# Using quaternions to calculate RMSD

@article{Coutsias2004UsingQT, title={Using quaternions to calculate RMSD}, author={Evangelos A. Coutsias and Chaok Seok and Ken A. Dill}, journal={Journal of Computational Chemistry}, year={2004}, volume={25} }

A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the root‐mean‐square deviation (RMSD). We present a simple derivation, based on quaternions, for the optimal solid body transformation (rotation‐translation) that minimizes the RMSD between two sets of vectors. We prove that the quaternion method is equivalent to the well‐known formula due to Kabsch. We analyze the various cases that may… Expand

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