It looks like RDMF theory inherits some of the many problems that affect DFT.
Fractional spin in reduced density-matrix functional theory
J. Chem. Phys. 135, 054109 (2011)
http://link.aip.org/link/doi/10.1063/1.3615955
J. Chem. Phys. 135, 054109 (2011)
http://link.aip.org/link/doi/10.1063/1.3615955