On the interpretative aspects of second‐order reduced density matrices

A division of the 2-matrix Γ, for a system of N identical fermions, into 2 parts is proposed in such a way that Γ has the same 1-matrix γ as does Γ and Γ has a vanishing 1-matrix (and therefore vanishing trace). This is accomplished by evaluating the natural spin orbital (NSO) occupation numbers Γ of Γ from (where the ni are NSO occupation numbers of γ); and letting γ0 have the same NSO's as does γ. The physical interpretation of Γ should be easier with this decomposition, since Γ is completely determined by γ and has a Hartree-Fock-like form, while Γ corrects the pair density of Γ without disturbing its 1-density.