Ab initio electron density functions of dilithium computed at the RHF, MP2, and CISD levels with extended basis sets and optimized bond lengths were analyzed topologically. Nonnuclear attractors were found at all levels. The nonnuclear attractor can be readily explained by the nodal properties of the valence electron density function. The analysis of their origin suggests that they might occur in long bonds of low polarity. Specific examples are cited that allow one to test this prediction. The existence of nonnuclear attractors shows that the theory of atoms in molecules does not invariably define a one-to-one relation between topologically defined basins and atoms. While the theory of atoms in molecules does not rely on such a relation, this requirement needs to be met for a chemically useful definition of atomic populations. Aside from this conclusion, the results point up a more general practical limitation of the partitioning scheme. If the electron density functions are extremely flat in the bonding region, whether a nonnuclear attractor is present or not, parameters of the topological theory that strongly depend on the locations of the partitioning surfaces might be greatly affected by the choice of the theoretical model. The crucial role is emphasized of the curvature in the direction of the bond path in judging the quality of the topological parameters of bonds of low polarity.