## 3 Results and Discussion
### Application as Anode Materials for Li, Na, K, Mg and Ca-Ions Batteries
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **Li** & **Na** & **K** & **Ca** \\ \hline \multirow{8}{*}{Most stable adsorption sites} & & E\({}_{\text{Ads}}=-2.026\) eV & E\({}_{\text{Ads}}=-2.476\) eV & E\({}_{\text{Ads}}=-3.013\) eV & E\({}_{\text{Ads}}=-2.428\) eV \\  & & L\({}_{\text{C1-A}}\) = 3.280 Å & L\({}_{\text{C1-N}}\) = 4.263 Å & L\({}_{\text{C1-K}}\) = 4.260 Å & L\({}_{\text{C1-C}}\) = 4.226 Å \\  & & L\({}_{\text{C2-N}}\) = 3.279 Å & L\({}_{\text{C2-N}}\) = 4.263 Å & L\({}_{\text{C2-K}}\) = 4.260Å & L\({}_{\text{C2-C}}\) = 4.226 Å \\  & & L\({}_{Z}\) = 0 Å & L\({}_{Z}\) = 0 Å & L\({}_{Z}\) = 0 Å & L\({}_{Z}\) = 0 Å \\  & & \(\Delta\)Q = 0.995 1 e \(\mid\) & \(\Delta\)Q = 0.996 1 e \(\mid\) & \(\Delta\)Q = 0.850 1 e \(\mid\) & \(\Delta\)Q = 1.620 1 e \(\mid\) \\ \cline{2-6}  & & E\({}_{\text{Ads}}\) = \(-1.703\)eV & E\({}_{\text{Ads}}\) = \(-1.735\)eV & E\({}_{\text{Ads}}\) = \(-2.368\) eV & E\({}_{\text{Ads}}=-1.804\) eV \\  & & L\({}_{\text{P1-A}}\) = 2.558 Å & L\({}_{\text{P1-N}}\) = 2.901 Å & L\({}_{\text{P1-K}}\) = 3.297 Å & L\({}_{\text{P1-Ca}}\) = 2.734 Å \\  & & L\({}_{\text{P2-Li}}\) = 2.559 Å & L\({}_{\text{P2-Na}}\) = 2.900 Å & L\({}_{\text{P2-K}}\) = 3.302 Å & L\({}_{\text{P2-Ca}}\) = 2.733 Å \\  & & L\({}_{Z}\) = 1.678 Å & L\({}_{Z}\) = 2.163 Å & L\({}_{Z}\) = 2.514 Å & L\({}_{Z}\) = 2.027 Å \\  & & \(\Delta\)Q = 0.993 1 e \(\mid\) & \(\Delta\)Q = 0.991 1 e \(\mid\) & \(\Delta\)Q = 0.932 1 e \(\mid\) & \(\Delta\)Q = 1.510 1 e \(\mid\) \\ \cline{2-6}  & & E\({}_{\text{Ads}}\) = \(-1.567\)eV & E\({}_{\text{Ads}}\) = \(-1.794\)eV & E\({}_{\text{Ads}}\) = \(-2.284\) eV & E\({}_{\text{Ads}}\) = \(-1.712\) eV \\  & & L\({}_{\text{C-Li}}\) = 2.505 Å & L\({}_{\text{C-Na}}\) = 3.255 Å & L\({}_{\text{C-K}}\) = 2.965 Å & L\({}_{\text{C-Ca}}\) = 2.408 Å \\  & & L\({}_{\text{P-Li}}\) = 2.482 Å & L\({}_{\text{P-Na}}\) = 2.819 Å & L\({}_{\text{P-K}}\) = 3.399 Å & L\({}_{\text{P-Ca}}\) = 2.882 Å \\  & & L\({}_{Z}\) = 1.024 Å & L\({}_{Z}\) = 0.216 Å & L\({}_{Z}\) = 2.397 Å & L\({}_{Z}\) = 1.819 Å \\  & & \(\Delta\)Q = 0.994 1 e \(\mid\) & \(\Delta\)Q = 0.993 1 e \(\mid\) & \(\Delta\)Q = 0.912 1 e \(\mid\) & \(\Delta\)Q = 1.615 1 e \(\mid\) \\ \cline{2-6}  & & E\({}_{\text{Ads}}\) = \(-1.551\) eV & E\({}_{\text{Ads}}\) = \(-1.793\) eV & E\({}_{\text{Ads}}\) = \(-2.513\) eV & E\({}_{\text{Ads}}\) = \(-1.560\) eV \\  & & L\({}_{\text{C-Li}}\) = 2.840 Å & L\({}_{\text{C-Na}}\) = 3.239 Å & L\({}_{\text{C-K}}\) = 3.729 Å & L\({}_{\text{C-Ca}}\) = 2.631 Å \\  & & L\({}_{\text{P-Li}}\) = 2.487 Å & L\({}_{\text{P-Na}}\) = 2.807 Å & L\({}_{\text{P-K}}\) = 3.214 Å & L\({}_{\text{P-Ca}}\) = 2.647 Å \\  & & L\({}_{Z}\) = 0 Å & L\({}_{Z}\) = 0 Å & L\({}_{Z}\) = 0 Å & L\({}_{Z}\) = 0 Å \\  & & \(\Delta\)Q = 0.993 1 e \(\mid\) & \(\Delta\)Q = 0.992 1 e \(\mid\) & \(\Delta\)Q = 0.910 1 e \(\mid\) & \(\Delta\)Q = 1.625 1 e \(\mid\) \\ \cline{2-6}  & & \({}_{\text{Ads}}\) = \(The charge transfers (\(\Delta\rho_{q}\)) between Li-, Na-, K-, and Ca-ions and the P-TpG nanosheet determine the configurations' efficiency. Therefore, we calculated three charge densities of the pristine structure (\(\rho_{S}\)), single adatom (\(\rho_{A}\)), and system compositions (\(\rho_{AS}\)):  
\[\Delta\rho_{q}=\rho_{AS}-\rho_{A}-\rho_{S} \tag{2}\]  
Figure 4 shows the Bader charge analysis [62] results, which gives insight about the charge transfer gradient variation in the presence of ions. We employ VESTA to visualize the variation of the charge transfer gradient. According to Table 1 and Figure 4, the charge transfer efficiencies from a single Li and Na adatom are always over 99%. These results suggest that a single Li and Na atom adsorbs effectively over the single-layer P-TpG. Moreover, according to Bader charge analysis results, upon the adsorption Li and Na adatoms are in the forms of Li+ and Na+, in agreement with the process in batteries, in which metal ions adsorb over the surface. The adsorption energy evaluation--by increasing the adatom coverage--is essential for anode materials.