  Functionals of the one-body reduced density matrix (1-RDM) are routinely
minimized under Coleman's ensemble $N$-representability conditions. Recently,
the topic of pure-state $N$-representability conditions, also known as
generalized Pauli constraints, received increased attention following the
discovery of a systematic way to derive them for any number of electrons and
any finite dimensionality of the Hilbert space. The target of this work is to
assess the potential impact of the enforcement of the pure-state conditions on
the results of reduced density-matrix functional theory calculations. In
particular, we examine whether the standard minimization of typical 1-RDM
functionals under the ensemble $N$-representability conditions violates the
pure-state conditions for prototype 3-electron systems. We also enforce the
pure-state conditions, in addition to the ensemble ones, for the same systems
and functionals and compare the correlation energies and optimal occupation
numbers with those obtained by the enforcement of the ensemble conditions
alone.
