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 Cu(II) 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 (S(i) . S(j)) nearest- and next-nearest-neighbor interactions, nearest-neighbor biquadratic [(S(i) . S(j))2] interactions and nearest-neighbor XY-interaction (S(ix)S(jy) + S(iy)S(jx)) 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-Dearest-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.