On Quantitative Estimation of the Degree of Similarity of Coordination Polyhedra
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TAL CHEMISTRY
On Quantitative Estimation of the Degree of Similarity of Coordination Polyhedra N. V. Somov* and P. V. Andreev Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603950 Russia *e-mail: [email protected] Received July 27, 2016
Abstract—A new method for quantitative description of the degree of similarity of coordination polyhedra has been proposed. The results of studying the five-coordination polyhedra of the antimony and bismuth complexes, in which the nearest coordination environment of metals consists of only oxygen and carbon atoms, have been presented. DOI: 10.1134/S1063774518010170
INTRODUCTION
In this study, we propose a new way for quantitative estimation of the similarity of two CPs with identical CNs. This method takes into account the distortion of chemical bond lengths and bond angles. The criterion is a dimensionless limited value. In contrast to the above methods, this algorithm is sensitive to enantiomers. The method was applied for the first time to analyze the CPs of lead(II) in chelating complexes with [Pb{μ6-NH(CH2PO3H)3}] and Na4[Pb2(H2O)2{μ3-N(CH2PO3)3H2}2] ⋅ 10H2O nitrilo-tris-methylene phosphonic acid [5].
It is often convenient to describe the atomic crystal structure in terms of coordination polyhedra (CPs). The geometrically regular CPs are found quite rarely in real atomic structures of crystals. Generally, the geometry of real CPs deviates from ideal, and these CPs are referred to as distorted. The CP geometry is generally described by a set of bond lengths and bond angles; however, this description is not always convenient, because it includes many parameters. It is convenient to perform a comparative analysis of several CPs by introducing a single numerical parameter, which replaces the set of bond lengths and bond angles. For example, a criterion for degree of trigonality, τ, was proposed in [1] for CPs with a coordination number (CN) equal to five. The τ value is calculated based on the two largest bond angles of the CP. The range of possible τ values is 0 ≤ τ ≤ 1. The CP is assumed to be a trigonal bipyramid at τ > 0.5 and a tetragonal pyramid otherwise. A criterion based on the analysis of the CP dihedral angles was proposed in [2]. The degree of distortion of an original CP was suggested to be characterized by the rms deviations of the corresponding dihedral angles from the standard values. The method was approved for CPs of three types: trigonal dodecahedron, trigonal prism with two capped lateral faces, and square antiprism. An alternative approach is the method for calculating the continuous symmetry (Continuous Symmetry Measures, CSM) [3], which is implemented in the SHAPE software [4]. The CSM method is based on analyzing the differences between the vectors of vertices of the original and standard polyhedra.
CALCULATION OF THE DEGREE OF SIMILARITY OF COORDINATION POLYHEDRA One of the ways to define a CP is to present it as a set of vectors connecting the center of the polyhedron and its vertices. It is convenient to use the central atom as th
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