  The predictive performance screening of novel compounds can significantly
promote the discovery of efficient, cheap, and non-toxic thermoelectric
materials. Large efforts to implement machine-learning techniques coupled to
materials databases are currently being undertaken, but the adopted
computational methods can dramatically affect the outcome. With regards to
electronic transport and power factor calculations, the most widely adopted and
computationally efficient method, is the constant relaxation time approximation
(CRT). This work goes beyond the CRT and adopts the proper, full energy and
momentum dependencies of electron-phonon and ionized impurity scattering, to
compute the electronic transport and perform power factor optimization for a
group of half-Heusler alloys. Then the material parameters that determine the
optimal power factor based on this more advanced treatment are identified. This
enables the development of a set of significantly improved descriptors that can
be used in materials screening studies, and which offer deeper insights into
the underlying nature of high performance thermoelectric materials. We have
identified $n_v$$\epsilon_r$ / $D_o^2m_{cond}$ as the most useful and generic
descriptor, a combination of the number of valleys, the dielectric constant,
the conductivity effective mass, and the deformation potential for the dominant
electron-phonon process. The proposed descriptors can accelerate the discovery
of new efficient and environment friendly thermoelectric materials in a much
more accurate and reliable manner, and some predictions for very high
performance materials are presented.
