Gaussian orbitals have the advantage that most integrals involving them can be evaluated analytically. They are a relatively localised basis set that are ideally suited to modelling rapidly varying functions such as wavefunction tail-off away from atomic cores such as oxygen. In this case the basis can easily be increased in the regions of a cluster where it is needed, whereas plane wave methods have to increase the plane waves throughout the supercell to achieve the same effect. However they do not individually approximate solutions to the Kohn-Sham equations in the same way as Slater orbitals. In addition, increasing the number of Gaussian orbitals used to fit the orbitals can quickly lead to `over-completeness'. In this case the system has functions which are very close with high overlaps, and can generate unphysical eigenvalues as a result.
States that are highly delocalised in space, for example weak bonding between distant molecular species, or fragments far from a surface, can suffer from the use of Gaussian orbitals, since they are by their nature localised. However they work well in large molecular clusters where often only a surprisingly small basis is required to accurately model the structure. Using fixed electronic charge means that it is impossible for a system to spontaneously lose or gain electrons. For example, O2- has a single very weakly bound electron that is distributed over a large space; this delocalisation is not correctly modelled by AIMPRO and the preference of the system to lose the electron is manifested in positive occupied eigenvalues.