All-electron method refers to electronic structure methods that consider all electrons in the system explicitly in solving for the wave functions (or electron densities). This is in contrast to the pseudopotential method where the influence of inner-shell electrons is taken into account through an effective potential (i.e., pseudopotential). All-electron methods are, in general, more accurate than pseudopotential methods. An additional merit is that all-electron methods are more suited for simulation of X-ray spectroscopy which involve inner-shell electrons. On the other hand, the calculation cost is higher than the pseudopotential method due to the larger number of electrons under consideration. Software codes employ various measures for efficiently handling steep variations in the inner-shell orbitals and gradual changes in interstitial regions at the same time.
Atom-localized basis/Gaussian basis
Many calculation codes expand the wave function using functions localized around atoms. Usually, numerical solutions to the Kohn-Sham equation for the atom or atom-localized Gaussians are used. Since the wave function in molecules and solids usually resemble a linear combination of atomic wave functions, atom-localized basis sets can describe the wave function accurately using a much smaller number of basis functions compared to the plane wave basis set. However, since atom-localized basis functions are not orthogonal in general, the improvement with increasing basis size is not always monotonic. Moreover, atom-localized basis sets are usually unsuitable for describing systems where electrons exist at positions away from atoms (such as in electrides or floating electron states).