## 2 Theoretical Framework  
### Density Functional Theory  
Here, we summarize the details of the first-principles based DFT calculations used in this study. The DFT calculations are performed with the Vienna Ab Initio Simulation Package (VASP) [30; 31] using the projector-augmented-wave (PAW) method [32; 33]. For UO\({}_{2}\) the electron exchange and correlation potential is described by the local density approximation (LDA) [34] and the Hubbard +\(U\) model is used for the strongly-correlated U 5f electrons [35]. To be in accordance with our earlier studies [11; 36], we employ the LDA functional for UO\({}_{2}\), and the \(U\) and \(J\) values are set to \(U=4.5\) eV and \(J=0.51\) eV; i.e., \(U-J=3.99\) eV. We adopt the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) functional [37] for silicon and LDA for GaAs to be consistent with reference literature [38; 39]. The energy cut-offs employed are 500 eV for UO\({}_{2}\), 520 eV for Si and 275 eV for GaAs. Defect properties in UO\({}_{2}\) are calculated using \(2\times 2\times 2\) and \(2\times 2\times 3\) supercells with \(2\times 2\times 2\) and \(2\times 2\times 1\) k-point meshes, respectively. Defect calculations are performed at both constant volume and fully relaxed (both in cell volume, shape, and atomic coordinates) conditions. Defects in silicon are simulated in a \(2\times 2\times 2\) and \(3\times 3\times 3\) size supercells with k-point meshes of \(4\times 4\times 4\) and \(3\times 3\times 3\), respectively, while those in GaAs are simulated in a \(3\times 3\times 3\) supercell with a k-point mesh of \(2\times 2\times 2\). The dielectric tensors are important for the correction schemes for the defect formation energies of charged systems and are calculated using density functional perturbation theory [40; 41] as implemented in VASP. The computed bulk properties of interest for UO\({}_{2}\), Si and GaAs are summarized in Table 1.  
We perform convergence tests of the final total energy with respect to the energy cut-off and k-point mesh sizes. The convergence tolerance for forces on each ion is 0.01 eV/A, resulting in total energies converged to less than \(10^{-5}\) eV. To ensure there are no issues associated with the change in plane wave basis and k-point density due to changing cell size, we also calculate the defect relaxation volume of point defects for higher energy cut-off and denser k-point mesh; we find that the relaxation volumes of neutral and charged defects are converged to 0.3-1.8 A\({}^{3}\) (which is within 5% of the relaxation volume) depending on the type of defect. Energy vs. volume calculations of defects are performed starting from the converged wave functions for the minimized defect structure. This is done to avoid the system becoming stuck in the metastable energy state associated with the possible configurations of the localized uranium f-electrons [42].  
Finally, to verify that our results are consistent across DFT codes, we performed calculations of the relaxation volume for defects in GaAs and Si with CASTEP [43], again using GGA-PBE with \"on the fly\"ultrasoft pseudopotentials with a cutoff energy of 450 eV. To ensure similarity with VASP simulations the same k-point grids are employed. The defect relaxation volumes as determined with CASTEP agree with those found with VASP, indicating that the behavior described here is not a consequence of a particular implementation of DFT.