Completeness of the exact muffin-tin orbitals: Application to hydrogenated alloys

We investigate the basis set convergence of the exact muffin-tin orbitals by monitoring the equation of state for Al, Cu, and Rh calculated in the conventional face-centered-cubic lattice (str-I) and in a face-centered-cubic lattice with one atomic and three empty sites per primitive cell (str-II). We demonstrate that three (spd) muffin-tin orbitals are sufficient to describe Al in both structures, but for str-II Cu and Rh at least five (spdfg) orbitals are needed to get converged equilibrium Wigner-Seitz radius (within <= 0.8%) and bulk modulus (<= 3.3%). We ascribe this slow convergence to the nearly spherical densities localized around the Cu and Rh atoms, which create strongly asymmetric charge distributions within the nearest cells around the empty sites. The potential sphere radius dependence of the theoretical results for structure str-II is discussed. It is shown that a properly optimized overlapping muffin-tin potential in combination with the spdfg basis yields acceptable errors in the equilibrium bulk properties. The basis set convergence is also shown on hydrogenated Sc and Sc-based alloys.