Recent refinements of the structure of trans-stilbene suggested the presence of disorder at only one of the two crystallographically independent sites of the unit cell. Calculations based on atom-atom intermolecular potentials have shown that this disorder is adequately described by a model in which some of the molecules at that site are misoriented in a manner which results in large positional changes for only a few of the atoms in each molecule. A technique has been developed for including the degree of misorientation into the lattice energy calculations and the results are compatible both with the preference for disorder at one site and with the degree of misorientation at that site as estimated from difference maps. The system was analysed at two temperatures (113 and 298 K). The calculations confirm that the probability of orientational disordering at low temperature is smaller than at high temperature and show that it is limited to about 20% in the latter case.
The transferability of (6-exp) interatomic n0n-bonded potential functions for hydrocarbons previously derived from low-temperature structures extrapolated to 0 K, sublimation heats and elasticity data of model molecular crystals, was tested by calculation of properties of other crystals not involved in the earlier optimization process. Equilibrium structures and sublimation heats were calculated, in agreement with experiment, for methane CH4, adamantane (CH2)6(CH)4, 2,2-paracyclophane (CH2)4(C6H4)2 and 3,3-paracyclophane (CH2)6(C6H4)2 crystals. The solid-solid phase-transition characteristics of adamantane were described consistently with the same potential force field. For the cubic phase of adamantane the orientationally disordered molecular arrangement, suggested by X-ray experiment, was predicted theoretically. The calculation of the structures and heats of sublimation of the same crystals were repeated with a set of potential functions derived recently [Williams, Acta Cryst. (1974). A30, 71-77] on the basis of experimental data not extrapolated to 0 K. The difference between the two approaches is discussed and illustrated by comparing the calculated results.
The widely used atom-atom approximation for evaluating intermolecular energies is deficient in its treatment of the electrostatic interactions. Latticeenergy calculations have been performed for three crystal structures with explicit incorporation of the electrostatic energy, at three levels of approximation, based on Hartree-Fock molecular charge distributions. Although the molecules chosen are all non-polar, the electrostatic term in each case provides most of the calculated lattice energy and leads to an appreciable contraction of the predicted equilibrium cell dimensions. In cyanogen the electrostatic contribution appears necessary to account for the observed orthorhombic structure rather than an alternative cubic form. Treating each molecule as a point quadrupole severely overestimates the interaction energies of nearest-neighbor molecules but for more distant neighbors agrees fairly well with more detailed models of the molecular charge distribution. Assigning point charges to the several atoms is an adequate approximation for the three systems examined but greater flexibility is likely to be required for molecules of lower symmetry.
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