  We present methods for generating computationally simple parameter-free pair
potentials useful for solids, liquids and plasma at arbitrary temperatures.
They successfully treat warm-dense matter (WDM) systems like carbon or silicon
with complex tetrahedral or other structural bonding features. Density
functional theory asserts that only one-body electron densities, and one-body
ion densities are needed for a complete description of electron-ion systems.
DFT is used here to reduce {\it both} the electron many-body problem and the
ion many-body problem to an exact one-body problem, namely that of the neutral
pseudoatom (NPA). We compare the Stillinger-Weber (SW) class of multi-center
potentials, and the embedded-atom approaches, with the NPA approach to show
that many-ion effects are systematically included in this one-center method via
one-body exchange-correlation functionals. This computationally highly
efficient "single-center" DFT-NPA approach is contrasted with the usual
$N$-center DFT calculations that are coupled with molecular dynamics (MD)
simulations to equilibriate the ion distribution. Comparisons are given with
the pair-potential parts of the SW, effective-medium `glue' models, and the
corresponding NPA pair-potentials to elucidate how the NPA potentials capture
many-center effects using only pair-potentials, based on single-center one-body
densities.
