Supramolecular Architecture in a Disordered Perhydrotriphenylene Inclusion Compound from Diffuse X-ray Diffraction Data

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The diffraction pattern from the disordered host-guest compound perhydrotriphenylene and 1-(4-nitrophenyl)piperazine (PHTP 5 .NPP) shows a complex variety of diffuse diffraction phenomena. A qualitative and semiquantitative interpretation of the diffuse intensities aided by group theoretical considerations provides detailed information concerning substitutional disorder of (R)- and (S)-PHTP molecules. On the basis of these results a Monte Carlo model for structure simulations has been developed, which comprises only five parameters. The parameters are determined with an evolutionary technique, testing 40 sets of parameters and improving them by mutation and recombination. It is found that the relevant structural information is available after relatively few generations from the average of all individuals rather than from the best individual within a population optimized through many generations. This realization accelerates the algorithm by at least an order of magnitude compared to its earlier implementations. R values between 0.125 and 0.13 indicate an agreement between experimental and simulated diffraction patterns that is pleasingly low for a disorder problem of this kind. The investigation of the structural properties of the host structure indicates that the most dominant structural features include sequences of 10-20 homochiral molecules along the c axis and a weak tendency of building heterochiral pairs in perpendicular directions. Strain associated with the difference in intermolecular contacts between homo- and heterochiral molecules is released by local shear deformations.