  Intermetallic semiconductors with the cubic Half-Heusler structure (XYZ) have
excellent thermoelectric properties. This has been attributed to the high
degeneracy of the carrier pockets in the band structure, but large differences
are found between different material compositions. Half-Heuslers are often
interpreted within Zintl chemistry, making a clear distinction between an
electropositive cation ($X^{n+}$) and an extended polyanion ($YZ^{n-}$). Based
on quantitative real space chemical bonding analysis, we unravel large degrees
of covalent bonding between the formal cation and anion, making the Zintl
distinction clearly invalid. This covalence is shown to strongly affect the
band structure, thermoelectric properties and response properties in the
materials, with improved thermoelectric properties observed for those materials
that least follow the Zintl concept. This expands our knowledge of the chemical
bonding motifs governing physical properties, and gives a critical view on the
simplistic chemical concepts too often applied for design of complex materials.
