The study of optical properties with mBJ-GGA approximation as a function of photons energy for a wide range between 0 and 27 eV reveals that the two half-Heusler CaCuP and CaAgP compounds display the maximum reflectivity and absorption in the ultra violet range. The electronic properties have pointed to a semiconductor behavior for the two compounds and have shown a direct gap Γ→Γ equal to 1.785 eV for CaCuP and 1.621 eV for CaAgP with mBJ-GGA approximation. The two compounds are mechanically stable the calculated elastic constants strictly obey the stability criteria with brittle behavior, isotropic, and ionic nature in cubic structure type I. Our two compounds are more stable in cubic structure type I structure and the lattices parameters obtained in good agreement with other available data. The mBJ-GGA approximation is also employed to give a better approximation of the energy bandgap for the two CaCuP and CaAgP compounds. The generalized gradient approximation (GGA) is used for studying exchange and correlation effects. Our comparative study is carried out on different structural, elastic, electronic, and optical properties of two new half-Heusler CaCuP and CaAgP compounds by using first-principles calculations based on density functional density. Finally, the ALIGNN model is used to predict the phonon spectra and properties for about 40,000 additional materials listed in the JARVIS-DFT database, which are validated as far as possible against other open-sourced high-throughput DFT phonon databases. The DOS-mediated ALIGNN model provides superior predictions when compared to a direct deep-learning prediction of these material properties as well as predictions based on analytic simplifications of the phonon DOS, including the Debye or Born-von Karman models. The model predictions are shown to capture the spectral features of the phonon density-of-states, effectively categorize dynamical stability, and lead to accurate predictions of DOS-derived thermal and thermodynamic properties, including heat capacity $C_$. The model is trained on a database of over 14,000 phonon spectra included in the JARVIS-DFT (Joint Automated Repository for Various Integrated Simulations: Density Functional Theory) database. Here, we present an atomistic line graph neural network (ALIGNN) model for the prediction of the phonon density of states and the derived thermal and thermodynamic properties. The phonon density-of-states (DOS) summarizes the lattice vibrational modes supported by a structure, and gives access to rich information about the material's stability, thermodynamic constants, and thermal transport coefficients. This uncommon combination of high electrical conductivity and low thermal conductivity is interesting and invites further attention. In Zr1.05NiSb, which has the highest electrical conductivity (≈4000Scm−1), κ is as low as ≈4Wm−1K−1 at 300K, of which almost 70% is estimated to be due to the electronic contribution resulting in a lattice contribution which is <1Wm−1K−1. Despite reasonably high electrical conductivity, the thermal conductivity (κ) of these compounds is found to be generally low (<15Wm−1K−1 near 300K). The average value of Seebeck coefficient is small, of the order of 10μVK−1. Near room temperature the thermopower is negative for ZrNiX (X = Si, Ge) and HfNiSi, and positive for NbCoSi and ZrNiSb as predicted theoretically. The electrical conductivity (σ) near room temperature is of the order of 103Scm−1, which is intermediate between that of the degenerate semiconductors and metallic alloys. In ZrNiSb no pseudogap is observed however, the density of states at EF is still small. A pseudogaplike feature is observed in the electronic density of states with Fermi energy (EF) located either slightly below (ZrNiSi, ZrNiGe, and HfNiSi) or above the pseudogap (NbCoSi). In NbCoSi and ZrNiSb, the majority carriers are holes. In ZrNiSi, ZrNiGe, and HfNiSi, the Fermi surface consists of small electron and hole pockets with electrons as the majority charge carriers. Our first-principles electronic band structure calculations reveal that they are semimetals. In ZrNiSb, 5% excess Zr is required to obtain the pure orthorhombic phase. Here, we show that all the named compounds actually crystallize with the orthorhombic TiNiSi structure type, which remains stable above room temperature up to at least 1100 K. Motivated by recent advances in half-Heusler based thermoelectric materials, we investigated the phase stability and thermoelectric properties of compounds ZrNiSi, ZrNiGe, HfNiSi, NbCoSi, and ZrNiSb, some of which were recently reported in literature as promising half-Heuslers for thermoelectric applications using the first-principles density functional theory based calculations.