## 3 Results and Discussion
### Single Vacancy in H-, O-, or N-Terminated C (001) Surfaces  
Single V in a diamond (001) surface is made by removing one C atom (in _L2_ to _L7_). The possible vacancy positions under H, O, or N termination are shown in Figure 2. In the case of Si and V, both interacted with one C atom, and therefore, they had the same possible positions near diamond (001) surfaces under different terminations.  
The formation energy \(E_{f}\) of single V positioned in the various C layers of H-, O-, or N-terminated diamond (001) surfaces, and in a 216-atom bulk diamond, calculated using Equation (1), are illustrated in Figure 4. The formation energies of the single V under the dimer rows (_configuration 1_) and between (_configuration 2_) again conformed to Figure 2.  
As shown in Figure 4, single V positioned at the _L2-1_ site of an N-terminated diamond (001) surface led to the smallest formation energy value of 3.14 eV, whereas all other configurations showed much larger formation energies (higher than 5 eV).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Bond Length (Å)**} \\ \hline  & \multicolumn{2}{c}{**H-Terminated**} & \multicolumn{2}{c}{**N-Terminated**} \\ \cline{2-6}  & **Site 1** & **Site 2** & & **Site 1** & **Site 2** \\ \hline X–X & & & & 1.62 & \\ X–C1 & 1.10 & & 1.50 & 1.53 & \\ C1–C1 & 1.62 & & & & \\ C1–C2 & 1.54 & & 1.54 & 1.52 & 1.59 \\ C2–C3 & 1.53 & 1.57 & 1.54 & 1.52 & 1.57 \\ C3–C4 & 1.52 & 1.56 & 1.54 & 1.52 & 1.57 \\ C4–C5 & 1.52 & 1.56 & 1.54 & 1.54 & \\ C5–C6 & 1.54 & & 1.54 & 1.55 & 1.53 \\ C6–C7 & 1.55 & 1.54 & 1.54 & 1.54 & 1.54 \\ C7–C8 & 1.54 & 1.54 & 1.54 & 1.54 & 1.54 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Bond lengths between different neighboring atoms in various layers for completely H-, O-, or N-terminated diamond (001) surfaces. Within the first column, X is the specific termination species, and C1 represents C atoms in the first C layer, C2 the second C layer, and so forth in a similar fashion. Sites \(I\) and \(2\) are the two different sites within the same layer, as in Figure 2.  
Figure 4: Formation energies of single vacancy in various positions (in _L2_ to _L7_) near a diamond (001) surface under H, O, or N termination and in bulk diamond as a reference. The possible vacancy sites under different surface states are depicted in Figure 2.  
Similar to the case of single Si, for single V positioned below the fifth C layer (including the fifth C layer), their formation energies were close to 6.6 eV under these three termination states. Additionally, using Equation (1), we calculated the formation energy of single V in a 216-atom bulk diamond as being 6.61 eV, which indicated similarities to existing results of 6.65 eV [48] and 6.98 eV [49]. The calculated formation energies of single V in diamond (001) surfaces below the fifth C layer under H, O, or N termination were similar to those in bulk diamond, which indicated that the surface effects declined to nearly negligible levels beneath the fifth C layer under the diamond (001) surface, as confirmed in Table 1.  
As a result, it was found that it is similarly easy, or difficult, for single vacancy to be created within the \(L2\) to \(L7\) C layers under H, O, or N termination, except for a configuration in which V is positioned at the \(L2\)-\(1\) site under a N-terminated surface, which indicated a much smaller formation energy as compared with others.