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We investigate the structure of the one-body Reduced Density Matrix (1RDM) ofthree electron systems, i.e. doublet and quadruplet spin configurations,corresponding to the smallest interacting system with an open-shell groundstate. To this end, we use Configuration Interaction (CI) expansions of theexact wave function in Slater determinants built from natural orbitals in afinite dimensional Hilbert space. With the exception of maximally polarizedsystems, the natural orbitals of spin eigenstates are generally spin dependent,i.e. the spatial parts of the up and down natural orbitals form two differentsets. A measure to quantify this spin dependence is introduced and it is shownthat it varies by several orders of magnitude depending on the system. We alsostudy the ordering issue of the spin-dependent occupation numbers which haspractical implications in Reduced Density Matrix Functional Theory minimizationschemes when Generalized Pauli Constraints are imposed and in the form of theCI expansion in terms of the natural orbitals. Finally, we discuss theaforementioned CI expansion when there are GPCs that are almost "pinned".

Structure of the first order Reduced Density Matrix in three electron systems: A Generalized Pauli Constraints assisted study