Pack-Monkhorst grid

The values of the total energy per cell reported in Table 1 as a function of the shrinking factor show that the size of the Pack-Monkhorst grid is related to the extent of the conduction-valence band gap (16.02, 6.25, 0 eV for the three cases considered, respectively). 

Pack and Monkhorst °° have suggested that a commensurate grid of points is a suitable option for this purpose. In their method, the grid size depends on a parameter, the shrinking factor s, that specifies how many equidistant k points must be taken along each direction of bi, hx, and bs inside one reciprocal lattice unit cell so that the total number of points in the grid, s, is equal to s , with n denoting the order of periodicity ( = 3 for three-dimensional crystals). 

Periodic conventional DFT was used in this study [47]. The calculations were performed using VASP [55, 56] with GGA [107] and using an energy cutoff of 270 eV (defined Irom plane wave convergence test performed on bulk NiO) and ultrasoft pseudopotenlials [108, 109]. The Brillouin zone integrations have been performed using a Monkhorst-Pack grid... 

DFT method SIESTA, GGA-PBE, 2x2 unit cell, four-layer slab, 5x5x1 k-points in the Monkhorst-Pack grid and energy cutoff of200 Ry. Corrected for thermodynamic... 

In a previous study, Warren et al. [37] have selected a finite 2x2x2 Monkhorst-Pack set of irreducible /c-points for all their configurations. However, because the variation of geometry induced by disorder has an important influence on the generation of an optimum k-points grid, different configurations must be treated with the same accuracy. Thus, only the first Brillouin zone centre point was considered in this study to integrate the DFT derived properties. 

A plane wave basis set with an orbital cutoff distance of 3.9 A was used. All-electron calculations and a double numerical basis set with polarization functions (DNP) were employed. Wave function integration in reciprocal space was performed via fine grid sampling of k points with a separation of 0.02 A . For the calculation of the density of states (DOS), a 5 X 8 X 3 Monkhorst-Pack grid was used. Charge transfer was calculated based on the Mulliken Population Analysis (MPA) (Mulliken 1955). 

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