Applying R-Matrix Theory to Atom-Molecule Inelastic Collisions: the case study of H$_2$O + H

TL;DR

This paper introduces an R-matrix theoretical framework for inelastic atom-molecule collisions, demonstrating high accuracy and significant computational speedups, especially when leveraging GPU acceleration, suitable for complex polyatomic systems.

Contribution

The study develops a rigorous R-matrix method for inelastic scattering, validated against traditional approaches, and optimized for high-performance computing environments.

Findings

R-matrix results match close-coupling accuracy

Achieves over tenfold speedup with GPU acceleration

Enables scalable studies of complex polyatomic collisions

Abstract

The present study presents a comprehensive theoretical investigation of atom and asymmetric top molecule inelastic scattering based on the R-matrix formalism. The proposed methodology establishes a rigorous framework for treating inelastic collisions in the space-fixed coordinate system. The excellent numerical performance of the method is demonstrated through the comparison of state-to-state rotationally inelastic R-matrix cross sections for the H + H$_2$O system with those obtained using conventional close-coupling (CC) theory. The R-matrix approach is shown to deliver results of comparable accuracy while achieving substantially reduced computation times. The method is furthermore shown to achieve more than one order-of-magnitude speedup by exploiting GPU-accelerated diagonalisation through the MAGMA library. This combination of accuracy and computational efficiency positions the R--matrix approach as a powerful and scalable tool for investigating inelastic scattering involving complex polyatomic systems, thereby paving the way for systematic studies of molecule-molecule interactions in astrophysical, atmospheric, and cold-matter environments.