If the energies of-occupied and empty orbitals as functions of N geometric parameters vary in different manners, single determinantal approaches such as the density functional ones may violate the Aufbau principle and the noncrossing rule, i.e., states of the same symmetry may cross in an (N-1)-dimensional parameter subspace. If dominant configuration mixing is simulated by a mixed ensemble density with fractional occupation numbers of the orbitals at the Fermi level, the density functional approaches recover the avoided crossing, as first pointed out by Dunlap and Mei [J. Chem. Phys. 78, 4997 (1983)]. However, present density functional approaches do not recover the nonavoided crossing in (N-2)-dimensional subspaces. The density functional-fractional occupation number approach yields reasonable pathways for the transition from the cyclic to the open ground state of O-3 and SO2 molecules.