The orbital occupation, which is the centerpiece of both self-interaction and several metal-insulator transition analyses, as well as of the local density or generalized gradient approximation with a Hubbard term, is not well defined, in the sense that it is partially ambiguous. A general treatment can be applied to both strongly and weakly correlated systems. When it is applied to an intermediate- and partially filled band within of the host semiconductor gap whose width is less than the semiconductor gap, the original single band can either split as in a Mott transition or not. The former situation is usual and almost always generalized. However the latter also takes place and results from a dilution effect of the self-interaction where a large orbital correlation is reduced if there are other orbital contributions with lower self-interaction in the band. The key is in the choice of the subspace of correlated orbitals. This effect can neither be ignored nor discarded for those systems where there is a substantial mix of states. Examples of these behaviors will be presented and compared to other results. Moreover, the combination of different Hubbard terms acting on different atomic state subspaces can also be used to correct the spurious self-interaction of the bands and the gap underestimation. The relationship between these terms applied to different subspaces of correlated electrons will be presented.