Bulk and surface properties of metals by full-charge-density screened Korringa-Kohn-Rostoker calculations

The full-charge-density screened Korringa-Kohn-Rostoker method is described and applied to calculate bulk and surface energies of transition metals. It is demonstrated that due to a truncated angular momentum expansion of the shape functions, the otherwise ultimate freedom of adding a constant to the potential in all space leads, in particular close to the cell boundaries, to potentials of fairly different shapes. Thus a dependence on this constant potential shift emerges for the calculated bulk total energies, equilibrium volumes, and bulk moduli, as well as for the surface energies and the work functions. A reasonable choice for the constant shift seems to set the bulk potential at the muffin-tin radius to zero. By making this choice the calculations give results that are in very good agreement to those calculated by other full-charge-density or full-potential methods.

Figure 1

${\upsilon }_{00}\left(r\right)∕\sqrt{4\pi }$ (solid line) and the resulting full-crystal potential (dashed line) for fcc Cu along a nearest-neighbor direction. The potential is shifted to $-0.8\mathrm{Ry}$ at the muffin-tin radii.

Figure 2

Full-crystal potential for Cu bulk in the nearest-neighbor direction for different shift parameters. Solid line: $V_{\mathrm{MT}}=-0.8\mathrm{Ry}$. Dashed line: $V_{\mathrm{MT}}=+0.2\mathrm{Ry}$. Dotted line: $V_{\mathrm{MT}}=0.0\mathrm{Ry}$.

Figure 3

Relative change of the total energy, $\mathrm{\Delta }{E}_{\mathrm{tot}}=E_{\mathrm{tot}}-E_{\mathrm{tot}}^{\max }$, of bulk Cu and Mo with respect to the potential at the muffin-tin radius, $V_{\mathrm{MT}}$.

Figure 4

Total energy of bulk Cu as a function of the lattice constant $a$ for different values of the potential at the muffin-tin radius, $V_{\mathrm{MT}}$ (in rydberg units).

Figure 5

Equilibrium lattice parameter $a_0$ and bulk modulus $B$ of bulk Cu as a function of the potential at the muffin-tin radius, $V_{\mathrm{MT}}$.

Figure 6

Surface energies $\gamma$ for (100) and (111) surfaces of Cu as calculated by using the FCD method and the ASA as a function of the potential at the muffin-tin radius, $V_{\mathrm{MT}}$.

Figure 7

Anisotropy ratio $\gamma \left(100\right)∕\gamma \left(111\right)$ of Cu and Mo as a function of the potential at the muffin-tin radius, $V_{\mathrm{MT}}$. The ideal value of $4∕3$ is indicated by the solid horizontal line.

Figure 8

Work functions for $\mathrm{Cu}\left(100\right)$ and $\mathrm{Cu}\left(111\right)$ as calculated by using the FCD method and the ASA as a function of the potential at the muffin-tin radius, $V_{\mathrm{MT}}$.

Figure 9

Work functions for (100) and (111) surfaces of Cu and Mo as a function of the potential at the muffin-tin radius, $V_{\mathrm{MT}}$.

Figure 10

Angular momentum convergence of the work function of fcc $\mathrm{Cu}\left(100\right)$ as calculated using the FCD scheme using $V_{\mathrm{MT}}=0$.