Fe-doped MoS₂ monolayers for CO, H₂S, and NO₂ detection: towards advanced environmental sensors

Abstract

In this study, density functional theory (DFT) calculations integrated with machine learning via the crystal graph convolutional neural network (CGCNN) were employed to systematically investigate the electronic, magnetic, thermomechanical, and optical properties of Fe-doped MoS₂ (Fe-MoS₂) monolayers before and after the adsorption of CO, H₂S, and NO₂ gas molecules. The computational results reveal that gas adsorption, particularly for CO and NO₂, induces strong interactions with the Fe-MoS₂ surface, leading to pronounced modifications in the electronic band structure, density of states, and charge redistribution. The thermomechanical and optical responses of the system are found to be sensitive to the nature of the adsorbed gas species, with notable variations observed in the elastic moduli and optical absorption coefficients. The Fe-MoS₂ monolayers exhibit strong optical absorption in the ultraviolet to visible spectral range (200–500 nm), alongside tunable electromagnetic characteristics modulated by gas adsorption. These findings highlight the potential of Fe-MoS₂ monolayers as a multifunctional material for applications in gas sensing and optoelectronic devices.

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1. Introduction

As electronic and optoelectronic devices continue to advance in intelligence and functionality, the demand for materials with novel and diverse properties becomes increasingly critical. This necessity has driven extensive research into the discovery and design of new materials, with nanomaterials emerging as a particularly promising class. Among the various structural forms under investigation, low-dimensional systems such as monolayers,^1–3 quantum dots,^4–6 quantum wells,^7–9 and quantum wires^10–12 have garnered significant attention due to their unique size-dependent properties.

Monolayer molybdenum disulfide (MoS₂) is a prototypical member of the two-dimensional (2D) transition metal dichalcogenide (TMD) family, structurally analogous to graphene but possessing a semiconducting character. It consists of a single layer of molybdenum (Mo) atoms sandwiched between two layers of sulfur (S) atoms, forming a trigonal prismatic coordination environment (S–Mo–S). Each Mo atom is coordinated by six S atoms, forming a stable hexagonal lattice.¹³ While bulk MoS₂ exhibits an indirect band gap of approximately 1.2 eV, the monolayer counterpart undergoes a transition to a direct band gap of about 1.8 eV at the K point in the Brillouin zone.¹⁴ This transition significantly enhances its optical activity, rendering monolayer MoS₂ highly attractive for applications in optoelectronic and photonic devices.

The direct band gap of monolayer MoS₂ results in strong photoluminescence (PL) emission in the visible spectrum, along with a pronounced excitonic effect characterized by a high exciton binding energy in the range of 0.5–0.9 eV – substantially greater than that of its bulk form.¹⁵ Furthermore, intrinsic monolayer MoS₂ behaves as an n-type semiconductor, though p-type conduction can be induced through chemical doping or electrostatic gating. The electron mobility in monolayer MoS₂ reaches approximately 200 cm² V⁻¹ s⁻¹ under ambient conditions and can be further enhanced under vacuum or when the monolayer is suspended.¹⁶

Monolayer MoS₂ can be further functionalized through elemental doping, enabling the formation of novel material systems with enhanced or tailored properties suitable for a broader range of technological applications.^17–19 Among various dopants, transition metal doping has attracted particular interest due to its potential to introduce magnetism and modify electronic characteristics. Using first-principles calculations based on density functional theory (DFT), the structural, electronic, and magnetic properties of a Mn-doped MoS₂ monolayer with the composition Mo_0.75Mn_0.25S₂ have been systematically investigated.²⁰ The results reveal that the spin-resolved electronic band structure exhibits metallic behavior for the spin-up channel and semiconducting behavior for the spin-down channel, indicating a robust half-metallic nature. This half-metallicity is highly desirable for spintronic applications. The substitutional doping of Mn atoms introduces strong ferromagnetic ordering in the system, which arises from the hybridization between the Mn(3d) orbitals and the Mo(4d) and S(3p) orbitals. To further elucidate the magnetic interactions, the spin-spiral dispersion relation as a function of wave vector was analyzed under generalized Bloch boundary conditions. The exchange coupling parameters J(i) (for i = 1–4) were extracted using the Heisenberg model. It was found that the nearest-neighbor exchange interaction J(1) dominates the magnetic coupling, while the next-nearest-neighbor term J(2) also contributes significantly and cannot be neglected. These findings underscore the critical role of both short- and medium-range magnetic interactions in determining the magnetic ground state of Mn-doped MoS₂ monolayers.

In a recent study, DFT was employed to explore the effects of Cr–Mn co-doping at both adjacent and spatially separated lattice sites on the electronic and optical properties of monolayer MoS₂.²¹ The computational results demonstrate that co-doping leads to a notable reduction in the band gap and induces a transition from a direct to an indirect band gap semiconductor, accompanied by the emergence of ferromagnetic ordering. Among the configurations considered, spatially separated Cr–Mn doping exhibits the most pronounced effects. From an optical standpoint, the spatially separated Cr–Mn co-doped MoS₂ structure displays significantly enhanced absorption in the visible and ultraviolet regions. This enhancement is accompanied by improved photoelectronic performance, as evidenced by increased optical conductivity, dielectric function components, and absorption coefficients. These findings suggest strong potential for applications in photodetectors, solar energy harvesting devices, and photocatalysis.

In a related investigation, Kumari Prajakta et al.²² conducted a comprehensive DFT analysis of the electronic and optical properties of pristine monolayer MoS₂, MoS₂ containing S/Mo vacancies, and MoS₂ doped with Nb, V, and Zn atoms. The study revealed that pristine MoS₂ exhibits a direct band gap of approximately 1.79 eV, while the doped systems show p-type semiconducting behavior. Optical anisotropy was observed in both the in-plane (x) and out-of-plane (z) directions, particularly in the photon energy range below 11 eV. These results underscore the viability of monolayer MoS₂ and its derivatives as promising candidates for integration into next-generation MOSFET-based nanoelectronic devices.

Surface adsorption studies on monolayer MoS₂ have garnered considerable attention in recent years.^23–25 In one such investigation, Shulin Yang and co-workers employed DFT to examine the adsorption behavior of H₂ molecules on transition metal-doped MoS₂ monolayers.²⁶ Their findings revealed that Os-doped MoS₂ exhibits the strongest interaction with H₂, characterized by an adsorption energy as low as −1.103 eV. This doped system can stably adsorb up to four H₂ molecules, with an average adsorption energy of approximately −0.792 eV. Furthermore, ab initio molecular dynamics simulations confirmed the structural stability of the H₂–Os–MoS₂ complex at 300 K, suggesting its potential applicability for room-temperature hydrogen storage.

In a separate study, Le Li et al. utilized first-principles calculations to investigate the adsorption capabilities of elemental mercury (Hg⁰) on non-metal-doped MoS₂ monolayers, where the dopants included B, C, N, O, and F.²⁷ The results indicated that MoS₂ doped with electron-accepting elements such as B, C, and N exhibited stronger adsorption of Hg⁰ compared to those doped with isoelectronic (O) or electron-donating (F) elements. A clear trend was observed in which the adsorption strength decreased with increasing valence electron count of the dopant, reaching a critical point at six valence electrons. Among the studied systems, B- and C-doped MoS₂ emerged as the most promising candidates for the effective capture and removal of elemental mercury in environmental pollution control applications.

Numerous recent studies have focused on the physical and chemical properties of MoS₂, driven by its potential for next-generation electronic and sensing applications.^28–31 Among various techniques, stress engineering has emerged as a crucial method for enhancing the electrical performance of semiconductor materials, particularly in silicon-based transistor technologies. In a study by Heechang Shin and colleagues, a biaxial tensile strain engineering strategy was developed for monolayer MoS₂ films synthesized via metal–organic chemical vapor deposition (MOCVD).³¹ Following the transfer of the MoS₂ film onto a SiO₂/Si substrate, the underlying silicon layer was selectively etched to release compressive stress in the oxide, thereby inducing uniform tensile strain in the overlying MoS₂ monolayer. The magnitude of induced stress was precisely controlled by adjusting the thickness of the stressed oxide layer. Transistors fabricated from these strained MoS₂ films were subsequently transferred onto soft plastic substrates, enabling the maintenance of uniform tensile stress across large areas and paving the way for applications in high-performance, flexible electronic devices.

In the present work, we conduct a comprehensive investigation into the properties of Fe-doped MoS₂ (Fe-MoS₂) monolayers, with particular emphasis on their gas adsorption capabilities. The adsorption behavior of three representative toxic gases – carbon monoxide (CO), hydrogen sulfide (H₂S), and nitrogen dioxide (NO₂) on the Fe-MoS₂ monolayer surface was systematically studied using a combination of DFT and machine learning techniques. This integrated approach provides a powerful framework for both understanding the atomic-scale mechanisms of gas adsorption and accelerating the prediction of material performance across diverse doping and adsorption configurations. The overarching aim is to elucidate the fundamental electronic and adsorption properties of Fe-MoS₂ monolayers and their interactions with gas molecules, thereby informing the design and optimization of materials for future applications in optoelectronic devices and chemical sensing technologies.

Among various transition metals, Fe was selected as the dopant in this study due to its unique ability to induce magnetic moments in non-magnetic 2D materials, particularly MoS₂. This property is essential for potential spintronic and magneto-electronic applications. Furthermore, Fe atoms can effectively hybridize with the MoS₂ lattice, leading to localized states near the Fermi level that may enhance surface reactivity toward gas molecules. Compared to heavier or more noble transition metals (such as Pd, Pt, or Au), Fe also offers advantages in terms of abundance, lower cost, and environmental compatibility, making it a promising candidate for scalable applications. This work aims to explore the dual roles of Fe in modulating both the magnetic and adsorption properties of MoS₂ monolayers.

2. Methods

The adsorption energy is calculated as follows:³²

E_a = E_t − E_p − E_gas

where, E_t, E_p, E_gas are respectively the total energy of the CO/H₂S/NO₂ adsorption system, the pristine system and of the isolated gas.

2.1. DFT calculations

First-principles calculations based on DFT were conducted using the Quantum ESPRESSO package to investigate the structural, electronic, and optical properties of Fe-doped monolayer MoS₂ (Fe-MoS₂), both in the pristine state and upon adsorption of CO, H₂S, and NO₂ gas molecules. The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional was employed to describe the exchange–correlation interactions, together with ultrasoft pseudopotentials. A kinetic energy cutoff of 50 Ry and a charge density cutoff of 500 Ry were used throughout the calculations.

A 4 × 4 supercell with a vacuum region of 20 Å along the out-of-plane direction was constructed to model the monolayer system. Brillouin zone sampling was performed using an 11 × 11 × 1 Monkhorst–Pack k-point grid. Structural relaxations were carried out until the forces on all atoms were less than 10⁻³ Ry bohr⁻¹ and the total energy change was below 10⁻⁶ Ry.

To properly account for dispersion interactions, which play a crucial role in physisorption, Grimme's DFT-D3 van der Waals correction was included in all total-energy and geometry optimization steps. Spin-polarized calculations were performed for all systems to capture magnetic effects induced by Fe doping and gas adsorption. The magnetic parameters were set using n_spin = 2, and the initial magnetic moment of the Fe dopant was defined through starting_magnetization(i) (with i corresponding to the Fe species). A commonly employed value of starting_magnetization = 0.5 was used to initiate spin polarization. Total and site-resolved magnetic moments were extracted from the self-consistent field (SCF) outputs.

2.2. CGCNN predictions

Thermo-mechanical properties – including bulk and shear moduli, heat capacities, Debye temperature, and thermal expansion coefficients – were predicted using the Crystal Graph Convolutional Neural Network (CGCNN). The model was trained on the Materials Project database, while the optimized DFT structures served as inputs for property inference.

The dataset was divided using an 80 : 20 training–testing ratio and evaluated through 5-fold cross-validation to ensure strong generalization performance. Training was performed with a learning rate of 0.01, a batch size of 256, and a maximum of 150 epochs. The learning objective was to minimize the mean absolute error (MAE), which converged to values below 0.12 eV for the targeted mechanical and thermodynamic property predictions.

3. Results and discussion

3.1. Stability results

Table 1 presents the adsorption energies (E_a) at various adsorption sites for the three gas molecules (CO, H₂S, NO₂) on the Fe-doped MoS₂ monolayer surface. For all three molecules, the lowest adsorption energy is consistently observed at the hollow site. Specifically, the adsorption energies at this site are −1.82 eV for CO, 2.51 eV for H₂S, and −1.62 eV for NO₂, respectively. Therefore, the hollow-site configurations are selected for subsequent calculations of electronic, magnetic, thermo-mechanical, and optical properties in this study. Both CO and NO₂ exhibit negative adsorption energies, indicating exothermic and thermodynamically favorable adsorption processes. Conversely, the H₂S-adsorbed configuration yields a positive adsorption energy, implying that the interaction between H₂S and the Fe-MoS₂ surface is energetically unfavorable under ambient conditions.

Table 1 Adsorption energy values at different sites of the configurations

Gas molecules	Top (eV)	Bridge (eV)	Valley (eV)	Hollow (eV)
CO	−1.21	−1.43	−1.37	−1.82
H2S	3.53	3.22	3.86	2.51
NO2	−1.02	−1.25	−1.18	−1.62

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Fig. 1 illustrates the optimized atomic configurations of the pristine Fe-doped MoS₂ (Fe-MoS₂) monolayer and the corresponding structures following the adsorption of CO, H₂S, and NO₂ gas molecules. The Fe-MoS₂ monolayer exhibits a hexagonal lattice composed of three atomic layers, with a central transition metal layer (Mo/Fe) sandwiched between two sulfur layers. The key structural parameters of the pristine and gas-adsorbed configurations are summarized in Table 2. Upon gas adsorption, noticeable distortions are observed in the local atomic environment surrounding the Fe dopant site. Specifically, the interatomic distances labeled as d₁, d₂, and d₃ exhibit slight elongations, indicative of localized lattice expansion. Among the studied systems, H₂S adsorption induces the most pronounced structural distortion, with d₂ = 2.430 Å, d₂ = 3.225 Å, and d₃ = 3.079 Å. In contrast, the CO- and NO₂-adsorbed configurations exhibit relatively minor structural perturbations, suggesting weaker lattice coupling.

Fig. 1 Top view of the pristine Fe-MoS₂ monolayer (a), top view and side view of the gas-adsorbed Fe-MoS₂ configurations (b and c).

Table 2 Structural parameters of Fe-MoS₂ monolayer and gas adsorption configurations of Fe-MoS₂ monolayer (d₁ is the distance between Mo and S atoms in the hexagon, d₂ is the distance between two S atoms in the same plane, d₃ is the distance between two S atoms in two different planes, µ is the magnetic moment in a unit cell)

Configurations	d1 (Å)	d2 (Å)	d3 (Å)	µ (µB)
Pristine Fe-MoS2	2.415	3.192	3.121	1.9878
CO adsorption	2.420	3.215	3.090	1.9865
H2S adsorption	2.430	3.225	3.079	2.0447
NO2 adsorption	2.425	3.219	3.096	0.7576

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Magnetic property analysis reveals that the pristine Fe-MoS₂ monolayer possesses a net magnetic moment of 1.9878µ_B. Upon adsorption of CO and H₂S, the magnetic moments change only marginally to 1.9865µ_B and 2.0447µ_B, respectively, indicating negligible perturbation of the spin distribution. However, NO₂ adsorption leads to a substantial reduction in the magnetic moment, decreasing to 0.7576µ_B. This significant drop suggests strong hybridization between the electronic states of NO₂ and the Fe-MoS₂ system, resulting in pronounced suppression of spin polarization.

In previous studies, pristine monolayer MoS₂ has been reported to interact weakly with common gas molecules such as CO, NO₂, and H₂S, typically exhibiting adsorption energies of only a few hundred meV (physisorption). Consequently, the undoped MoS₂ substrate generally shows weak adsorption behavior. This trend was clearly demonstrated in the DFT investigation by Yue et al., where molecules such as CO and NO₂ exhibited small adsorption energies (≈0.1–0.3 eV) on pristine MoS₂.³⁵ The introduction of dopants or defects significantly enhances the surface reactivity; several reports have shown that both transition-metal doping and sulfur vacancies increase adsorption strength through the formation of localized d-states and stronger orbital hybridization between the dopant and gas molecules.^36,37 Specifically, studies on metal-doped MoS₂ systems (e.g., Ni-, Co-, and Fe-doped MoS₂) have reported substantially larger adsorption energies (up to ∼1 eV or higher) for molecules such as H₂S and NO₂, consistent with a chemisorption mechanism arising from strong interactions between the metal d-orbitals and the molecular orbitals.^36,38 Our results – CO (E_a ≈ −1.82 eV) and NO₂ (E_a ≈ −1.62 eV) at the hollow site – are in agreement with the enhanced adsorption commonly observed in transition-metal-doped MoS₂ systems and fall well above the typical range for pristine MoS₂. This indicates that Fe doping robustly promotes chemisorption, consistent with previous findings on TM-doped MoS₂.^37,39

Regarding electronic and magnetic properties, numerous prior studies have demonstrated that transition-metal dopants (including Fe) can introduce d-states near the Fermi level, induce spin splitting, and even convert nonmagnetic semiconductors into spin-polarized semimetals. The results obtained in this work – the emergence of spin-polarized semimetallicity in the pristine-doped system and the transition to fully metallic behavior accompanied by a strong reduction of the magnetic moment upon NO₂ adsorption – are consistent with earlier DFT analyses on the effects of doping and defects on the band structure and magnetism of MoS₂.^38,39

To comprehensively assess the thermomechanical properties of the material systems, key parameters including bulk modulus (B), shear modulus (G), heat capacity at constant pressure (C_P), heat capacity at constant volume (C_V), Debye temperature (T_D), and thermal expansion coefficient (α) were predicted for the pristine Fe-MoS₂ monolayer and the corresponding gas-adsorbed configurations (CO, H₂S, and NO₂) using the Crystal Graph Convolutional Neural Network (CGCNN) deep learning framework. CGCNN is a graph-based convolutional neural network architecture that encodes the crystal structure as a graph, enabling efficient extraction of local and global structural features and accurate prediction of physical properties.

The predicted values are summarized in Table 3 and reveal notable changes in several thermomechanical characteristics upon gas adsorption. The bulk modulus of the pristine configuration was calculated to be 25.82 GPa, which is significantly lower than that of bulk MoS₂ (∼50.86 GPa (ref. 33)), yet consistent with the expected behavior of a doped two-dimensional material. Upon gas adsorption, the bulk modulus increases markedly for the CO- and NO₂-adsorbed systems, reaching 33.85 GPa and 32.49 GPa, respectively. This increase indicates enhanced volumetric stiffness, likely attributed to the strong chemical interaction between the adsorbed molecules and the Fe-MoS₂ surface, which locally reinforces the lattice structure. In contrast, H₂S adsorption results in only a marginal change (B = 26.69 GPa), remaining close to the pristine value, consistent with a relatively weaker interaction in terms of elastic response.

Table 3 Thermo-mechanical parameters of the configurations

Configurations	B (GPa)	G (GPa)	CP (kB per atom)	CV (kB per atom)	TD (K)	α (K^−1)
Pristine Fe-MoS2	25.82	21.73	2.84	2.77	395.86	6.12 × 10^−5
CO adsorption	33.85	21.40	2.79	2.77	335.17	6.09 × 10^−5
H2S adsorption	26.69	9.01	2.88	2.79	362.00	6.04 × 10^−5
NO2 adsorption	32.49	15.99	2.79	2.78	354.71	6.09 × 10^−5

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The shear modulus G exhibits more pronounced variations, highlighting the anisotropic nature of the mechanical response in the 2D system. For the pristine Fe-MoS₂ monolayer, G is calculated to be 21.73 GPa, lower than the bulk value of MoS₂ (46.76 GPa (ref. 33)), as expected for atomically thin structures. Following gas adsorption, G remains nearly unchanged for CO (21.40 GPa), decreases moderately for NO₂ (15.99 GPa), and decreases significantly in the case of H₂S adsorption, dropping to just 9.01 GPa – approximately 41% of the pristine value. This substantial reduction in shear modulus suggests a severe weakening of the material's shear strength upon H₂S adsorption, which aligns with the large structural deformation observed in the geometric analysis. These results indicate that different gas adsorption scenarios can modulate the mechanical resilience of Fe-MoS₂ to varying degrees, with H₂S exerting the most detrimental effect.

To evaluate the consistency and reliability of machine learning predictions, the bulk modulus (B) and shear modulus (G) of the pristine Fe-MoS₂ monolayer were independently calculated using DFT methods, yielding values of 24.31 GPa and 20.26 GPa, respectively. These results are in close agreement with the corresponding values predicted by the CGCNN model, which produced B = 25.82 GPa and G = 21.73 GPa. The relative deviation between the DFT and CGCNN results is less than 7%, confirming that the CGCNN model provides quantitatively reliable estimates of the elastic properties for this system. This agreement validates the application of CGCNN as a complementary and efficient approach for large-scale screening of mechanical properties in doped two-dimensional materials.

From a thermal perspective, both the isobaric heat capacity (C_P) and isochoric heat capacity (C_V) per atom remain relatively stable across all configurations, fluctuating within a narrow range of 2.77–2.88k_B per atom. Among them, the H₂S-adsorbed configuration exhibits the highest C_P value (2.88k_B per atom), which can be attributed to increased vibrational amplitudes arising from structural deformation. Nevertheless, the variation in heat capacity values is minor, suggesting that the overall heat storage capacity of the Fe-MoS₂ system is not significantly affected by gas adsorption.

The Debye temperature (T_D), a key parameter reflecting lattice vibrational stiffness and thermal stability, offers further insight into the thermal behavior of the material. Compared to the T_D of bulk MoS₂ (∼278.35 K (ref. 33)), the pristine Fe-MoS₂ monolayer displays a substantially higher value (395.86 K), indicating lattice stiffening induced by Fe doping. Upon gas adsorption, T_D decreases across all configurations, with values of 335.17 K (CO), 354.71 K (NO₂), and 362.00 K (H₂S), suggesting a softening of the vibrational network due to gas–surface interactions. Despite these reductions, all T_D values remain above that of bulk MoS₂, indicating that the Fe-MoS₂ monolayer retains good thermal stability even after gas adsorption.

Finally, the thermal expansion coefficient (α) remains nearly constant across the studied systems, ranging from 6.04 × 10⁻⁵ K⁻¹ to 6.12 × 10⁻⁵ K⁻¹. These values are in close agreement with the reported thermal expansion coefficient of monolayer MoS₂ (α ≈ 6.49 × 10⁻⁵ K⁻¹ (ref. 34)). This consistency suggests that gas adsorption does not significantly alter the material's macroscopic thermal expansion behavior, although localized lattice distortions are evident at the adsorption sites.

As CGCNN directly learns atomic and bonding environments from the crystal graph, the model captures local structural features that govern thermo-mechanical responses. Across all predicted properties – including bulk modulus (B), shear modulus (G), heat capacities (C_P, C_V), Debye temperature (T_D), and thermal expansion coefficient (α) – the model consistently assigned higher importance to the atomic environment surrounding the Fe dopant and the neighboring S atoms. Key features such as bond lengths, local coordination, and atomic connectivity were found to strongly influence the predictive performance, reflecting their critical role in determining lattice stiffness, vibrational behavior, and anharmonic effects. This result underscores the physical interpretability of CGCNN in modeling doped 2D systems and highlights its ability to learn chemically meaningful representations for complex property prediction.

3.2. Electronic results

The electronic band structures and total density of states (TDOS) of the pristine Fe-MoS₂ monolayer and its gas-adsorbed configurations (CO, H₂S, and NO₂) are presented in Fig. 2. As illustrated, the pristine Fe-MoS₂ system, as well as the CO- and H₂S-adsorbed structures, exhibit spin-polarized semimetallic behavior in which the spin-up channel displays metallic characteristics while the spin-down channel retains semiconducting features. In contrast, the NO₂-adsorbed configuration shows metallic behavior in both spin channels, indicating strong electronic hybridization between the NO₂ molecular orbitals and the Fe-MoS₂ substrate. For pristine Fe-MoS₂, the TDOS reveals finite states around the Fermi level, suggesting that Fe doping introduces additional electronic states primarily originating from Fe–S hybridization, thereby reducing the effective bandgap and enhancing carrier availability. Upon gas adsorption, the TDOS becomes noticeably modified, particularly for NO₂. The pristine, CO-, and H₂S-adsorbed structures show no TDOS at the Fermi level in the spin-down channel, whereas distinct TDOS contributions appear around the Fermi level for both spin channels in the NO₂-adsorbed configuration. This confirms that NO₂ induces the strongest electronic perturbation among the examined gases and significantly alters the spin-dependent electronic structure of Fe-MoS₂.

Fig. 2 Energy band structure and total density of states in the structures: Fe-MoS₂ (a), CO adsorption (b), H₂S adsorption (c), NO₂ adsorption (d).

Pristine monolayer MoS₂ and bulk MoS₂ are both spin-unpolarized semiconductors, possessing direct and indirect band gaps of approximately 1.8 eV and 1.2 eV, respectively.¹⁴ The emergence of spin polarization and metallicity in the Fe-doped systems underscores the critical role of Fe dopants in tailoring the electronic structure, enabling modulation of both the magnetic and conductive properties of the material.

Adsorption on the Fe-MoS₂ monolayer caused distinct shifts in the Fermi level (E_F), which was initially calculated at −1.6877 eV. Upon gas exposure, two primary interaction mechanisms were confirmed. Firstly, CO adsorption and NO₂ adsorption both resulted in an upward E_F shift, the E_F moved to −1.6371 eV for CO (a shift of +0.0506 eV) and −1.6099 eV for NO₂ (a shift of +0.0778 eV). In contrast, H₂ adsorption led to a marginal downward E_F shift to −1.6972 eV (a shift of −0.0095 eV). The magnitude and direction of these E_F shifts directly correlate with the induced change in carrier concentration, predicting that NO₂ and CO interactions will yield the highest sensor response due to the substantial alteration of the electronic structure.

Fig. 3 illustrates the state contributions of individual atoms in the Fe-MoS₂ structures and their gas-adsorbed configurations. For the pristine structure (Fig. 3a), Mo, S, and Fe atoms collectively contribute to the TDOS, with S dominating the low-energy region and Mo–Fe contributing significantly near the Fermi level. Upon CO adsorption (Fig. 3b), O atoms exhibit substantial contributions across multiple energy regions, while the contribution of C is mainly localized around −4.5 eV and 1.5 eV, reflecting the hybridization between the CO molecule and the Fe-MoS₂ surface. For H₂S adsorption (Fig. 3c), H atoms contribute only minimally to the TDOS, whereas the S atoms from both the molecule and the substrate dominate the spectral features, indicating a weaker interaction compared to CO. In contrast, the NO₂-adsorbed configuration (Fig. 3d) shows significant contributions from O atoms near the Fermi level, while the contribution from N is much smaller, which partially accounts for the metallic behavior observed in the NO₂-adsorbed structure.

Fig. 3 The state contributions of individual atoms in the structures: Fe-MoS₂ (a), CO adsorption (b), H₂S adsorption (c), NO₂ adsorption (d).

The partial density of states (PDOS) profiles of pristine and gas-adsorbed Fe-MoS₂ (Fig. 4) reveal observable changes in the orbital contributions of Mo, Fe, and S atoms upon adsorption of CO, H₂S, and NO₂. Although these variations are not large, they provide useful insights into the electronic interactions between the gas molecules and the substrate.

Fig. 4 Partial density of states of the pristine Fe-MoS₂ monolayer structure (a) and the Fe-MoS₂ monolayer structures adsorbed with gases: CO (b), H₂S (c), NO₂ (d).

A notable feature observed in all gas-adsorbed configurations is the pronounced reduction in the intensity of the Mo(5s) peak. In the pristine Fe-MoS₂ structure, a sharp Mo(5s) peak appears near −4.5 eV; however, upon adsorption of CO, H₂S, or NO₂, the magnitude of this peak decreases significantly.

The sulfur-derived S(3s) and S(3p) states also exhibit reduced spectral intensity after gas adsorption, indicating that S atoms in the MoS₂ lattice participate in electron redistribution upon binding. This depletion arises from hybridization between S orbitals and the constituent atoms of the incoming molecules, signifying perturbation of the valence-band bonding network.

The Fe(4s) states decrease substantially from ∼0.21 states per eV in the pristine configuration to 0.10, 0.14, and 0.09 states per eV for the CO-, H₂S-, and NO₂-adsorbed structures, respectively. This reduction confirms that Fe acts as an active site mediating electronic coupling between the adsorbates and the MoS₂ lattice, and highlights the essential role of Fe doping in enhancing gas sensitivity.

For the CO-adsorbed configuration, the electronic states associated with C and O near −8.9 eV, −4 eV, and +1.8 eV overlap significantly with Mo(5s), Fe(4s), and S(3p) states. This clear orbital alignment is characteristic of chemisorption, producing strong hybridization and considerable charge redistribution at the interface.

In the case of H₂S adsorption, the broad distribution of H-derived molecular states indicates weak and delocalized hybridization. Unlike CO, the frontier orbitals of H₂S couple inefficiently with Mo and Fe due to their lower reactivity and unfavorable symmetry. This weaker coupling explains both the unfavorable (positive) adsorption energy and the limited PDOS perturbation. The accompanying structural distortions and the reduction in shear modulus G further suggest that H₂S disrupts the lattice mechanically rather than forming strong chemical bonds.

For NO₂ adsorption, substantial hybridization occurs from −7 eV to +3 eV, where N- and O-derived states strongly overlap with Mo, Fe, and S orbitals. This interaction leads to significant charge redistribution and the observed suppression of the magnetic moment. The strong coupling between NO₂ and the substrate is fully consistent with its chemisorption behavior, driven by the high electronegativity of the molecule.

The charge density difference (CDD) plots reveals distinct interaction mechanisms between the Fe-MoS₂ monolayer and the adsorbed gas molecules (CO, H₂S, and NO₂) (Fig. 5). Quantitatively, the computed charge transfer from the gas molecules to the substrate was approximately +0.011 e (CO), −0.0191 e (H₂S), and +0.0178 e (NO₂), respectively, where positive values denote electron transfer to the substrate.

Fig. 5 Charge density difference in adsorbed configurations (the yellow and blue regions represent increases and decreases in charge, respectively): CO adsorption (a), H₂S adsorption (b), NO₂ adsorption (c).

For the CO-adsorbed system, a slight electron donation to the substrate was observed, suggesting moderate orbital hybridization, particularly involving the Fe-3d and CO-2π orbitals. This is consistent with the moderate adsorption energy (−1.8 eV) and implies a predominantly physisorption-driven interaction, with minor charge polarization effects. In contrast, H₂S exhibited a net charge transfer away from the substrate (−0.0191 e), indicating that the gas molecule acts as a weak electron acceptor. This result aligns with the positive adsorption energy (+2.5 eV), confirming the thermodynamic instability of H₂S adsorption on the Fe-MoS₂ surface. The minimal charge redistribution observed in the CDD further supports the conclusion that H₂S only weakly perturbs the electronic structure of the host material.

For the NO₂-adsorbed configuration, the substrate gains a small amount of charge (+0.0178 e), which may be attributed to the high electron affinity of NO₂ and the potential formation of partial charge transfer complexes. The corresponding adsorption energy (−1.6 eV) and visible charge accumulation around the adsorption site suggest stronger physisorption or weak chemisorption. Notably, the electron density rearrangement also contributes to the observed suppression of magnetic moments in this configuration. The low magnitude of charge transfer (<0.02 e in all cases) indicates that the interactions between gas molecules and Fe-MoS₂ are primarily governed by weak van der Waals forces and electrostatic polarization, rather than strong covalent bonding. These findings are in good agreement with the electronic and magnetic properties discussed in subsequent sections.

The Joint Density of States (JDOS) serves as a fundamental quantity for assessing the optical absorption characteristics, electron–hole pair generation, and modifications in electronic structure under the influence of electromagnetic radiation. Fig. 6 presents the calculated JDOS for the pristine Fe-MoS₂ monolayer and for three gas-adsorbed configurations: CO, H₂S, and NO₂. The results indicate that, within the low-energy photon range (ħω < 9 eV), the JDOS profiles of all configurations remain relatively similar, suggesting that the electronic states responsible for transitions in this region are not significantly perturbed by gas adsorption. This implies that the low-energy optical properties of the material are largely preserved across the different adsorption states.

Fig. 6 Joint density of states (JDOS) of pristine Fe-MoS₂ monolayer structures and gas-adsorbed Fe-MoS₂ structures.

A key observation is the presence of non-zero JDOS values at very low photon energies, indicating the availability of accessible electronic states near the Fermi level that can participate in optical transitions even under low-energy excitation. This behavior is characteristic of semi-metallic systems and corroborates the findings from band structure analysis. Specifically, the pristine Fe-MoS₂, as well as the CO- and H₂S-adsorbed configurations, exhibit spin-polarized semi-metallic characteristics, while the NO₂-adsorbed system displays a fully metallic nature. The metallicity of the NO₂-adsorbed configuration facilitates continuous low-energy transitions, thereby enhancing its optical activity in the infrared-to-visible spectral range.

In the photon energy range of 3–7 eV, corresponding to the visible and near-ultraviolet (UV) regions, all configurations – including the pristine Fe-MoS₂ monolayer and the gas-adsorbed systems – exhibit pronounced Joint Density of States (JDOS) values. This indicates a high density of available electronic transitions, which directly correlates with efficient photon absorption in this spectral range. Such behavior confirms the suitability of Fe-MoS₂ systems, regardless of adsorption state, for optoelectronic applications such as photovoltaic devices and optical sensors operating in the visible – UV domain.

However, notable divergence between configurations emerges in the higher-energy range of 9–12 eV. While the pristine, H₂S-adsorbed, and NO₂-adsorbed structures exhibit JDOS values that remain close to zero – indicating a lack of accessible transitions – distinct features appear in the CO-adsorbed configuration. Specifically, several small peaks are observed, suggesting the activation of new high-energy optical transitions. This phenomenon is likely associated with strong orbital hybridization between CO molecular states, particularly O(2p), and Fe/S atomic states, which gives rise to defect-like or mid-gap states within this energy range.

In the deep ultraviolet region (19–25.5 eV), a similar pattern is observed. Only the NO₂-adsorbed configuration presents multiple JDOS peaks, whereas the pristine and H₂S-adsorbed systems display JDOS values that remain effectively zero throughout this range, indicating the absence of transition-active states. The emergence of these high-energy features in the NO₂ system signifies substantial perturbation of the electronic structure due to NO₂ adsorption, extending well beyond the vicinity of the Fermi level. The induced modifications enable additional intraband and interband transitions, which are characteristic of strong molecular hybridization and electronic asymmetry. Additionally, the CO-adsorbed system also exhibits non-zero JDOS values in the 21.7–24 eV range, though with a lower intensity and fewer peaks compared to the NO₂ configuration. This suggests a moderate influence of CO adsorption on high-energy electronic states.

3.3. Optical results

Fig. 7 shows the real part of the dielectric function, ε₁(ω), along the in-plane x and y crystallographic directions for the pristine Fe-MoS₂ monolayer and the gas-adsorbed configurations (CO, H₂S, and NO₂). As the primary descriptor of the material's polarization response under an external electric field, ε₁(ω) governs key optical behaviors such as refractive index, transmittance, and absorption.

Fig. 7 Real part of dielectric function of the pristine Fe-MoS₂ monolayer structure (a) and the Fe-MoS₂ monolayer structures adsorbed with gases: CO (b), H₂S (c), NO₂ (d).

For pristine Fe-MoS₂, ε₁(ω) along the x and y directions overlaps nearly perfectly throughout the full photon-energy range considered, indicating strong in-plane dielectric isotropy. This behavior is consistent with the intrinsic hexagonal symmetry and uniform electronic distribution within the basal plane of the monolayer. Upon adsorption of CO, H₂S, and NO₂, a slight but noticeable deviation emerges between the ε₁(ω) responses along the two crystallographic directions. Although the induced anisotropy remains modest, it clearly indicates a partial breaking of in-plane symmetry due to the localized electronic perturbation introduced by the adsorbed species. This demonstrates that gas adsorption modifies the polarization pathways of the substrate and introduces mild direction-dependent dielectric behavior.

Across all configurations, the first major peak in ε₁(ω) appears near 1 eV, falling within the near-infrared (NIR) region. This feature originates from low-energy interband transitions close to the Fermi level and is characteristic of two-dimensional semiconductors. Furthermore, ε₁(ω) maintains relatively high values across the 1–3 eV range, spanning the NIR and the lower visible spectrum. A large real dielectric response in this region reflects strong material polarization and the associated attenuation of internal electric fields, often referred to as optical shielding. This suggests that Fe-MoS₂ efficiently reflects or absorbs incident light in this spectral window, consistent with behaviors typically exploited in photodetection or optical-filtering contexts.

At higher photon energies (3–8 eV), corresponding to the near-UV to mid-UV range, ε₁(ω) decreases sharply, indicating suppression of low-energy polarizable transitions and increased optical transparency. Beyond ∼10 eV, ε₁(ω) approaches a nearly constant baseline, consistent with dielectric saturation and the dominance of transitions from deeper core states. This asymptotic response is characteristic of inertial, weakly dispersive dielectric behavior at very high excitation energies. The curves corresponding to the gas molecules serve only as complementary information to illustrate how adsorption perturbs the optical response of F-MoS₂ monolayer.

Fig. 8 presents the imaginary part of the dielectric function, ε₂(ω), for pristine Fe-MoS₂ and the gas-adsorbed configurations (CO, H₂S, and NO₂). Since ε₂(ω) quantifies the material's dissipative response to incident electromagnetic radiation, it is directly linked to the probability of optical absorption arising from interband electronic transitions. In this subsection, our discussion focuses primarily on how adsorption modifies the optical response of the Fe-MoS₂ monolayer; the spectra associated with the adsorbed molecules are included as complementary information to illustrate their perturbative effects on the substrate.

Fig. 8 Imaginary part of dielectric function of the pristine Fe-MoS₂ monolayer structure (a) and the Fe-MoS₂ monolayer structures adsorbed with gases: CO (b), H₂S (c), NO₂ (d).

For the pristine Fe-MoS₂ monolayer, the ε₂(ω) curves along the x and y directions overlap exactly across the entire photon-energy range, reflecting the strong in-plane optical isotropy expected from a two-dimensional system with high structural symmetry. This uniformity indicates that optical transitions in the pristine configuration do not favor any crystallographic direction, consistent with a homogeneous charge distribution throughout the basal plane.

Gas adsorption leads to a modest divergence between the x- and y-direction ε₂(ω) spectra, particularly within selected low- and mid-energy regions. Although the induced anisotropy remains small, it reflects a partial breakdown of the in-plane symmetry caused by local electronic rearrangements at the adsorption site. The interaction between the adsorbed molecules and the Fe-MoS₂ lattice perturbs the orbital hybridization near the Fermi level, producing slight direction-dependent modifications to the optical absorption profile. Nevertheless, the overall magnitude of this anisotropy is limited, indicating that Fe-MoS₂ retains an essentially isotropic dissipative response even after adsorption-consistent with the trends observed in the real dielectric component ε₁(ω).

A key spectral feature across all configurations is the pronounced absorption peak in ε₂(ω) centered around ∼3 eV, which lies in the visible range. This peak arises from strong interband transitions between occupied valence-band states and low-lying conduction-band states. Its persistence across all gas-adsorption scenarios shows that the fundamental optical absorption mechanism of Fe-MoS₂ remains intact, with the adsorbed molecules acting only as perturbations rather than fundamentally altering the intrinsic transition channels of the monolayer.

At higher photon energies (>8.5 eV), within the deep ultraviolet (DUV) regime, ε₂(ω) rapidly decays toward near-zero values. This decline reflects the limited availability of accessible unoccupied states at these high energies and the suppression of dipole-allowed transitions. As a result, the system becomes largely transparent to DUV radiation and exhibits minimal energy dissipation through absorption. This behavior is consistent across all configurations and underscores the intrinsic inertial, weakly dispersive nature of Fe-MoS₂ at high excitation energies.

Fig. 9 shows the optical absorption coefficient, α(ω), for pristine Fe-MoS₂ and the gas-adsorbed configurations (CO, H₂S, and NO₂) along the three principal crystallographic directions. As α(ω) reflects the material's ability to attenuate incident light through interband transitions, these spectra allow us to assess how gas adsorption perturbs the intrinsic optical response of the Fe-MoS₂ monolayer. Across all configurations, the strongest absorption occurs in the 200–500 nm wavelength range, covering the near-ultraviolet (NUV) and the entire visible region. This prominent absorption arises from efficient interband transitions involving states near the Fermi level, and its persistence in both pristine and adsorbed structures indicates that the fundamental optical activity of Fe-MoS₂ remains intact despite adsorption. These trends characterize the spectral regime where the monolayer intrinsically exhibits strong light–matter interaction, providing a baseline for understanding how external perturbations such as gas adsorption modulate the optical performance.

Fig. 9 Absorption coefficient of the pristine Fe-MoS₂ monolayer structure (a) and the Fe-MoS₂ monolayer structures adsorbed with gases: CO (b), H₂S (c), NO₂ (d).

At wavelengths longer than ∼500 nm, α(ω) decreases rapidly for all configurations. In the out-of-plane (z) direction – perpendicular to the monolayer surface – the absorption drops sharply beyond 300 nm and approaches nearly zero for the pristine, CO-adsorbed, and H₂S-adsorbed systems. This behavior is characteristic of two-dimensional materials, in which optically active states are largely confined within the xy-plane. Due to limited orbital overlap and weak electronic dispersion along the z-axis, optical transitions in this direction are strongly suppressed, resulting in minimal absorption.

A notable deviation from this trend occurs for the NO₂-adsorbed configuration. Although α(ω) in the z direction still decreases at longer wavelengths, it remains finite instead of vanishing. This behavior signifies partial breaking of out-of-plane symmetry and can be attributed to the stronger electronic interaction between NO₂ and the Fe-MoS₂ substrate. The associated charge redistribution and enhanced orbital hybridization introduce small but active electronic states with out-of-plane character, enabling weak absorption perpendicular to the monolayer surface. It demonstrates that adsorption can subtly tune vertical optical responses in Fe-MoS₂, an effect that may be useful in understanding interlayer coupling or out-of-plane optical behavior in more complex stacked or heterostructured systems.

4. Conclusions

In this study, the structural, electronic, thermo-mechanical, and optical properties of Fe-doped monolayer MoS₂ (Fe-MoS₂) were systematically investigated in both pristine form and in the presence of adsorbed CO, H₂S, and NO₂ molecules, employing DFT in combination with a Crystal Graph Convolutional Neural Network (CGCNN) machine-learning framework. The adsorption analysis reveals that CO and NO₂ exhibit negative adsorption energies, indicating thermodynamically favorable interactions with the Fe-MoS₂ surface, whereas H₂S shows a positive adsorption energy, signifying an energetically unfavorable adsorption process under the considered conditions. These distinctions highlight the differing adsorption behaviors among the gas species and their varying impacts on the physicochemical properties of Fe-MoS₂.

Electronic structure analysis revealed that the pristine, CO-, and H₂S-adsorbed Fe-MoS₂ systems preserved a spin-polarized semimetallic character, whereas NO₂ adsorption induced a transition to metallic behavior and significantly suppressed the magnetic moment. The projected density of states (PDOS) and charge density difference (CDD) analyses indicated substantial charge redistribution upon adsorption, highlighting distinct charge transfer mechanisms and hybridization patterns depending on the adsorbed gas species.

Thermo-mechanical evaluations demonstrated anisotropic mechanical responses to gas adsorption: CO and NO₂ enhanced the bulk modulus, suggesting increased stiffness, while H₂S caused a marked reduction in shear modulus, indicative of localized lattice softening. Thermal properties – including isochoric/isentropic heat capacities, Debye temperature, and thermal expansion coefficient – remained relatively stable across configurations, confirming thermal robustness of the system post-adsorption.

Optical analysis, including the real and imaginary parts of the dielectric function, absorption coefficient, and joint density of states (JDOS), confirmed strong light absorption in the 200–500 nm spectral range (UV-visible), with retained or tunable optical activity after gas adsorption. JDOS results corroborated the presence of high transition state densities in the visible-UV region, with selective enhancement at high energies depending on the gas species.

Overall, the results suggest that Fe-MoS₂ monolayers show potential for selective gas detection toward specific molecules such as CO and NO₂, in addition to 2D optoelectronic applications. The unfavorable adsorption of H₂S further emphasizes the selective nature of the gas detection response, indicating that this material may not be suitable for all gas species.

Author contributions

N. V. Hoang researched, surveyed and set up input files. Tr. Q. Trieu prepared the figures, the tables. N. V. Hoang and Tr. Q. Trieu wrote the main manuscript. All authors reviewed the manuscript.

Conflicts of interest

We declare we have no competing interests.

Data availability

Data supporting the findings of this study are available within the article.

Acknowledgements

The authors gratefully acknowledge the support of the HPC system at the Institute for Advanced Study in Technology (IAST), Ton Duc Thang University.

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