  Data from recent laser-shock experiments, density-functional theory (DFT)
with molecular-dynamics (MD), and path-integral Monte Carlo (PIMC) simulations
on carbon are compared with predictions from the neutral-pseudo-atom (NPA)+
hyper-netted-chain (HNC) approach for carbon, a complex liquid in the
warm-dense matter regime. The NPA results are in good agreement, not only with
high-density regimes that have been studies via PIMC, but even at low densities
and low temperatures where transient covalent bonding dominates ionic
correlations. Thus the `pre-peak' due to the C-C bond at $\sim$1.4-1.6 \AA$\,$
and other features found in the pair-distribution function from DFT+MD
simulations at 0.86 eV and 3.7 g/cm$^3$ etc., are recovered accurately in the
NPA+HNC calculations. Such C-C bonding peaks have not been captured via
average-atom ion-sphere (IS) models. Evidence for an unusual liquid $\to$ vapor
and metal$\to$ semi-metal transition occurring simultaneously is presented.
Here a strongly correlated metallic-liquid with transient C-C bonds, i.e.,
carbon at density $\sim$ 1.0 g/cm$^3$ and mean ionization $Z=4$ transits
abruptly to a disordered mono-atomic vapour at 7 eV, with $Z\simeq$ 3. Other
cases where $Z$ drops abruptly are also noted. The nature of $Z$, its
discontinuities, and the role of exchange correlation, are reviewed. The
limitations of IS models in capturing the physics of transient covalent bonding
in warm dense matter are discussed.
