Model for the crystal packing and conformational changes of biphenyl in incommensurate phase transitions

Standard atom–atom potentials for hydrocarbons and a torsional potential to account for the π-electron conjugation energy were used to model the crystal structures and phase transitions of biphenyl. The model describes the high-temperature phase (I) with its planar molecule as a stationary point of the energy hypersurface. Phase I represents a low-energy barrier between the symmetry minima of the ground state (phase III), in which the molecule is twisted with torsion angles of opposite sign. Global-energy minimization was carried out by considering both regular structures, with one or two independent molecules, and quasi-one-dimensional superstructures built of N cells (N up to 16) of the high-temperature structure. The various energy-minimized biphenyl structures demonstrate remarkable similarity in their crystal packing; in particular, there are characteristic rows of cooperatively twisted molecules parallel to the superstructure dimension b. The structures built of centrosymmetric rows (P, Z = 4 and 8) are almost as low in energy as the basic structure (an N = 2 superstructure, Pa, Z = 4); moreover, one of them is isostructural with the low-temperature p-quaterphenyl structure. With N > 8, structures of lower energy than that of the basic structure (N = 2) were found; their common feature is an M-fold modulation of the twist angle over the supercell period, with M smaller than N and generally not a simple fraction of it. The global minimum was found to conform to the ratio k = M/N = 6/14, which is close to the experimentally observed k = 6/13 in the incommensurate phase III. Enthalpy minimization showed an overall decrease in the magnitude of the twist angle down to τ ≃ 0°, as well as the evolution of the modulated structures towards the high-temperature structure with increasing pressure, in agreement with evidence for the high-pressure limit of the incommensurate biphenyl phases.