Kneller G R
Laboratoire Léon Brillouin, CEA-CNRS, F-91191 Gif-sur-Yvette, France.
J Comput Chem. 2005 Nov 30;26(15):1660-2. doi: 10.1002/jcc.20296.
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 sense that the Kabsch method may yield an improper optimal rotation, which must be explicitly checked for, whereas the quaternion method does not mix proper and improper rotations. Nevertheless, both types of solutions can be considered by solving the same eigenvector problem. The relation between the two types of solutions is briefly discussed and bounds for the eigenvalues are given.
库齐亚斯等人最近发表了一种寻找两个分子结构最佳旋转叠加的方法,该方法基于四元数对旋转的表示(《计算化学杂志》25(15),1849(2004))。之前其他作者也提出过该方法,并将其与卡布斯方法进行了比较,在卡布斯方法中,旋转矩阵的元素直接用作优化问题的变量。两种方法等效的说法具有误导性,因为卡布斯方法可能会产生不适当的最佳旋转,必须对此进行明确检查,而四元数方法不会混淆适当旋转和不适当旋转。然而,通过求解相同的特征向量问题可以考虑这两种类型的解。简要讨论了两种类型解之间的关系,并给出了特征值的界限。