## 3 Results and Discussion
### Mulliken Bond Populations and Hirsfield Charge  
The bond populations [32] can quantitatively confirm the strengthening or weakening of chemical bonds. After the geometry optimization, the P atom of PV complex finally bonds with six surrounding C atoms and the P atom of PVH complex bonds with four surrounding C atoms. The vacancies of these two complexes eventually disappear. As shown in Tables 5-7, there is an obvious decrease in the P-C bond populations in the PV complex compared with the bonds around the single P atom and PVH complex. This is related to two factors: (1) the increase in the bond length weakens the covalent bond and (2) the lack of electrons involved in the formation of the surrounding bonds. Compared with the bonds around the PVH complex, the lower PV complex bond populations are related to the lack of valence electrons for the P atom during the formation of the six P-C bonds. Because of the H atoms, the P atom only has to bond with five nearby carbon atoms, so the PVH complex bond populations are higher and the C-P bonds around the PVH complex are more stable than those around the PV complex. The H-C bond populations around the PVH complex remain near 1.00, consistent with earlier results that the bond lengths of the H-C bonds remain almost constant. The P-C bond populations around the single P atom are higher than those around the PV and PVH complexes, which is related to their smaller structural deformation and fewer P-C bonds around the P atom. The P-C bond populations in the second C layer around the single P atom and PV complex on the (001) diamond surface are smaller than those around the single P atom and PV complex in other locations, indicating that the covalent bonds around the single P atom and PV complex in the second layer on the (001) surface are weaker than those around the single P atom and PV complex in other locations. The Hirshfeld charge [33] of the doped P and H atom of different complex is also represented in Tables 5-7. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Surface** & **Layer** & **Position of P** & **Position of V** & \multicolumn{4}{c}{**P-C Bond Population**} & \multicolumn{2}{c}{**P Atomic Charge (e)**} \\ \hline \multirow{5}{*}{(001)} & 2 & A & B & 0.47 & 0.47 & 0.38 & 0.55 & 0.55 & 0.22 \\  & 3 & B & B & 0.57 & 0.57 & 0.59 & 0.57 & 0.43 & 0.43 & 0.25 \\  & 4 & A & A & 0.57 & 0.57 & 0.55 & 0.55 & 0.43 & 0.22 \\  & 5 & A & A & 0.60 & 0.60 & 0.53 & 0.53 & 0.56 & 0.52 & 0.22 \\  & 6 & A & C & 0.53 & 0.57 & 0.56 & 0.55 & 0.55 & 0.53 & 0.23 \\ \hline \multirow{5}{*}{(111)} & 2 & A & A & 0.58 & 0.58 & 0.56 & 0.53 & 0.53 & 0.53 & 0.23 \\  & 3 & A & A & 0.58 & 0.58 & 0.56 & 0.53 & 0.53 & 0.53 & 0.23 \\ \cline{1-1}  & 4 & A & B & 0.54 & 0.58 & 0.53 & 0.57 & 0.51 & 0.50 & 0.23 \\ \cline{1-1}  & 5 & A & B & 0.58 & 0.58 & 0.54 & 0.54 & 0.51 & 0.50 & 0.23 \\ \cline{1-1}  & 6 & A & B & 0.58 & 0.58 & 0.54 & 0.54 & 0.51 & 0.51 & 0.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Atomic charges and electron bond population of the PV complex with the lowest formation energy in each layer. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Surface** & **Layer** & **Impurity Position** & \multicolumn{2}{c}{**P-C Bond Population**} & \multicolumn{2}{c}{**P Atomic Charge (e)**} \\ \hline \multirow{5}{*}{(001)} & 2 & A & 0.58 & 0.58 & 0.46 & 0.51 & 0.24 \\  & **A** & 0.83 & 0.83 & 0.79 & 0.79 & 0.31 \\  & **B** & 0.83 & 0.80 & 0.82 & 0.82 & 0.35 \\  & **A** & 0.86 & 0.86 & 0.83 & 0.83 & 0.32 \\  & **B** & 0.80 & 0.80 & 0.84 & 0.85 & 0.34 \\  & **5** & **A** & 0.82 & 0.84 & 0.84 & 0.84 & 0.33 \\  & **6** & **A** & 0.83 & 0.84 & 0.84 & 0.85 & 0.33 \\ \hline \multirow{5}{*}{(111)} & 2 & A & 0.81 & 0.81 & 0.81 & 0.82 & 0.36 \\  & **3** & **A** & 0.82 & 0.82 & 0.83 & 0.84 & 0.34 \\ \cline{1-1}  & **4** & **A** & 0.85 & 0.85 & 0.85 & 0.82 & 0.33 \\ \cline{1-1}  & **5** & **A** & 0.82 & 0.82 & 0.83 & 0.85 & 0.33 \\ \cline{1-1}  & **6** & **A** & 0.83 & 0.83 & 0.83 & 0.84 & 0.33 \\ \hline \hline \end{tabular}
\end{table}