  The choice of exchange functional is a critical factor in determining the
energy bandgap of semiconductors. Ab initio calculations using different
exchange functionals, including the conventional generalized-gradient
approximation (GGA) functionals, meta-GGA functionals, and hybrid functionals,
show significant differences in the calculated energy bandgap for
semiconducting half-Heusler compounds. These compounds, which have 18 valence
electrons per unit cell, are of great interest due to their thermoelectric
properties, making them suitable for energy conversion applications. In
addition, accounting for electronic correlations using the GW method also
affects the calculated energy bandgaps compared to standard GGA calculations.
The variations in calculated energy bandgaps are specific to each material when
using different functionals. Hence, a detailed investigation of the electronic
properties of each compound is necessary to determine the most appropriate
functional for an accurate description of the electronic properties. Our
results indicate that no general rules can be established and a comparison with
experimental results is required to determine the most appropriate functional.
