  We investigate electronic structures and thermoelectric properties of recent
synthetic half-Heusler $\mathrm{ZrNiPb}$ by using generalized gradient
approximation (GGA) and GGA plus spin-orbit coupling (GGA+SOC). Calculated
results show that $\mathrm{ZrNiPb}$ is a indirect-gap semiconductor. Within the
constant scattering time approximation, semi-classic transport coefficients are
performed through solving Boltzmann transport equations. It is found that the
SOC has more obvious influence on power factor in p-type doping than in n-type
doping, leading to a detrimental effect in p-type doping. These can be
explained by considering the SOC influences on the valence bands and conduction
bands near the Fermi level. The lattice thermal conductivity as a function of
temperature is calculated, and the corresponding lattice thermal conductivity
is 14.5 $\mathrm{W m^{-1} K^{-1}}$ at room temperature. By comparing the
experimental transport coefficients with calculated ones, the scattering time
is attained for 0.333 $\times$ $10^{-14}$ s. Finally, the thermoelectric figure
of merit $ZT$ can be attained, and the $ZT$ value can be as high as 0.30 at
high temperature by choosing appropriate doping level. It is possible to reduce
lattice thermal conductivity by point defects and boundaries, and make
half-Heusler $\mathrm{ZrNiPb}$ become potential candidate for efficient
thermoelectricity.
