On the importance of local orbitals using second energy derivatives for d and f electrons

The all-electron linearized augmented plane wave (LAPW) methods are among the most accurate to solve the Kohn-Sham equations of density functional theory for periodic solids. In the LAPW methods, the unit cell is partitioned into spheres surrounding the atoms, inside which the wave functions are expanded into spherical harmonics, and the interstitial region, where the wave functions are expanded in Fourier series. Recently, Michalicek et al. (2013) reported an analysis of the so-called linearization error, which is inherent to the basis functions inside the spheres, and advocated the use of local orbital basis functions involving the second energy derivative of the radial part (HDLO). In the present work, we report the implementation of such basis functions into the WIEN2k code, and discuss in detail the improvement in terms of accuracy. From our tests, which involve atoms from the whole periodic table, it is concluded that for ground-state properties (e.g., equilibrium volume) the use of HDLO is necessary only for atoms with d or f electrons in the valence and large atomic spheres. For unoccupied states which are not too high above the Fermi energy, HDLO systematically improve the band structure, which may be of importance for the calculation of optical properties.