Local basis sets

The initial step in projection is finding a suitable choice of local auxiliary basis functions. For reasons of simple chemical interpretation, LOBSTER employs minimal basis sets that nonetheless carry the correct nodal behavior in the core region, which is necessary to fit PAW wavefunctions. LOBSTER first came with contracted primitive Slater‐type orbitals (STOs) fitted to atomic functions,14 a reasonable choice for post‐processing bonding information. There are also systems, however, where the bonding situation requires additional basis functions which deviate from those of the corresponding free atoms. In elemental beryllium, for example, its 2p levels are unoccupied in the free atom. For bulk Be, however, the 2p levels do get involved into bonding and define the metallic character, so the Be basis set must also include 2p functions.

For demonstration, let's look at the high‐temperature phase,15 body‐centered cubic beryllium, β‐Be. Its electronic structure was calculated with ABINIT employing the JTH atomic datasets16 and the GGA‐PBE parametrization for exchange and correlation.17 On the LOBSTER side, the original basis set^[14a] and its basis functions (1s and 2s) somehow manage to reconstruct the PAW electronic structure but with an unacceptable absolute charge spilling of roughly 19% (see below for definitions). For analysis, the differences between the original and projected wavefunctions were calculated and an isosurface at 65% of the maximum resulting density was plotted for several bands at Γ. The fourth band showed enormous deviations (Fig. ​(Fig.2,2, left) because the basis lacks an orbital of p‐symmetry, as reasoned before. Adding a 2p function strongly reduces the absolute charge spilling to 1.73%. For comparison, the 65% density‐difference maxima decrease by two orders of magnitude (Fig. ​(Fig.2,2, right). While the functions were added by fitting VASP data, they turn out to be general enough to easily fit other PAW wavefunctions, for example, those calculated by ABINIT, too.

Isosurfaces (in Å⁻³) at 65% of the differences between the ABINIT‐based PAW densities and the LOBSTER‐projected densities for the fourth band of β‐Be at Γ. On the left side, the basis contains only 1s and 2s functions as given by Bunge et al., whereas on the right this basis was enlarged by 2p functions. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Hence, free‐atom calculations in large supercells have been performed for all elements up to Z = 96 (curium) using GGA‐PBE17 as implemented in VASP.18 In nearly all cases up to Z = 80 (mercury) did the new basis functions match the previously given ones well, and they allowed us to numerically fit and add missing (polarization) functions. Obviously, these new functions had to be orthogonalized with regard to the existing functions of the same l azimuthal quantum number to enlarge the basis sets already available in LOBSTER. In the next step, visual evaluation of the calculated PAW atomic orbitals yielded wavefunctions of the desired symmetry and shape; hence they were corroborated as a valid basis choice.

While the basis functions are aligned with the Cartesian axes by default, LOBSTER 2.0.0 supports user‐defined rotations of the basis functions as has been described recently;19 this new feature can be especially useful when isolated, orbital‐wise interactions must be studied.