  For more than three decades, nearly free electron elemental metals have been
a topic of debate because the computed bandwidths are significantly wider in
the local density approximation to density-functional theory (DFT) than
indicated by angle-resolved photoemission experiments. Here, we systematically
investigate this using first-principles calculations for alkali and
alkaline-earth metals using DFT and various beyond-DFT methods such as
meta-GGA, G$_0$W$_0$, B3LYP, and DFT+eDMFT. We find that the static non-local
exchange and correlation, as partly included in the B3LYP hybrid functional,
significantly increase the bandwidths even compared to LDA, while the
G$_0$W$_0$ bands are only slightly narrower than in LDA. The agreement with the
ARPES is best when the local approximation to the self-energy is used in the
DFT+eDMFT method. We infer that even moderately correlated systems with
partially occupied s-orbitals, which were assumed to approximate the uniform
electron gas, are very well described in terms of short-range dynamical
correlations that are only local to an atom.
