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Updated: Aug 11, 2025

Spatial Separation of Molecular Conformers and Clusters
Published on: January 9, 2014
A Practical Algorithm to Solve the Near-Congruence Problem for Rigid Molecules and Clusters
José Manuel Vásquez-Pérez1, Luis Ángel Zárate-Hernández2, Carlos Zepactonal Gómez-Castro1
1CONACyT Research Fellow, Universidad Autónoma del Estado de Hidalgo, Pachuca42184, México.
Abstract:
We present an improved algorithm to solve the near-congruence problem for rigid molecules and clusters based on the iterative application of assignment and alignment steps with biased Euclidean costs. The algorithm is formulated as a quasi-local optimization procedure with each optimization step involving a linear assignment (LAP) and a singular value decomposition (SVD). The efficiency of the algorithm is increased by up to 5 orders of magnitude with respect to the original unbiased noniterative method and can be applied to systems with hundreds or thousands of atoms, outperforming all state-of-the-art methods published so far in the literature. The Fortran implementation of the algorithm is available as an open source library (https://github.com/qcuaeh/molalignlib) and is suitable to be used in global optimization methods for the identification of local minima or basins.
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