Wavefunction augmented plane wave

The APW (augmented plane wave) method was devised by Slater (1937,1965), and is based on the solution of the Schrodinger equation for a spherical periodic potential using an expansion of the wavefunction in terms of solutions of the atomic problem near the nucleus, and an expansion in plane waves outside a predetermined sphere in the crystal. 

Augmented Plane Waves (APW) This method, introduced by Slater [45], consists of expanding the wavefunctions in plane waves in the regions between the atomic spheres, and in functions with spherical symmetry within the spheres. Then the two expressions must be matched at the sphere boundary so that the wave-functions and their first and second derivatives are continuous. For core states, the wavefunctions are essentially unchanged within the spheres. It is only valence states that have significant weight in the regions outside the atomic spheres. 

The projector augmented-wave (PAW) DFT method was invented by Blochl to generalize both the pseudopotential and the LAPW DFT techniques [81]. PAW, however, provides all-electron one-particle waveflmctions not accessible with the pseudopotential approach. The central idea of the PAW is to express the all-electron quantities in terms of a pseudo-wavefunction (easily expanded in plane waves) term that describes interstitial contributions well, and one-centre corrections expanded in terms of atom-centred functions, that allow for the recovery of the all-electron quantities. The LAPW method is a special case of the PAW method and the pseudopotential formalism is obtained by an approximation. Comparisons of the PAW method to other all-electron methods show an accuracy similar to the FLAPW results and an efficiency comparable to plane wave pseudopotential calculations [82. 83]. PAW is also formulated to carry out DFT dynamics, where the forces on nuclei and wavefunctions are calculated from the PAW wavefunctions. (Another all-electron DFT molecular dynamics technique using a mixed-basis approach is applied in [84]. )... 

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