## 4 Conclusions  
The energetic stability, geometric structures, and DOS of neutral SiV color centers under H-, O-, or N-terminated diamond (001) surfaces were calculated using DFT methods, under periodic boundary conditions. Our results elicited the following conclusions:  
1. The effects of the termination species on inner diamond atoms decayed to be negligible below the fifth C layer. The formation energies of SiV\({}^{0}\) under H-, O-, or N-terminated diamond (001) surfaces converged to the corresponding value in bulk diamond when they were positioned below the fifth C layer. Additionally, when deeper than the fifth C layer, regardless of H, O, or N termination, the C-C bond lengths reached a stable value, almost the same as that in bulk diamond.
2. Regarding formation energy, it was generally easier for SiV\({}^{0}\) to be embedded in an O-terminated diamond (001) surface when this was above the fifth C layer. Formation energies were almost the same when placed below the fifth C layer among H, O, and N terminations. However, it was similarly easy for SiV\({}^{0}\) to form as both _configuration 1_ (i.e., its original (prior to geometry optimization) Si or V site was positioned in the third C layer, below the dimer rows) and _configuration 2_ (i.e., its original (prior to geometry optimization) Si or V site was positioned in the third C layer, between the dimer rows) at the second and to third layers under N termination, and as _configuration 2_ (i.e., both of its original (prior to geometry optimization) Si and V site were positioned in the third or fourth C layers, between the dimer rows) at the third and fourth layers under H termination as compared with O termination.
3. Si generally showed a lower formation energy than SiV near H-, O-, or N-terminated diamond (001) surfaces. However, SiV centers exhibited rather high energetic stability once formed, as indicated by their binding energies.
4. H termination exhibited a contracting effect on inner surface atoms. For O termination, there was a small expanding effect on inner surface atoms. Similar to H termination, N termination showed a small contracting effect on inner surface atoms.
5. H termination species introduced heavy impurity energy levels deep down in the CBM, and even worse, deep impurity energy levels were introduced not only above the VBM but also below CBM under O termination, in the DOS of diamond (001) surfaces. Our calculations revealed that there were almost no such impurity energy levels above the VBM or below the CBM for N termination, which indicates that an N-terminated diamond (001) surface is a suitable medium for the use of single SiV\({}^{0}\) as a single-photon source.  
Y.P. and W.S. contributed equally to this work; conceptualization, S.S. and H.L.; data curation, Y.P. and W.S.; formal analysis, Y.P. and W.S.; funding acquisition, W.S., S.S. and H.L.; investigation, Y.P. and W.S.; methodology, Y.P. and W.S.; project administration, S.S. and H.L.; resources, Y.P., W.S., S.S., and H.L.; Software, Y.P. and W.S.; Supervision, S.S. and H.L.; Validation, Y.P. and W.S.; Visualization, Y.P. and W.S.; writing--original draft, Y.P. and W.S.; writing--review and editing, S.S. and H.L.  
This research was funded by the International Cooperation Research Project of Shenzhen, grant number GJHZ20180413182004161.  
The authors declare no conflict of interest.