  On the basis of density functional theory and semi-classical Boltzmann
theory, we have investigated the structural, elastic, electronic, optical and
thermoelectric properties of 18--valence electron count rhodium based
half-Heusler alloys focusing on RhTiP, RhTiAs, RhTiSb, and RhTiBi. The absence
of imaginary frequencies in the phonon dispersion curve for these system
verifies that they are structurally stable. RhTiP is ductile in nature, while
others are brittle. The alloys are found to be semiconducting with indirect
band gaps ranging from 0.94 to 1.01 eV. Our calculations suggest these
materials to have high absorption coefficient and optical conductivity in the
ultraviolet as well as visible region. While considering thermoelectricity, we
found that $p$--type doping is more favorable in improving the thermoelectric
properties. The calculated values of power factor with $p$-type doping are
comparable to some of the reported half-Heusler materials. The optimum figure
of merit \zt\ is $\sim1$ for RhTiBi suggesting it as a promising candidate for
thermoelectric applications while RhTiP, RhTiAs, and RhTiSb with optimum \zt \
values between 0.38 to 0.67 are possible candidates for use in thermoelectric
devices.
