Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain.

The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges such as the lack of the Kohn-Sham scheme and the complexity of the pure N-representability conditions are still impeding its wild utilization. Fortunately, ensemble N-representability conditions derived in the natural orbital basis are known and trivial such that almost every functional of the 1-RDM is actually natural orbital functional, which does not perform well for all the correlation regimes.