The unit cell of phosphorene consists of four phosphorus atoms in an orthorhombic space group, as shown in Fig. 1A, with a lattice parameter of 4.61 and 3.29 Å, which is in good agreement with the previous reports [1]. We used a 3 × 3 supercell consisting of 36 atoms to model the gas molecule interaction studies as shown in Fig. 1B, with lattice dimensions of 13.85 Å × 9.89 Å. As can be seen, the structure of pristine phosphorene is anisotropic along the x and y directions, which are labeled as armchair and zigzag directions, respectively. After relaxation, the bond length of the P-P bond [d₁(inter-layer distance)] was 2.26 Å in the armchair direction and 2.22 Å [d₂(intra-layer distance)] in the zigzag direction, which are consistent with the literature [1]. Here, d₁ and d₂ are found to be slightly different but are very close to each other due to the covalent bonds between phosphorus 3p orbitals.

In order to investigate the mono-vacancy, we removed one phosphorus atom from the 3 × 3 supercell structure. The structure of the MVP is shown in Fig. 1C. The formation energy (Ef) of the mono-vacancy configuration was computed using the relation Ef=EMVP−NpEp, where EMVP denotes the energy of phosphorene containing a single vacancy, Np is the number of phosphorus atoms in the defective model, and Ep corresponds to the per-atom energy extracted from pristine phosphorene. The calculated formation energy is 2.07 eV, indicating that vacancy creation is endothermic but energetically feasible. This value is in excellent agreement with earlier work by Ramachandran et al. [35], who reported a formation energy of 2.09 eV using DFT-GGA. The relatively low value implies that mono-vacancies can be introduced experimentally and may play an active role in modulating the sensing performance of phosphorene.

Close to this defect, the armchair bond length of P-P bond measures 2.26 Å, while in zig-zag direction, it was 2.34 Å. In contrast, the bond lengths away from the defect region were 2.26 and 2.22 Å along armchair and zig-zag directions, respectively, which are comparable to those of phosphorene.

We next investigated the interaction of phosphorene sheets with different molecules by placing molecules close to the sheet in the orientation as shown in the Fig. 2. Interaction lengths between different gas molecules and P & MVP sheets is shown in Fig. 3, while geometry of gas molecules after interaction with sheets is shown in the Figs. 2 and 4, respectively. First, the interaction was investigated on a pristine phosphorene sheet, where we found almost no change in P-P bond length. We found that the interaction length (d) between NH₃, AsH₃, PH₃, CO₂ and CH₄ and the pristine phosphorene sheet was 3.01, 3.45, 3.40, 3.62 and 3.19 Å, respectively with calculated interaction energies to be −0.166, −0.163, −0.157, −0.112 and −0.104 eVs for respective gases showing weak physisorption interactions. The interaction energy data suggest that the interaction ability of these five gas molecules on pristine phosphorene is in the order NH₃ > AsH₃ > PH₃ > CO₂ > CH₄. In a pristine phosphorene sheet, each phosphorus atom is covalently bonded with three neighboring phosphorus atoms. Each phosphorus atom has five valence electrons (3s²3p³). Three of these electrons form three σ bonds with adjacent phosphorus atoms. The remaining two valence electrons create a lone pair that resides in an out-of-plane orbital. This arrangement gives rise to the distinctive puckered honeycomb structure. When a gas molecule interacts with a pristine phosphorene sheet, then Van der Waals interaction between the gas molecules and P sheet leads to higher values of interaction length.

Next, we studied the interaction of various gases on a mono-vacancy phosphorene (MVP) sheet by placing a gas molecule near the vacancy of MVP and allowing the system to relax without any constraints. The interaction lengths between gas molecules and the MVP sheet were 0.69, 1.26, 1.07, 2.58 and 2.04 Å for NH₃, AsH₃, PH₃, CO₂, CH₄ gases, respectively. In case of MVP, at the vacancy site each phosphorus atom is bonded with only two adjacent phosphorus atoms compared to three phosphorus atoms in pristine phosphorene sheet. This creates the local deformation and changes in orbital hybridization (Figs. S2 and S3). When NH₃, AsH₃, or PH₃ gas atoms interact with MVP sheet then these gas atoms covalently bind with phosphorus atoms close to the vacancy site. This results in strong interaction and a remarkable reduction in the interaction length. As compared to the pristine phosphorene sheet (P), we observed stronger interactions between vacancy-defected phosphorene sheet and different molecules. The relaxed structures of the MVP sheets after adsorption of NH₃, AsH₃, PH₃, CO₂ and CH₄ gas molecules are shown in Fig. 4A–J.

In case of mono-vacancy phosphorene, the interaction energies of NH₃, AsH₃, PH₃, CO₂, CH₄ gas molecules were −0.343, −0.045, −0.272, −0.522, and −0.519 eV, respectively. The interaction ability of these five gas molecules on MVP is in the order CO₂ > CH₄ > NH₃ > PH₃ > AsH₃.

On comparing the interaction energies of NH₃, AsH₃, PH₃, CO₂, and CH₄ gas molecules on pristine phosphorene and MVP, it was found that vacancy could enhance the bonding strength of all the gas molecules except AsH₃. We have given a comparison of the interaction energies of NH₃, AsH₃, PH₃, CO₂, and CH₄ gas molecules on pristine phosphorene (P) (blue color) and mono vacancy phosphorene (MVP) in Fig. S1.

This exception in the case of AsH₃ arises mainly due to electronic and structural factors. The mono-vacancy introduces unsaturated phosphorus atoms with dangling bonds that generally promote charge transfer and covalent bonding with incoming gas molecules. However, AsH₃ possesses a larger atomic radius and weaker electronegativity compared to NH₃ and PH₃, leading to poor orbital overlap between As–4p and P–3p states at the defect site. As a result, AsH₃ fails to form a strong P–As bond and instead exhibits lower interaction energy and a negative Bader charge transfer value (–0.469 e⁻) (discussed in next section), indicating electron withdrawal rather than bond stabilization. Therefore, unlike other gases, AsH₃ interacts less strongly with the defective phosphorene sheet.

In the chemisorbed cases (NH₃, PH₃, and to a lesser extent AsH₃ on MVP), the interaction is predominantly covalent in nature. The mono-vacancy creates unsaturated phosphorus atoms with dangling bonds, which act as active sites for adsorption. The lone-pair electrons on N or P atoms in NH₃ and PH₃ interact with the P-3p orbitals at the vacancy site, leading to dative (coordinate) covalent bond formation. This is confirmed by the significant reduction in adsorption distance (0.69–1.07 Å), large negative adsorption energies (−0.272 to −0.343 eV), and notable Bader charge transfer (0.256 e⁻ for NH₃ and −0.362 e⁻ for PH₃) (discussed in next section). In contrast, AsH₃ shows a weakly chemisorbed or transition-type interaction due to poor orbital overlap between the larger As–4p orbitals and P–3p defect orbitals, which explains its lower adsorption energy. Meanwhile, CO₂ and CH₄ exhibit van der Waals-type physisorption, as indicated by larger adsorption distances (>2.0 Å), small charge transfer, and minimal deformation of the MVP lattice.

To investigate further the gas molecule interaction and their sensing properties, we studied the electronic properties of systems by analysing their electronic band structures (Fig. 5). Fig. 5A shows the band structure of pristine phosphorene, while Fig. 5B–F shows the band structure of the phosphorene sheets after their interaction with gas molecules NH₃, AsH₃, PH₃, CO₂, and CH₄, respectively. We observed that due to the weak interaction between different gas molecules and the pristine phosphorene sheet, the electronic bands profile remains almost unaltered.

We have given the band structures of MVP sheets before and after gas molecule interaction in Fig. 6. The presence of the defect is shown to induce hole doping within the phosphorene, evidenced by the Fermi level shifting upwards towards the valence band. The band gap identified was indirect, measuring approximately 0.77 eV. Additionally, it was observed that the defect creates localized states in the valence band, indicated by the relatively flat band just below the Fermi level. These localized states act as possible active states for interacting with gas molecules.

The band gaps of P-sheet, MVP sheet, and the ad-systems are shown in Table 1. The band gap of the pristine phosphorene sheet was found to be 0.87 eV, which reduces to 0.77 eV in the MVP sheet as a result of vacancy. As in the case of pristine phosphorene sheet all gases show weak physisorption interactive nature with no chemical bond formation between molecule and the sheet, a similar interaction is reflected in the electronic band gap analysis, where we observed that band gap remains almost unaltered after different gas molecules interaction (Table 1) indicating very low amount of charge transfer between pristine phosphorene sheet and gas molecules. We have presented a comparative chart of the band gap in Fig. 7. In the case of gas molecules interacting with the MVP sheet, we see significant changes in the band gap values as a result of molecule interaction. The band gap of MVP changes from its original value of 0.77 eV to 0.66, 0.41, 0.65, 0.87, and 0.88 eV after interaction of gas molecules NH₃, AsH₃, PH₃, CO₂, and CH₄, respectively, which reflects larger charge transfer compared to that in the pristine phosphorene sheet. This was again confirmed through the Bader charge transfer analysis, where a considerable amount of charge transfer is observed between different molecules and the MVP sheet.

In order to gain a deeper insight into the electronic characteristics, the density of states (DOS) plots for all systems were analyzed (Fig. 8). We found that when NH₃, AsH₃, PH₃ gas molecules interact with pristine phosphorene, there is a slight change in DOS of pristine phosphorene and the Bader charge transfer are −0.039, −0.011, and −0.013 e⁻, respectively, which shows that there is less transfer of charge from the sheet to gas molecules, behaving NH₃, AsH₃, PH₃ are electron acceptors. While in the case of CO₂ and CH₄ gas molecules interaction with pristine phosphorene, there are significantly higher values of DOS in the conduction band, and CO₂ and CH₄ gas molecules interaction show the electron donor characteristics, as the Bader charge transfer are 0.017 and 0.006 e⁻, respectively.

The DOS of the MVP sheet underwent significant modifications after the sheet’s interaction with NH₃, AsH₃, PH₃, CO₂, and CH₄ gases. After NH₃ interaction, DOS of MVP increases significantly towards the lower energy side near the Fermi level, which further leads to a higher Bader charge transfer of 0.256 e⁻ showing electron donor properties of ammonia gas. AsH₃ and PH₃ interactions increase the DOS values in the vicinity of the Fermi level and lead to large Bader charge transfer of −0.469 and −0.362 e⁻, respectively that indicating the electron acceptor behavior of AsH₃ and PH₃ gas molecules. While CO₂ and CH₄ interaction slightly changes DOS of MVP towards the higher energy side near the Fermi level, and an increase in peak value of DOS in the conduction band leads to a smaller Bader charge transfer with values 0.021, and 0.014 e⁻. Hence, CO₂ and CH₄ molecules show the behavior of an electron donor.

Significant changes of DOS in the vicinity of the Fermi level are anticipated to lead to marked changes in the associated electronic properties. This is highly advantageous for gas sensing purposes. Therefore, the MVP demonstrates greater suitability for sensing NH₃, AsH₃, PH₃, CO₂, and CH₄ compared to pristine phosphorene. We have given projected-density-of-states (pdos) of NH₃ and AsH₃ molecules interacting with pristine and MVP sheets in Figs. S2 and S3, respectively. We note that a stronger overlap occurs, with noticeable As-sp³ mixing with defect-P (s–p hybrid) orbitals, indicating significant hybridization (Fig. S3).

The sensor responses for all the ad-systems were determined by analyzing the band gap before and after the interactions with the gases. Fig. 9 illustrates the sensitivity (S%), while Table 2 provides the sensitivities measured for NH₃, AsH₃, PH₃, CO₂, and CH₄ to be 39.65%, 10.34%, 17.7%, 15.62%, and 9.28%, respectively. For pristine phosphorene, the band gap shows nearly no changes following the interaction of AsH₃ and CH₄. However, there is a slight change in band gap noted after the interaction of NH₃, PH₃ and CO₂. Therefore, pristine phosphorene demonstrates a higher sensitivity towards NH₃, PH₃ and CO₂, while it has lower sensitivity towards AsH₃ and CH₄.

In case of MVP, the sensitivity for NH₃, AsH₃, PH₃, CO₂, and CH₄ are 88.71%, 99.9%, 90.13%, 86.82% and 87.56%, respectively. In this case, the increased value of S can be attributed to a significant alteration in the band gap. The changes in the band gap occur due to the interaction of NH₃, AsH₃, PH₃, CO₂, and CH₄ gas molecules on the MVP sheet, which leads to enhanced Bader charge transfer between the MVP and the gas molecules with values 0.256, −0.469, −0.362, 0.021, and 0.014 e⁻, respectively in contrast to −0.039, −0.011, −0.013, 0.017 and 0.006 e⁻ in pristine phosphorene. Upon AsH₃ interaction with MVP, although the interaction energy is low, the sensitivity is very high. This indicates that AsH₃ is better sensed by MVP. The sensitivity of NO₂-doped graphene and Ti₃C₂ MXene is found to be 25.3% and 6.13%, respectively for NH₃ gas [36].

We have also computed the recovery time using Eq. (4). A short recovery time is crucial because it ensures that the sensor is prepared for further measurements, improving the overall efficiency and reliability of gas detection, particularly in applications where gas concentrations fluctuate quickly. The recovery times for various ad-systems are presented in Table 2. The recovery time ranges from milliseconds to picoseconds. At room temperature, physisorbed systems (e.g., CO₂, CH₄ on P and on MVP) exhibit short lower-bound recovery times in the ps–ms range within the desorption energy, Ea≈intercation energy,∣Eint∣ approximation. By contrast, chemisorbed cases on MVP (notably NH₃, PH₃) can involve additional barriers arising from bond formation and local deformation; hence their practical recovery can be considerably longer than the lower-bound τ reported here and may benefit from temperature- or light-assisted desorption. The overall trend across gases and substrates remains unchanged. Consequently, both phosphorene-based sensors can be classified as reusable sensors, with MVP being slightly favored for its stable performance. This observation supports the conclusion that the MVP monolayer can be regarded as a highly sensitive and reusable sensor for these gases. For comparison, the recovery time of Zr₃C₂O₂-based gas sensor for NH₃ gas was found to be 1 ms and for W-doped graphene it was 10 s for CH₄ gas molecules [31].

The interactions between the surface and the adsorbate result in modifications to the work function of the nanomaterial. Therefore, we further determined the work function values and found that the interaction of these gas molecules on both P and MVP sensors caused a reduction in the work function. The work function values are presented in Table 2. The gas molecules NH₃, AsH₃, PH₃, CO₂, and CH₄ tend to exhibit weaker physisorption on pristine phosphorene, leading to only minor changes in the work function, although some modulation occurs due to decreased charge transfer. Consequently, the work function of pristine phosphorene sheet in the presence of these gases is found to be low. In contrast, the covalent adsorption of NH₃, AsH₃, and PH₃ on MVP leads to significant charge transfer, resulting in significant work function changes. Moreover, the physisorption of CO₂ and CH₄ on MVP causes lower charge transfer and, as a result, lower work function changes as well.