Green’s function method for elimination of the spurious multipole interaction in the surface/interface slab model

When modeling a surface/interface using a slab geometry that imposes the periodic boundary condition, there are spurious dipole and higher-order multipole interactions with the image slabs. Here, we show that the effective screening medium (ESM) method [M. Otani and O. Sugino, Phys. Rev. B 73, 115407 (2006)] can deal with such electrostatic issues rigorously in a slab calculation. After benchmark calculations for a hypothetical water layer, we show that there is an error in the total energy caused by the multipole interaction, but this can be treated efficiently using the ESM method. The accurate treatment of the electrostatic interaction is essential for performing large-scale surface/interface calculations.

Figure 1

(Color online) Convergence of the total energy (in eV) of the ${\text{H}}_2\text{O}$ layer for the dipole correction and ESM methods. The values depicted are decimal logarithms of the difference between the total energy calculated at each self-consistency step $\left(E\right)$ and the converged value $\left(E_0\right)$.

Figure 2

(Color online) Hypothetical NaCl sheets used in the calculation: (a) $\left(2\times 1\right)$ and (b) $\left(4\times 1\right)$ unit cells.

Figure 3

(Color online) Total energy (per unit cell) as a function of the cell length in the direction normal to the surface $\left(L_z\right)$ for (a) $\left(2\times 1\right)$ and (b) $\left(4\times 1\right)$ cells.

Figure 4

(Color online) ${\mathit{g}}_{\parallel }$ components of the electrostatic potential $V$ for the $\left(4\times 1\right)$ cell. ${\mathit{g}}_{\parallel }$’s are expressed in terms of the basic reciprocal lattice vectors.