First-principles calculations were used to perform a cross-material investigation on the electronic structures of 13 parent compounds for thermoelectric materials. Boltzmann transport equations were used to calculate carrier doping level dependence of the Seebeck coefficient, electrical conductivity with respect to relaxation time, effective Lorenz numbers and the maximum possible thermoelectric figure of merit (Z_eT) in the limit of zero phonon thermal conductivity. High Z_eT was obtained only in semiconductors with finite band gaps. High Z_eT for high doping level was achieved in compounds that had a steep density of states at the band edge. Calculations were combined with experimental transport properties to evaluate electron relaxation time of the samples. These analyses can be used to understand the nature of electron scattering mechanisms in specific thermoelectric materials and reduce the number of experiments required to develop new thermoelectric materials.