## 3 Results and Discussion
### Single Neutral Silicon Vacancy in the H-, O-, or N-Terminated C (001) Surfaces
#### 3.3.3 Geometric Structures  
In this section we will investigate the geometric structures by analyzing the bond lengths and bond populations. Positive and negative bond population values indicate bonding and antibonding states between atoms, respectively. A value of zero stands for a completely ionic bond, and values greater than zero indicate increasing levels of covalent interaction. Therefore, a high positive value indicates a covalent bond, while a low positive value corresponds to an ionic interaction [53; 54]. Table 3 indicates the bond lengths and bond populations of Si-C bonds of SiV\({}^{0}\) in bulk diamond and fully H-, O-, or N-terminated diamond (001) surfaces. These selected SiV\({}^{0}\) near the surfaces were the three with the lowest formation energy, i.e., in the third to fourth layers (_configuration 2_) under H termination; in the second to third layers under O termination; and in the second to third layers (_configuration 2_) under N termination. We calculated the distance between Si and C in bulk diamond as being 1.98 A, which agreed well with the existing studies (1.97 A [55] and 1.944 A [56]).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Bond** & **Bond Length** (Å) & **Bond Population** \\ \hline \multirow{2}{*}{**Bulk**} & & & 0.54 \\  & & & 0.55 \\  & & & 0.57 \\ \hline \multirow{3}{*}{**H-terminated**} & Si–C2 & 1.85 & 0.68 \\  & Si–C3 & 2.02 & 0.65 \\  & Si–C4 & 1.94 & 0.70 \\  & Si–C5 & 2.37 & 0.22 \\ \hline \multirow{3}{*}{**O-terminated**} & Si–C1 & 2.08 & 0.45 \\  & Si–C2 & 1.97 & 0.49 \\ \cline{1-1}  & Si–C3 & 1.98 & 0.57 \\ \cline{1-1}  & Si–C4 & 1.91 & 0.63 \\ \hline \multirow{3}{*}{**N-terminated**} & Si–C1 & 1.94 & 0.57 \\ \cline{1-1}  & Si–C2 & 2.01 & 0.54 \\ \cline{1-1}  & Si–C3 & 1.96 & 0.64 \\ \cline{1-1}  & Si–C4 & 2.19 & 0.40 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Bond lengths and bond populations of the Si–C bonds of SiV\({}^{0}\) for completely H-, O-, or N-terminated diamond (001) surfaces as compared with those in bulk diamond. C1 to C5 represent C atoms in the \(L1\) to \(L5\) C layer from the surface.  
As shown in Table 3, the bond length of Si-C2 under H termination was 1.85 A, lower than its corresponding value of 1.98 A in bulk diamond, and its bond population was 0.68, higher than in bulk diamond. Both of these results indicate that Si-C2 possessed stronger covalent interaction in this instance as compared with bulk diamond. Additionally, in this instance, Si-C5 had a bond length of 2.37 A, much longer than in bulk diamond, and its bond population of 0.22 was much smaller than in bulk diamond, which indicates that this Si-C5 was weaker than in bulk diamond. The other bonds within these two boundaries showed similar values to those in bulk diamond. Accordingly, we can observe a contracting effect of H termination on inner surface atoms.  
For the O-terminated surface, Si-C1 showed a longer bond length of 2.08 A as compared with bulk diamond, and its bond population was 0.45, which was smaller than in bulk diamond. These results indicate weaker covalent interaction than that between Si-C in bulk diamond. Furthermore, Si-C4 was equal to 1.91 A, which was shorter than that in bulk diamond and possessed a larger bond population of 0.63 than that in bulk. The other bonds between were similar to those in bulk diamond. These results indicate that O termination species exhibits a small expanding effect on inner surface atoms.  
Under N termination, Si-C1 indicated a bond length value of 1.94 A, shorter than in bulk diamond. Additionally, Si-C4 had a longer bond length of 2.19 A than 1.98 A in bulk diamond, and a smaller bond population of 0.40 as compared with bulk diamond. The other bonds between showed similar properties to those in bulk diamond. The above results indicate a small contracting effect of N termination on inner surface atoms.