  To investigate the physical characteristics of the half-Heusler BaHgSn
molecule, we used theoretical calculations within the Density Functional Theory
(DFT) framework utilizing the LSDA+mBJ technique in this study. Using the
optimal lattice parameters, we discover that half-Heusler BaHgSn exhibits a
Dirac semimetal behavior with a band gap of 0.1 eV. Thomas Charpin's numerical
first-principles calculation approach was applied to determine the elastic
constants of hexagonal BaHgSn alloys. The material's optical characteristics
verified its prospective use in infrared-visible devices. According to a
thermo-electric properties analysis, at 20x10^18 {\Omega}-1.m-1.s-1, the
electrical conductivity reaches its maximum after increasing gradually up to
500 K. Compared to other compounds, these results indicate that BaHgSn has
potential for use in opto-electronic and thermo-electric devices.
