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).