Localized atomic basis set in the projector augmented wave method

We present an implementation of localized atomic-orbital basis sets in the projector augmented wave (PAW) formalism within the density-functional theory. The implementation in the real-space GPAW code provides a complementary basis set to the accurate but computationally more demanding grid representation. The possibility to switch seamlessly between the two representations implies that simulations employing the local basis can be fine tuned at the end of the calculation by switching to the grid, thereby combining the strength of the two representations for optimal performance. The implementation is tested by calculating atomization energies and equilibrium bulk properties of a variety of molecules and solids, comparing to the grid results. Finally, it is demonstrated how a grid-quality structure optimization can be performed with significantly reduced computational effort by switching between the grid and basis representations.

Figure 1

(Color online) The pseudovalence states of iron calculated with PAW and the norm-conserving HGH pseudopotentials. Both methods produce smooth wave functions for the delocalized $4s$ state but the lack of norm conservation allows the short-ranged $3d$ state in PAW to be accurately sampled on a much coarser grid.

Figure 2

(Color online) Basis function generation for the nitrogen $2s$ state: the all-electron orbital of the free atom, the confined all-electron orbital, and the corresponding pseudowave function after applying the inverse PAW transformation. The augmentation sphere and basis function cutoffs are indicated.

Figure 3

(Color online) PBE atomization energies from the G2-1 data set, relative to the grid values. The corresponding mean absolute errors with respect to the grid values are: 1.71 eV (20.4%) for DZ; 0.36 eV (4.45%) for DZP; 0.25 eV (3.02%) for triple zeta polarized; and 0.20 eV (2.44%) for triple zeta double polarized.

Figure 4

(Color online) Deviations in lattice parameter (a), cohesive energy (b), and relative bulk modulus (c) from the converged results. The largest bars have been truncated and are shown with dotted edges. See Table for the precise values.

Figure 5

(Color online) The energy as a function of iteration count (top) as well as CPU time (bottom) in structure optimizations. Shows a grid-based optimization and an LCAO-based structure optimization plus the continuation of the LCAO optimization after switching to the grid representation.