Hazardous gas adsorption and sensing by pristine and Pd/Mo-decorated TiS₂: a first-principles study

Abstract

The rapid expansion of industrial activities necessitates the development of cost-effective and highly sensitive gas sensors for the detection of hazardous gases such as NO₂, SO₂, NO, and H₂S. Two-dimensional TiS₂ has attracted considerable attention due to its tunable electronic properties and large surface area. However, its inherently weak interaction with gas molecules limits its practical sensing performance. In this study, first-principles density functional theory (DFT) calculations within the CASTEP framework are employed to systematically investigate the adsorption and sensing characteristics of pristine, palladium (Pd), and molybdenum (Mo) decorated TiS₂ monolayers. Pristine TiS₂ exhibits physisorption for SO₂, NO₂, and H₂S, with chemisorption observed only for NO. In contrast, Pd and Mo decoration (Pd/Mo/TiS₂) significantly enhance the adsorption capability of TiS₂, leading to stronger chemisorption with higher adsorption energies, shorter adsorption distances, and pronounced charge transfer. Mo/TiS₂, in particular, demonstrates strong interactions with adsorption energies ranging from −1.01 eV to −3.421 eV. Electronic structure analysis reveals that NO₂ and NO adsorption on Mo/TiS₂ induces a transition to metallic behavior, resulting in markedly enhanced conductivity and superior sensitivity (392.732 at room temperature), surpassing both pristine and Pd/TiS₂. Recovery time analysis shows that Mo/TiS₂ undergoes extremely slow desorption, with values of 5.544 × 10³⁷ s for NO₂ and 6.8 × 10⁴⁵ s for NO under ambient conditions. In contrast, Pd/TiS₂ demonstrates more practical recovery behavior, with SO₂, NO, and H₂S desorbing within 8.598 × 10⁻³, 0.003, and 65.08 s, respectively. Work function analyses further confirm that Pd and Mo decoration improve charge transport efficiency and enhance sensor selectivity. These results highlight Pd/Mo-decorated TiS₂ as promising candidates for high-performance gas sensors in industrial applications.

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1. Introduction

The advancement of human civilization requires a balance between industrial progress, environmental sustainability, and protection of public health. Rapid industrialization in modern urban environments has caused severe contamination from hazardous waste, particularly toxic gases and heavy metals. Among these pollutants, nitrogen dioxide (NO₂), sulfur dioxide (SO₂), nitric oxide (NO), and hydrogen sulfide (H₂S) are considered highly dangerous due to their significant environmental and health consequences.^1–3 NO₂ is a toxic reddish-brown gas that causes respiratory inflammation and contributes to acid rain.⁴ SO₂, a colorless irritant, also leads to acid rain, vegetation damage, and respiratory issues.^5,6 NO from industrial and vehicular sources contributes to smog formation, while excess levels harm lung function.^7,8 H₂S, a flammable and poisonous gas with a rotten-egg odor, poses serious occupational and respiratory hazards, even at low concentrations.⁹ The design of highly sensitive, reliable, and cost-effective gas sensors has therefore become essential to mitigate these risks.

Recent studies have explored diverse sensing materials, including graphene,^10,11 phosphorene,^12,13 carbon nanotubes (CNTs),^14,15 MXenes,¹⁶ ZnO,^17,18 CuO,¹⁹ and two-dimensional (2D) transition metal dichalcogenides (TMDs),^20,21 due to their promising sensitivity, selectivity, and low power consumption.^22,23 2D TMDs have recently emerged as attractive candidates for hazardous gas sensing owing to their tunable electronic properties, large surface-to-volume ratio, efficient charge transfer ability, and low power consumption.^21,24–26 In addition to gas sensing, TMDs have been widely explored for applications in energy storage,^27,28 biosensing,²⁹ optoelectronics,³⁰ and piezoelectric devices.³¹ These compounds possess the general formula XY₂, where X represents a transition metal (e.g., Ti, Zr, W) and Y denotes a chalcogen element such as sulfur (S) or selenium (Se). TMDs consist of a transition metal layer between two chalcogen layers, with tunable band gaps that make them suitable for sensing applications.³² Titanium disulfide (TiS₂) is particularly noteworthy among TMDs due to its excellent chemical stability, high carrier mobility, and favorable electrical and thermal conductivity.³³ It can be synthesized in diverse nanostructured forms, including nanoribbons, nanosheets, nanoflakes, and nanodiscs.^34–36 Several experimental studies have demonstrated their potential for gas sensors. Wagh et al. synthesized TiS₂ nanostructures via hydrothermal methods for NO₂ detection, reporting enhanced sensitivity at 160 °C for 600 ppm NO₂.³⁷ Sakhuja et al. fabricated TiS₂ nanoflake sensors, achieving strong responses of 395% to 4 ppm H₂S in dry air and 234% to oxygen under ambient conditions.³⁸ Manzoor et al. studied CO₂ sensing using TiS₂ nanodiscs and observed a detection limit of 5 ppm, a 60% response rate, and a rapid response time of 37 s toward 500 ppm CO₂ under ambient conditions.³⁹ Sharma et al. reported a 72% response to 200 ppm NH₃ at atmospheric pressure with commendable selectivity.⁴⁰ These findings confirm the versatility of TiS₂ for gas sensing, although studies remain limited compared to widely investigated TMDs such as MoS₂, MoSe₂, and WS₂. Despite its potential, pristine TiS₂ often exhibits weak interactions with certain gas molecules, which restricts its sensitivity and selectivity, restricting its broader applicability.

To overcome this limitation, surface modification strategies such as metal doping, vacancy engineering, and transition metal (TM) decoration have been widely employed. TM decoration, in particular, introduces foreign metal atoms onto the TMDs surface, generating active sites that enhance adsorption strength, promote charge transfer, and improve overall sensing performance.⁴¹ Transition metals such as palladium (Pd) and molybdenum (Mo) are especially attractive because of their catalytic properties and strong interactions with gas molecules.^42,43 For instance, Zhu et al. demonstrated enhanced SO₂ adsorption on Pd- and Pt-decorated ZrS₂ monolayers using density functional theory (DFT),⁴⁴ while Vu and Pham reported improved SO₂ sensing using Ni-, Pd-, and Pt-decorated HfS₂.⁴⁵ Similarly, Dong et al.⁴⁶ reported that Mo-doped WSe₂ exhibited stronger adsorption toward CO₂ and N₂O than CH₄, confirming the role of transition-metal (TM) doping in enhancing TMD-based gas sensing. Huang et al.⁴⁷ showed that Mo₃-doped TiS₂ improves conductivity, humidity tolerance, and oxygen adsorption, while significantly strengthening CO₂ and SO₂ adsorption through strong orbital hybridization. Saleem et al.⁴⁸ studied the adsorption of toxic gases (CO, CO₂, H₂S, NH₃, NO, NO₂, SO, and SO₂) on pristine and Li-decorated TiS₂ monolayers using DFT calculations. It demonstrates that Li decoration transforms TiS₂ into a metallic system with enhanced adsorption energies, faster recovery times, improved charge transfer. In our previous computational study, the sensing behavior of pristine TiS₂ toward NO₂ and SO₂ was investigated using DFT.⁴⁹ The results showed that pristine TiS₂ interacts weakly with these gases via van der Waals forces, displaying limited adsorption strength and minor changes in electronic properties, particularly demonstrating very low sensing ability toward SO₂.

Despite these advances, no systematic DFT investigations have explored the adsorption and sensing behavior of Pd/Mo-decorated TiS₂ monolayers toward multiple industrially relevant toxic gases. This represents a critical knowledge gap in understanding the full potential of TiS₂ for high-performance gas sensing. The present study addresses this gap by investigating the adsorption and gas-sensing properties of pristine, and Pd/Mo-decorated TiS₂ monolayers toward four toxic gases of industrial importance such as NO₂, NO, SO₂, and H₂S. Using DFT within the Cambridge Serial Total Energy Package (CASTEP), key parameters including adsorption energy, adsorption distance, charge transfer, band structure, density of states, work function, conductivity, sensitivity, and recovery time are systematically analyzed. The findings are expected to provide theoretical insights into TiS₂-based sensor performance and to guide the design of practical, high-performance gas sensors for industrial applications.

2. Computational details in DFT

In this study, all first-principles calculations were performed using CASTEP⁵⁰ program based on DFT.⁵¹ For exchange–correlation interactions, the Perdew–Burke–Ernzerhof (PBE) functional and the Generalized Gradient Approximation (GGA)⁵² were employed. van der Waals forces were computed by DFT-D corrections suggested by TS (Tkatchenko–Scheffler).⁵³ Initially, we optimized the unit cell of TiS₂, characterized by the space group P3̄m1. Subsequently, we bisected this unit cell along the 001 direction and enlarged it to a 3 × 3 × 1 supercell, optimizing the supercell with a 15 Å vacuum along the Z direction. For unit cell optimization, the cut-off energy was set to 500 eV, and the Monkhorst–Pack grid k-point was 6 × 6 × 1. For supercell optimizations and further calculations, a 3 × 3 × 1 Monkhorst–Pack grid k-point and 500 eV cut-off energy were used. The cut-off energy and k-point were determined through systematic convergence tests, where the total energy change was monitored with respect to increasing plane-wave cutoff energy and k-point density, shown in Fig. S1. The total energy became nearly constant beyond 450 eV and 3 × 3 × 1 k-points; thus, 500 eV and 3 × 3 × 1 were selected for subsequent calculations to ensure accuracy and efficiency. Simulations were performed using ultrasoft pseudopotentials⁵⁴ and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) minimization algorithm.⁵⁵ The convergence criteria were set as follows: maximum stress of 0.10 GPa, maximum force of 0.05 eV Å⁻¹, maximum displacement of 0.002 Å, and energy tolerance of 2.0 × 10⁻⁵ eV per atom, following values commonly adopted in previous study on similar dichalcogenide systems.⁵⁶ After the optimization of the TiS₂ supercell, selected transition metals (Pd and Mo) were introduced to decorate the TiS₂ surface. The most energetically favorable decorated configurations were determined by calculating the binding energy or cohesive energy of each configuration. To check the structural stability of the optimized supercells binding energy will be calculated using the following formula:^57,58Here, E_coh, E_total(TiS₂/TM@TiS₂), E(Ti), E(S) represents the cohesive energy of TiS₂ or transition metal (TM) decorated TiS₂, total energy of TiS₂ or transition metal decorated TiS₂, the energy of isolated transition metal, the energy of isolated Ti, and the energy of isolated S, respectively.

Besides optimization of supercells, each gas molecule was built and optimized. Then, optimized gas molecules were adsorbed on the supercell's surface. After gas adsorption, the structures of the gas-adsorbed systems were further optimized. The adsorption energy of the gas molecules on the monolayer was calculated using the following equation:⁵⁹

E_ads = E_total − (E_substrate + E_gas) (2)

Here, E_ads, E_total, E_substrate, and E_gas represent the adsorption energy of gas molecules, the total energy of systems after gas adsorption, the total energy of systems before gas adsorption, and the total energy of the isolated gas molecule, respectively.

Charge transfer (ΔQ) was calculated via the Hirshfeld charge analysis method to ascertain the adsorption capacity, with the corresponding calculation formula presented below:^60,61

ΔQ = Q_after − Q_before (3)

In this context, ΔQ, Q_after, and Q_before represent the charge transfer between the gas and the monolayer, the charge of the gas molecules after it has been adsorbed, and the charge of the isolated gas before it has been adsorbed, respectively. Charge density differential maps (CDD) were produced to visualize charge accumulation and depletion surrounding the gas molecules and monolayer surface.

Electronic properties were computed using the spin-polarized GGA-PBE functional with a cutoff energy of 500 eV and a 3 × 3 × 1 Monkhorst–Pack k-point grid, consistent with the geometry optimization setup. Alterations in electronic characteristics during gas adsorption will facilitate the analysis of the sensor's behavior. For this purpose, electronic band structures, as well as partial (PDOS) and total (TDOS) density of states, were calculated for all systems before and after gas adsorption. The conductivity of any substance is related to its band gap. The conductivity of the adsorbent, both prior to and after gas adsorption, is determined using the following equation:⁶²

In this expression, A denotes a constant, E_g refers to the band gap, K is the Boltzmann constant, and T represents the absolute temperature in Kelvin.

Sensitivity (S) is a key parameter used to assess the effectiveness of materials in gas sensing applications. A higher sensitivity signifies stronger gas–material interactions, indicating improved adsorption and surface activity. Evaluating sensitivity is therefore essential to determine how effectively pristine and decorated TiS₂ monolayers respond to different gases, which directly influences their gas-sensing performance. The sensitivity of an adsorbent toward specific gas molecules was evaluated by monitoring changes in their electrical conductivity upon gas exposure, typically expressed as the difference in conductivity with and without the presence of the gas.⁶³

σ_pure, and σ_{substrate+gas} represent the conductivity of the adsorbent before gas adsorption and after adsorption, respectively. Selectivity was calculated using the following formula:⁶⁴Here, K represents selectivity, S_target is the sensitivity of highest sensitive gas towards a specific system and S_intereferent is the other interfering gases.

Recovery time refers to the period required for a material to restore its initial conductivity after being exposed to a gas.⁶⁵ A shorter recovery time indicates quicker desorption of gas molecules from the material's surface.⁶⁶ Sensor recovery time was calculated using the van't-Hoff–Arrhenius equation:⁶⁷

Here, K, T, E_ad, and f represent Boltzmann's constant, the absolute temperature, adsorption energy, and the frequency of UV radiation (ranging from 10¹² to 3 × 10¹⁴ Hz), respectively.

The minimum energy required to excite an electron from inside a solid to the vacuum level, where it becomes free to escape the material, is known as the work function (WF). The WF is strongly influenced by the surface properties of a material. Any modification at the surface can alter the WF, which in turn affects how easily electrons can escape. In the field of photovoltaics, the WF plays a vital role in determining a material's electrical conductivity and chemical reactivity.^68,69 Gas adsorption leads to a pronounced change in the work function (ϕ), which can be exploited for developing work function-based sensors. These variations in ϕ can be experimentally measured using the Kelvin probe method, providing a practical route for sensor fabrication.⁷⁰ The work function (ϕ) is defined by the difference between the vacuum electrostatic potential (E_vacuum) and the Fermi level (E_Fermi):⁷¹

ϕ = E_vacuum − E_Fermi (8)

3. Results and discussion

3.1 Structural analysis of pristine TiS₂ and Pd/Mo decorated TiS₂

Before the adsorption of gas molecules on monolayer surfaces, all gases and the adsorbents (where gas molecules are adsorbed) should be optimized. The selected gas molecules' geometries, including NO₂, SO₂, NO, and H₂S, were optimized using the CASTEP module. The optimized gas molecule structures are shown in Fig. 1. The bond lengths and angles of optimized gases are listed in Table 1. Bond lengths of NO₂, SO₂, NO, and H₂S are 1.230, 1.195, 1.448, and 1.350 Å, respectively. These values are close enough to the previous findings.^45,66,72 The optimized 3 × 3 × 1 supercell of pristine TiS₂, most stable Pd-decorated TiS₂ (Pd/TiS₂), and Mo-decorated TiS₂ (Mo/TiS₂) are shown in Fig. 2(a), (b) and (c), respectively. The lattice parameters of optimized pristine TiS₂ are a = b = 3.414 Å, which is very close to previously documented values, previous experimental value is 3.3976 Å (ref. 73) and computational value is 3.407 Å.⁷⁴ The optimized pristine TiS₂ is thermodynamically stable as the calculated cohesive energy using eqn (1) is negative (−6.48 eV per atom). The Ti–S bond length of pristine TiS₂ is 2.433 Å, in the case of Pd/TiS₂, this bond length increases to 2.504 Å, and for Mo/TiS₂, the Ti–S bond length is 2.514 Å. The increase in bond length may arise from the interaction of the decorated atoms with TiS₂, which have diverse sizes and charge distributions. The trend in Ti–S bond length is TiS₂ < Pd/TiS₂ < Mo/TiS₂. Here, the greater bond elongation in Mo/TiS₂ reflects more enhanced electronic interaction, higher degree of charge delocalization between the Mo atom and the TiS₂ layer, which in turn increases the availability of active sites for gas adsorption. Therefore, it serves as an indicator of increased surface reactivity arising from electronic modulation which may lead to stronger adsorption energies in case of Mo/TiS₂. The Ti–S–Ti bond angle is 89.52° for pristine TiS₂, S–Pd–S, and S–Mo–S bond angles are 111.62° and 111.83°, respectively.

Fig. 1 Optimized gas molecule structures (a) NO₂, (b) SO₂, (c) NO, and (d) H₂S.

Table 1 Bond lengths and angles of optimized monolayers and gas molecules

Compounds	Bond lengths before gas adsorption (Å)						Bond lengths after gas adsorption (Å)				Angles (°)
	Ti–S	Pd–Ti	Mo–Ti	N–O	S=O	H–S	Ti–S
							NO2	SO2	NO	H2S
TiS2	2.433	—	—	—	—	—	2.431	2.433	2.406	2.428	89.52 (Ti–S–Ti)
Pd/TiS2	2.504	2.294, 2.292	—	—	—	—	2.487	2.457	2.530	2.483	111.62 (S–Pd–S)
Mo/TiS2	2.514	—	2.248, 2.250	—	—	—	2.535	2.518	2.562	2.515	111.83 (S–Mo–S)
NO2	—	—	—	1.230	—	—	—				133.32 (O–N–O)
SO2	—	—	—	—	1.448	—	—				119.34 (O–S–O)
NO	—	—	—	1.195	—	—	—				180 (N–O)
H2S	—	—	—	—	—	1.350	—				91.63 (H–S–H)

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Fig. 2 (a) Optimized TiS₂ monolayer showing three possible decoration sites, (b and c) most energetically favorable Pd-decorated TiS₂ and Mo-decorated TiS₂ monolayers, respectively.

One of the principal concerns was the geometric stability subsequent to the Pd and Mo decoration in the pristine TiS₂ layer. For this purpose, three positions on the TiS₂ layer were selected, illustrated in Fig. 2(a), where Pd and Mo atoms were decorated: above the Ti atom, above the S atom, and above the hollow site. Upon complete geometry optimization of the structure, the binding energies at these three places are computed using eqn (1) to ascertain the most stable configuration of the Pd/Mo/TiS₂ monolayer. The more negative binding energy indicates the favorable stable systems. In case of Pd/TiS₂, the computed binding energies for these locations are −6.37, −6.33, and −6.38, respectively and for Mo/TiS₂, the binding energies are −6.59, −6.6096, −6.6099 eV, respectively. The maximum binding energy, found at the hollow site (−6.38 eV for Pd/TiS₂) and (−6.6099 eV for Mo/TiS₂), indicates that the hollow site is the most stable for both Pd/TiS₂ and Mo/TiS₂ monolayers. These stable structures are shown in Fig. 2(b) and (c), where Pd and Mo create covalent bonds with surrounding S atoms. The Pd–S and Mo–S connections have an average bond length of 2.293 Å and 2.249 Å, respectively, which are less than the total of the atomic covalent radii of S (1.04 Å) + Pd (1.39 Å) and S (1.04 Å) + Mo (1.54 Å),⁷⁵ suggesting a substantial covalent nature and a strong metal–sulfur interaction. The Pd and Mo atoms appear to be firmly anchored in the hollow site, the most energetically advantageous configurations for the Pd/TiS₂ and Mo/TiS₂ monolayers, based on strong covalent bonds. Further calculations of gas adsorptions were conducted on these most stable structures. Additionally, to confirm that the pristine and Pd/Mo-decorated TiS₂ structures are stable at high temperatures, we performed ab initio molecular dynamics (AIMD) simulations at 398 K with a 1 fs time step for a total simulation period of 5 ps. As shown in Fig. S2, the total energy of each system (Figs. S2(a), (c) and (e)) fluctuates slightly around a constant mean value throughout the simulation period, indicating the absence of any structural distortion or bond breaking. Correspondingly, the temperature profiles (Fig. S2(b), (d) and (f)) remain stable around the target value, showing only minor fluctuations typical of thermal equilibrium conditions. These observations confirm that the TiS₂, Pd/TiS₂, and Mo/TiS₂ monolayers maintain their structural integrity at elevated temperatures, demonstrating their excellent dynamic and thermal stability, which is essential for reliable sensing performance under practical operating conditions.

3.2 Gas adsorption properties on pristine and Pd/Mo decorated TiS₂

After the geometry optimization of the TiS₂ monolayer, NO and H₂S gas molecules are adsorbed on the TiS₂ monolayer surface in different positions. Adsorbed systems are then optimized, and the most stable systems are identified based on the minimum adsorption energy.⁷⁶ These most stable systems are shown in Fig. 3. The calculated adsorption characteristics, for instance, adsorption energy (E_ads), adsorption distance (D), charge transfer (ΔQ), changes in bond length of gas molecules (L_g), and band gap (E_g) are listed in Table 2. The adsorption energy is calculated using eqn (2). The minimum adsorption energies for NO and H₂S on pristine TiS₂ are −0.188 eV and −0.602 eV, respectively. Additionally, the minimum adsorption distances between the gas molecules and TiS₂ monolayer are 2.114 Å for NO and 3.321 Å for H₂S. The adsorption energy and distance both suggest that NO adsorption on TiS₂ is chemisorption. In the case of H₂S gas, the adsorption energy is low and the adsorption distance is much greater than the sum of the covalent radii of H and S.⁷⁵ The connection between the sulfur atom of TiS₂ and the hydrogen atom in H₂S occurs through weak van der Waals bonds, and this sort of adsorption is classified as physisorption.⁶⁰ Significant alterations in bond lengths of the adsorbed gas molecules are seen upon adsorption, as illustrated in Table 2. The N–O bond in NO is shortened by 0.001 Å, and the H–S bond in H₂S is elongated by 0.001 Å. The alteration in bond length of gas molecules during gas adsorption indicates the interaction between the gas molecules and the TiS₂ monolayer surface. For getting more insights into interactions between gas molecules and TiS₂ monolayer, charge transfer due to gas adsorption is calculated using eqn (3), employing Hirshfeld charge distributions for both gases and monolayers. NO and H₂S both act as electron donors; here, NO transfers 0.17 electrons and H₂S transfers 0.01 electrons to the TiS₂ monolayer. These findings also suggest that the interaction between NO and the TiS₂ monolayer is a strong chemisorption, whereas H₂S shows a weak physical interaction. Furthermore, we have examined the charge density difference map (CDD) to visualize charge accumulation and depletion surrounding the gas molecules and the TiS₂ surface. The CDD of NO@TiS₂ and H₂S@TiS₂ are shown in Fig. 3(c) and (f), where purple color indicates charge accumulation and green color denotes charge depletion. There is significant charge accumulation and depletion between the N–S bond in NO@TiS₂; in contrast, between H from H₂S and S from TiS₂, we found very little charge distribution. In our previous study, we investigated the adsorption characteristics of NO₂ and SO₂ on the pristine TiS₂ monolayer. For comparing their adsorption characteristics with NO@TiS₂ and H₂S@TiS₂, we have added the adsorption properties in Table 2. While comparing these four gas molecules' adsorptions on TiS₂, only NO shows chemisorption, and the other three gases (NO₂, SO₂, and H₂S) show weak physical interactions.

Fig. 3 Most stable optimized systems of adsorbed gas molecules on TiS₂ monolayer: (a and b) top and side views of NO@TiS₂; (d and e) top and side views of H₂S@TiS₂; and (c and f) the corresponding charge density difference (CDD) of NO@TiS₂ and H₂S@TiS₂.

Table 2 Computed adsorption properties, adsorption energy (E_ads), charge transfer (ΔQ), adsorption distance (D), bond length (L_g) of gas molecules after adsorption, band gap (E_g)

Compound	Gas	Eads (eV)	ΔQ (e)	D (Å)	Lg (Å)	Eg (eV)
TiS2	—	—	—	—	—	0.098
	NO2 (ref. 49)	−0.204	−0.06	3.608	1.234	0
	SO2 (ref. 49)	−0.235	−0.01	3.684	1.449	0.099
	NO	−0.602	0.17	2.114	1.194	0
	H2S	−0.188	0.01	3.321	1.351	0.103
Pd/TiS2	—	—	—	—	—	0.079
	NO2	−0.979	−0.21	2.130	1.248	0
	SO2	−0.588	−0.09	2.343	1.450	0.144
	NO	−1.455	0.07	1.887	1.196	0
	H2S	−0.817	0.16	2.489	1.355	0.182
Mo/TiS2	—	—	—	—	—	0.307
	NO2	−2.942	−0.22	2.018	1.386	0
	SO2	−1.01	−0.1	2.345	1.456	0.351
	NO	−3.421	−0.17	1.795	1.219	0
	H2S	−1.312	0.17	2.544	1.408	0.398

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After completing structural relaxation, Fig. 4 illustrates the lowest energy adsorption configurations for the Pd/TiS₂ and Mo/TiS₂ monolayers interacting with four gas molecules, including NO₂, SO₂, NO, and H₂S. The adsorption characteristics for these gas molecules on the Pd/TiS₂ and Mo/TiS₂ monolayers are presented in Table 2. The adsorption energies for NO₂, SO₂, NO, and H₂S on Pd/TiS₂ are −0.979, −0.588, −1.455, and −0.817 eV, respectively, suggesting that these gases and the Pd/TiS₂ surface have a substantial interaction. The observation is additionally supported by the adsorption structures illustrated in Fig. 4(a)–(d) and the adsorption distances presented in Table 2, indicating the formation of Pd–N, Pd–S, Pd–N, and Pd–H chemical bonds in adsorbed systems. This suggests the chemisorption-type adsorption behavior for all gas molecules on the Pd/TiS₂ monolayer. The adsorption strength of these gases on the Pd/TiS₂ surface adheres to the following hierarchy: NO > NO₂ > H₂S > SO₂. This pattern indicates that the surface interactions with NO are the most robust, perhaps due to the establishment of strong Pd–N bonds, whereas SO₂ demonstrates relatively weaker interactions compared to other gases. Although SO₂ shows relatively weaker interactions, its adsorption energy notably increases upon Pd decoration compared to pristine TiS₂. Upon adsorption on the Pd/TiS₂ monolayer, noticeable alterations in the bond lengths of the adsorbed gas molecules are observed, as summarized in Table 2. Specifically, the N–O bond in NO₂, one of the S–O bonds in SO₂, the N–O bond in NO, and one of the H–S bonds exhibit elongations of 0.018 Å, 0.002 Å, 0.001 Å, and 0.005 Å, respectively. These variations in bond lengths suggest different strengths and natures of interactions between the gas molecules and the Pd/TiS₂ surface. Hersfield charge transfer analysis further indicates that NO and H₂S act as electron donors, transferring approximately 0.07 and 0.16 electrons, respectively, to the Pd/TiS₂ monolayer. Conversely, NO₂ and SO₂ function as electron acceptors, receiving about 0.21 and 0.09 electrons, respectively, from the substrate. Additionally, charge density difference (CDD) plots (Fig. 5) illustrate significant charge redistribution, including both accumulation and depletion, primarily around the Pd–X bonds (X = N, S, O) formed during adsorption. This charge reorganization, along with evidence for orbital overlapping, indicates strong interaction between the gases and the Pd site. Overall, the combination of adsorption energies, adsorption distance, charge transfer values, and CDD analysis confirms that the interactions between NO, NO₂, SO₂, H₂S, and the Pd/TiS₂ monolayer are predominantly chemical in nature, involving substantial electron exchange.

Fig. 4 Most stable optimized systems of adsorbed gas molecules on decorated-TiS₂ monolayers: (a) NO₂@Pd/TiS₂, (b) SO₂@Pd/TiS₂, (c) NO@Pd/TiS₂, (d) H₂S@Pd/TiS₂, (e) NO₂@Mo/TiS₂, (f) SO₂@Mo/TiS₂, (g) NO@Mo/TiS₂, and (h) H₂S@Mo/TiS₂.

Fig. 5 Charge density difference (CDD) mapping of gas adsorbed systems: (a) NO₂@Pd/TiS₂, (b) SO₂@Pd/TiS₂, (c) NO@Pd/TiS₂, (d) H₂S@Pd/TiS₂, (e) NO₂@Mo/TiS₂, (f) SO₂@Mo/TiS₂, (g) NO@Mo/TiS₂, and (h) H₂S@Mo/TiS₂. Here, purple and green colors denote charge accumulation and depletion, respectively.

In the case of the Mo-decorated TiS₂ monolayer, adsorption energies for NO₂, SO₂, NO, and H₂S were calculated to be −2.942, −1.01, −3.421, and −1.312 eV, respectively. These values reflect a strong interaction between the gas molecules and the modified surface, which are significantly larger than pristine TiS₂ and Pd-decorated TiS₂. These suggest the strong chemisorption of these gas molecules on the Mo/TiS₂ surface. Their adsorption distances tabulated in Table 2 and Fig. 4(e)–(h) also imply the strong covalent bonding between the gas molecules and the Mo atom of the substrate. This interaction also induces noticeable changes in the molecular structures of the adsorbed species. For NO₂, SO₂, NO, and H₂S, the bond lengths are elongated by 0.156, 0.008, 0.024, and 0.58 Å, respectively, compared to their isolated forms. The bond length change is also more prominent for Mo/TiS₂ compared to pristine and Pd/TiS₂. The change in Ti–S bond length is also observed in all three systems after gas adsorption. Though the change is less in pristine TiS₂ compared to decorated TiS₂. Ti–S bond length changes after gas adsorption are depicted in Table 1. For pristine TiS₂, Ti–S bond lengths changes are 0.002 and 0.00 for NO₂ and SO₂ gases, these little changes also matched with their weak physical interaction characteristics whereas in case of NO, Ti–S bond length changes more indicating strong interaction of NO with TiS₂. For both decorated systems significant changes in Ti–S bond length can match their strong chemical interactions.

Further insights were obtained from Hirshfeld charge transfer analysis, which indicates that H₂S acts as an electron donor, transferring 0.17 electrons to the Mo/TiS₂ surface. Conversely, NO₂ and SO₂, and H₂S act as electron acceptors, gaining 0.22, 0.1, and 0.17 electrons, respectively, from the substrate. These results are consistent with the charge density difference (CDD) plots shown in Fig. 5, which reveal significant electron accumulation and depletion around the Mo–X (X = N, O, S) bonding regions. This charge redistribution confirms strong orbital hybridization and underlines the chemical nature of the interaction.

Overall, these findings suggest that Mo-functionalized TiS₂ is a more promising candidate for detecting these toxic gases than pristine and Pd/TiS₂ monolayers based on adsorption characteristics. The interaction strength of the gases with the monolayers decreases in the following order: Mo/TiS₂ > Pd/TiS₂ > pristine TiS₂. Such comparative analysis provides valuable guidance for the rational design of selective and efficient gas sensors based on the transition of metal-decorated 2D materials.

3.3 Electronic properties of pristine/Pd/Mo TiS₂ before and after gas adsorption

To investigate how gas molecules interact with the pristine and Pd/Mo-decorated TiS₂ monolayers and influence their electronic characteristics and thus their conductivity, the band structures of the adsorption systems were examined. This analysis illustrates the modifications in the electronic response of the monolayer upon gas adsorption, offering valuable insights for enhancing gas-sensing efficiency. Fig. 6 depicts the band structures of pristine TiS₂, Pd/TiS₂, and Mo/TiS₂ before gas adsorption and the band structures of adsorbed systems (NO@TiS₂ and H₂S@TiS₂). Here, band structures are shown for only the spin-up state, as the band structures for both spin states are similar. The bandgap of the pristine TiS₂ monolayer is found to be 0.098 eV (indirect) using the GGA-PBE functional, which is close to previous literature (0.112 eV).⁷⁴ Pd-decoration and Mo-decoration tune the band gap of TiS₂ to 0.079 eV (indirect) and 0.307 eV (direct), respectively.

Fig. 6 Electronic band structures (a) pristine TiS₂, (b) Pd/TiS₂, (c) Mo/TiS₂, (d) NO@TiS₂, and (e) H₂S@TiS₂.

Here band gap change is more pronounced for Mo/TiS₂ than for Pd/TiS₂. These serve as reference points for assessing the impact of adsorbates on the electronic properties of the systems. As shown in Fig. 6(d) and (e), the adsorption of NO on TiS₂ reduces the band gap of TiS₂ to 0 eV, which is metallic, and H₂S increases the band gap of pristine TiS₂ slightly (0.103 eV). Band gap results listed in Table 2 from our previous study⁴⁹ depict that NO₂ adsorption makes NO₂@TiS₂ again metallic, and SO₂ increases the band gap very little (0.099 eV). Conductivity and sensitivity are directly influenced by the band gap. Upon gas adsorption, an increase in the band gap leads to reduced conductivity, while a decrease in the band gap results in enhanced conductivity. The conductivity results for different adsorption systems at three different temperatures (298, 358, and 398 K) are listed in Table 3. The conductivity increases for NO₂ and NO from 0.149 to 1.00 A per ohm per m, whereas for SO₂ and H₂S conductivity decreases very little (0.149 to 0.146 A per ohm per m for SO₂ and 0.135 A per ohm per m for H₂S). Electronic band structures of gas adsorbed systems on Pd/TiS₂ and Mo/TiS₂ are shown in Fig. 7. In the case of Pd/TiS₂, the corresponding bandgap values are 0.00 eV for NO and NO₂, 0.144 eV for SO₂, and 0.182 eV for H₂S. In the case of NO₂ and NO, adsorption systems again exhibit metallic nature, thus increasing the conductivity. For SO₂ and H₂S, the conductivity decreases significantly. When it comes to Mo/TiS₂, the band gap undergoes remarkable shifts after the adsorption of gas species. After adsorption, the band gap narrows dramatically to 0 eV from 0.307 eV for NO₂ and NO, indicating a transition toward metallic character and pointing to a significant rise in electrical conductivity (0.003 to 1.00 A per ohm per m). This pronounced effect indicates that NO₂ and NO exert the strongest influence on the electronic behavior of Mo/TiS₂ compared to the other studied gases. SO₂ and H₂S adsorption result in band gaps of 0.351 eV and 0.398 eV, respectively, both larger than the band gap of Mo/TiS₂, suggesting diminished conductivity relative to the Mo/TiS₂ monolayer surface.

Table 3 Conductivity (σ), sensitivity (S) of gas adsorption systems at three different temperatures (298 K, 358 K, and 398 K), and selectivity (K) at 298 K

System	σ (A per ohm per m) K = 298 K	σ (A per ohm per m) T = 358 K	σ (A per ohm per m) T = 398 K	S (T = 298 K)	S (T = 358 K)	S (T = 398 K)	K (T = 298 K)
TiS2	0.149	0.204	0.2397	—	—	—	—
NO2@TiS2	1.00	1.00	1.00	5.737	3.893	3.171	1.00
SO2@TiS2	0.146	0.201	0.236	0.019	0.016	0.015	301.95
NO@TiS2	1.00	1.00	1.00	5.737	3.893	3.171	1.00
H2S@TiS2	0.135	0.189	0.223	0.093	0.078	0.070	61.688
Pd/TiS2	0.215	0.279	0.317	—	—	—	—
NO2@Pd/TiS2	1.00	1.00	1.00	3.645	2.591	2.158	1.00
SO2@Pd/TiS2	0.061	0.097	0.123	0.719	0.652	0.613	5.07
NO@Pd/TiS2	1.00	1.00	1.00	3.645	2.591	2.158	1.00
H2S@Pd/TiS2	0.013	0.026	0.038	0.942	0.906	0.881	3.87
Mo/TiS2	0.003	0.007	0.012	—	—	—	—
NO2@Mo/TiS2	1.00	1.00	1.00	392.723	143.625	86.727	1.00
SO2@Mo/TiS2	0.002	0.004	0.007	0.576	0.51	0.474	681.81
NO@Mo/TiS2	1.00	1.00	1.00	392.723	143.625	86.727	1.00
H2S@Mo/TiS2	0.001	0.002	0.004	0.83	0.772	0.735	473.16

---

Fig. 7 Electronic band structures (a) NO₂@Pd/TiS₂, (b) SO₂@Pd/TiS₂, (c) NO@Pd/TiS₂, and (d) H₂S@Pd/TiS₂, (e) NO₂@Mo/TiS₂, (f) SO₂@Mo/TiS₂, (g) NO@Mo/TiS₂, and (h) H₂S@Mo/TiS₂.

The comparative analysis of band structures demonstrates that adsorption of NO₂ and NO markedly reduces the band gap of TiS₂-based systems to metallic states, thereby enhancing their conductivity, while SO₂ and H₂S interactions induce only slight band gap increases associated with reduced conductivity. Notably, Mo/TiS₂ exhibits the most substantial electronic modulation among the studied monolayers, underscoring its strong potential as a highly sensitive and selective candidate for gas-sensing applications.

In order to gain deeper insights into the influence of adsorbed molecules on the electronic structure of the substrate, a density of states (DOS) analysis was conducted. The outcomes for the pristine TiS₂, Pd/TiS₂, and Mo/TiS₂ adsorption systems are illustrated in Fig. 8. The total density of states (TDOS) and partial density of states (PDOS) for pristine TiS₂ and Pd/TiS₂ are presented in Fig. 8(a). The TDOS curves reveal that decorating with Pd induces notable modifications in the electronic structure, Pd/TiS₂ exhibiting additional states near the Fermi level (E_F). The PDOS analysis further elucidates the contributions of specific atomic orbitals: Ti-3d states dominate near E_F, while S-3p states are spread across a broader energy range. Notably, the Pd-4d state contributes significantly near the Fermi level in Pd/TiS₂, suggesting that Pd incorporation introduces new electronic states primarily derived from Pd orbitals. Fig. 8(b) shows the TDOS and PDOS for pristine TiS₂ and Mo/TiS₂. Mo decoration introduces states near the Fermi level. The PDOS indicates that additional Mo-4d contributions appear and hybridize with Ti-3d states, leading to a redistribution of states around E_F. These electronic modifications suggest that decoration may facilitate faster charge transfer with adsorbed gas molecules and improve TiS₂'s sensitivity and performance in gas sensors.

Fig. 8 TDOS and PDOS for various configurations (a) Pd/TiS₂ and (b) Mo/TiS₂, (c) NO@TiS₂, (d) H₂S@TiS₂, (e) NO₂@Pd/TiS₂, (f) SO₂@Pd/TiS₂, (g) NO@Pd/TiS₂, and (h) H₂S@Pd/TiS₂, (i) NO₂@Mo/TiS₂, (j) SO₂@Mo/TiS₂, (k) NO@Mo/TiS₂, and (l) H₂S@Mo/TiS₂.

The TDOS for NO adsorption on TiS₂ shown in Fig. 8(c) reveals a clear modification of the DOS near the Fermi level compared to pristine TiS₂, indicating a strong interaction between NO molecules and the TiS₂ surface. The PDOS confirms that the newly introduced states originate mainly from the N-2p and O-2p orbitals, which overlap with Ti-3d states near E_F. This orbital hybridization facilitates efficient charge transfer, suggesting a chemisorption-type interaction. In contrast, H₂S adsorption causes relatively weaker changes in the DOS distribution around E_F. The contributions from H-1s and S2-3p (S from H₂S) orbitals are small and show limited overlap with Ti-3d states, indicating a weaker electronic coupling compared to NO adsorption. This implies that the interaction of H₂S with TiS₂ is more physisorptive in nature, with lower charge transfer efficiency. These analyses are also inconsistent with the Hersfield charge analysis. In the case of NO₂ adsorption on Pd/TiS₂, substantial perturbation of the TDOS occurs around the Fermi level, driven mainly by the hybridization of N-2p/O-2p states with Pd-4d orbitals. This demonstrates strong chemisorption with considerable charge transfer. For SO₂ adsorption on Pd/TiS₂, the TDOS shows a clear modification near the Fermi level compared to pristine Pd/TiS₂, indicating strong orbital hybridization. The PDOS reveals hybridization of Pd-4d, Ti-3d, with S2-3p and O-2p (from SO₂), confirming charge transfer and orbital overlap. These modifications suggest chemisorption, which enhances the sensing response toward SO₂. For NO adsorption, notable changes are observed in the electronic states near the Fermi level. The hybridization of N-2p with Pd-4d orbitals suggests stable chemisorption. Interestingly, H₂S adsorption on Pd/TiS₂ causes relatively weaker changes in the DOS distribution around E_F. The contributions from H-1s and S2-3p (S from H₂S) orbitals are small and show limited overlap with Ti-3d states, indicating a weaker electronic coupling compared to other gases. But the adsorption energy of −0.87 eV and charge transfer of 0.16 electrons confirm that H₂S interacts through chemisorption with small orbital hybridization.

Now, for NO₂ adsorption on Mo/TiS₂, the PDOS reveals pronounced hybridization between the O-2p/N-2p states of NO₂ and the Mo-4d orbitals, extending from −3 eV up to the Fermi level. This indicates a strong chemical interaction. In the case of SO₂ adsorption, considerable changes are also observed in the TDOS, although slightly weaker than NO₂. The PDOS shows strong overlap between O-2p states of SO₂ and Mo-4d orbitals. For NO adsorption, the DOS profile exhibits moderate modification around the Fermi level. The PDOS indicates hybridization between N-2p states of NO and Mo-4d orbitals, confirming the chemisorption nature. In contrast, H₂S adsorption induces only minor changes in the TDOS. The PDOS shows limited contributions from H-1s and S2-3p (from H₂S) states overlapping with the Mo-4d orbitals. This implies a weaker interaction compared to other gases, though it can still be chemisorptive in nature, as the adsorption energy and charge transfer are higher.

3.4 Sensitivity, selectivity, and recovery characteristics

The sensitivity (S) values of pristine, Pd/TiS₂, and Mo/TiS₂ toward various gases were computed for three different temperatures (298, 358, and 398 K) using eqn (5) and are summarized in Table 3. Fig. 9 depicts the sensitivity comparison for adsorbed gas molecules. For all gas molecules, sensitivity decreases with increasing temperature. Pristine TiS₂ shows the highest sensitivity toward NO₂ (5.737), and NO (5.737), both of which are considerably greater than SO₂, and H₂S gases at room temperature. Pd/TiS₂ also exhibits the same pattern of gas sensitivity (NO₂ & NO > H₂S > SO₂), however, the room temperature sensitivity increases for SO₂ (0.719) and H₂S (0.942), and decreases for NO₂ & NO (3.645 for each) compared to pristine TiS₂. Interestingly, Mo/TiS₂ shows significantly the highest sensitivity for NO₂ (392.732) and NO (392.732) at room temperature and at high temperature also holds a significant sensitivity (143.625 at 358 K and 86.727 at 398 K), indicating its strong potential for stable and efficient gas sensor performance across a wide temperature range. In contrast, for SO₂ and H₂S gas molecules, Mo/TiS₂ doesn't show such a huge change in sensitivity. Pd/TiS₂ exhibits better sensitivity for SO₂ and H₂S gases compared to pristine TiS₂ and Mo/TiS₂. However, all three configurations follow the sensitivity order in such that: NO₂ & NO > H₂S > SO₂. Overall, despite variations in magnitude among the different monolayer modifications, all three TiS₂-based configurations consistently show the highest sensitivity toward NO₂ and NO, followed by H₂S and then SO₂, highlighting their selective gas-sensing behavior. To further quantify this selectivity, the selectivity coefficients (K) were determined as the ratio of the target gas sensitivity (NO or NO₂) to that of other interfering gases, using eqn (6). The calculated K values at 298 K listed in Table 3 reveal a clear trend in gas discrimination capability across the systems. For pristine TiS₂, NO₂ and NO shows significantly higher selectivity over SO₂ (K = 301.95) and H₂S (K = 61.69), indicating strong preferential adsorption of NO₂ or NO molecules. Pd functionalization results in a reduction of selectivity, with moderate K values toward SO₂ (5.07) and H₂S (3.87), implying weaker gas discrimination. In contrast, Mo decoration markedly enhances the selectivity, producing exceptionally large K values for SO₂ (681.81) and H₂S (473.16) relative to NO₂ and NO. This trend demonstrates that the Mo/TiS₂ surface possesses superior selectivity toward the target gases, particularly NO₂ and NO, followed by TiS₂, while Pd/TiS₂ exhibits the lowest selectivity. Interestingly, all three systems show similar selectivity towards both NO₂ and NO, that indicates these two gases may not be detected altogether but can be detected if one of them mixed with SO₂, and H₂S based on these selectivity results. This selectivity is calculated from sensitivity comparison only, where sensitivity is calculated from conductivity variation using eqn (5) that depends on band gap change after gas adsorption. After adsorption of NO₂ and NO, all systems band gaps become zero for both gases, that's why the conductivity and sensitivity values remain same for both gases. However, other properties such as, charge transfer, change in work function show different results for NO₂ and NO. These differences may provide alternative measurable signals (work function shifts)⁷⁷ for discrimination of NO₂ and NO.

Fig. 9 Sensitivity of gas molecules on adsorption systems, (a) pristine TiS₂, (b) Pd/TiS₂, (c) Mo/TiS₂.

The recovery time (τ) for all adsorbed gases was evaluated using eqn (7) at three different temperatures: 298 K, 348 K, and 398 K, and taking the frequency as 10¹² Hz, and summarized in Table 4. For pristine TiS₂, all studied gases exhibit ultrafast recovery times in the range of 10⁻⁹ to 10⁻⁵ s. This indicates highly reversible physisorption and may not retain gases long enough for accurate detection. These systems can be used only when a very fast recovery is required. NO₂@Pd/TiS₂ shows exceedingly long recovery times (up to 10¹² s at 298 K), indicative of strong chemisorption. Although this enhances gas capture, the excessively slow desorption hinders sensor reusability and response speed. In contrast, SO₂@Pd/TiS₂ displays moderate recovery times (from 8.598 × 10⁻³ s at 298 K to 2.744 × 10⁻⁵ s at 398 K), suggesting a balanced adsorption–desorption behavior favorable for sensing. The recovery time for H₂S@Pd/TiS₂ is 65.08 s at 298 K and decreases to 0.022 s at 398 K, which indicates that H₂S can be detected by Pd/TiS₂ at room temperature and also slightly elevated temperatures. Mo decoration results in even stronger gas adsorption, as evidenced by extremely high recovery times for NO₂ and NO (10²⁵ to 10⁴⁵ s), rendering them impractical under ambient conditions due to irreversible binding. However, SO₂ and H₂S on Mo/TiS₂ show more manageable recovery behaviors at elevated temperatures (e.g., 6.157 s for SO₂ at 398 K and 4.11 × 10⁴ s for H₂S at 398 K), suggesting these systems could be viable for high-temperature sensing applications.

Table 4 Recovery time (T_rec) at three different temperatures (298 K, 358 K, and 398 K) and work function of gas adsorption systems

Compound	Trec (T = 298 K)	Trec (T = 358 K)	Trec (T = 398 K)	Work function (eV)
TiS2	—	—	—	5.539
NO2@TiS2	2.754 × 10^−9	7.302 × 10^−10	3.764 × 10^−10	5.632
SO2@TiS2	9.333 × 10^−9	2.017 × 10^−9	9.387 × 10^−10	5.561
NO@TiS2	0.0149	0.0003	4.134 × 10^−5	5.255
H2S@TiS2	1.526 × 10^−9	4.466 × 10^−10	2.419 × 10^−10	5.422
Pd/TiS2	—	—	—	5.277
NO2@Pd/TiS2	3.963 × 10^12	2.988 × 10^8	2.616 × 10^6	5.769
SO2@Pd/TiS2	8.598 × 10^−3	1.86 × 10^−4	2.744 × 10^−5	5.635
NO@Pd/TiS2	0.003	6.586 × 10^−5	1.079 × 10^−5	5.299
H2S@Pd/TiS2	65.08	0.315	0.022	5.019
Mo/TiS2	—	—	—	5.316
NO2@Mo/TiS2	5.544 × 10^37	2.552 × 10^29	1.759 × 10^25	5.465
SO2@Mo/TiS2	1.21 × 10^5	165.339	6.157	5.81
NO@Mo/TiS2	6.8 × 10^45	1.38 × 10^36	2.003 × 10^31	5.358
H2S@Mo/TiS2	1.54 × 10^10	2.95 × 10^6	4.11 × 10^4	5.186

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3.5 Work function analysis

To further evaluate the gas sensing performance of pristine TiS₂, Pd/TiS₂, and Mo/TiS₂ upon the adsorption of NO₂, SO₂, NO, and H₂S, the corresponding WF values were calculated using eqn (8). Fig. 10 presents the WF variations, and the detailed results are summarized in Table 4. The work function (WF) of pristine TiS₂ was calculated as 5.539 eV, which provides the baseline for comparison with gas-adsorbed and decorated systems. Upon adsorption of gases on pristine TiS₂, slight variations in WF were observed: NO₂ (5.632 eV) and SO₂ (5.561 eV) increased the WF, indicating weak electron withdrawal from the surface, while NO (5.255 eV) and H₂S (5.422 eV) reduced the WF, suggesting electron donation to the substrate. These modest changes imply limited charge transfer between pristine TiS₂ and the target gases.

Fig. 10 Work function comparison for (a) pristine TiS₂, (b) Pd/TiS₂, (c) Mo/TiS₂ to different gases.

Decorating with Pd significantly modified the surface electronic structure, lowering the WF to 5.277 eV, thereby facilitating electron mobility. When gases were adsorbed on Pd/TiS₂, pronounced WF variations were observed: NO₂ (5.769 eV) and SO₂ (5.635 eV) induced substantial increases, reflecting strong electron transfer from the substrate to the oxidizing gases. In contrast, H₂S adsorption reduced the WF to 5.019 eV, highlighting enhanced electron donation and strong interaction with the Pd-modified surface.

Similarly, Mo decoration reduced the WF to 5.316 eV, improving the electron transfer capability of TiS₂. Among the gases, SO₂ adsorption produced the highest WF (5.81 eV), indicating strong interaction and significant charge redistribution at the Mo/TiS₂ surface. NO₂ and NO also caused moderate increases to 5.465 eV and 5.358 eV, respectively, while H₂S lowered the WF to 5.186 eV, suggesting its electron-donating behavior.

Overall, these results demonstrate that Pd and Mo decoration effectively lowers the WF, improves electron mobility, and enhances the gas sensing performance of TiS₂. Interestingly, the trend in work function variation does not perfectly coincide with the net charge transfer values obtained from Hirshfeld charge analysis listed in Table 2. SO₂ adsorption on Mo/TiS₂ yields a relatively small charge transfer than other gases but induces one of the largest work function shifts. This discrepancy arises because the work function is governed not only by charge magnitude but also by the adsorption-induced surface dipole, which depends on charge redistribution, molecular orientation, and interface effects.^78,79 Moreover, Hirshfeld analysis provides only an approximate measure of charge transfer, often underestimating interfacial polarization, while the work function reflects the overall electrostatic response, including dipole formation and Pauli push-back effects.^80,81 However, Pd and Mo decoration improve the gas sensing performance of TiS₂ based on both work function analysis and Hersfield charge transfer analysis.

3.6 Comparative analysis of gas-sensing performance with reported studies

Table 5 compares the gas-sensing properties of Pd/TiS₂ and Mo/TiS₂ systems investigated in this work with previously reported materials toward NO₂, SO₂, NO, and H₂S gases. The parameters considered include adsorption energy (E_ads), charge transfer (ΔQ), and sensitivity (S) at 298 K.

Table 5 Comparison of gas sensing properties of NO₂, SO₂, NO, and H₂S gases with other studies

System	Gas	Adsorption energy, Eads (eV)	Charge transfer, ΔQ (e)	Sensitivity, S (T = 298 K)	References
Li/TiS2	NO2	−0.73	−0.253	—	82
Pt/ZrS2	NO2	−0.685	−0.130	0.99	72
Pd/TiS2	NO2	−0.979	−0.21	3.645	This work
Mo/TiS2	NO2	−2.942	−0.22	392.723	This work
Li/TiS2	SO2	−0.95	0.014	—	82
Pd/ZrS2	SO2	−1.02	−0.08	—	83
Rh/HfS2	SO2	−0.406	−0.083	—	85
Pd/TiS2	SO2	−0.588	−0.09	0.719	This work
Mo/TiS2	SO2	−1.01	−0.1	0.576	This work
Li/TiS2	NO	−0.99	0.186	—	82
Pt/ZrS2	NO	−0.944	0.0511	5.74	72
Pd/TiS2	NO	−1.455	0.07	3.645	This work
Mo/TiS2	NO	−3.421	−0.17	392.723	This work
Rh/ZrSe2	H2S	−1.274	0.250	—	84
Pt/ZrS2	H2S	−0.905	0.228	11.08	72
Pd/TiS2	H2S	−0.817	0.16	0.906	This work
Mo/TiS2	H2S	−1.312	0.17	0.772	This work

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For NO₂ sensing, the Mo/TiS₂ system exhibits the highest adsorption energy (−2.942 eV) among all the compared materials. In contrast, Pd/TiS₂ shows relatively moderate E_ads of −0.979 eV, which still surpasses that of Li/TiS₂ (−0.73 eV)⁸² and Pt/ZrS₂ (−0.685 eV).⁷² The charge transfer values also support this trend, where both Pd/TiS₂ (−0.21e) and Mo/TiS₂ (−0.22e) exhibit greater electron exchange compared to other reported systems. The exceptionally high sensitivity value for Mo/TiS₂ (392.723) further confirms its superior response capability toward NO₂ gas. In the case of SO₂ adsorption, both Pd/TiS₂ and Mo/TiS₂ display favorable adsorption characteristics with E_ads values of −0.588 eV and −1.01 eV, respectively. These are comparable to Pd/ZrS₂ (−1.02 eV)⁸³ and Li/TiS₂ (−0.95 eV),⁸² suggesting effective interaction while maintaining good reversibility. The charge transfer for Mo/TiS₂ (−0.1e) is slightly higher than that of Pd/TiS₂ (−0.09e), both are higher compared to other reported values. For NO gas, Mo/TiS₂ again demonstrates remarkably higher adsorption energy (−3.421 eV) compared to Pd/TiS₂ (−1.455 eV) and other materials such as Li/TiS₂ (−0.99 eV)⁸² and Pt/ZrS₂ (−0.944 eV).⁷² Mo/TiS₂ also show extraordinarily high sensitivity (392.723) compared to other materials, indicating its excellent potential for NO detection. Regarding H₂S sensing, Pd/TiS₂ and Mo/TiS₂ exhibit adsorption energies of −0.817 eV and −1.312 eV, respectively, which are comparable to or higher than those of previously reported systems such as Pt/ZrS₂ (−0.905 eV)⁷² and Rh/ZrSe₂ (−1.274 eV).⁸⁴ Both systems also show notable charge transfer values (0.16e for Pd/TiS₂ and 0.17e for Mo/TiS₂) comparable to other materials. However, Pd/TiS₂ and Mo/TiS₂ show poorer sensitivity compared to Pt/ZrS₂.

4. Conclusions

This first-principles density functional theory study comprehensively investigated the gas-sensing properties of pristine and transition metal Pd/Mo-decorated TiS₂ monolayers toward industrial toxic gases (NO₂, SO₂, NO, H₂S). The thermodynamic stability of pristine TiS₂ was confirmed through negative cohesive energy, and the hollow site was identified as the most energetically favorable position for both Pd and Mo decoration, where strong covalent bonds were formed between Pd/Mo–S atoms. Pristine TiS₂ exhibited strong chemisorption only for NO, while displaying weak physisorption for NO₂, SO₂, and H₂S. However, both Pd and Mo decoration significantly enhanced the adsorption characteristics for all target gases, transforming weak physisorption into strong chemisorption. Mo/TiS₂, in particular, demonstrated the strongest adsorption energies for all target gases. Electronically, adsorption of NO₂ and NO on both decorated systems (especially Mo/TiS₂) consistently led to a metallic state (0 eV band gap), indicating a drastic increase in electrical conductivity and high sensitivity. This enhancement was corroborated by density of states analysis, which revealed significant orbital hybridization and efficient charge transfer between gas molecules and the decorated metal atoms. In terms of sensing performance, Mo/TiS₂ showed exceptionally high sensitivity to NO₂ and NO (392.732 at room temperature). While pristine TiS₂ offered ultrafast recovery due to physisorption, Mo/TiS₂ exhibited excessively long recovery times for NO₂ and NO at ambient conditions, suggesting irreversible binding. However, SO₂ and H₂S on Mo/TiS₂ demonstrated more manageable recovery (6.571 and 4.11 × 10⁴ s) at elevated temperatures, making them viable for high-temperature applications. Pd/TiS₂ provided a balanced adsorption–desorption for SO₂, NO, and H₂S at room temperature. Work function analysis further supported that Pd and Mo decoration effectively lowered the work function of TiS₂, enhancing electron mobility and overall gas sensing performance. These findings suggest that transition metal decoration, particularly with Mo and Pd, is an effective strategy to greatly enhance the gas-sensing performance of TiS₂ monolayers. Though Mo/TiS₂ exhibits high sensitivity and strong adsorption toward NO₂ and NO, its slow desorption behavior limits practical application, whereas Pd/TiS₂ shows comparatively more favorable recovery characteristics. These insights offer useful guidance for the rational design of next-generation 2D material-based gas sensors.

Author contributions

Tasmi Akter: conceptualization, writing – original draft, methodology, software, validation, formal analysis, investigation, data curation, visualization. Md. Jahirul Islam: conceptualization, writing – review & editing, validation, supervision. Md. Tawabur Rahman: writing – review & editing, validation, supervision. Jahirul Islam: writing – review & editing, visualization, validation.

Conflicts of interest

The authors declare that there are no known financial or personal conflicts of interest that could have influenced the work presented in this paper.

Data availability

The data supporting the findings of this study are available from the corresponding authors upon reasonable request.

Supplementary information is available. See DOI: https://doi.org/10.1039/d5ra06850a.

Acknowledgements

The computational work of this research was performed at the Computational Materials Science Laboratory in the Department of Materials Science and Engineering at Khulna University of Engineering & Technology, Khulna 9203, Bangladesh.

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