Comment on “Using quaternions to calculate RMSD” [J. Comp. Chem. 25, 1849 (2004)]

  title={Comment on “Using quaternions to calculate RMSD” [J. Comp. Chem. 25, 1849 (2004)]},
  author={Gerald R. Kneller},
  journal={Journal of Computational Chemistry},
  • G. Kneller
  • Published 2005
  • Mathematics, Medicine, Computer Science
  • Journal of Computational Chemistry
Coutsias et al. have recently published a method to find the optimal rotational superposition of two molecular structures, which is based on a representation of rotations by quaternions ( J. Comp. Chem. 25(15), 1849 (2004) ). The method, which has been suggested by other authors before, is compared to the one by Kabsch, where the elements of the rotation matrix are directly used as variables of the optimization problem. The statement that the two methods are equivalent is misleading in the… Expand
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Acta Crystallogr A
  • Acta Crystallogr A
  • 1989
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  • Acta Crystallogr A
  • 1988