In quantal density functional theory (Q-DFT), any nondegenerate or degenerate ground or excited state of a system of electrons may be mapped to one of noninteracting fermions such that the equivalent density, energy, and ionization potential are obtained. As these model fermions are noninteracting, their effective potential energy, a local (multiplicative) operator, is the same for a particular state of the model system. The state of the noninteracting fermions, however, is arbitrary in that they could be in a ground or excited state. Hence, within Q-DFT, there exist, in principle, an infinite number of local effective potential energy functions that can generate the same density as that of the interacting electrons. In this article, we demonstrate this state arbitrariness by mapping a (nondegenerate) ground state of the Hookean atom to two different noninteracting fermion systems: one in a singlet ground state (1s2) and the other in a singlet first excited state (1s2s). In each case, the density and energy determined are equivalent to that of the Hookean atom in the ground state, with the highest occupied eigenvalues of the model system being the negative of the ionization potential. The contrast with the mapping within traditional Kohn–Sham and generalized adiabatic connection Kohn–Sham density functional theories is also made. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
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