Comment on "nonuniqueness of algebraic first-order density-matrix functionals"

Wang and Knowles (WK) [Phys. Rev. A 92, 012520 (2015)PLRAAN1050-294710.1103/PhysRevA.92.012520] have given a counterexample to the conventional in reduced density-matrix functional theory representation of the second-order reduced density matrix (2RDM) Γij,kl in the basis of the natural orbitals as a function Γij,kl(n) of the orbital occupation numbers (ONs) ni. The observed nonuniqueness of Γij,kl for prototype systems of different symmetry has been interpreted as the inherent inability of ON functions to reproduce the 2RDM, due to the insufficient information contained in the 1RDM spectrum. In this Comment, it is argued that, rather than totally invalidating Γij,kl(n), the WK example exposes its symmetry dependence which, as well as the previously established analogous dependence in density functional theory, is demonstrated with a general formulation based on the Levy constrained search.