Solids modeled by crystal field ab initio methods : 5. the phase transitions in biphenyl from a molecular point of view
Faculty of Sciences. Chemistry
Acta crystallographica: section B: structural science. - Copenhagen
, p. 96-106
University of Antwerp
Using ab initio calculations at the 4-21G level and procedures for extrapolation to r(g) geometry as well as using the electrostatic crystal field (ECF-MO) approach, the geometry and torsion potential were calculated for 1,1'-biphenyl in the gas phase, in the P2(1)/a lattice with Z = 2 and in the Pa lattice with Z = 4. At all stages excellent agreement is obtained with available diffraction data, including L22 librational components between 293 and 40 K. The following molecular picture emerged when the molecule goes from the gas phase through the solid-state phases biphenyl I, biphenyl II and biphenyl III. In the gas phase biphenyl is twisted (\pi\ = 45.7-degrees) with a relatively high torsion barrier [DELTAE(phi) = 7.9 kJ mol-1], decreasing to \phi\ = 27-degrees and DELTAE(phi) = 3.0 kJ mol-1 in the P2(1)/a lattice of biphenyl I. In P2(1)/a, each molecule is librating (in dynamical disorder) between an image form (phi = +27-degrees) and a mirror-image form (phi = -27-degrees). At 40 K a phase transition to biphenyl II takes place in which half of the molecules freeze into the image and half into the mirror-image enantiomer. They form racemic pairs along the ab diagonals of the Pa lattice. Since Z = 4 in the Pa lattice, there are two types of racemic pairs, viz. AA' and BB' with \phi(A)\ = 37.7 and \phi(B)\ = 38.9-degrees. The observed incommensurability along a*b* between 17 and 40 K (biphenyl II) is associated with order/disorder competition of AA' and BB' pairs. The observed incommensurability along b* below 17 K (biphenyl III) is associated with the slow disappearance of domain boundaries. These are stacking faults as a result of glide planes left as relics of the original P2(1)/a structure. The calculations attribute DELTAH = 0.33 kJ mol-1 to the transition at 40K and DELTAH = 0.17 kJ mol-1 to the transitions through the various incommensurate phases including that at 17 K. The values compare very well with those obtained by calorimetry. The model also rationalizes observations such as the approximate doubling of the b axis at 40 K, the quasi-temperature independent long-range order of 0.67 and \[phi]\ = 10-degrees in biphenyl II, as well as the length of the incommensurate wavevector in biphenyl III.