FPLAPW

FPLAPW stands for Full-Potential Linearized Augmented Plane Wave, an all-electron method used in electronic-structure calculations within density functional theory for solids and molecules. It belongs to the family of augmented plane-wave methods and is distinguished by a full-potential treatment, avoiding the spherical approximation to the potential that is common in simpler approaches. The method is valued for its accuracy in handling complex materials and heavy elements.

In FPLAPW, space is partitioned into non-overlapping atomic spheres around each nucleus and the interstitial region between them. The basis functions are plane waves in the interstitial region and atom-centered radial functions multiplied by spherical harmonics inside the spheres. The radial functions solve the radial equation for the local potential, and the plane waves and spherical solutions are matched at the sphere boundaries, yielding a complete basis for the Kohn-Sham states. The approach is linearized in energy to yield a tractable eigenvalue problem, and Local Orbitals can be added to improve the description of semicore and tightly bound states.

FPLAPW can incorporate spin polarization and spin-orbit coupling, and it is recognized for delivering high-precision results for total energies, electron densities, and band structures. It is widely used in solid-state physics and materials science, particularly for systems with transition metals, heavy elements, surfaces, and complex crystal structures. Notable software packages implementing FPLAPW include WIEN2k and ELK.

Compared with methods that employ approximations to the potential, FPLAPW is computationally intensive, especially for large systems, but provides rigorous all-electron results and serves as a benchmark standard in density functional theory calculations.