## 1 Introduction
Various research studies have explored the impact of adsorption behavior from TM active sites on different TMDs. [PERSON] et al. conducted a comprehensive study on the adsorption of small molecule gases on TM-atom-doped MoS\({}_{2}\). They discovered that different TM active sites yield varying adsorption strengths and selectivity for small inorganic gases like CO, NO, NO\({}_{2}\), and NH\({}_{3}\)[33]. Through the manipulation of different elements, the adsorption effect of MoTe\({}_{2}\) on CO can be enhanced and differentiated [34]. Similar adjustments in the adsorption effect were also observed for NO\({}_{2}\) adsorption [35]. [PERSON] et al. [36] reported on the adsorption of CO\({}_{2}\), NO\({}_{2}\), and NO on different TM-doped WSe\({}_{2}\). By comparing work functions, they determined that Ag doping is suitable for NO\({}_{2}\) detection. Among the noble metal dopants, Ag stands out as one of the most affordable noble metal options. Furthermore, Ag sites exhibit high reactivity toward the adsorption of small molecules and can lower the operation temperature of the sensors [37]. For instance, [PERSON] et al. found that Ag decoration leads to the maximum sensitivity improvement in NH\({}_{3}\) detection compared to other noble metal modifications, including Pt and Au, for the reason that Ag nanoparticles bring higher activity for O\({}_{2}\) decomposition and detect gas molecule adsorption [38]. Moreover, Ag on TMDs belongs to n-type doping and can adjust the electron transfer for modulating the potential barrier. [PERSON] et al. discussed the sensing performance using Ag-doped MoSe\({}_{2}\) sensing materials, and the sensitivity to H\({}_{2}\)S was obviously improved [39]. [PERSON] et al. discovered that Ag nanostructure on WS\({}_{2}\) can enhance the sensitivity as well as recovery performance of NO\({}_{2}\) because of the n-type doping and synergistically catalytic effect [40]. From the above discussion, Ag doping is beneficial to simultaneously improve the electronic structure and catalytic performance for detected gas adsorption and decomposition, and Ag-WSheterostructure can bring excellent carrier characteristics of optical excitation [41]. Given the limited adsorption behavior and selective detection of several toxic gas molecules on pristine WS\({}_{2}\) and the advantageous of Ag active sites, it is imperative to further investigate adsorption performance, gas sensitivity and selectivity. In this research, first-principles calculations based on density functional theory (DFT) to investigate the adsorption of three representative hazardous gases (CO, NO\({}_{2}\), and SO\({}_{2}\)) on an Ag-doped WS\({}_{2}\) monolayer were employed. Detailed calculations of atomic structures and adsorption parameters were conducted, followed by a comprehensive comparison. Moreover, the alterations in electronic properties before and after adsorption were discussed, and the sensing properties were also evaluated. To summarize, this study offers a theoretical perspective on the sensing properties of modified WS\({}_{2}\). It opens up extensive possibilities for exploring diverse TMDs as sensing materials and varying surface modifications to enhance sensing characteristics.