Projector-basis technique and Car-Parrinello scaling in mixed-basis, linearized-augmented-plane-wave, and extended linearized-augmented-plane-wave electronic-structure methods

It is shown that by exploiting auxiliary or projector-basis functions as a local representation of plane waves, highly efficient implementations of several band-structure techniques can be obtained. Examples are nonlocal pseudopotential methods with (1) plane-wave and (2) mixed (plane waves plus local orbitals) basis sets, and the all-electron (3) linearized-augmented-plane-wave and (4) extended linearized-augmented-plane-wave methods. The computation in all of the proposed techniques scales as ${\mathit{N}}^2$ln(N), where N is the number of atoms in the unit cell. Early calculations are presented for the plane-wave and mixed-basis approaches.