Some aspects of the adiabatic connection method are studied for two-particle spherically symmetric systems. Ground-state wave functions that are constrained by means of a set of moments to have the same density as a corresponding fully interacting system are obtained for noninteracting or partially interacting systems. Local one-body potentials that support these constrained wave functions are generated using a simple method. We examine an interacting two-particle system with a parameter-dependent one-body potential, which for a particular value of that parameter exhibits an intersection between the S-3 and the P-3 states, whereas the 2s and 2p eigenvalues of the corresponding Kohn-Sham potentials do not intersect along with the total energies. These results show that there do exist cases where occupying the orbitals from below in energy may not lead to the ground state, and that the inherent assumptions behind the adiabatic connection can sometimes be violated. (C) 2004 American Institute of Physics.