IRA

IRA identifies optimal correspondences between atomic arrangements with unknown atom assignments by iteratively rotating atom-centered reference frames and minimizing a permutationally invariant Hausdorff distance.

Key Features:

• Iterative atom-centered frame rotation and assignment: A parameter-less algorithm iteratively proposes rotations and assigns atom-centered reference frames to identify matches between structures.
• Permutationally invariant matching: Uses the Hausdorff distance as a permutationally invariant set–set metric to determine minimal-value solutions for matching problems.
• Versatile rigid transformations: Handles rotations, reflections, translations, and permutations and accommodates structures with varying numbers of atoms.
• Distortion handling via singular value decomposition: Applies singular value decomposition (SVD) to refine optimal rotation and translation for distorted structures.
• Constrained Shortest Distance Assignments (CShDA): Computes atomic assignments under a one-to-one constraint to establish precise correspondence between atoms of different structures.
• Benchmarking: Validated through extensive testing against other shape matching algorithms to assess performance across diverse scenarios.

Scientific Applications:

• Exploration of collective coordinates: Identifies relevant collective coordinates for clustering molecular dynamics data, exemplified by a replica-exchange trajectory of a cyanine molecule.
• Structural distortion analysis: Computes distortion scores for amorphous models such as SiO2 and compares them with classical strain-based potentials.

Methodology:

IRA iteratively adjusts atom-centered reference frames to minimize the Hausdorff distance, uses singular value decomposition to refine rotations and translations for distorted structures, and applies the Constrained Shortest Distance Assignments (CShDA) algorithm to compute one-to-one atomic assignments.