Zirconium hydride serves as a critical moderator in advanced nuclear reactors, and its thermal scattering law (TSL) data are vital for reactor design. First-principles calculations based on lattice dynamics or molecular dynamics generally rely on the harmonic approximation (HA) or classical mechanics, thereby neglecting quantum effects (QEs), which remain significant for hydrogen atoms even at 0 K.

In this work, we employ an integrated computational approach that combines the quasi-harmonic approximation (QHA), polynomial machine learning potentials (MLPs), and the stochastic self-consistent harmonic approximation (SSCHA) to evaluate the phonon density of states (PDOS) and TSL of zirconium hydride. First, the equilibrium lattice parameters at 0 K are determined using QHA. Subsequently, ab initio lattice dynamics (AILD) is employed to compute energies and atomic forces for a broad set of atomic configurations, generating a high-quality training dataset. Based on this dataset, a polynomial MLPs is trained to accurately reproduce the Born-Oppenheimer energy and Hellmann-Feynman forces. Finally, within the SSCHA framework, the trained MLP enabled efficient sampling of large-scale ensembles, and the PDOS incorporating quantum effects is obtained through variational minimization of the free energy.

The results reveal that accounting only for quantum-induced volume expansion within QHA leads to a softening of the PDOS, whereas further inclusion of quantum corrections via SSCHA markedly suppresses this softening trend. For \epsilon\text-ZrH_2 , the quantum-corrected PDOS demonstrates significantly improved agreement with experimental data compared to the HA, reducing the \chi^2 deviation for cylindrical and slab samples by 64.1% and 37.7%, respectively. The peak positions of the double-differential scattering cross-section, derived from this quantum-corrected PDOS, align more closely with the ENDF/B-VIII.1 evaluated library. Moreover, the calculated total scattering cross-section exhibits trends consistent with existing theoretical results and shows good agreement with experimental measurements. Furthermore, criticality benchmark validation indicates that incorporating quantum effects can enhance the accuracy of k_\texteff calculations under specific conditions. The datasets presented in this paper are openly available at https://doi.org/10.57760/sciencedb.33601.