Explanation for the stacking disorder in tris(bicyclo[2.1.1]hexeno)benzene using lattice-energy minimisations

Abstract

AbstractThe stacking disorder in the hexagonal polymorph of tris(bicyclo[2.1.1]hexeno)benzene, C18H18, is explained by lattice-energy minimisations. The compound crystallises in layers withP(-6)2mlayer-group symmetry. Each layer can be placed in one of three possible positions. Possible stacking sequences were derived from order-disorder (OD) theory and by a combinatorial approach. The resulting periodic model structures were optimised by lattice-energy minimisations. The calculations show thateclipsedarrangements of layers (sequencee.g. ABA) are energetically less favourable thannon-eclipsedones (sequencee.g. ABC). The reason was found in the deviation fromP(-6)2msymmetry. Molecules ineclipsedlayers are almost parallel to the layer plane, whereas molecules innon-eclipsedlayers are inclined to it by about 3° leading to a more efficient packing. The influence of the next-nearest layers was found to be not a direct one, but mediated by the distortion of the layers between them. Using Boltzmann statistics, the stacking probabilities for all four-layer sequences were calculated. The results match well with the probabilities derived from the diffuse scattering by Bürgiet al.(2005) (Z. Kristallogr. 220, 1066–1075). The lattice-energy minimisations allowed to determine the actual local structures in all individual layers including packing effects like rotation of molecules, lateral shifts, and to calculate the stacking layer thickness, depending on the actual layer sequences.The diffraction pattern, calculated from a lattice-energy optimised structure with 54 layers, is similar to the experimental one, and even approximates the diffuse scattering.