  We investigate the effect of electronic correlations onto the
thermoelectricity of semi-conductors and insulators. Appealing to model
considerations, we study various many-body renormalizations that enter the
thermoelectric response. We find that, contrary to the case of correlated
metals, correlation effects do not per se enhance the Seebeck coefficient or
the figure of merit, for the former of which we give an upper bound in the
limit of vanishing vertex corrections. For two materials of current interest,
FeAs2 and FeSb2, we compute the electronic structure and thermopower. We find
FeAs2 to be well described within density functional theory, and the therefrom
deduced Seebeck coefficient to be in quantitative agreement with experiment.
The capturing of the insulating ground state of FeSb2, however, requires the
inclusion of many-body effects, in which we succeed by applying the GW
approximation. Yet, while we get qualitative agreement for the thermopower of
FeSb2 at intermediate temperatures, the tremendously large Seebeck coefficient
at low temperatures is found to violate our upper bound, suggesting the
presence of decisive (e.g. phonon mediated) vertex corrections.
