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 pi-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 (1) over bar 1, 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 tau similar or equal to 0degrees, 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.