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A mathematical model for the stacking patterns of planar copper(II) halide oligomers

A mathematical model for the stacking patterns of planar copper(II) halide oligomers Planar bibridged CunX2nL2 oligomers, where X is a halide ion and L a halide ion or neutral ligand, with values of n ranging from 1 to 7, occur in numerous copper(II) halides. Within the oligomers, each CuII ion assumes an approximate square-planar primary coordination geometry. Common examples include Cu2X62-, Cu3X82- and Cu4X102- anions and neutral species such as CuCl2(H2O)2, Cu2Br4(pyridine)2 and Cu3Cl6(CH3CN)2. The oligomers aggregate through the formation of long semicoordinate Cu-X linkages, creating stacks of oligomers. A wide variety of stacking arrangements (polytypes) is possible, corresponding to different sequences of relative translations between adjacent oligomers. The ground states of a one-dimensional Hamiltonian are developed to account for a subset of the observed polytypism. Terms included in the Hamiltonian include quadratic (Si Sj) nearest- and next-nearest-neighbor interactions, nearest-neighbor biquadratic Si Sj2 interactions and nearest-neighbor XY-interaction (SixSjy + SiySjx) terms. The XY term accounts for the four allowable relative translations, the nearest-neighbor terms parameterize the energies of these four relative translations and the next-nearest-neighbor term gives rise to the development of the stacking patterns. The model predicts the existence of five of the observed polytypes and, in addition, eight new polytypes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Foundations of Crystallography International Union of Crystallography

A mathematical model for the stacking patterns of planar copper(II) halide oligomers

A mathematical model for the stacking patterns of planar copper(II) halide oligomers


Abstract

Planar bibridged CunX2nL2 oligomers, where X is a halide ion and L a halide ion or neutral ligand, with values of n ranging from 1 to 7, occur in numerous copper(II) halides. Within the oligomers, each CuII ion assumes an approximate square-planar primary coordination geometry. Common examples include Cu2X62-, Cu3X82- and Cu4X102- anions and neutral species such as CuCl2(H2O)2, Cu2Br4(pyridine)2 and Cu3Cl6(CH3CN)2. The oligomers aggregate through the formation of long semicoordinate Cu-X linkages, creating stacks of oligomers. A wide variety of stacking arrangements (polytypes) is possible, corresponding to different sequences of relative translations between adjacent oligomers. The ground states of a one-dimensional Hamiltonian are developed to account for a subset of the observed polytypism. Terms included in the Hamiltonian include quadratic (Si Sj) nearest- and next-nearest-neighbor interactions, nearest-neighbor biquadratic Si Sj2 interactions and nearest-neighbor XY-interaction (SixSjy + SiySjx) terms. The XY term accounts for the four allowable relative translations, the nearest-neighbor terms parameterize the energies of these four relative translations and the next-nearest-neighbor term gives rise to the development of the stacking patterns. The model predicts the existence of five of the observed polytypes and, in addition, eight new polytypes.

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Publisher
International Union of Crystallography
Copyright
Copyright (c) 1993 International Union of Crystallography
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S0108767392012170
Publisher site
See Article on Publisher Site

Abstract

Planar bibridged CunX2nL2 oligomers, where X is a halide ion and L a halide ion or neutral ligand, with values of n ranging from 1 to 7, occur in numerous copper(II) halides. Within the oligomers, each CuII ion assumes an approximate square-planar primary coordination geometry. Common examples include Cu2X62-, Cu3X82- and Cu4X102- anions and neutral species such as CuCl2(H2O)2, Cu2Br4(pyridine)2 and Cu3Cl6(CH3CN)2. The oligomers aggregate through the formation of long semicoordinate Cu-X linkages, creating stacks of oligomers. A wide variety of stacking arrangements (polytypes) is possible, corresponding to different sequences of relative translations between adjacent oligomers. The ground states of a one-dimensional Hamiltonian are developed to account for a subset of the observed polytypism. Terms included in the Hamiltonian include quadratic (Si Sj) nearest- and next-nearest-neighbor interactions, nearest-neighbor biquadratic Si Sj2 interactions and nearest-neighbor XY-interaction (SixSjy + SiySjx) terms. The XY term accounts for the four allowable relative translations, the nearest-neighbor terms parameterize the energies of these four relative translations and the next-nearest-neighbor term gives rise to the development of the stacking patterns. The model predicts the existence of five of the observed polytypes and, in addition, eight new polytypes.

Journal

Acta Crystallographica Section A: Foundations of CrystallographyInternational Union of Crystallography

Published: Jul 1, 1993

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