Modeling the phase change in crystalline biphenyl by using a temperature-dependent potential

The structures of two crystalline phases of biphenyl (C₁₂H₁₀) were modeled using an exp-6-1 nonbonded potential and (1 - cos² φ) terms for the phenyl-phenyl conjugation energy. Preliminary calculations were made by minimizing the energy of a model starting from the 110 K structure, space group P2₁/a, with planar molecules. Doubling the b axis and relaxing all symmetry caused the model to transform to a structure with twisted molecules, space group Pa, essentially the same as the approximate structure reported from neutron diffraction studies at 22 K. Increasing the contribution of the conjugation energy reversed the transformation, and calculations show that the potential that produces planar molecules in the crystal predicts twisted molecules in the gas phase, in agreement with experiment. A new temperature-dependent potential is described in which the nonbonded terms are modified according to the thermal motions of the atoms involved. Motion parallel to the interaction vector tends to push atoms apart, whereas motion perpendicular to it permits their mean positions to get closer together. Ways of combining the motions of the two atoms involved are considered. This new potential was applied to biphenyl to calculate successfully the observed unit-cell volumes and thermal expansion. The model reproduces the torsion angles in the 22 K structure, and increasing temperature produces the experimental phase change, although the predicted transition temperature is higher than that observed.