  Recently, we introduced (e-print arXiv:1407.7128) {\em local reduced density
matrix functional theory} (local RDMFT), a theoretical scheme capable of
incorporating static correlation effects in Kohn-Sham equations. Here, we apply
local RDMFT to molecular systems of relatively large size, as a demonstration
of its computational efficiency and its accuracy in predicting single-electron
properties from the eigenvalue spectrum of the single-particle Hamiltonian with
a local effective potential. We present encouraging results on the
photoelectron spectrum of molecular systems and the relative stability of
C$_{20}$ isotopes. In addition, we propose a modelling of the fractional
occupancies as functions of the orbital energies that further improves the
efficiency of the method useful in applications to large systems and solids.
