  We investigate the structure of the one-body Reduced Density Matrix (1RDM) of
three electron systems, i.e. doublet and quadruplet spin configurations,
corresponding to the smallest interacting system with an open-shell ground
state. To this end, we use Configuration Interaction (CI) expansions of the
exact wave function in Slater determinants built from natural orbitals in a
finite dimensional Hilbert space. With the exception of maximally polarized
systems, the natural orbitals of spin eigenstates are generally spin dependent,
i.e. the spatial parts of the up and down natural orbitals form two different
sets. A measure to quantify this spin dependence is introduced and it is shown
that it varies by several orders of magnitude depending on the system. We also
study the ordering issue of the spin-dependent occupation numbers which has
practical implications in Reduced Density Matrix Functional Theory minimization
schemes when Generalized Pauli Constraints are imposed and in the form of the
CI expansion in terms of the natural orbitals. Finally, we discuss the
aforementioned CI expansion when there are GPCs that are almost "pinned".
