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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.
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.
