B97D	–0.114	3.45
rGO-ZnO–Ag-Pd film	GGA-PBE	–0.720	59.00	14.00		Pal et al.
W-doped graphene	GGA-PBE-D2	–1.035	24.85	2.44 × 105	NH3, CH4, CO, SO2 and H2S	Yang et al.
AlP-decorated graphene	M06–2X	–0.218	4.68	4.65 × 10–9		Zakeri et al.
Pt-doped g-C3N4	GGA-PBE	–1.830	26.19		CH4 and CO2	Luo et al.
Pt-ZnONT	B3LYP-D3	–1.360	4.19	1.35 × 10–9		Li and Asad
Pt-decorated WS2	GGA-PBE-D	–1.300	27.00	1.85	CO, H2S, NH3, and CH4	Li et al.
Pt-doped MoTe2	GGA-PBE-D	–1.791	12.41	1.32 × 106	CO, C2H4, and C2H2	Jiang et al.
NiN4S-doped SWCNT	ωB97XD	–0.082	50.94	2.20 × 10–11		Imeni et al.
Al12C12 nanocage	B3LYP	H2–Al = −0.550	0.21	1.97 × 10–3	CH4, CO, NO, and NH3	Huang et al.
		H2–C = −0.560	0.21	2.90 × 10–3
Y@b64	B3LYP-D3	–0.960	74.94	166.80	CH4, CO, H2S, and N2	this work

^aValue calculated from E _gap data.

^bValue found in the article.

^cValue calculated by the equation S = [(R – R ₀)/R ₀] × 100%.

^dValue calculated at 598 K.

^eValue calculated at 538 K.

^fValue calculated at 498 K.

The comparison among different theoretical studies of H₂ sensors highlights the central role of computational modeling in identifying materials with superior performance in terms of sensitivity, selectivity, and stability. The detailed evaluation of electronic, structural, and adsorption properties not only guides the rational selection of promising candidates but also reduces experimental costs and directs the development of more efficient devices. These advances hold potential for application in leak-monitoring systems, safety devices for hydrogen production, and technologies associated with fuel cells. Thus, theoretical results not only deepen the understanding of detection mechanisms but also strengthen the integration between computational research and the implementation of technological solutions, driving the transition toward the growing hydrogen economy.

4. Conclusions

In this study, density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations revealed that yttrium modification of B₁₂N₁₂ nanocages significantly enhances H₂ adsorption performance. Geometric, electronic, energetic and optical properties were analyzed, and the results presented that while the pristine B₁₂N₁₂ nanocage exhibited weak physisorption (E _ads = −0.04 eV; ΔG _ads = +0.25 eV), all Y-modified configurations displayed spontaneous adsorption (ΔG _ads < 0) with markedly increased interaction energies. Among the studied systems, the Y@b₆₄–H₂ configuration exhibited chemisorption (E _ads = −0.96 eV) with adequate recovery time (τ = 166.8 s), substantial electronic sensitivity (ΔE _gap = 74.94%), structural stability under molecular dynamics simulations, and a detectable optical response in the UV–Vis region. Furthermore, it demonstrated superior selectivity against common interfering gases (CH₄, CO, H₂S, and N₂), highlighting its potential as a dual-mode electronic and optical H₂ sensor. These results position Y@b₆₄ as a highly promising candidate for hydrogen monitoring and industrial safety applications. Experimental validation will be essential to confirm these theoretical predictions under practical conditions, particularly in industrial safety and hydrogen monitoring environments. Future directions include investigating the integration of this material into real sensing platforms, as well as assessing its performance in miniaturized devices operating under variable environmental conditions, targeting applications in intelligent detection networks and in the emerging infrastructure of the hydrogen economy.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c11273.

• DOS of hydrogen gas adsorption on pure B₁₂N₁₂, YB₁₁N₁₂, B₁₂N₁₁Y, Y@b₆₄, Y@b₆₆ and Y@B₁₂N₁₂ nanocages (Figure S1); IR spectra of the of the B₁₂N₁₂ nanocage and the yttrium metal-modified nanocages: doped (YB₁₁N₁₂ and B₁₂N₁₁Y), decorated (Y@b₆₄ and Y@b₆₆), and encapsulated (Y@B₁₂N₁₂) (Figure S2); IR spectra of the hydrogen gas (H₂) adsorption on the surfaces of pure and Y-modified B₁₂N₁₂ nanocages (Figure S3); Multiplicity, sum spin population, Mulliken Spin Population, Electron Population, S ², deviation, effective magnetic moment (μ_ef), and magnetism for all systems studies (Table S1); Vibrational frequencies (cm^–1) for all systems studies (Table S2); Wavelengths (λ_max), oscillator intensities (f), energies (E), and main electronic transitions associated with the absorption peaks of the Y@b₆₄ and Y@b₆₄-H₂ systems (Table S3) (PDF)

The Article Processing Charge for the publication of this research was funded by the Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES), Brazil (ROR identifier: 00x0ma614).

The authors declare no competing financial interest.