Theoretical Study of SO₂ Selective Detection from the Cr-Modified B₁₂N₁₂

Abstract

Sulfur dioxide is a toxic gas with serious environmental and health implications, making the development of selective and efficient sensors an urgent need. In this work, we investigate, using density functional theory (DFT)/B3LYP-D3/6–31G­(d,p) calculations, the potential of B₁₂N₁₂ nanocages functionalized with Cr in different configurations (doped, decorated, and encapsulated) for application in SO₂ chemical sensing. The results show that the encapsulated configuration (Cr@B₁₂N₁₂) exhibits the best combination of properties, including high electronic sensitivity (ΔE _gap = 79.3%), moderate adsorption energy (E _ads = −0.96 eV), and an appropriate recovery time (τ = 167 s), key parameters for reusable sensors under atmospheric conditions. In addition, the system demonstrates high selectivity toward interfering gases such as CO, CO₂, COCl₂, CH₄, H₂S, N₂, and H₂O, corroborated by molecular dynamics simulations. The data analysis suggests that Cr functionalization represents a promising strategy for SO₂ sensor design, although the system’s performance remains dependent on the adsorption energy range and the experimental feasibility of metal encapsulation.

1. Introduction

In the context of modern industries, air pollution has become a severe threat to the environment and human health. Among the polluting gases, we can mention SO₂, a colorless, poisonous, and hazardous gas that poses a significant risk to human health. − Obeso et al. highlighted that developing technologies capable of precisely monitoring specific air pollutants in diverse settings is essential to control emissions and ensure safe exposure limits are not exceeded. Detection and control of gases in residential and industrial environments are necessary, and the study and development of sensors for detecting toxic gases can prevent potentially serious health problems.

In recent decades, theoretical and experimental studies have been carried out to promote the development of new gas sensors and nanoscale materials for removing toxic gases from the environment. − Nanomaterials have aroused interest among research groups, motivated by their potential for rapid detection, high sensitivity, and low recovery time. − In particular, the B₁₂N₁₂ nanocage modified with metal atoms has received special attention for improving the sensitivity, adsorption capacity, and selectivity. ,−

The interaction of SO₂ gas with various surfaces has already been investigated in theoretical studies using density functional theory (DFT). − Soltani et al. tested the doping of Al₁₂N₁₂ with Ga and Mg and observed that although the Mg-doped Al₁₂N₁₂ cluster exhibits high sensitivity to the presence of SO₂ and NO₂ molecules, nickel-decorated B₁₂N₁₂ were shown to differentiate SO₂ from O₃, and the B₂₄N₂₄ nanocage, which differentiates SO₂ from CS₂. Badran et al. showed that Be₁₂O₁₂ and Mg₁₂O₁₂ nanocages can be used to detect and remove H₂S and SO₂ gases. In a study using the Zn₂₄ cluster, Mohammadi et al. showed that the material can act as an adsorbent for SO₂, NO, and NO₂ gases. Albargi et al. showed that the Cu₂Zn₁₀O₁₂ nanocage is a promising candidate for H₂S and SO₂ detecting applications. Hussain et al. demonstrated that the modification in B₁₂P₁₂ nanocage, particularly the inclusion of zinc, enhances the SO₂ adsorptive and sensitivity capacities.

The aza-macrocycle and g-C₃N₄, both pure and modified, emerged as promising materials for SO₂ and SO₃ selective detection. The g-C₃N₄ showed a higher sensitivity to SO₂, underscoring its potential for gas detection. Rad and collaborators tested Pt-decorated graphene and showed that the system detects SO₂ and O₃ gases, with better electronic sensitivity. Shamim and collaborators tested T-graphene (TG), T-boron nitride (TBN), and their heterostructure (TG-TBN) toward CO, SO₂, NO, and NO₂ gas molecules and observed that TBN can be used as a gas sensor for SO₂ and NO₂ gases. An et al. and Parkar et al. tested Fe-doped and Si-doped carbon nanotubes and showed that both systems could detect and remove SO₂, although Si-doped carbon nanotubes exhibited greater sensitivity. Ahmed et al. reported that phosphorus-doped T-graphene nanocapsule is a promising candidate for SO₂ and O₃ detection.

In addition to the studies cited above, − recently, others have been developed using chromium as a surface-modifying element. − Hou et al. tested the Cr₃-doped GaSe monolayer to detect and remove Cl₂, NO, and SO₂ gases and observed that Cr₃–GaSe monolayer, as a substrate material of disposable resistive sensors and removers (with high recovery times), has enormous potential in the area of detection and removal of these toxic gases. Shao et al. showed that Cr-doped armchair graphene nanoribbons performed more efficiently than zigzag graphene nanoribbons for SO₂ detection. Yan et al. suggested that Cr- and Ti-decorated graphene systems were able to detect SO₂ and SO₃. Wu et al. reported that Cr-NbS₂ and Mo-NbS₂ systems could eliminate sulfur-containing gases (SO₂, H₂S, and SO₃) in the atmosphere. Tang et al. using V-, Cr-, and Mn-decorated MoTe₂ systems or hazardous gases adsorption observed that Cr-MoTe₂ and Mn-MoTe₂ were effective in detecting CH₄, HCHO, SO₂, and NO₂ gases. In this sense, these findings motivated us to design a system by modifying the B₁₂N₁₂ nanocage with Cr metal, aiming for efficient SO₂ adsorption and detection in the environment.

Notably, studies on Cr-modified B₁₂N₁₂ nanocages for SO₂ adsorption and sensing are absent in the current literature. In the meantime, the objective of this study is to develop a theoretical study at the DFT level to investigate how different B₁₂N₁₂ nanocage modifications (doped, decorated, and encapsulated) by chromium affect the interaction with SO₂ and the potential application as a material for SO₂ selective detection in the environment.

2. Computational Methodology

The ground state geometry calculation of isolated B₁₂N₁₂ and all systems formed by Cr-modified B₁₂N₁₂ and its interaction with SO₂ were made using the 6–311G­(d,p) basis set in the ORCA 5.0 program. The B3LYP functional, which is based on the normalized gradient approximation (GGA), was used because this functional is able to describe pure and modified B₁₂N₁₂ very well. , To improve the description of long-range interaction, ,,, the Grimme dispersion function (B3LYP-D3) was used. The selected basis set seeks to maintain consistency with previous works − and has been extensively used in the literature for studies involving B₁₂N₁₂ nanocages modified with transition metals, ,− showing consistent results and lower computational costs when compared to more elaborate basis sets. Frequency analysis was also performed at the same level of theory to confirm true global minima, and no imaginary frequencies were recorded. The RMS gradient, RMS displacement, maximum gradient, and maximum displacement were 5 × 10^–6 Hartree, 1 × 10^–4 Hartree/Bohr, 2 × 10^–3 Bohr, 3 × 10^–4 Hartree/Bohr, and 4 × 10^–3 Bohr, respectively.

The inclusion of Cr metal in B₁₂N₁₂ was done in five different configurations: doped (CrB₁₁N₁₂ and B₁₂N₁₁Cr, with the replacement of one boron atom and one nitrogen atom by one Cr atom, respectively); decorated (Cr@b₆₄ and Cr@b₆₆, with a Cr atom positioned above the atomic bond between the tetragonal and hexagonal rings and above the atomic bond between two hexagonal rings, respectively) and encapsulated (Cr@B₁₂N₁₂, in which a Cr atom is positioned inside the B₁₂N₁₂ nanocage). The structures were optimized with zero charge and different spin multiplicities, and the lowest energy structures were used in the analyses.

The HOMO–LUMO gap (E _gap) value was calculated for all investigated structures using the equation defined as the energy difference between the frontier molecular orbitals (FMOs).

$$E_{\mathrm{gap}}=E_{\mathrm{LUMO}}-E_{\mathrm{HOMO}}$$ 1

where E _LUMO and E _HOMO are the energies of the lowest unoccupied molecular orbital and the highest occupied molecular orbital, respectively. The cohesive energy (E _coh in eq ) was used to investigate the nanocage’s stability ,

$$E_{\mathrm{coh}}=\frac{1}{N}(E_{\mathrm{nanocage}}-x{E}_{\mathrm{B}}-y{E}_{\mathrm{N}}-z{E}_{\mathrm{Cr}})$$ 2

where E _nanocage is the nanocage total energy (pure or Cr-modified); E _B, E _N, and E _Cr are the B, N, and Cr atom energies, respectively; x, y, and z are the B, N, and Cr quantities in the structure, respectively, and N indicates the total number of atoms.

The ionization potential (IP), electron affinity (eA), chemical hardness (η), and chemical potential (μ) were calculated as a FMOs function, as shown in eqs , , , and : −

$$\mathrm{IP}\approx -E_{\mathrm{HOMO}}$$ 3

$$\mathrm{eA}\approx -E_{\mathrm{LUMO}}$$ 4

$$\eta \approx \frac{1}{2}(\mathrm{IP}-\mathrm{eA})$$ 5

$$\mu \approx -\frac{1}{2}(\mathrm{IP}+\mathrm{eA})$$ 6

A comparison between the stability and reactivity of isolated B₁₂N₁₂ and the nanocages after interaction with Cr was made since the stability and reactivity of molecular systems can be evaluated using DFT calculations. Thus, as proposed by Parr et al., electrophilicity (ω) can be calculated by the chemical potential and chemical hardness (eq )­

$$\omega =\frac{{\mu }^2}{2\eta }$$ 7

After modification of the B₁₂N₁₂ nanocage with Cr, a SO₂ molecule was adsorbed on the surface of the nanocages and the adsorption energy (E _ads) was calculated using eq

$$E_{\mathrm{a}\mathrm{d}\mathrm{s}}=E_{(\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{g}\mathrm{e}‐\mathrm{S}{\mathrm{O}}_2)}-(E_{(\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{g}\mathrm{e})}+E_{(\mathrm{S}{\mathrm{O}}_2)})+E_{\mathrm{B}\mathrm{S}\mathrm{S}\mathrm{E}}$$ 8

where E _{(nanocage‑SO2)} is the system energy with adsorbed SO₂, E _(nanocage) is the energy of the pure or modified nanocage, E _(SO2) is the SO₂ energy, and E _BSSE is the basis set superposition error (BSSE).

The charge transfer (Q) between the nanocage and SO₂, which is the charge difference between adsorbed SO₂ (Q _{(nanocage‑SO2)}) and free SO₂ (Q _(SO2)), was calculated with eq .

$$Q=Q_{(\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{g}\mathrm{e}‐\mathrm{S}{\mathrm{O}}_2)}-Q_{(\mathrm{S}{\mathrm{O}}_2)}$$ 9

To aid the adsorption analyses, S–O stretching (v _S–O), Gibbs free energy change (ΔG _ads), distance, and bond order (B.O.) were obtained. Data regarding the density of states (DOS) and molecular electrostatic potential (MEP) were generated with the Multiwfn and ChimeraX.

To investigate the potential of nanocages as a material for a chemoresistive sensor for SO₂ detection, the electronic sensitivity of the material to the gas (ΔE _gap), which is related to the electrical conductivity (σ), sensor recovery time (τ), sensitivity (S) and selectivity coefficient (κ), and highest occupied molecular orbital-lowest-unoccupied molecular orbital gap (HOMO–LUMO) (E _gap) were calculated. The electrical conductivity (σ) of the sensor is experimentally dependent on the gap energy and can be calculated according to eq : ,

$$\sigma =A{T}^{3/2}/{\mathrm{e}}^{-E_{\mathrm{gap}}/2k_{\mathrm{B}}T}$$ 10

where A (electron/m³ K^3/2) is a constant, T is the thermodynamic temperature (K), E _gap is the gap energy, and k _B is Boltzmann’s constant (8.62 × 10^–5 eV K^–1).

After determining the most sensitive nanocage that best adsorbs SO₂, the recovery time (τ) was calculated using eq . −

$$\tau =v_0^{-1}{\mathrm{e}}^{-E_{\mathrm{gap}}/k_{\mathrm{B}}T}$$ 11

where v ₀ are attempt frequencies (1.0 × 10¹², 5.2 × 10¹⁴, and 1.0 × 10¹⁶ s^–1). −

The system with the best result for detecting SO₂ was also subjected to interaction with other gases (CO, COCl₂, CH₄, H₂O, N₂, CO₂, H₂S, and N₂O), to compare the selectivity of the system for adsorption of SO₂ with that of other gases. For this, the sensor response (S) and selectivity coefficient (κ _SO2‑int) were calculated using eqs and : −

$$S=\frac{|R_{\mathrm{gas}}-R_{\mathrm{pure}}|}{R_{\mathrm{pure}}}=\frac{\left|\frac{1}{{\sigma }_{\mathrm{gas}}}-\frac{1}{{\sigma }_{\mathrm{pure}}}\right|}{\frac{1}{{\sigma }_{\mathrm{pure}}}}=\frac{|{\sigma }_{\mathrm{gas}}-{\sigma }_{\mathrm{pure}}|}{{\sigma }_{\mathrm{gas}}}$$ 12

$${\kappa }_{\mathrm{S}{\mathrm{O}}_2‐\mathrm{int}}=\frac{S_{\mathrm{S}{\mathrm{O}}_2}}{S_{\mathrm{int}}}$$ 13

In eq , σ_gas represents the conductivity of the gas adsorbed on the nanocage surface, σ_pure is the conductance of the isolated nanocage, and R is the resistance, which is inversely proportional to the electrical conductivity (see eq ). In eq , S _SO2 is the SO₂ sensitivity and S _int is the sensitivity of other gases.

The SO₂ sensibility and structural stabilities of the adsorption system were assessed through molecular dynamics (MD) simulations conducted for 500 ps, with a 2 fs integration time step and a dump of 500 fs at room temperature. Interatomic force uses the GFN1 Hamiltonian as implemented in the xTB software package.

3. Results and Discussion

3.1. Spin Multiplicities

Different spin multiplicities of the Cr-modified B₁₂N₁₂ nanocages (i.e., singlet, triplet, and quintet) were evaluated to determine the most stable configuration of each structure formed. The energy values of the different spin states, referenced to the most stable spin configuration, are presented in Table . It is possible to observe that Cr is more stable with a singlet spin state in the encapsulated system (Cr@B₁₂N₁₂), triplet in the doped systems (CrB₁₁N₁₂ and B₁₂N₁₁Cr), and quintet when decorated in B₁₂N₁₂ (Cr@b₆₄ and Cr@b₆₆). The formation of Cr-decorated systems is more stable when the metal assumes a high-spin multiplicity; this observation is in agreement with the results published by Arshad et al.

1. Relative Energy Values (in Hartree) for Different Cr Spin Multiplicities, Referenced to the Most Stable Cr-Modified B₁₂N₁₂ System.

Cr spin	CrB11N12	B12N11Cr	Cr@b64	Cr@b66	Cr@B12N12
1	0.036	0.035	0.106	0.114	0.000
3	0.000	0.000	0.044	0.440	0.012
5	0.075	0.030	0.000	0.000	0.024

The spin contamination analysis for Cr-functionalized B₁₂N₁₂ nanocage revealed varying degrees of spin state purity depending on the metal’s doping or encapsulation position. Table summarizes the obtained values for the total spin operator expectation value, $⟨{\hat{\mathrm{S}}}^2⟩$ , their theoretical expectations, and the corresponding deviations. All systems exhibited deviations below 10%, indicating adequately described spin states with negligible contamination. This supports the stability of the spin states and the appropriate application of the chosen functional-basis set combination for the studied systems.

2. Spin Contamination Analysis of Cr-Modified B₁₂N₁₂ Nanocages.

nanocage	system spin	$⟨{\hat{\mathrm{S}}}^2⟩$	$⟨{\hat{\mathrm{S}}}^2⟩$ expected	deviation
CrB11N12	4	3.811014	3.750000	0.061014
B12N11Cr	4	4.097592	3.750000	0.347592
Cr@b64	5	6.094094	6.000000	0.094094
Cr@b66	5	6.154875	6.000000	0.154875
Cr@B12N12	1	0.000000	0.000000	0.000000

3.2. Structural Analysis

Initially, it was observed that the B₁₂N₁₂ nanocage ground state geometry is symmetrical and formed by eight hexagonal rings and six tetragonal rings (see Figure ), with bond lengths of b ₆₄ = 1.484 Å and b ₆₆ = 1.437 Å. This symmetry confers a zero electric dipole moment to B₁₂N₁₂, and all data are consistent with works from the literature. − Furthermore, MEP analysis confirmed that negative charge accumulation occurs around N atoms (red region) and decreases around B atoms (blue region) in the B₁₂N₁₂ nanocage. For the orbitals, the HOMO is concentrated exclusively on the N atoms, while the LUMO is on the B atoms regions. DOS analysis showed that the pristine B₁₂N₁₂ nanocage presented an E _gap = 6.88 eV, which is in good agreement with the results published by Beheshtian et al. (E _gap = 6.84 eV) and by Escobedo-Morales et al. (E _gap = 6.67 eV).

1.

Ground state geometry, MEP, FMOs, and DOS for the B₁₂N₁₂ nanocage.

The ground-state geometry of the Cr-modified nanocages can be seen in Figure . In these systems, the doped structures exhibit local structural deformation caused by the displacement of the Cr atom outward from the nanocage surface; this can be attributed to the larger atomic radius of Cr compared to B and N atoms. For the decorated Cr@b₆₆ and Cr@b₆₄ nanocages, it was observed that the B–N bond lengths adjacent to the Cr atom are 0.208 and 0.889 Å longer than those of pure B₁₂N₁₂, respectively, indicating that decoration also promotes local structural changes. In the encapsulated nanocage (Cr@B₁₂N₁₂), the B–N bond distances (b ₆₆ = 1.485 Å and b ₆₄ = 1.520 Å) are close to the values found for the unmodified B₁₂N₁₂ nanocage, indicating that the Cr atom is well accommodated inside the B₁₂N₁₂ nanocage.

2.

Ground state geometry for B₁₂N₁₂ nanocages modified with Cr: CrB₁₁N₁₂, B₁₂N₁₁Cr, Cr@b₆₄, Cr@b₆₆, and Cr@B₁₂N₁₂.

3.3. Energy and Stability Properties

Properties of interest of this work for the pure and modified B₁₂N₁₂ are presented in Table , and from this, it is possible to notice a significant increase in the dipole moment after the modification with Cr (0.51–5.58 D); this occurs due to an asymmetry in the nanocage (see Section ). This effect was less pronounced for Cr@B₁₂N₁₂, and is associated with a little distortion of the nanocages that promotes a smaller separation of charges.

3. Dipole Moment (DM) Energies, Ionization Potential (IP), Electron Affinity (eA), Chemical Hardness (η), Chemical Potential (μ), Electrophilicity (ω), Mulliken Charge for Cr Atom (Q _Cr), and Cohesion Energy (E _coh) Values for the Isolated Nanocages.

systems	DM/Debye	IP/eV	eA/eV	H/eV	μ/eV	ω/eV	QCr/|e|	Ecoh/eV
B12N12	0.00	7.63	0.75	3.44	–4.19	2.56	-	–7.401
CrB11N12	3.94	7.14	2.20	2.47	–4.67	4.41	0.81	–7.428
B12N11Cr	5.17	6.13	2.37	1.88	–4.25	4.79	0.53	–7.180
Cr@b64	5.58	5.69	2.10	1.80	–3.89	4.22	0.55	–7.319
Cr@b66	5.17	5.47	2.48	1.50	–3.98	5.29	0.46	–7.308
Cr@B12N12	0.51	4.98	1.46	1.76	–3.22	2.94	–0.53	–7.086

The results showed that the Cr atom exhibits a positive net charge in the doped and decorated structures, suggesting a preferential interaction with the regions of highest electron density of the SO₂ molecule, i.e., with the oxygen atoms. In contrast, in the encapsulated Cr@B₁₂N₁₂ nanocage, the Cr atom acquires a negative charge, resulting in a lower electron density (i.e., more positive partial charges) on the surrounding boron atoms. This behavior also explains the interaction of the encapsulated nanocage with the negative or partially negative regions of the SO₂ molecule, as will be further discussed in the next section.

To gain deeper insight into the stability and reactivity of the studied systems, it is necessary to examine the quantum chemical descriptors: chemical hardness (η), chemical potential (μ), and electrophilicity index (ω). The results show that the Cr-modified nanocages present lower η and higher ω values than pristine B₁₂N₁₂ (see Table ), indicating that the unmodified nanocage is thermodynamically more stable. According to Parr et al. and Pearson, systems with lower η and higher ω values are generally more reactive, supporting the conclusion that Cr-functionalized nanocages exhibit enhanced reactivity compared to the pristine B₁₂N₁₂. The negative cohesive energy (E _coh) values confirm the thermodynamic feasibility of all studied structures, with CrB₁₁N₁₂ being the most stable, consistent with previous results, and, among them, the Cr@B₁₂N₁₂ nanocage exhibiting notable kinetic stability.

From a practical perspective, experimental studies have demonstrated the feasibility of synthesizing B₁₂N₁₂ nanocages via top-down approaches, such as plasma discharge and plasma-assisted chemical vapor deposition. Additionally, the synthesis of BN nanocages modified with encapsulated transition metals such as Fe, Y, Ag, and La has already been achieved, as reported by Oku et al. − Therefore, based on the present theoretical results and existing experimental evidence, the synthesis of the Cr@B₁₂N₁₂ nanocage at both laboratory and industrial scales appears feasible, opening the path for experimental studies involving toxic gases and indicating promising prospects for real-world applications.

3.4. SO₂ Adsorption

In this stage, the adsorption of a single SO₂ molecule was evaluated, forming the following systems: B₁₂N₁₂–SO₂, CrB₁₁N₁₂–SO₂, B₁₂N₁₁Cr–SO₂, Cr@b₆₄–SO₂, Cr@b₆₆–SO₂, and Cr@B₁₂N₁₂–SO₂. The corresponding ground-state geometries are shown in Figure . It was observed that the most favorable interaction occurs through the oxygen atom of SO₂, in agreement with previous studies. ,, The adsorption sites exhibiting the strongest interactions are the positively charged Cr atoms in the CrB₁₁N₁₂, B₁₂N₁₁Cr, Cr@b₆₄, and Cr@b₆₆ structures, and the positively charged B atoms in the encapsulated Cr@B₁₂N₁₂ structure.

3.

Ground state geometry for the systems: B₁₂N₁₂–SO₂, CrB₁₁N₁₂–SO₂, B₁₂N₁₁Cr–SO₂, Cr@b₆₄–SO₂, Cr@b₆₆–SO₂, and Cr@B₁₂N₁₂–SO₂.

For both the isolated and SO₂-adsorbed systems, the HOMO energy (E _H), LUMO energy (E _L), HOMO–LUMO gap (E _gap), and electronic sensitivity (ΔE _gap) were calculated and are summarized in Table . A significant decrease in E _gap was observed for the Cr-modified systems, with values ranging from 2.69 to 4.95 eV, indicating an increase in the electronic reactivity. This decrease is consistent with previous findings for: (i) B₁₂N₁₂ doped with Fe, Co, Ni, Cu, and Zn; (ii) encapsulated 3d, 4d, and 5d transition metals in B₁₂N₁₂ nanocages; and (iii) B₁₂N₁₂ nanocages decorated with first-row transition metals. Among the Cr-functionalized structures, the Cr@b₆₆-decorated nanocage exhibited the most pronounced gap reduction, indicating its elevated reactivity. However, the electronic sensitivity did not correlate directly with this increased reactivity: the pristine B₁₂N₁₂ nanocage showed a higher sensitivity to SO₂ adsorption than most Cr-modified systems. Notably, the Cr@B₁₂N₁₂ nanocage exhibited a sensitivity of 79.3%, highlighting its potential for SO₂ detection and reinforcing the relevance of its future experimental synthesis, in line with previous transition-metal-based studies − and its demonstrated performance in N₂O detection.

4. HOMO Energy (E _H), LUMO Energy (E _L), HOMO-LUMO Gap (E _gap), and Electronic Sensitivity in Percentage (ΔE _gap) Values, for Isolated and SO₂ Adsorbed Systems for Pure and Modified Nanocages .

		isolated			with SO2 adsorbed
system		EH (eV)	EL (eV)	Egap (eV)	EH (eV)	EL (eV)	Egap (eV)	ΔE gap (%)
B12N12		–7.63	–0.75	6.88	–7.50	–4.02	3.48	49.33
CrB11N12	α	–6.83	–2.79	4.04	–6.59	–3.68	2.91	28.0
	β	–7.14	–2.20	4.95	–7.46	–3.71	3.74	24.3
B12N11Cr	α	–6.13	–2.37	3.76	–6.44	–2.96	3.48	7.4
	β	–5.56	–2.45	3.12	–6.00	–3.70	2.29	26.5
Cr@b64	α	–5.65	–2.38	3.27	–5.93	–2.88	3.05	6.7
	β	–5.69	–2.10	3.60	–5.88	–2.23	3.65	1.4
Cr@b66	α	–5.47	–2.48	2.99	–5.89	–2.89	3.00	0.4
	β	–4.86	–2.17	2.69	–5.89	–2.22	3.68	36.8
Cr@B12N12		–4.98	–1.46	3.53	–4.73	–4.00	0.73	79.3

^aα and β indicate spin-up and spin-down, respectively, for the systems that presented an open shell.

Table presents the geometric, spectroscopic, energetic, and electronic parameters used to elucidate the adsorption mechanism of SO₂ gas on the surfaces of both pristine and chromium-modified B₁₂N₁₂ nanocages. The equilibrium distances between the SO₂ molecule and the nanocage surfaces, obtained from ground-state geometries, reveal that SO₂ remains farther from the pristine B₁₂N₁₂ nanocage (corroborated by a low bond order <0.1) and significantly closer to the Cr-modified structures, which exhibit markedly higher bond orders ranging from 0.38 to 0.79. These findings indicate that Cr modification enhances the interaction strength between the nanocage and the adsorbed molecule. This conclusion is further supported by the variations in the S–O bond lengths and S–O stretching frequencies observed in the SO₂-adsorbed complexes (Nanocage–SO₂) relative to the isolated SO₂ molecule. For the B₁₂N₁₂–SO₂ system, both parameters closely match those of the free SO₂ molecule, confirming the physisorption character of the interaction. In contrast, the Cr-modified nanocages exhibit longer S–O bond distances and significant red shifts in the S–O stretching frequencies, indicating substantial orbital overlap and electron density redistribution (clear evidence of chemisorption). It is worth noting that this spectroscopic criterion has previously been employed by our research group to distinguish between physisorption and chemisorption in analogous systems involving modified B₁₂N₁₂ nanocages interacting with NO, CNCl, N₂O, and CO. These precedents reinforce the validity of our current interpretation regarding the nature of the SO₂ adsorption process.

5. Calculated Values of Adsorption Energy (E _ads), Bond Length Cage-SO₂ (d _cage‑SO2 ), Bond Length SO₂ (d _S–O), Mulliken Charge SO₂ and Cr (Q _SO2 and Q _Cr), Dipole Moment (DM), Stretching Frequencies (v _S–O), Cage-SO₂ Mayer Bond Order (B.O.), and Adsorption Gibbs Free Energy Changes (ΔG _ads) for the Complexes between SO₂ and Isolated Nanocages.

system	Eads/eV	dcage‑SO2 /Å	dS–O(1)/Å	dS–O(2)/Å	QSO2 /|e|	QCr/|e|	DM/Debye	vS–O/cm–1	B.O.	ΔG ads/eV
B12N12–SO2	–0.19	2.286	1.475	1.461	0.07	-	1.47	1129.48	<0.1	+ 0.20
CrB11N12–SO2	–1.17	1.869	1.618	1.618	–0.31	0.82	1.48	805.10	0.79	–0.91
B12N11Cr–SO2	–1.79	2.024	1.572	1.570	–0.36	0.59	1.98	922.53	0.55	–1.62
Cr@b64–SO2	–2.03	1.443	1.627	1.485	–0.37	0.67	4.86	814.22	0.70	–1.93
Cr@b66–SO2	–2.27	1.907	1.612	1.489	–0.37	0.66	5.11	818.68	0.71	–2.18
Cr@B12N12–SO2	–0.96	1.766	1.700	1.492	–0.21	–0.43	3.41	812.48	0.38	–0.63
SO2	-	-	1.464	1.464	0.00	-	1.79	1337.49	-	-

The adsorption energy (E _ads) analysis for SO₂ on the nanocages indicates that the interaction between the SO₂ molecule and pristine B₁₂N₁₂ is weak, characterized by a low E _ads value of 0.21 eV, a bond order below 0.1, and a minimal charge transfer of 0.07|e|. ,, These results confirm the physisorption nature of the process, which is further supported by the positive ΔG _ads, indicating a nonspontaneous adsorption under the simulated conditions. In contrast, the introduction of Cr atoms significantly enhanced the adsorption properties of the nanocages. As shown in Table , all Cr-modified systems exhibited spontaneous adsorption processes (ΔG _ads < 0). However, the E _ads values for the CrB₁₁N₁₂–SO₂, B₁₂N₁₁Cr–SO₂, Cr@b₆₄–SO₂, and Cr@b₆₆–SO₂ systems were higher than −1.0 eV, ranging between −1.17 and −2.27 eV, thus making their application as chemical sensors unfeasible, as it makes the adsorption process irreversible, with a prolonged adsorption–desorption cycle. ,, Notably, these high E _ads values are confirmed by the high bond orders ranging from 0.55 to 0.79, and by the high charge transfers (greater than −0.31|e|). The E _ads value of −0.96 eV for the Cr@B₁₂N₁₂–SO₂ system, on the other hand, was shown to be adequate since the value is in the range −0.3 eV < E _ads < −1.0 eV. This adequacy converges with the moderate values of charge transfer for the SO₂ molecule (−0.21|e|) and of bond order between the nanocage and the SO₂ gas (0.38). Furthermore, it is noteworthy that after the interaction with SO₂, there was an increase in the dipole moment only for Cr@B₁₂N₁₂, among the modified nanocages, increasing the charge separation sensitivity, which is highly desired for electrochemical sensors.

The interaction between the modified nanocages and the SO₂ molecule causes changes in E _gap (see Table ), as well as in the energy and shape of the frontier molecular orbitals (HOMO and LUMO), as shown in Figure , from which it is possible to infer the chemical interaction between the nanocages with Cr and SO₂. In general, the adsorption of the SO₂ gas causes a slight stabilization of the HOMO and the LUMO orbitals for the CrB₁₁N₁₂, B₁₂N₁₁Cr, Cr@b₆₄, and Cr@b₆₆ nanocages. On the other hand, for the Cr@B₁₂N₁₂ nanocage, there was a weak destabilization of the HOMO (0.25 eV) and a significant stabilization of the LUMO (2.54 eV), which resulted in a greater electronic sensitivity for the Cr@B₁₂N₁₂ nanocage. Furthermore, from the DOS diagrams, it is possible to observe a preponderant role of the cage in the formation of frontier molecular orbitals after interaction with SO₂. However, a greater participation of chromium in the formation of LUMO was observed for the Cr@B₁₂N₁₂–SO₂ system, confirming that the Cr-encapsulated nanocage is more sensitive to the SO₂ molecule. The MEPs confirm an increase in the electron density distribution in SO₂ (accumulation of electronic charges), meaning that SO₂ receives a certain amount of charge from the modified nanocages (negative Mulliken charges).

4.

DOS, MEP, and HOMO and LUMO data, for ground state geometry of the CrB₁₁N₁₂–SO₂, B₁₂N₁₁Cr–SO₂, Cr@b₆₄–SO₂, Cr@b₆₆–SO₂, and Cr@B₁₂N₁₂–SO₂ systems.

3.5. Recovery Time

The interaction of the SO₂ molecule on the Cr@B₁₂N₁₂ nanocage surface showed moderate adsorption energy (−0.96 eV) and high sensitivity to SO₂ (79.3%); for this reason, the recovery time (τ) for the Cr@B₁₂N₁₂ nanocage was also evaluated. The value was approximately 167 s, a suitable recovery time for chemical sensor applications. Different recovery times depending on the temperature (T) and the attempt frequency (v ₀) can be observed in Table , , and it is possible to observe that the recovery times calculated for Cr@B₁₂N₁₂–SO₂ varied between 0.51 μs and 4.63 h for the attempt frequencies and temperatures tested. Confirming that, at 298.15 K and under visible light, the recovery time of the Cr@B₁₂N₁₂ nanocage presents a suitable result for applications such as the SO₂ sensor, it was also possible to observe that the recovery time can be reduced with the use of ultraviolet light or with the increase in temperature.

6. Calculated Values of Recovery Time (τ) for SO₂ Adsorption on Cr@B₁₂N₁₂ Nanocage Using Three Different Attempt Frequencies and Temperatures.

		recovery time
light	v0 (s–1)	298.15 K	398.15 K	498.15 K
infrared	1.0 × 1012	4.63 h	1.41 s	5.12 ms
yellow	5.2 × 1014	166.8 s	14 ms	0.05 ms
ultraviolet	1.0 × 1016	1.67 s	0.14 ms	0.51 μs

A more comprehensive approach to the recovery time (τ) behavior for the Cr@B₁₂N₁₂–SO₂ system as a function of a temperature variation from 250 to 450 K can be observed in Figure , considering the evaluated temperatures. It is possible to notice that τ tends to 10 s, for example, at 280 K (ultraviolet light), 325 K (yellow light), and 380 K (infrared light), indicating that it is possible to adjust the desorption process of a molecule on a sensitive surface. When room temperature is available, it is observed that for infrared light, the time for desorption of the SO₂ molecule is greater than 4 h, which makes it impossible to apply the Cr@B₁₂N₁₂ nanocage as a sensor for intermittent use in the detection of SO₂. In this sense, the Cr@B₁₂N₁₂ nanocage is suitable for application in disposable chemical sensors to rapidly detect the toxic gas SO₂, taking advantage of the high electronic sensitivity and adequate recovery time using visible light and adsorption energy.

5.

Variation in recovery time of the Cr@B₁₂N₁₂–SO₂ adsorption system as a function of the temperature and attempt frequency.

3.6. Effect of Interfering Gases

The selectivity of the Cr@B₁₂N₁₂ nanocage toward SO₂ was further evaluated in the presence of potential interfering gases, namely, CO, COCl₂, CH₄, H₂O, N₂, CO₂, H₂S, and N₂O. The optimized geometries of the adsorption complexes are shown in Figure .

6.

Optimized structures of the Cr@B₁₂N₁₂ nanocage and the adsorbed gases CO, COCl₂, CH₄, H₂O, N₂, CO₂, H₂S, and N₂O.

Table summarizes the key parameters associated with the adsorption of each gas on the Cr@B₁₂N₁₂ nanocage, including adsorption energy (E _ads), HOMO–LUMO energy gap (E _gap), electronic sensitivity (ΔE _gap), sensor response (S), selectivity coefficient (κ), and charge transfer to the gas (Q _gas). The data clearly indicate that SO₂ exhibits the strongest interaction with the nanocage, with the highest electronic sensitivity among all gases studied. Notably, only H₂O was found to be chemisorbed, whereas CO, COCl₂, CH₄, N₂, CO₂, H₂S, and N₂O showed weak physisorption, with absolute E _ads values below 0.3 eV, indicating limited interaction with the Cr@B₁₂N₁₂ surface.

7. Values of Adsorption Energy (E _ads), HOMO-LUMO Gap (E _gap), Electronic Sensitivity (ΔE _gap), Sensitivity (S), Selectivity Coefficient (κ), and Mulliken Charge SO₂ (Q _SO2 ) Calculated for the Interaction of Gases CO, COCl₂, CH₄, H₂O, N₂, CO₂, H₂S, and N₂O with Cr@B₁₂N₁₂ .

system	Eads/eV	Egap/eV	ΔE gap/%	S	κSO2‑int	QSO2 /|e|
Cr@B12N12–SO2	–0.96	0.73	79.30	4.5 × 1023		–0.207
Cr@B12N12–CO	–0.07	1.97	44.14	1.4 × 1013	3.0 × 1010	0.070
Cr@B12N12–COCl2	–0.19	2.30	34.96	2.7 × 1010	1.7 × 1013	0.088
Cr@B12N12–CH4	–0.06	3.60	2.03	0.75	5.9 × 1023	0.015
Cr@B12N12–H2O	–0.67	3.47	1.64	2.08	2.1 × 1023	0.243
Cr@B12N12–N2	–0.06	3.51	0.57	0.48	9.4 × 1023	0.019
Cr@B12N12–CO2	–0.13	3.51	0.49	0.40	1.1 × 1024	0.022
Cr@B12N12–H2S	–0.26	3.52	0.24	0.18	2.5 × 1024	0.269
Cr@B12N12–N2O	–0.13	3.52	0.14	0.10	4.3 × 1024	0.040

Charge transfer analysis revealed that, for the Cr@B₁₂N₁₂–SO₂ system, electron flow occurs from the nanocage to the SO₂ molecule (−0.207|e|), suggesting the presence of back-donation mechanisms in the interaction, in agreement with previous studies. , Conversely, for all other interfering gases, the direction of charge transfer was predominantly from the gas molecules to the nanocage.

The sensitivity parameter (S) quantifies the change in electronic properties of the nanocage upon gas adsorption, while the selectivity coefficient (κ) reflects the nanocage’s capability to distinguish SO₂ in a gas mixture. Higher values of κ indicate a better discrimination capability. The results confirm that the Cr@B₁₂N₁₂ nanocage exhibits excellent selectivity and sensitivity toward SO₂ detection, suggesting its applicability in the development of high-performance chemical sensors for atmospheric monitoring.

To investigate the thermodynamic stability of the studied adsorption system and to reinforce the analysis of the nanocage’s selectivity toward SO₂ in the presence of interfering gases, a more realistic system was subjected to a 500 ps molecular dynamics (MD) simulation. The system consisted of a Cr@B₁₂N₁₂ nanocage surrounded by SO₂ gas and all other gases tested. The graph in Figure (left side) shows an abrupt drop in the system’s energy at around 100 ps of the MD simulation, which is related to the dispersion of CH₄, N₂, CO₂, and N₂O gases, none of which bind to the nanocage. CO, H₂S, and water molecules bind to the nanocage, whereas COCl₂ remains near the system but does not interact directly with the cage. In contrast, the SO₂ molecule binds both to the metal center and to a neighboring boron site via its two oxygen atoms, establishing a stronger interaction with the nanocage throughout the trajectory, as illustrated in the system snapshot at the end of the MD run (Figure , right).

7.

Molecular dynamics analysis of the Cr@B₁₂N₁₂ nanocage with SO₂, CO, COCl₂, CH₄, N₂, CO₂, H₂S, and N₂O gases. Trajectory graph (left) and final state of the trajectory (right).

The molecular dynamics analysis showed that interactions with higher sensitivity (such as CO ΔE _gap = 44.14%) or with higher relative adsorption energy values (such as H₂O E _ads = −0.67 eV and H₂S E _ads = −0.26 eV) are possible in realistic systems. However, these do not interfere with the detection or adsorption of the SO₂ gas. The MD results reaffirm the system’s stability and selectivity. The MD results, therefore, corroborate both the thermodynamic stability and selectivity of the Cr@B₁₂N₁₂ nanocage toward SO₂, reinforcing its potential as a robust sensing material under practical operational conditions.

Finally, a comparative analysis between the Cr@₁₂N₁₂ nanocage and other materials reported in the literature for SO₂ adsorption − is presented in Table . The Cr@B₁₂N₁₂ nanocage demonstrated one of the highest electronic sensitivities (ΔE _gap = 79.3%) among the systems investigated, outperforming most candidates and closely followed by the MgB₁₁N₁₂ nanocage (ΔE _gap = 75.37%) and the phosphorus-doped tetragonal graphene nanocapsule (P-doped TGC, ΔE _gap = 74.19%). Despite its high sensitivity, the P-doped TGC presents a weak interaction with SO₂ (E _ads = −0.21 eV), which may impair selectivity in the presence of interfering gases. , Conversely, the MgB₁₁N₁₂ nanocage exhibits excessively strong binding (E _ads = −3.39 eV), which compromises sensor reusability due to irreversible adsorption. In contrast, the Cr@B₁₂N₁₂ nanocage achieves an optimal balance between adsorption energy and sensitivity, combining selective SO₂ detection with feasible desorption and regeneration properties. These findings highlight the Cr@B₁₂N₁₂ nanocage as a highly promising candidate for the design of efficient, selective, and reusable chemoresistive sensors for SO₂ monitoring in atmospheric environments.

8. Comparison of Sensing Materials for the Detection of Sulfur Dioxide (SO₂).

sensor	functional/basis set	Eads/eV	ΔE gap/%	refs
GaB11N12	B3LYP/6–31G(d)	–2.80	67.45	Soltani et al.
MgB11N12	B3LYP/6–31G(d)	–3.39	75.37	Soltani et al.
Ni-decorated B12N12	B3LYP/6–31G(d,p)	–1.82	36.90	Rad and Ayub
B24N24	B3LYP-D3/6–31G(d)	–0.49	45.87	Ding and Gu
Be12O12	B3LYP-D3/6–31G(d,p)	–0.68	15.97	Badran et al.
Mg12O12	B3LYP-D3/6–31G(d,p)	–2.11	2.60	Badran et al.
Zn24	TPSSh/Lanl2DZ	–4.26	46.08	Mohammadi et al.
Zn12O12	TPSSh/Lanl2DZ	–0.54	55.13	Mohammadi et al.
Cu2Zn10O12	B3LYP/LanL2DZ	–2.64	4.98	Albargi et al.
B12P12	B3LYP/6–31G(d,p)	–0.15	45.67	Hussain et al.
Zn–B12P12	B3LYP/6–31G(d,p)	–1.08	55.97	Hussain et al.
aza-macrocycle	ωB97XD/6–31 + G(d,p)	–0.24	1.29	Siddique et al.
g-C3N4	B3LYP/6–31G(d,p)	–0.28	7.45	Ashiq et al.
Pt-decorated graphene	B3LYP/6–31G(d,p)	–0.85	25.10	Rad and Zareyee
T-boron nitride (TBN)	PBE/DNP	–0.911	6.5	Shamim et al.
Fe-CNT	PBE/DNP	–1.298	28.40	An et al.
Si-CNT	PBE/DNP	–1.66	42.59	Parkar et al.
P-doped TGC	B3LYP-D3/6–31G(d)	–0.21	74.19	Ahmed et al.
Cr@B12N12	B3LYP-D3/6–31G(d,p)	–0.96	79.30	This work

^aWithout BSSE correction.

^bWith BSSE correction.

^cCalculated value using E _gap from the literature.

^dLiterature data.

4. Conclusions

In this theoretical study, pristine and chromium-modified B₁₂N₁₂ nanocages (doped, decorated, and encapsulated) were evaluated as potential candidates for the selective sulfur dioxide (SO₂) detection. Among the investigated systems, the Cr@B₁₂N₁₂ nanocage exhibited the most balanced performance, with moderate adsorption energy (E _ads = −0.96 eV), high electronic sensitivity (ΔE _gap = 79.3%), and an adequate recovery time at room temperature (τ = 167 s). These values indicate a favorable balance between effective detection and reversible adsorption, which are key features for reusable gas sensors.

Importantly, Cr@B₁₂N₁₂ showed remarkable selectivity toward SO₂ in the presence of common atmospheric interfering gases, including CO, COCl₂, CH₄, N₂O, N₂, CO₂, H₂S, and water, confirmed by molecular dynamics tests. While H₂O exhibited chemical adsorption, its electronic sensitivity (ΔE _gap = 1.64%) was significantly lower than that of SO₂. All other gases showed weak physisorption (E _ads < 0.3 eV) and minimal gap variation, confirming SO₂-specific detection.

Taken together, these findings position Cr@B₁₂N₁₂ as a promising platform for SO₂ chemoresistive sensing applications. Nevertheless, the adsorption energy is near the upper limit for reversible detection, and the experimental synthesis of encapsulated Cr within the nanocage remains a challenge. Therefore, additional studies, particularly experimental validation and stability assessments, are necessary to support the practical implementation of this system in real-world sensor technologies.

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.

§.

Date of death: June 10, 2024