**Figure 7.** *Calculation of the diamond lattice constant in the case of PBE0 and PBE.*


#### **Table 5.**

*Resulting Γ- Γ and Γ-X gaps obtained for PBE and PBE0 in eV.*

convergent properties such as the density of states in smaller unit cells. Oscillations in the lattice constant are typical, and it can be difficult to achieve high levels of convergence. Best practice is to use the same k-point sampling grid in the calculations when possible and dense (high number of k-points) otherwise. It is important to verify convergence in these cases. The larger the unit cells, the smaller the number of kpoints required. For example, if a 1 1 1 fcc unit cell shows convergent results in a 12 12 12 k-point grid, then a 2 2 2 fcc unit cell would show the same level of convergence with a 6 6 6 k-point grid. In other words, doubling the unit cell vectors results in a halving of the number of k-points [28].

Sometimes k-points are described as k-points per reciprocal atom. For example, a 12 12 12 k-point grid for a primitive fcc unit cell corresponds to 1728 k-points per reciprocal atom. A 2 2 2 fcc unit cell has eight atoms (i.e., 0.125 reciprocal atoms), and thus, a 6 6 6 k-point grid has 216 k-points, (216/0.125 = 1728 k-points per reciprocal atom) [28].

In this k-point convergence study, we use an 8 8 8 k-point grid on a unit cell containing two atoms, resulting in 1024 k-points per reciprocal atom.
