## 3 Results and Discussion
### Adsorption of Single Molecule, Double Molecules on Pt-Graphene
#### 3.2.3 Analysis of Frontier Molecular Orbital  
The HOMO, LUMO and the value of \(E_{g}\) of the system after adsorbing a single gas molecule are shown in Table 2. It was found that \(E_{g}\) increased to some extent during all the adsorption processes. Before Pt-graphene adsorbed gas molecules, HOMO and LUMO were mainly distributed at Pt atoms and their opposite sides (Figure 9a). The corresponding energy gap width \(E_{g}\) was 0.28 eV. As shown in Figure 9b, after adsorption of SO\({}_{2}\), the HOMO and LUMO were slightly transferred to the SO\({}_{2}\) adsorption site, and more uniformly distributed on the surface of Pt-graphene. \(E_{g}\) increases to 0.601 eV. We estimate that with the increase of \(E_{g}\) leads to the slightly decreased conductivity of the system. When a single SOF\({}_{2}\) molecule is adsorbed on Pt-graphene, it is not much different from the adsorption of SO\({}_{2}\), and the \(E_{g}\) is increased to 0.667 eV. There was almost no change in HOMO. The SOF piece causes change in LUMO. For SO\({}_{2}\)F\({}_{2}\) adsorption, the \(E_{g}\) value is 0.716 eV, and HOMO and LUMO were significantly reduced. The HOMO and LUMO adsorption configurations of Pt-graphene adsorbed SO\({}_{2}\)F\({}_{2}\) are shown in Figure 9d. There are few orbits around the adsorbed SO\({}_{2}\)F\({}_{2}\).  
The HOMO, LUMO and \(E_{g}\) of the system after adsorption of mixed gas molecules are shown in Table 3. The HOMO and LUMO distribution (Figure 10b) has been extended to the adsorbed SO\({}_{2}\) and SOF\({}_{2}\) molecule, and the \(E_{g}\) is broadened to 0.564 eV. Therefore, we evaluate that the effect of SO\({}_{2}\) and SOF\({}_{2}\) adsorption slightly increases the conductivity of Pt-graphene. Although the SO\({}_{2}\)F\({}_{2}\) molecule is too far away to affect the frontier molecular orbital (Figure 10c), the adsorbed SO\({}_{2}\) increasing the HOMO and LUMO distribution to change the system conductivity. For the HOMO and LUMO  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**System** & **LUMO (eV)** & **HOMO (eV)** & \(E_{g}\) **(eV)** \\ \hline Pt-graphene & \(-3.798\) & \(-4.229\) & 0.489 \\ Pt-graphene/SO\({}_{2}\) & \(-4.105\) & \(-4.706\) & 0.601 \\ Pt-graphene/SO\({}_{2}\) & \(-4.218\) & \(-4.884\) & 0.667 \\ Pt-graphene/SO\({}_{2}\)F\({}_{2}\) & \(-4.330\) & \(-5.046\) & 0.716 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), \(E_{g}\) before and after adsorption of single SO\({}_{2}\), SOF\({}_{2}\), SO\({}_{2}\)F\({}_{2}\) by Pt-graphene.  
Figure 9: Distribution of HOMO (red-green) and LUMO (blue-yellow) (**a**) before and after (**b**) single SO\({}_{2}\), (**c**) single SOF\({}_{2}\) and (**d**) single SO\({}_{2}\)F\({}_{2}\) adsorption on Pt-graphene.  
distributions of SOF\({}_{2}\)-SO\({}_{2}\)F\({}_{2}\) adsorption shown in Figure 10d, part of the HOMO is distributed on the bonded F surface and one SOF\({}_{2}\) molecule, and LUMO is uniformly distributed on the C atom as compared with before adsorption. In addition, with \(E_{g}\) rising to 0.706 eV, HOMO and LUMO mainly distribute around F-Pt bond and SOF\({}_{2}\) molecule.