Augmented functions: linear methods
The great disadvantage of augmentation is that the basis functions are energy dependent, so that matching conditions must be satisfied separately for each eigenstate at its (initially unknown) eigenenergy. This leads to non-linear equations that make such methods much more complicated than the straightforward linear equations for the eigenvalues of the hamiltonian expressed in fixed energy-independent bases such as plane waves, atomic orbitals, gaussians, etc. Linearization is achieved by defining augmentation functions as linear combinations of a radial function ψ(Ev, r) and its energy derivative evaluated at a chosen fixed energy Ev. In essence, ψ(Ev, r) and form a basis adapted to a particular ...