## 4 Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Defects** & \(\Sigma\Delta\Omega^{\prime}\) & **Defect** & \(\Delta\Omega^{\prime}\) \\ \hline \(V_{\text{O}}+\text{O}_{i}^{\prime}\) & 3.26 & \(V_{\text{O}}+\text{O}_{i}^{\prime}\) (OS) & 3.63 \\ \(V_{\text{U}}^{\prime\prime\prime}+4\text{{H}}\) & \(-6.26\) & \(V_{\text{U}}^{\prime\prime}\) & \(-9.07\) \\ \(\text{O}_{i}^{\prime}+2\text{{H}}\)- & \(-3.20\) & \(\text{O}_{i}^{\prime\prime}\) & \(-3.38\) \\ \(V_{\text{O}}^{\prime}+2\text{{e}}^{\prime}\) & 6.52 & \(V_{\text{O}}^{\prime\prime}\) & \(0.56\) \\ \(V_{\text{Ga}}^{\prime}+3\text{{H}}\) & \(-33.83\) & \(V_{\text{Ga}}^{\prime\prime}\) & \(-26.29\) \\ \(V_{\text{Si}}^{\prime}+2\text{{e}}^{\prime}\) & \(-12.39\) & \(V_{\text{Si}}^{\prime\prime}\) & \(-14.69\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the defect relaxation volume (Å\({}^{3}\)) of neutral individual defects computed within a single (one) supercell (labeled OS) or via a sum of defect relaxation volumes of individual charge defects computed in separate supercells. contribution of the change in charge to the volume of the electron reservoir is missing. The change in the volume of the bulk with charge can be attributed to the volume contribution per electron as coming from the change in volume of the electron reservoir, \(\Delta\Omega^{ref}\). Therefore, a complete definition of defect formation volume should be given as:  
\[\Delta\Omega^{f}(X,\,q)=\Delta\Omega^{r}(X,\,q)-q\Delta\Omega^{ref}\pm\Omega_{0} \tag{16}\]  
\(\Delta\Omega^{ref}\) is determined by the slope of the bulk relaxation volume as a function of charge. Values of \(\Delta\Omega^{ref}\) are system dependent and for UO\({}_{2}\), GaAs, and Si we find \(-\)11.6 A\({}^{3}\), \(-\)23.6 A\({}^{3}\) and \(-\)16.14 A\({}^{3}\) per unit charge, respectively. For Si, Windl and [PERSON] [13] reported a value of about \(-\)15 A\({}^{3}\) from the slope of the change in volume of the bulk with net charge, similar to the value we have obtained. One can then recompute defect formation volumes by accounting for \(\Delta\Omega^{ref}\) in all three systems, as summarized in Table 7. Reaction volumes are not affected by \(\Delta\Omega^{ref}\) as the reaction is overall charge neutral and, hence, the change in volume of the electronic reservoir due to charge cancels out exactly. In our discussion so far we have assumed negligible contribution to volume from the potential alignment correction, consistent with the results described in Figure 3a. However, as discussed in Section 3.1.2, the volume correction from potential alignment can be significant, depending on the adopted approach. As mentioned above, the difference in the two potential alignment approaches (Figure 4) comes down to how the volume of the reference bulk calculation is treated. That is, when considering the volume change induced by a charged defect and the associated corrections, do we compare to the original neutral bulk or a bulk cell expanded to the same volume as the defective state? Figure 4 indicates that the major contribution to the correction is associated with adding charge to the bulk. Comparing the change in volume of the electron reservoir \(\Delta\Omega^{ref}\) from Figure 9 with the volume correction from potential alignment correction \(\Delta\Omega^{PA}_{corr}\), we find that both are large (c.f. Figure 4) and