  We study the electronic structure and thermoelectric properties of recently
synthesized CoAsSb. The calculated bandgap becomes more accurate for
increasingly-complex electronic structure methods: generalized gradient
approximation, hybrid functionals, self-consistent linearized quasiparticle GW
method (LQSGW), and LQSGW with simplified vertex corrections. By equating the
bandgaps of each method from a rigid shift of the bands, we evaluate the
contributions made to thermoelectric properties beyond the bandgap. In doing
so, we evaluate the efficacy of a common-practice: a rigid shift applied to
less-costly electronic structure methods in order to gain some accuracy of the
more-costly methods. We find that while the shift made the Seebeck coefficients
much closer to one another than from the original electronic structures, there
remain differences in the Goldsmid-Sharp (thermoelectric) bandgap between the
methods and from the intended electronic bandgap. Additionally, some lasting
differences in temperature dependence remain between the methods.
