  Within the method of spectral moments it is possible to construct the
spectral function of a many-electron system from the first $2P$ spectral
moments ($P=1,2,3,\dots$). The case $P=1$ corresponds to standard Kohn-Sham
density functional theory (KS-DFT). Taking $P>1$ allows us to consider
additional important properties of the uniform electron gas (UEG) in the
construction of suitable moment potentials for moment-functional based spectral
density-functional theory (MFbSDFT). For example, the quasiparticle
renormalization factor $Z$, which is not explicitly considered in KS-DFT, can
be included easily. In the 4-pole approximation of the spectral function of the
UEG (corresponding to $P=4$) we can reproduce the momentum distribution, the
second spectral moment, and the charge response acceptably well, while a
treatment of the UEG by KS-DFT reproduces from these properties only the charge
response. For weakly and moderately correlated systems we may reproduce the
most important aspects of the 4-pole approximation by an optimized two-pole
model, which leaves away the low-energy satellite band. From the optimized
two-pole model we extract \textit{parameter-free universal} moment potentials
for MFbSDFT, which improve the description of the bandgaps in Si, SiC, BN, MgO,
CaO, and ZnO significantly.
