ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
The distortion of an observed coordination polyhedron can be evaluated from a comparison of this polyhedron with the least-squares best-fit polyhedron with optimum location, orientation, size parameters and prescribed symmetry. A set of atoms at positions, x(1) .... x(n), may be fitted to the set y(1) .... y(n) by rearranging the matrix equations: y(i) = t + Rλ(i)x(i) (i = 1,n) and solving for the unknown parameters of the translation vector, t, the rotation matrix, R, and the (diagonal) dilation matrices, λ(i), which optimize the fit between the two sets. The elements of the (one or more) dilation matrices may be constrained to fix the fitted set to the desired symmetry. The solution is effected by means of a two-stage iterative least-squares technique employing the so-called 'small- angle' rotation matrix. The average distance between corresponding atoms of the two sets, which is a minimum at the point of optimum fit, provides a unique one-parameter characterization of the degree of distortion between the two configurations. The magnitudes of the operations needed to produce the best fit are also recoverable from the least-squares solution.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0567739474001239
