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In this study, we have reported electronic structure, lattice dynamics, andthermoelectric (TE) transport properties of a new family of pentanarysubstituted TiNiSn systems using the 18 valence electron count (VEC) rule. Fromour calculated band structures and density of states, we show that bypreserving the 18 VEC through aliovalent substitutions at the Ti site of TiNiSnsemiconducting behavior can be achieved, and hence one can tune the bandstructure and band gap to maximize the thermoelectric figure of merit (ZT)value. Two approaches have been used for calculating the lattice thermalconductivity ($\kappa_{L}$), one by fully solving the linearized phononBoltzmann transport (LBTE) equation from first$-$principles anharmonic latticedynamics calculations implemented in Phono3py code and other using Slack'sequation with calculated Debye temperature and Gr\"{u}neisen parameter usingthe calculated elastic constant values. The calculated $\kappa_{L}$ valuesdecrease from parent TiNiSn to pentanary substituted TiNiSn systems as expecteddue to fluctuation in atomic mass. The calculated $\kappa_{L}$ for Hfcontaining systems La$_{0.25}$Hf$_{0.5}$V$_{0.25}$NiSn and non Hf containingsystem La$_{0.25}$Zr$_{0.5}$V$_{0.25}$NiSn calculated from Phono3py (Slack'sequation) are found to be 0.37 (1.04) and 0.16 (0.95) W/mK, at 550\,K,respectively and the corresponding ZT value are found to be 0.54 (0.4) and 0.77(0.53). Among the considered systems, the calculated phonon spectra and heatcapacity show that La$_{0.25}$Hf$_{0.5}$V$_{0.25}$NiSn has moreoptical$-$acoustic band mixing which creates more phonon$-$phonon scatteringand hence lower the $\kappa_{L}$ value and maximizing the ZT. Based on thecalculated results we conclude that one can design high-efficiencythermoelectric materials by considering the 18 VEC rule with aliovalentsubstitution.

First principle design of new thermoelectrics from TiNiSn based pentanary alloys based on 18 valence electron rule