DFT insights into the gas sensing performance of M₂X (M = Zr, Hf; X = C, N) MXenes and their Janus derivatives for toxic gases

Abstract

Widespread air pollution caused by toxic, flammable, and hazardous gases has been linked to numerous health issues. Gas sensors play a crucial role in the detection and monitoring of these harmful substances. In this study, Zr and Hf-based carbide and nitride MXenes (Zr₂C, Zr₂N, Hf₂C, and Hf₂N) and their Janus structures (ZrHfC and ZrHfN) were investigated for their sensing performance towards the toxic CO, NO, NO₂, and SO₂ gas molecules using density functional theory (DFT). The adsorption behavior in terms of adsorption energy, charge transfer, recovery time, electronic properties in terms of band structures, density of states (DOS), and work function were examined to understand the sensing behavior of the nanosheets. Chemisorption interactions were found for all of the complexes except CO and SO₂ adsorption on ZrHfC. Favorable adsorption characteristics were observed for the CO and NO gases on all the nanosheets. The adsorption energies ranged from −1.65 to −3.37 eV for CO and −4.42 to −5.32 eV for NO, with corresponding Mulliken charge transfers of −0.152 to −1.00e and −0.172 to −1.038e, respectively. But in the case of NO₂ and SO₂, very high adsorption characteristics with high deformation of the gases in the complexes were found, which leads to unfavorable adsorption performances. Furthermore, the work functions of the nanosheets varied during the adsorption of gas molecules. Thus, all calculations indicate that all six nanosheets can be useful for monitoring CO and NO.

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1. Introduction

The existence of hazardous gas molecules in the environment is increasing rapidly due to rapid industrialization, which is alarming for the environment. Hazardous, poisonous, combustible, and explosive gases such as ethanol (C₂H₆O), formaldehyde (HCHO), nitrogen oxides (NO_x), acetone (C₃H₆O), ammonia (NH₃), sulfur oxides (SO_x), and carbon monoxide (CO) pose serious threats to human health, environmental safety, and urban air quality and contribute significantly to carbon emissions and other global concerns. Toxic gases are the prime cause of cardiovascular diseases, cardiac dysfunction, nausea, acute headaches, respiratory issues, asthma, neural damage, and so on.^1,2 CO is a poisonous gas without smell, color, or taste. It forms when fuels such as wood, coal, or gas don’t burn completely or when gas doesn’t get enough fresh air. When inhaled, it binds to blood cells faster than oxygen, developing a lack of oxygen in the body and leading to tissue hypoxia, brain injury, or even death.³ SO₂ is a colorless, corrosive, and highly irritant gas that can cause significant health effects. It causes bronchoconstriction in asthmatic subjects, exacerbates asthma, chronic bronchitis, and chronic obstructive pulmonary disease, and contributes to acid rain.⁴ Nitric oxide (NO) and nitrogen dioxide (NO₂) are major air pollutants that harm both health and the environment by contributing to acid rain, ozone depletion, and the greenhouse effect.⁵ Air contamination disturbs the natural atmospheric conditions and creates an ecological imbalance, resulting in 9 out of 10 people inhaling highly contaminated air, according to WHO.⁶

Researchers have concentrated on developing complex gas sensors that offer high accuracy and speed in detecting the concentrations of gases to enable the rapid identification of these gas molecules. These sensors have several applications, such as the detection of explosives, medical diagnostics, food and beverage quality evaluation, and air quality monitoring. Many two-dimensional (2D) nanomaterials, including phosphorene, graphene, related 2D crystals, and even MXenes, have been utilized as gas-sensing materials over the past few decades due to their ultrahigh surface area, strong exterior actions, high mobility, outstanding thermal and electrical conductivity values, and high chemical and thermodynamic durability.^7–9 A new class of two-dimensional materials called MXenes was discovered in 2011. It comprises nitrides, carbides, oxycarbides, and nitrocarbides of transition metals. These substances have generated considerable attention due to their various applications in energy storage, hydrogen generation, gas sensing, biological sensing catalysis, and water purification.^10,11 The structures are composed of 2–5 sections of initial metals that transition (M), linked with 1–4 stages of X (C or N) that can be prepared by eliminating “A” sections (including Al or Si) via MAX indicators and by employing non-MAX ones.¹² By taking out the “A” element from the bulk MAX phases, 2D MXene systems as suitable models were built.^13,14 For simplicity, the focus was placed on M₂X-type MXenes, the thinnest members of the MXene family, where M represents transition metals such as Sc, Ti, Zr, Hf, V, Nb, Ta, and Cr, and X stands for either carbon (C) or nitrogen (N). Finally, the overall findings were discussed on thicker MXene systems.^15–18 It is anticipated that the produced metal surfaces will undergo chemical termination following the removal of the “A” element.^13,19 When hydrofluoric acid (HF) acid solutions chemically exfoliate the MXenes, it has been observed experimentally that the exterior layers dissolve via F and/or OH groups.^20,21 Additionally, O-terminated surfaces could be created chemically or by post-processing OH-terminated systems, for example, by thermal treatment or an ultraviolet-ozone cleaning method.^19,22,23

From Table 1, it is clear that most previous DFT investigation focused on single-component MXenes that were utilized for detecting various toxic gases. These studies reported good charge transfer and sensitivity. However, they did not investigate Janus or heterostructure MXenes and were mainly restricted to conventional MXenes. Furthermore, common defects in MXenes, such as vacancies or missing atoms, can significantly affect the gas sensing properties. They often create additional active sites, enhancing adsorption and charge transfer with gas molecules, which can improve sensitivity and selectivity. However, a high concentration of defects may reduce structural stability. In recent years, numerous theoretical investigations have reported promising gas sensing properties of Janus material transition metal dichalcogenides beyond MXenes. Therefore, in this work, we focused on Janus MXenes. For instance, H. Dou et al.³² and B. Paul et al. explored Janus WSTe and WSeTe monolayers to determine toxic gases including CO, NO, and O₂, while L. Ju et al. demonstrated that Se-vacancies in Janus WSSe enhance sensitivity toward NO₂.^32–34 The selective adsorption of SO₂ and NO₂ on Janus MoSSe was also reported by B. Babariya et al.³⁵ Our exploration of Janus MXenes as novel gas sensing materials is further motivated by these works, which demonstrate how the intrinsic asymmetry of Janus structures can greatly enhance the gas sensing performance. Therefore, the current work depends on DFT to methodically investigate Hf₂C, Hf₂N, Zr₂C, Zr₂N, and their Janus heterostructures (ZrHfC and ZrHfN).

Table 1 Comparison of gas sensing materials based on MXenes

Author	Sensing materials	Targeted gases	Methods	Key findings	Ref.
J. Liang et al.	MXene-based biosensor	Biomolecules	DFT	Good biocompatibility; potential piezoresistive biosensor.	24
Q. Zhou et al.	Ni-doped Zr2CO2/MoS2	HCN	DFT	Enhanced adsorption/sensing via O-vacancies and doping.	25
R. K. Choudhury	W2CT2 (T = O, F)	NH3	DFT	Strong physisorption, charge transfer, and conductivity.	26
Z. Li et al.	Ti3C2O2	NH3, H2S, CO2	DFT	Strong adsorption; excellent sensitivity to toxic gases.	27
R. P. Reji et al.	Sc2CO2	VOCS (ethanol, acetonitrile, 2-propanol)	DFT	Dual-mode sensing; high sensitivity, fast recovery.	28
J. Su et al.	Zn–Co doped Ti3C2O2	NO	DFT	Enhanced NO adsorption; improved sensitivity.	29
K. Boonpalit et al.	Sc@Zr3C2O2, Y@Zr3C2O2	CO	DFT	Good sensitivity, stability, and fast recovery.	30
Xi. Li et al.	Zr3C2O2	Multiple gases	DFT	Gas sensing tunable via surface groups and strain.	31

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2. Computational details

Using the DMol³ component in the Materials Studio software, DFT calculations were performed to investigate the interactions among six nanosheets and unique gas molecules, such as CO, NO, SO₂, and NO₂.^36,37 The exchange–correlation functions were analyzed using the GGA (generalized gradient approximation) with the Perdew–Burke–Ernzerhof (PBE) approach.³⁶ To adjust for relativistic impacts in the core region, a double numerical basis set with polarization (DNP) and the DFT semi-core pseudopotential (DSPP) were utilized.^38,39 All the calculations were completed with Grimme dispersion correction (DFT-D2) for van der Waals forces and large interactions.⁴⁰ We used the spin-unrestricted method, which employed separate orbitals for spin-up and spin-down electrons, to acquire a more accurate representation of uncoupled electron systems. Furthermore, the Tkatchenko–Scheffler (TS) dispersion correction was utilized to account for interactions produced by van der Waals forces.^41–43 For this study, we used a 3 × 3 × 1 supercell with a 20 Å vacuum layer, containing 34 atoms. Earlier studies confirm that a 3 × 3 supercell works well for gas adsorption, and a 20 Å vacuum space prevents interactions between neighboring units.^44,45 All calculations were performed using an established k-point grid of 4 × 4 × 1 and an entire cut-off radius of 5.4 Å. In an optimization process, the maximum force, displacement convergence, and energy tolerance are 0.002 Ha Å⁻¹, 0.005 Å, and 1 × 10⁻⁵ Ha, respectively.^46,47

The cohesive energy of our proposed nanosheets was calculated using the following equation to investigate their structural stability.⁴⁶

where, E_TM and E_X represent the energies of the transition metal atoms (Zr or Hf) and the non-metal atoms (N or C), respectively. The variables A and B indicate the number of transition metal and non-metal atoms, respectively.

The adsorption energy was obtained to explore the ability of gas molecules and nanosheets to adsorb,⁴⁸

E_ads = E_{nanosheet+gas} − E_nanosheet − E_gas (2)

where E_{nanosheet+gas} is the total energy of the nanosheets with the absorbed gas molecules; E_nanosheets and E_gas are the energy of the nanosheets and the energy of the gas molecules before adsorption, respectively.

Through Mulliken and Hirshfeld's charge evaluation, the total charge transfer (Q_t) between the gas molecules and the nanosheets was studied. Q_t was determined by,⁴⁹

Q_t = Q_ads-gas − Q_iso-gas (3)

In this case, Q_ads-gas denotes the net charge of the gas molecules following adsorption, while Q_iso-gas denotes the net charge of the isolated gas molecules. The CASTEP module was employed to generate the charge density difference (CDD) maps with a cutoff energy of 400 eV and a k-point grid of 3 × 3 × 1 to enable determination of the charge transfer behavior,⁴⁷

Δρ = ρ_{nanosheet+gas} − ρ_nanosheet − ρ_gas (4)

In this case, ρ_{nanosheet+gas}, ρ_nanosheet and ρ_gas are the charge density of the nanosheets with the absorbed gas molecules, nanosheets and gas molecules, respectively.

3. Results and discussion

3.1 Geometry and structural stability

In this investigation, four 3 × 3 × 1 supercells of carbide and nitride MXenes (Hf₂C, Hf₂N, Zr₂C, and Zr₂N) and their Janus MXenes (ZrHfC and ZrHfN) were chosen. The Janus MXenes were created by replacing one Zr/Hf layer of any of the initial four nanosheets (Hf₂C/N or Zr₂C/N) with Hf/Zr, forming ZrHfC and ZrHfN. Each of these nanosheets has 27 atoms. Hf₂N, Zr₂N, and ZrHfN contain 9 N atoms each, and the same goes for Hf₂C, Zr₂C, and ZrHfC, but here they have 9 C atoms each. In both the Hf₂N and Hf₂C structures, 18 Hf atoms are present, and 18 Zr atoms are present in both the Zr₂N and Zr₂C structures. Additionally, 9 N or C atoms, along with 9 Hf and Zr atoms, respectively, are present in the ZrHfN and ZrHfC structures. The N–Hf bond length and bond angle of Hf–N–Hf in the optimized Hf₂N structure are determined to be 2.204 Å and 87.150°, respectively, consistent with previous findings.⁵⁰ For Hf₂C, the C–Hf bond length and bond angle of Hf–C–Hf are determined to be 2.204 Å and 87.150°, respectively, and are comparable to the prior value.⁵¹ Additionally, the obtained value is the same in the instances of Zr₂N and Zr₂C. The ZrHfC monolayer, as seen in Fig. 1, is made up of three distinct atom layers: Hf, Zr, and N. The C layer is located in the center of the Hf and Zr layers. In the same way, the ZrHfN monolayer is composed of three layers, with the N layer remaining in the midst of the Hf and Zr layers. The ZrHfC and ZrHfN heterolayer structures show the maximum stability and lowest formation energies of all the mixed phases. The Hf–C and Zr–C bond lengths in the ZrHfC structure are optimized to be 2.192 Å and 2.218 Å, respectively, and the Hf–N–Zr bond angle is calculated to be 92.909°. For ZrHfN, the optimized Hf–N–Hf bond angle is 46.128°, and the Hf–N bond length is 2.192 Å, both in useful agreement with previously revealed findings.⁵⁰ It is shown in Fig. 2–5 that no structural deformation occurs in these nanosheets after optimization. Therefore, the stability of the structure remains unchanged in this gas sensor. In this investigation, we also relaxed four hazardous gases, namely CO, NO, NO₂, and SO₂, in the ground state. The optimized structures of these gas molecules are shown in Fig. 1. In CO and NO, the C–O and N–O bonds have lengths of 1.145 Å and 1.166 Å, respectively. The N–O bond length in the NO₂ molecule is 1.213 Å, while the S–O bond length in the SO₂ molecule is 1.464 Å. NO₂ and SO₂ have V-shaped structures, with calculated O–N–O and O–S–O bond angles of 133.271° and 119.712°, respectively.

Fig. 1 Top and side views of the optimized structures of the nanosheets.

Fig. 2 Top and side views of (a) CO, (b) NO, (c) NO₂, and (d) SO₂ adsorbed on the Hf₂C (top two rows) and Hf₂N (bottom two rows) nanosheets.

We calculated the cohesive energy using eqn (1) to understand the bond strength in the crystal structures—the more negative the cohesive energy, the more stable the structure. The cohesive energies are −6.96, −6.59, −6.97, −6.61, −6.98, and −6.62 eV for Hf₂C, Hf₂N, Zr₂C, Zr₂N, ZrHfC, and ZrHfN, respectively, which is consistent with previous findings.⁵⁰ In our findings, the cohesive energy is larger (more negative) in the carbide MXene than that of nitride ones, which was also found by Shein et al.⁵² The cohesive energies increase in this order: Hf₂N < Zr₂N < ZrHfN < Hf₂C < Zr₂C < ZrHfC, which shows that ZrHfC is the most stable among the nanosheets.

3.2 Adsorption behavior of Hf₂C and Hf₂N towards the CO, NO, NO₂, and SO₂

The adsorption properties of CO, NO, NO₂, and SO₂ on the Hf₂C and Hf₂N nanosheets were evaluated by analyzing the adsorption energy (E_ads), minimum adsorption distance (d_min), and charge transfer (Q_t). The calculated values are summarized in Table 2, and the corresponding optimized structures are illustrated in Fig. 2. When the adsorption process is positive, it indicates an endothermic reaction; conversely, the negative adsorption value indicates an exothermic reaction and also illustrates the attractive connection between gas molecules and nanosheets.⁵³ Here, the significant values of E_ads are −2.32, −4.42, −7.63, and −9.61 eV for CO, NO, NO₂, and SO₂ gas molecule adsorption on the Hf₂C nanosheet at a distance of about 2.155, 2.102, 2.085, and 2.048 Å, respectively. Similarly, in the case of the Hf₂N nanosheet, the values of E_ads are −1.65, −4.82, −7.38, and −11.52 eV for CO, NO, NO₂, and SO₂ gas molecules at a distance of 2.354, 2.054, 2.040, and 2.034 Å, respectively. Based on the study findings by Yong et al., the highest E_ads values for CO, NO, NO₂, and SO₂ on the C₂N monolayer are −0.239 eV, −0.471 eV, −1.665 eV, and −1.304 eV, respectively.⁵⁴ Aghaei et al. observed that the adsorption energies of toxic gas molecules (NO, CO, and NO₂) on graphene-like boron carbide (BC₃) were −1.11 eV, −1.34 eV, and −1.13 eV, respectively.⁵⁵ Q. Hu et al. demonstrated Hf₃C₂O₂ MXene's gas sensing potential through its moderate adsorption energies of −0.197 eV (CO) and −0.174 eV (NO).⁵⁶ According to Salih et al., gold (Au) and silver (Ag) co-doped molybdenum disulfide (Au–Ag–MoS₂) demonstrated promising NO and NO₂ gas sensing capabilities, with adsorption energies of −0.553 eV and −2.603 eV, respectively.⁵⁶ Based on the current comprehensive study, the E_ads energy for the Hf₂C and Hf₂N nanosheets is better than the previous ones, confirming the superior sensing potential of Hf-based MXenes compared with many other 2D materials.

For both Hf₂C and Hf₂N nanosheets, the E_ads increases in the order CO < NO < NO₂ < SO₂, while d_min follows the reverse trend. Furthermore, all of the E_ads values are observed to be negative, indicating an exothermic reaction. NO₂ and SO₂ molecules show a stronger interaction with Hf₂C and Hf₂N nanosheets than CO and NO molecules, which are also adsorbed on the surfaces of Hf₂C and Hf₂N in chemisorption. However, when the adsorption energy is too high, the desorption process slows, i.e., the recovery time increases, which is unsuitable for a good conductor. This indicates that these two nanosheets show better performance as a gas sensor material for detecting CO and NO rather than NO₂ and SO₂.

Mulliken and Hirshfeld charge analysis also indicates that Hf₂C and gas molecules interact strongly by sharing a vast amount of charge (Mulliken) −0.200e (CO), −0.432e (NO), −1.906e (NO₂) and −1.964e (SO₂), where Hf₂C plays the role of electron donor and toxic gas molecules are used as electron acceptors. Charge transfer analysis reveals that the Hf₂C nanosheets exhibit a slightly greater charge transfer with gas molecules than Hf₂N. However, a significant amount of electron transfer occurs in Hf₂N. The Hirshfeld charge of 0.214e and Mulliken charge of 0.359e, 0.522e, and 0.327e are transferred to the gas molecules CO, NO, NO₂, and SO₂, respectively. The Q_t values for CO, NO, NO₂, and SO₂ adsorption indicate that Hf₂N serves as an electron donor. Thus, for Hf₂C, the charge transfer follows the order: CO < NO < NO₂ < SO₂, while for Hf₂N, the trend is CO < SO₂ < NO < NO₂. Previously, Yong et al. reported charge transfers of 0.031e, 0.294e, −0.017e, and −0.088e between C₂N and CO, NO, NO₂, and SO₂ gas molecules, respectively.⁵⁴ According to S. M. Aghaei et al., charge transfers occur between BC₃ and gas molecules as follows: 0.09e from BC₃ to CO, 0.65e from NO to BC₃, and 0.48e from NO₂ to BC₃.⁵⁵ E. Salih et al. demonstrated significant charge transfer from NO (0.220e) and NO₂ (0.448e) to the Au–Ag–MoS₂.⁵⁷ Our results, in particular, exhibit higher charge transfer values, proving that the material according to this study interacts with these gas molecules more strongly, which implies it has promising potential for gas-sensing purposes.

3.3 Adsorption behavior of Zr₂C and Zr₂N towards the CO, NO, NO₂, and SO₂

To measure the adsorption capacity of the aforementioned gas molecules on other nanosheets, specifically Zr₂C and Zr₂N, we calculated the adsorption energy with adsorption distance and net charge transfer using eqn (2) and (3), which are listed in Table 1, and Fig. 3 depict the top and side views of the following gas molecule adsorption on the Zr₂N and Zr₂C nanosheets. The various adsorption sites on the nanosheets and gas molecules' orientations were investigated to find the most stable complex. The significant values of E_ads are −2.84, −4.97, −9.27, and −10.60 eV, respectively, for CO, NO, NO₂, and SO₂ gas molecule adsorption on Zr₂C nanosheets from distances of 2.176, 2.136, 2.108, and 2.063 Å, respectively. Again, the values of E_ads are −3.37, −5.13, −9.87, and −6.56 eV for CO, NO, NO₂, and SO₂ gas molecule adsorption on Zr₂N nanosheets at a distance of 2.139, 2.154, 2.165, and 2.099 Å, respectively. According to H. Y. Ammar et al., the E_ads values of CO and NO are significantly enhanced when the B₁₂N₁₂ nanocage is doped with transition metals (Mn and Fe). Specifically, MnB₁₁N₁₂ exhibits adsorption energies of −0.510 eV (CO) and −0.740 eV (NO), while FeB₁₁N₁₂ shows higher adsorption energies of −0.760 eV (CO) and −1.013 eV (NO).⁵⁸ Y. Wu et al. calculated adsorption energies on B-doped graphdiyne (B-GDY), showing weak CO interaction (−0.068 eV), moderate SO₂ adsorption (−0.173 eV), and stronger NO_x capture (−0.458 eV for NO, −0.541 eV for NO₂).⁵⁹ J. Ren et al. demonstrated that pristine hexagonal boron arsenide (BAs) exhibits distinct gas adsorption capabilities, with calculated adsorption energies of −0.27 eV for CO, −0.18 eV for NO, −0.43 eV for NO₂, and a significantly stronger −0.92 eV for SO₂.⁶⁰ Our study shows that Zr₂C and Zr₂N nanosheets have stronger adsorption energy than the previous findings. Numerically, the adsorption energy trend upon adsorption on Zr₂C is CO < NO < NO₂ < SO₂, while for Zr₂N it follows CO < NO < SO₂ < NO₂. From the above observation, we have seen that the maximum adsorption occurs for SO₂ in the case of Zr₂C nanosheets, and for Zr₂N nanosheets, it occurs for NO₂ gas molecules. Also, the adsorption energy for CO and NO for both of these nanosheets is in the chemisorption range.

Fig. 3 Top and side views of (a) CO, (b) NO, (c) NO₂, and (d) SO₂ adsorbed on the Zr₂C (top two rows) and Zr₂N (bottom two rows) nanosheets.

Mulliken charge analysis also shows that a considerable amount of charge is transferred to the nanosheets, indicating a strong interaction between the gas molecules and these two nanosheets. In terms of Zr₂C, the charge transfer increases in the order: CO (−0.913e) < NO (−1.030e) < NO₂ (−1.871e) < SO₂ (−1.959e), while for Zr₂N the trend follows CO (−0.152e) < SO₂ (−0.329e) < NO₂ (−0.440e) < NO (−0.477e). H. Y. Ammar et al. found that CO transferred 0.222e to MnB₁₁N₁₂ and 0.269e to FeB₁₁N₁₂, while NO received 0.045e from MnB₁₁N₁₂ and transferred 0.053e to FeB₁₁N₁₂.⁵⁸ Y. Wu et al. reported charge sharing between the B-GDY supercell and gas molecules, with values of −0.008e (CO), 0.083e (NO), −0.563e (NO₂), and −0.071e (SO₂).⁵⁹ J. Ren et al. reported minimal charge transfer between monolayer BAs and CO/NO molecules, while stronger interactions were observed with NO₂ (−0.231e) and SO₂ (−0.179e).⁶⁰

From this table (Table 2), the atomic-level characteristics of the gases and the MXene surfaces can be used to explain the adsorption energies and charge transfer trends seen for distinct gas molecules on different MXenes. Because of their high electronegativity and polarity, which enable them to draw more electrons from the MXene surface, SO₂ and NO₂ exhibit the strongest adsorption and largest charge transfer. CO, on the other hand, has the smallest charge transfer and the weakest adsorption because of its smaller size and lower electronegativity. Furthermore, compared to carbides, nitride-based MXenes (Hf₂N, Zr₂N) frequently exhibit slightly greater adsorption because nitrogen atoms offer more active sites for electron transfer, improving the interaction with polar gas molecules.

3.4 Adsorption behavior of ZrHfC and ZrHfN towards the CO, NO, NO₂, and SO₂

To get more insight into the adsorption phenomena of Janus carbide and nitride MXene, we similarly observed the adsorption behavior of ZrHfC and ZrHfN towards the gas molecules. Fig. 4 and 5 show the top and side views after gas molecule adsorption on the ZrHfC and ZrHfN nanosheets. To better investigate the adsorption behavior, gas molecules are adsorbed on the Zr and Hf sites of the nanosheets. The significant values of E_ads at the Zr sites are −2.77, −4.98, −9.17, and −0.40 eV, respectively, for CO, NO, NO₂, and SO₂ gas molecule adsorption on the ZrHfC nanosheets at a distance of 2.455, 2.097, 2.092, and 2.046 Å, respectively (Table 3). The significant values of E_ads at the Hf sites are −0.29, −4.57, −9.50, and −10.68 eV, respectively, for CO, NO, NO₂, and SO₂ gas molecule adsorption on the ZrHfC nanosheets at a distance of 2.134, 2.183, 2.135, and 2.046 Å, respectively. Numerically, the absolute values of adsorption energy for the Zr sites are SO₂ < CO < NO < NO₂, and for the Hf sites are CO < NO < NO₂ < SO₂. In these nanosheets, the Zr site for CO and the Hf site for SO₂ are substantially more reactive. Comparing the above two adsorption sites, we observe that the maximum adsorption occurs at NO₂ gas molecules, which is −9.17 eV for Zr sites, and for the Hf sites, it occurs for SO₂ (−10.68 eV) gas molecules. The most favorable adsorption sites are found at distances of 2.115 Å, 2.051 Å, 2.039 Å, and 1.098 Å on the Zr site of ZrHfN, with adsorption energies of approximately −3.30 eV, −4.78 eV, −10.13 eV, and −6.54 eV for CO, NO, NO₂, and SO₂, respectively.

Fig. 4 Top and side views of (a) CO, (b) NO, (c) NO₂, and (d) SO₂ adsorbed on the ZrHfC, where the top two rows are Hf sites and the bottom two rows are Zr sites of the nanosheets.

Fig. 5 Top and side views of (a) CO, (b) NO, (c) NO₂, and (d) SO₂ adsorbed on the ZrHfN, where the top two rows are Hf sites and the bottom two rows are Zr sites of the nanosheets.

Table 2 Calculated values of the adsorption energy (E_ads), minimum adsorption distance (d_min), and charge transfer between the gas molecules and the Hf₂C, Hf₂N, Zr₂C and Zr₂N nanosheets

Nanosheets	Gas molecules	E ads (eV)	d min (Å)	Q t (e) (Mulliken)	Q t (e) (Hirshfeld)
Hf2C	CO	−2.32	2.155	−0.200	−0.162
	NO	−4.42	2.102	−0.432	−0.288
	NO2	−7.63	2.085	−1.906	−0.673
	SO2	−9.61	2.048	−1.964	−0.822
Hf2N	CO	−1.65	2.354	−0.109	−0.214
	NO	−4.82	2.054	−0.359	−0.276
	NO2	−7.38	2.04	−0.522	−0.437
	SO2	−11.52	2.034	−0.327	−0.228
Zr2C	CO	−2.84	2.176	−0.913	−0.333
	NO	−4.97	2.136	−1.030	−0.349
	NO2	−9.27	2.108	−1.871	−0.657
	SO2	−10.60	2.063	−1.959	−0.812
Zr2N	CO	−3.37	2.139	−0.152	−0.107
	NO	−5.13	2.154	−0.477	−0.29
	NO2	−9.87	2.165	−0.44	−0.331
	SO2	−6.56	2.099	−0.329	−0.276

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According to Table 3, SO₂ and NO₂ show the greatest amount of adsorption and strongest charge transfer on both ZrHfC and ZrHfN due to their high electronegativity and polarity, while CO exhibits the weakest because of its tiny dimensions and low electronegativity. Since nitrogen provides more active sites for electron transfer, nitride-based MXenes (ZrHfN) generally adsorb gases more strongly than carbides (ZrHfC).

Table 3 Calculated values of the adsorption energy (E_ads), minimum adsorption distance (d_min), and charge transfer between the gas molecules and the ZrHfC and ZrHfN nanosheets

Nanosheets	Gas molecules	Sites	E ads (eV)	d min (Å)	Q t (e) (Mulliken)	Q t (e) (Hirshfeld)
ZrHfC	CO	Zr	−2.77	2.455	−0.915	−0.364
		Hf	−0.29	2.134	−0.027	−0.038
	NO	Zr	−4.98	2.097	−0.172	−0.124
		Hf	−4.57	2.183	−1.033	−0.367
	NO2	Zr	−9.17	2.092	−1.88	−0.656
		Hf	−9.50	2.135	−1.887	−0.677
	SO2	Zr	−0.40	2.046	−0.245	−0.252
		Hf	−10.68	2.046	−1.945	−0.830
ZrHfN	CO	Zr	−3.30	2.115	−1.00	−0.384
		Hf	−2.76	2.167	−0.955	−0.340
	NO	Zr	−4.78	2.051	−0.701	−0.349
		Hf	−5.32	2.146	−1.038	−0.358
	NO2	Zr	−10.13	2.039	−1.908	−0.667
		Hf	−10.14	2.039	−2.585	−1.018
	SO2	Zr	−6.54	1.098	−0.053	−0.504
		Hf	−11.55	2.038	−1.923	−0.805

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Similarly, for the Hf site, CO, NO, NO₂, and SO₂ molecules adsorb on ZrHfN at minimum distances of 2.167 Å, 2.146 Å, 2.039 Å, and 2.026 Å, with corresponding adsorption energies of about −2.76 eV, −5.32 eV, −10.14 eV, and −11.52 eV, respectively. The adsorption energies on the Zr site follow the trend: CO < NO < SO₂ < NO₂, and on the Hf site, that is, CO < NO < NO₂ < SO₂. The adsorption energies indicate that all four gases interact with both ZrHfC and ZrHfN through chemisorption, with substantially larger values for NO₂ and SO₂ gas molecules. Previous study by Kharb et al. demonstrates that O-functionalized TiVC MXene exhibits exceptional gas adsorption capabilities, with energies of −0.88 eV (CO), −0.72 eV (NO), −1.06 eV (NO₂), and −0.28 eV (SO₂).⁶¹ The highest adsorption energy was found on Pt-decorated Hf₂CO₂, with values of −3.45 eV for CO as reported by Boonpalit et al.³⁰ Hu et al. reported adsorption energies of 2.07 eV for CO, 3.05 eV for NO, and 2.53 eV for NO₂ on Cr–C₉N₄, while for Fe₂–C₉N₄, the E_ads values were 2.60 eV for CO, 3.07 eV for NO, and 2.45 eV for NO₂.⁶² Compared to these earlier findings, our nanosheets demonstrate stronger adsorption.

We also noticed that the electron transfer between the gases and the heterostructures is significantly larger on both sites of the nanosheets when considering Mulliken and Hirshfeld charge analysis. The Mulliken charge transfer from ZrHfC to gas molecules is significant, with approximately 0.915e for CO, 0.172e for NO, 1.88e for NO₂, and 0.245e for SO₂ at the Zr site during the interaction between the nanosheets and gas molecules. The charge transfers of 0.027e, 1.033e, 1.887e, and 1.945e at the Hf site from ZrHfC to CO, NO, NO₂, and SO₂ gas molecules, respectively. For ZrHfN, a notable amount of charge is transferred from the nanosheets to the toxic gases. At the Zr site, Mulliken charges of 1.00e, 0.701e, 1.908e, and 0.504e (Hirshfeld) are transferred to CO, NO, NO₂, and SO₂, respectively. Meanwhile, at the Hf site, the Mulliken charge transferred to CO, NO, NO₂, and SO₂ has values of 0.955e, 1.038e, 2.585e, and 1.93e, respectively. K. Ma et al. reported charge transfers of −0.98e (CO–Zr–stanene), −1.293e (NO–Nb–stanene), −0.63e (NO₂–Zr–stanene), and −0.67e (SO₂–Nb–stanene).⁶³ Z. Wu et al. found charge transfers of 0.108e (CO), 0.306e (NO), 0.513e (NO₂), and 0.589e (SO₂) for adsorption on Al-doped Ti₂CO₂ nanosheets.⁶⁴ Mushtaq et al. observed the highest charge transfers: −2.52e (NO on a hollow site) and −3.59e (NO₂ on a Si-atom site), with negative values indicating electron donation from the CFMS (001) surface to NO_x.⁶⁵ Compared to previous studies, our proposed heterostructure demonstrates significantly higher charge transfer values.

3.5 Electronic properties

To better understand the performance of these MXene nanosheets, the electronic characteristics of all six nanosheets have been examined. We checked their band structures, density of states (DOS) spectra, and charge density difference (CDD) maps. The electronic band structures were computed along a high-symmetry path through the Brillouin zone: starting at Γ (0,0,0), then to F (0,0.5,0), next to K (−0.333,0.667,0), and back to Γ (0,0,0) (Fig. 6). In all cases, the results clearly indicate that several bands cross the Fermi level, confirming the metallic character of the system, which matches with previous findings.⁵⁰ The absence of a band gap ensures a continuous distribution of electronic states at the Fermi level, which is favorable for fast electron transport. In addition, the presence of steeply dispersive bands near the Fermi level suggests low effective mass and high carrier mobility. The DOS plots represent the distribution of electronic states at different energy levels. To investigate how gas adsorption affects the electronic properties of the nanosheets, we analyzed both the total density of states (TDOS) and partial density of states (PDOS), as illustrated in Fig. 7. After adsorption of the CO and NO gases on the nanosheets, no significant DOS peak was found at the Fermi level, but minor changes were found near the Fermi level after the adsorption of NO₂ and SO₂ gas molecules. From the DOS spectra, it also confirmed that all the optimized complexes exhibited metallic behavior due to the non-zero DOS at the Fermi level (E_F). From the plots, it is evident that there is significant overlap between the orbitals of the gas molecules and the MXene surface atoms, particularly near the Fermi level. This orbital hybridization indicates strong electronic interactions between the gas molecules and MXenes, confirming the chemisorption mechanism. The intensity and position of the peaks also suggest that Hf- and Zr-based MXenes interact more strongly with NO and NO₂ compared to CO and SO₂, consistent with the adsorption energy and charge transfer results.

Fig. 6 The band structures of the nanosheets (a) Hf₂C, (b) Hf₂N, (c) Zr₂C, (d) Zr₂N, (e) ZrHfC, and (f) ZrHfN.

Fig. 7 The total and partial DOS for (a) Hf₂C, (b) Hf₂N, (c) Zr₂C, (d) Zr₂N, (e) ZrHfC, and (f) ZrHfN nanosheets before and after adsorption of CO, NO, NO₂, and SO₂ gas molecules.

We also studied the charge density difference (CDD) maps to examine charge redistribution, bonding interactions, and electric charge transfer behavior. The CDD maps in Fig. 8 illustrate the charge transfer process, where cyan and yellow colors indicate regions of charge loss and gain, respectively. For clearer visualization, the iso-surface value was set to 0.03e Å⁻³ to effectively represent charge density distributions. The CDD map clearly shows electron redistribution throughout the system by highlighting these regions. From Fig. 8, the transfer of a significant amount of charges between the gas molecules (CO) and the nanosheets is clearly observed. From the Mulliken charge analysis, we observe electron transfers of 0.200e (for CO) to Hf₂C, 0.109e to Hf₂N, 0.913e to Zr₂C, 0.152e to Zr₂N, 0.915e to ZrHfC, and 1.000e to ZrHfN. Charge transfer took place between the gas molecules and the adjacent atoms on the nanosheet surface.

Fig. 8 CDD maps of the CO gas adsorbed nanosheets, where the iso-value was set at ±0.03e Å⁻³.

3.6 Recovery time

In nanosheets, the recovery time (τ) is the time needed for gas molecules to desorb from the surface. Higher performance and accurate repeated use require faster sensor renewal, which is indicated by a shorter recovery time. An increase in adsorption energy leads to the recovery time τ being boosted exponentially, and standard transition state theory may clarify this fact as:⁶⁶where ϑ₀ denotes the attempt frequency, Boltzmann's constant is represented as k_B, and T is the absolute temperature in Kelvin. According to the equation, a longer recovery time occurs with a higher adsorption energy. While our proposed nanosheets have significantly higher adsorption energy, this also creates a drawback, like gas molecules taking much longer to desorb. The experiment's results revealed that exposure to vacuum UV light at various frequencies (10¹² s⁻¹, 3 × 10¹⁴ s⁻¹, and 10¹⁸ s⁻¹) and at varying temperatures (300 K, 400 K, and 500 K) was suitable for recovering the detector.^54,55,66 In our observations, all the nanosheets exhibit stronger adsorption of gases, leading to significantly longer recovery times. The adsorption energy for SO₂ and NO₂ is much higher compared to that for CO and NO across all nanosheets. As a result, molecular desorption from the surface is hindered, resulting in a slower recovery process. For CO adsorption (E_ads = 1.65 eV) on Hf₂N nanosheets, the recovery time is predicted to be 2.34 minutes at 500 K, along with a frequency of 3 × 10¹⁴ s⁻¹. Since the absorption energies are greater in all instances, the recovery time is considerably longer. At a frequency of 10¹⁸ s⁻¹ and a temperature of 500 K, the recovery time for NO on Hf₂N is 3.249 × 10³¹ s. For Hf₂C, the recovery times are 2.98 × 10⁵ s for CO and 3.45 × 10⁶² s for NO. In the case of Zr₂C, the recovery times are 4.141 × 10¹⁰ s (CO) and 1.202 × 10³² s (NO), whereas for Zr₂N, they are 9.07 × 10⁵ s (CO) and 4.92 × 10³³ s (NO), respectively. For the heterostructures at the Zr site, ZrHfC exhibits recovery times of 8.16 × 10⁹ s (CO) and 1.52 × 10³² s (NO). Similarly, ZrHfN shows recovery times of 1.79 × 10¹⁵ s (CO) and 1.46 × 10³⁰ s (NO).

3.7 Sensitivity

It's crucial to examine a material's work function (φ) before using it as a sensing device. Because the work function of material surfaces influences the adsorption energy and charge transfer process, it is important for gas sensing. We studied how gas molecules change the work function of the nanosheets. To account for the interaction of dipoles, particular attention has been paid to the dipole slab correction in the work function calculation.⁵⁵ In φ-based sensors, adsorbed gas molecules modify the work function, altering the material's electron emission. This work function shift changes the gate voltage, creating a detectable electrical signal for gas sensing.^67,68 The variation in work function due to gas adsorption was computed by,⁴⁷where φ_c is the work function after the absorption of gas molecules, and φ_n is the nanosheets' work function before adsorption. The bar diagram of the φ variation following gas molecule adsorption is displayed in Fig. 9. The results of our investigation showed that the work functions for Hf₂C, Hf₂N, Zr₂C, Zr₂N, ZrHfC, and ZrHfN nanosheets were, respectively, 5.14 eV, 5.13 eV, 5.24 eV, 5.24 eV, 5.19 eV, and 5.18 eV. Following the adsorption of gas molecules, a negative change implies a decrease in work function, whereas a positive change suggests an increase. A major transfer in charge resulted in an increase. During gas adsorption on the nanosheets, the work function increases for all systems except in the following cases: Hf₂C with CO, NO₂, and SO₂; Hf₂N with CO; Zr₂N with NO and SO₂; and ZrHfC with CO.

Fig. 9 The variation in the nanosheets' work function after the gas molecules' adsorption.

After the adsorption of CO, NO₂, and SO₂ on Hf₂C, the φ values decreased, with the most significant negative change in φ observed for NO₂ (about 3.11%). For Hf₂N, the greatest positive change in φ was observed for SO₂ (approximately 4.11%) due to a significant Δq of around 0.327e from the Hf₂N to SO₂. For Zr₂C, φ experiences minor changes while adsorbing CO, NO, and NO₂ gas molecules, but it significantly rises with SO₂ adsorption (around 3.82%) because of high Δq values of about 1.959e from Zr₂C to SO₂. For Zr₂N, the only positive variation in the work function is found for the adsorption of NO₂ of about 4% because there is a large charge transfer of 0.329e to SO₂, and for other gas adsorption, it is reduced minimally. For the heterostructures, φ varies significantly for the adsorption of SO₂ at about 3.85% and 2.12% for ZrHfC and ZrHfN, respectively, due to the significant charge transfer of about 1.945 and 1.93, respectively.

4 Conclusions

Many harmful gases are currently present in our environment, which affect not only plants and animals but also human health and our daily lives. These harmful gases must be eliminated or filtered to ensure a healthy existence. MXenes have attracted a great deal of attention for their gas-sensing applications. The adsorption characteristics of Hf₂C, Hf₂N, Zr₂C, Zr₂N, ZrHfC, and ZrHfN nanosheets for CO, NO, NO₂, and SO₂ gas molecule adsorption have been examined in this study by employing the DFT approach. Our four MXenes and their Janus MXenes show stable thermodynamic stability, which was confirmed by the negative values of cohesive energies. All nanosheets show metallic behavior. To comprehend the adsorption behavior, the adsorption energy, charge transfer, work function, and electronic characteristics were investigated. The chemisorption of CO and NO on all nanosheets demonstrated better results, according to the adsorption energy, charge transfer, and electric characteristics. However, the adsorption behavior of NO₂ and SO₂ gas molecules was higher, but the recovery time was comparatively much larger for these two gases. The adsorption energies demonstrate strong CO and NO affinity across all six nanosheets, with values of −2.32 eV (CO) and −4.42 eV (NO) for Hf₂C, −1.65 eV (CO) and −4.82 eV (NO) for Hf₂N, −2.84 eV (CO) and −4.97 eV (NO) for Zr₂C, −3.37 eV (CO) and −5.13 eV (NO) for Zr₂N, −2.77 eV (CO) and −4.98 eV (NO) for ZrHfC at the Zr site, and −3.30 eV (CO) and −4.78 eV (NO) for ZrHfN at the Zr site. A significant amount of charge is shared between the nanosheets and the gas molecules, which are also visualized in the CDD maps. The DOS spectra demonstrate that no additional electronic states are created at the Fermi level for CO and NO adsorption on the nanosheets, but a minor contribution has been found near to the Fermi level in the case of NO₂ and SO₂. Moreover, there is a notable variation in the work functions of the nanosheets when gas molecules are adsorbed. Consequently, every computation suggests that every one of the six nanosheets could be helpful in tracking CO and NO toxic gas molecules.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included in the manuscript.

Acknowledgements

We thankfully acknowledge the Bangladesh Research and Education Network (BdREN) for their computational access.

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