On a method of nonlinear optimization for the comparison of spatial structure of molecules

To compare the geometry of two or more geometric structures consisting of N ordered points, and which can be considered as solids in three-dimensional space, we developed a method based on the minimization of a certain comparison function. This function is the sum of squared distances between pairs of elements of the two structures under comparison with the same indices. Distances change when changing the mutual orientation of the structures with all possible shifts and rotations of the structures as rigid bodies. The comparison function is minimized with respect to Euler angles, provided that centers of mass of two compared structures are superposed. The minimization of the comparison function with respect to Euler angles is carried out numerically by the Rosenbrock method. The developed method for comparison of geometric structures is used to solve problems in structural chemistry, that is to compare molecules with the same structural formula in one crystal. © 2020 Faculty of Organizational Sciences, Belgrade. All rights reserved.

Authors
Number of issue
1
Language
English
Pages
91-99
Status
Published
Volume
30
Year
2020
Organizations
  • 1 Peoples' Friendship University of Russia, Moscow, Russian Federation
  • 2 Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, Russian Federation
Keywords
Conformer; Euler angles; Optimization; Rosenbrock Method; Rotation Matrix
Date of creation
02.11.2020
Date of change
02.11.2020
Short link
https://repository.rudn.ru/en/records/article/record/65313/
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