IRA: A Shape Matching Approach for Recognition and Comparison of Generic Atomic Patterns

Area of Science:

• Computational chemistry and materials science
• Structural analysis and comparison
• Algorithm development for scientific applications

Background:

• Atomic structure matching is crucial for understanding materials.
• Existing methods often require prior atomic assignments or are limited in scope.
• Handling unknown atomic permutations and structural distortions presents a significant challenge.

Purpose of the Study:

• To develop a versatile, parameter-less algorithm for shape matching of atomic structures.
• To address the challenge of unknown atomic assignments and potential distortions.
• To provide a robust method for comparing and identifying atomic structures and fragments.

Main Methods:

• Iterative Rotations and Assignments (IRA) algorithm utilizing Hausdorff distance for frame selection.
• Singular Value Decomposition (SVD) for optimal rotation and translation in distorted structures.
• Constrained Shortest Distance Assignments (CShDA) for one-to-one atomic mapping.
• Benchmarking against existing shape matching algorithms.

Main Results:

• IRA successfully identifies rigid rotations, reflections, translations, and permutations between structures with varying atom counts.
• The method accurately handles periodic and non-periodic structures, including those with distortions.
• Performance benchmarks demonstrate superior efficiency compared to two other shape matching algorithms.
• Application examples show utility in analyzing molecular dynamics trajectories and amorphous material models.

Conclusions:

• The proposed IRA and CShDA approach offers a powerful and flexible solution for atomic structure matching.
• It enables detailed analysis of structural similarities, distortions, and permutations without prior assignments.
• The algorithm has broad applicability in materials science, cheminformatics, and structural biology for data exploration and comparison.