We present a computational scheme for orbital-free density functional theory (OFDFT) that simultaneously provides access to all-electron values and preserves the OFDFT linear scaling as a function of the system size. Using the projector augmented-wav
e method (PAW) in combination with real-space methods we overcome some obstacles faced by other available implementation schemes. Specifically, the advantages of using the PAW method are two fold. First, PAW reproduces all-electron values offering freedom in adjusting the convergence parameters and the atomic setups allow tuning the numerical accuracy per element. Second, PAW can provide a solution to some of the convergence problems exhibited in other OFDFT implementations based on Kohn-Sham codes. Using PAW and real-space methods, our orbital-free results agree with the reference all-electron values with a mean absolute error of 10~meV and the number of iterations required by the self-consistent cycle is comparable to the KS method. The comparison of all-electron and pseudopotential bulk modulus and lattice constant reveal an enormous difference, demonstrating that in order to assess the performance of OFDFT functionals it is necessary to use implementations that obtain all-electron values. The proposed combination of methods is the most promising route currently available. We finally show that a parametrized kinetic energy functional can give lattice constants and bulk moduli comparable in accuracy to those obtained by the KS PBE method, exemplified with the case of diamond.
A combined experimental and theoretical study is presented of the band gap of AlInN, confirming the breakdown of the virtual crystal approximation (VCA) for the conduction and valence band edges. Composition dependent bowing parameters for these quan
tities are extracted. Additionally, composition dependent band offsets for GaN/AlInN systems are provided. We show that local strain and built-in fields affect the band edges significantly, leading to optical polarization switching at much lower In composition than expected from a VCA approach.
We demonstrate that cation-related localized states strongly perturb the band structure of $text{Al}_{1-x}text{In}_x$N leading to a strong band gap bowing at low In content. Our first-principles calculations show that In-related localized states are
formed both in the conduction and the valence band in $text{Al}_{1-x}text{In}_x$N for low In composition, $x$, and that these localized states dominate the evolution of the band structure with increasing $x$. Therefore, the commonly used assumption of a single composition-independent bowing parameter breaks down when describing the evolution both of the conduction and of the valence band edge in $text{Al}_{1-x}text{In}_x$N.
