Calculated energy and conformation of clusters of benzene molecules and their relationship to crystalline benzene

The detailed conformations of benzene clusters containing 2, 3, 5, 7, 9, 11, 13 and 15 molecules were calculated. The nonbonded potential energy of the clusters was minimized by the Newton-Raphson method with exp-6-1 potential functions. All of the clusters exhibited a predominating edge-to-side or herringbone pattern of packing. The concept of intershell coordination, as contrasted to ligand coordination, was introduced and illustrated with the undecamer and larger clusters. The pentadecamer clearly showed the beginning of a second coordination shell. The tridecamer conformation was related to a 13-molecule fragment from crystalline orthorhombic benzene. This crystal fragment has a higher energy than the tridecamer. The fragment can convert to the tridecamer conformation by a process of plane slippage with cooperative molecular motion. Two examples, an isoheptamer and an isotridecamer conformation, are given of clusters with lower total cluster energy but with a higher energy for the reference molecule. In neither case do the conformations follow a smooth trend with increasing cluster size. The isotridecamer has approximate threefold symmetry and has a conformation quite different from the crystal fragment.