## 3 Results
### Electronic Structure  
The partial density of states (PDOS) are shown for select Pu atoms within the structure with varying distances from the Ga atom (Table 3) for the Pu-Ga structures with no defects and defects. First, we will discuss the PDOS with no defects shown in Figure 8, where Pu-1 and Pu-2 are atoms that are 1 nn distance from the Ga and Pu-3 is from a nearest neighbor shell further away in order to gauge the effects on Pu near or far from the Ga. Clearly, in Figure 8, the Ga 4p states are located in the same energy region and the Pu 5f states exhibit similar features for all three concentrations. The PDOS for Pu-1 has an increased 5f intensity at \(\sim\)0.4 eV as compared to Pu-2 and Pu-3. Due to the induced tetragonal distortion from the Ga, Pu-1 is slightly closer to the Ga atom than Pu-2, and this enables Ga 4p and Pu 6d hybridization at approximately 2.25 eV below the Fermi energy. Not shown is the fact that the Pu 6d orbital states allow for hybridization with the Ga 4p states where the Pu 5f orbital states are heavily weighted at the Fermi energy. Another note is that the Ga 4p\({}_{\text{y}}\) and 4p\({}_{\text{z}}\) states are equivalent in the 0.926 at. % Ga concentration apparently due to the tetragonal distortion that occurs in the y-z plane. Increasing the Ga content in the structure, the Ga 4p\({}_{\text{y}}\) and 4p\({}_{\text{z}}\) states shift from one another but have similar structure, and the Pu 6d states decrease in intensity with an emergence of higher intensity 6d state in the Pu-3 atom at an energy of around \(-\)2 eV, indicating competing interactions of the Ga atoms within the structure. It has been previously calculated that when spin-orbit coupling is taken into account, the Pu-Ga interactions are still dominated by Pu 6d and Ga 4p hybridization [25]. The importance of spin as part of the electronic correlation is highlighted further in the Supplementary Materials. In Figure S1, when the PDOS is calculated for a pure \(\delta\)-Pu (at the AFM theoretical lattice constant) for a non-magnetic configuration, the Pu 5f electrons intensity significantly increases right below the Fermi energy in contrast with the AFM configuration. This causes the Pu 6d states to shift to higher energies. Hence, this changes the bonding mechanism when Ga is introduced into the lattice where the Ga 4p states hybridizes with the Pu 5f states when considering a non-magnetic configuration in the AFM structure (Figure S2). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Pu-Ga Distance (Å)**} & \multicolumn{3}{c}{**Pu-vacancy Distance (Å)**} \\ \hline
**at. \% Ga** & **Defect Distance to Ga** & **Pu-1** & **Pu-2** & **Pu-3** & **Pu-1** & **Pu-2** & **Pu-3** \\ \hline
0.926 & No Defect & 3.07 & 3.14 & 10.58 & - & - & - \\
1.852 & No Defect & 3.08 & 3.18, 3.18 & 8.47 & - & - & - \\
2.778 & No Defect & 3.06 & 3.16, 3.15 & 8.42 & - & - & - \\
0.926 & 1 nn & 3.07 & 3.88 & 10.60 & 2.57 & 3.10 & 10.59 \\
1.852 & 1 nn & 3.06 & 3.10, 3.17 & 8.48 & 2.53 & 3.16 & 10.59 \\
2.778 & 1 nn & 3.10 & 5.40 & 8.39 & 2.97 & 3.00 & 10.57 \\
2.788 & 1 nn bw 2 Ga & 3.03 & 3.12, 3.19 & 8.39 & 3.03 & 2.99 & 10.57 \\
2.788 & 2 nn bw 3 Ga & 3.13 & 5.49 & 8.39 & 3.12 & 3.19 & 10.54 \\
2.788 & 4 nn & 3.02 & 5.53 & 5.45 & 3.79 & 1.94 & 5.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Pu-Ga and Pu-vacancy distances in various at. % Ga concentrations and defect structures represented in the partial density states in Figures 8–10. Note: bond lengths are contracted from experimental bond lengths due to a contracted lattice at 0K as shown in Figure 2.  
With the introduction of a mono-vacancy at the first nearest neighboring distance from the Ga, there is minimal change in the Ga 4p states, while there are distinct changes in the Pu 5f and 6d states (Figure 9). For instance, in the 0.926 at.