Augmented functions: APW, KKR, MTO
Augmentation provides a method of constructing a basis that is in some ways the “best of both worlds:” the smoothly varying parts of the wavefunctions between the atoms represented by plane waves or other smoothly varying functions, and the rapidly varying parts near the nuclei represented as radial functions times spherical harmonics inside a sphere around each nucleus. The solution of the equations becomes a problem of matching the functions at the sphere boundary. The original approach is the augmented plane wave (APW) method of Slater, which leads to equations similar to the pseudopotential and OPW equations, but with matrix elements of a more complicated, energy-dependent potential operator. ...