  We study LiFeP, LiFeAs and NaFeAs in their paramagnetic metallic phase
including dynamical electronic correlations within a density functional theory
+ slave-spin mean-field framework. The three compounds are found to lie next to
the crossover between a normal and a Hund's metal, where a region of enhanced
electronic compressibility that may boost superconductivity is systematically
present in this type of systems. We find that LiFeP lies in the normal metallic
regime, LiFeAs at the crossover, and NaFeAs is in the Hund's metal regime,
which possibly explains the different experimental trends for the pressure- and
doping-dependence of superconductivity in these compounds. Our picture captures
the orbitally-resolved mass renormalizations measured in these materials, while
an analysis of the Sommerfeld specific-heat coefficient highlights some
limitations of currently used implementations of density-functional theory for
the correct prediction of the details of band structures in the iron-based
superconductors.
