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

@article{Kneller2005CommentO,
  title={Comment on “Using quaternions to calculate RMSD” [J. Comp. Chem. 25, 1849 (2004)]},
  author={Gerald R. Kneller},
  journal={Journal of Computational Chemistry},
  year={2005},
  volume={26}
}
  • 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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Using quaternions to calculate RMSD
TLDR
It is proved that the quaternion method is equivalent to the well‐known formula due to Kabsch, and an expression for the gradient of the RMSD as a function of model parameters is presented. Expand
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Abstract An algorithm is developed that finds the optimal orientation of a rigid molecular structure, represented by N reference sites, with respect to the same number of sites in an observedExpand
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A rotation axis vector with magnitude tan (θ/2) for a rotation angle θ and a closely related unit vector of dimension 4 are used to show that : (i) the quadratic residual (weighted sum of squares ofExpand
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Quaternions are a simple and powerful tool for handling rotations and double groups. This book gives a complete treatment of finite point groups as subgroups of the full rotation group and emphasizesExpand
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It is shown that in the rotational superposition method proposed by Diamond (1988), which always produces orthogonal transformations with positive determinants, a simple test exists for the existenceExpand
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Rotation matrices that minimize or maximize the sum of the squared distances between corresponding atoms for two structures are found using a constrained least-squares procedure solved analyticallyExpand
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A simple procedure is derived which determines a best rotation of a given vector set into a second vector set by minimizing the weighted sum of squared deviations. The method is generalized for anyExpand
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