## 3 Results
### Electronic Properties of Ag-WS\({}_{2}\) Monolayer after Gas Adsorption  
To compare the electronic properties of Ag-WS\({}_{2}\) before and after adsorption, the calculations of the band structure and DOS after adsorption were conducted, as shown in Figure 5. It is evident that all gas adsorptions result in a reduction in the band gap, as illustrated in Figure 5a,d,g. The calculated band gaps are 1.19 eV, 1.06 eV, and 0.96 eV for CO, NO\({}_{2}\), and SO\({}_{2}\) adsorption, respectively. Notably, both NO\({}_{2}\) and SO\({}_{2}\) adsorptions lead to band rearrangements around 0 eV. Specifically, NO\({}_{2}\) adsorption introduces a new band at 0 eV, contributing to the reduction in bandgap. Conversely, SO\({}_{2}\) adsorption presents a distinct scenario where the new bands form below the conduction band. Additionally, alterations in the morphology of these two curves of new bands are also observed. For an in-depth analysis of the changes in bandgap and a thorough investigation of the molecular orbitals before and after adsorption, the TDOS of Ag-WS\({}_{2}\) after adsorption and the molecular orbitals of CO, NO\({}_{2}\), and SO\({}_{2}\) are shown in Figure 5b,e,h. Isolated CO exhibits occupied 5\(\sigma\) molecular orbitals and unoccupied 2\(\pi^{\star}\)[51]. Following adsorption, the previously occupied 5\(\sigma\) orbitals nearly vanish, and the 2\(\pi^{\star}\) orbitals exhibit a flattened profile with unoccupied characteristics. This observation supports the notion that CO loses electrons upon adsorption. Isolated NO\({}_{2}\) displays an asymmetric DOS, implying inherent magnetism before adsorption [52]. Upon adsorption, the PDOS of NO\({}_{2}\) becomes symmetric. The 3\(\pi^{\star}\) orbitals, which were partly occupied before adsorption, undergo a leftward shift and become nearly fully occupied after adsorption. In contrast, for SO\({}_{2}\), the 3b orbitals are entirely unoccupied before adsorption [53]. However, after adsorption, these orbitals experience partial occupation. This molecular orbital analysis underscores the transition of certain orbitals within NO\({}_{2}\) and SO\({}_{2}\) from an unoccupied to an occupied state, providing evidence that they function as electron acceptors during the adsorption process.  
The chemical interactions were investigated via the calculation of atomic orbitals of Ag and atoms within molecules. Upon CO adsorption, overlapping states are discernible above 0 eV, indicating unoccupied orbitals. Consequently, the chemical interactions manifest within the vacant atomic orbitals of Ag 4d and C 2p (within CO). However, minimal chemical interactions are observed within the occupied orbitals. Regarding NO\({}_{2}\) adsorption, hybridization between Ag 4d and O 2p (in NO\({}_{2}\)) is evident around energy levels of approximately \(-7\) eV, \(-6\) eV, \(-1.5\) eV, and \(-0.5\) eV. These orbitals are all occupied, highlighting the prevalence of chemical interactions within occupied atomic orbitals of Ag 4d and O 2p (in NO\({}_{2}\)). In the case of SO\({}_{2}\) adsorption, hybridizations occur within the energy range of about \(-7.5\) eV to \(-6\) eV, in proximity to \(-3\) eV, and around +0.6 eV. Consequently, both occupied and unoccupied orbitals display chemical interactions. In essence, all three molecules exhibit chemical interactions with Ag atoms, with hybridization occurring across both occupied and unoccupied orbitals for different molecules.  
Figure 4: CDD configurations and the projection curve of \(Z\)-direction of CO, NO\({}_{2}\), and SO\({}_{2}\) on Ag-WS\({}_{2}\) monolayer: (**a**) CO on Ag-WS\({}_{2}\) monolayer; (**b**) NO\({}_{2}\) on Ag-WS\({}_{2}\) monolayer; (**c**) SO\({}_{2}\) on Ag-WS\({}_{2}\) monolayer (the isosurface is 0.01 e/Å\({}^{3}\), and the pink and yellow represent the electron accumulation and depletion region, respectively).