Zirconium hydride serves as a critical moderator in advanced nuclear reactors, and its thermal scattering law (TSL) data are of importance for reactor design. First-principles calculations based on lattice dynamics or molecular dynamics generally rely on the harmonic approximation(HA) or classical mechanics, neglecting quantum effects（QEs), which are significant for hydrogen atoms even at 0 K.
In this work, we employ an integrated computational method combining Quasi-Harmonic Approximation (QHA), Polynomial Machine Learning Potentials (MLPs), and 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 were determined via QHA. Subsequently, ab initio lattice dynamics (AILD) was utilized to compute energies and atomic forces for a broad set of structures to construct a high‑quality training dataset. Based on this, a polynomial MLPs was trained to accurately describe the Born–Oppenheimer energy and Hellmann–Feynman forces. Finally, within the SSCHA framework, the trained MLPs facilitated efficient sampling of large-scale ensembles, and the PDOS incorporating QEs was obtained through variational minimization of the free energy.
The results reveal that only considering the quantum‑induced volume expansion within QHA leads to a softening of the PDOS, whereas further inclusion of quantum corrections via SSCHA noticeably 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 follows trends consistent with existing theoretical results and matches well with experimental measurements. Furthermore, criticality benchmark validation indicates that considering quantum effects can further improve the calculation accuracy of k_\texteff under specific conditions. The datasets presented in this paper are openly available at https://doi.org/10.57760/sciencedb.33601 Please use the private access link https://www.scidb.cn/s/fAF3I3 to access the dataset during the peer review process).