Representability of Bloch states on Projector-augmented-wave (PAW) basis sets

Design of small, yet `complete', localized basis sets is necessary for an efficient dual representation of Bloch states on both plane-wave and localized basis\footnote{Agapito, Ferretti, Calzolari, Curtarolo and Buongiorno Nardelli, PRB {\bf 88}, 165127 (2013).}. Such simultaneous dual representation permits the development of faster more accurate (beyond DFT) electronic-structure methods for atomistic materials (e.g. the ACBN0 method\footnote{Agapito, Curtarolo and Buongiorno Nardelli, \texttt{arXiv:1406.3259 [cond-mat.str-el]}}.) by benefiting from algorithms (real and reciprocal space) and hardware acceleration (e.g. GPUs) used in the quantum-chemistry and solid-state communities. Finding a `complete' atomic-orbital basis (partial waves) is also a requirement in the generation of robust and transferable PAW pseudopotentials. We have employed the atomic-orbital basis from available PAW data sets, which extends through most of the periodic table, and tested the representability of Bloch states on such basis. Our results show that PAW data sets allow systematic and accurate representability of the PAW Bloch states, better than with traditional quantum-chemistry double-zeta- and double-zeta-polarized-quality basis sets.