Full-Dimensional Time-Independent Quantum Dynamics Approach to Rovibrationally Inelastic Scattering between Triatomic and Diatomic Molecules: A Case Study for H ₂ O + H ₂

Quantum mechanical treatment of intermolecular scattering involving polyatomic molecules encounters formidable computational challenges via time-independent coupled-channel (TICC) methods. This work reports the first rigorous TICC framework for triatom-diatom collisions in full dimensionality with applications for vibrational and rotational relaxation processes for H₂O + H₂. The dimensional scaling limitations are overcome by implementation of Radau coordinates with bisector-<i>z</i> embedding for the triatomic monomer, which optimally reduces basis set requirements while inherently preserving its exchange symmetry. Body-fixed formulation is used to simplify the potential matrix formula. By comparing with prior reduced-dimensional results, which uses a H₂ rigid rotor model and space-fixed formulation, we validate the numerical robustness of this newly proposed approach and the usage of H₂ rigid rotor approximation. Furthermore, the matrix decoupling scheme with the nearest-neighbor Coriolis coupling included preserves key resonance structures while eliminating unphysical artifacts observed in conventional coupled-states approaches. This work establishes a new paradigm for high-dimensional quantum scattering dynamics, particularly enabling investigation of vibration-to-vibration energy transfer mechanisms for triatom-diatom scatterings in future studies.