Title:

Interactions of molecules and the properties of crystals

In this thesis the basic theory of the lattice dynamics of molecular crystals is considered, with particular reference to the specific case of linear molecules. The objective is to carry out a critical investigation of a number of empirical potentials as models for real systems. Suitable coordinates are introduced, in particular vibrational coordinates which are used to describe the translational and rotational modes of the free molecule. The Taylor expansion of the intermolecular potential is introduced and its terms considered, in particular the (firstorder) equilibrium conditions for such a system and the (secondorder) lattice vibrations. The elastic properties are also considered, in particular with reference to the specific case of rhombohedral crystals. The compressibility and a number of conditions for elastic stability are introduced. The total intermolecular interaction potential is divided into three components using perturbation methods, the electrostatic energy, the repulsion energy and the dispersion energy. A number of models are introduced for these various components. The induction energy is neglected. The electrostatic interaction is represented by atomic multipole and molecular multipole models. The repulsion and dispersion energies are modelled together in a central interaction potential, either the LennardJones atomatom potential or the anisotropic BernePechukas moleculemolecule potential. In each case, the Taylor expansion coefficients, used to calculate the various molecular properties, are determined. An algorithm is described which provides a relatively simple method for calculating cartesian tensors, which are found in the Taylor expansion coefficients of the multipolar potentials. This proves to be particularly useful from a computational viewpoint, both in terms of programming and calculating efficiency. The model system carbonyl sulphide is introduced and its lattice properties are described. Suitable parameters for potentials used to model the system are discussed and the simplifications to the Taylor expansion coefficients due to crystal symmetry are detailed. Four potential parameters are chosen to be fitted to four lattice properties, representing zero, first and second order Taylor expansion coefficients. The supplementary tests of a given fitted potential are detailed. A number of forms for the electrostatic interaction of carbonyl sulphide are considered, each combined with a standard atomatom potential. The success of the molecular octupole model is considered and the inability of more complex electrostatic potentials to improve on this simple model is noted. The anisotropic BernePechukas potential, which provides an increased estimate of the compressibility is considered as being an improvement on the various atomatom potentials. The effect of varying the exponents in the atomatom (or moleculemolecule) potential, representing a systematic variation of the repulsion and dispersion energy models, is examined and a potential which is able to reproduce all of the given lattice properties for carbonyl sulphide is obtained. The molecular crystal of cyanogen iodide is investigated. Superficially it is similar to the crystal of carbonyl sulphide and the potentials used with success for the latter are applied to cyanogen iodide to determine whether they are equally as effective models for this molecule. These potentials are found to be far less successful, in all cases yielding a number of unrealistic results. Reasons for the failure of the model are considered, in particular the differences between the electrostatic properties of the two molecules are discussed. It is concluded that some of the simplifications which proved satisfactory for carbonyl sulphide are invalid for simple extension to the case of cyanogen iodide. A first estimate of the differences in the electrostatic properties is attempted, calculating the induction energies of the two molecules. The assumption that the induction energy may be neglected is justified for the case of carbonyl sulphide but found to be far less satisfactory for cyanogen iodide. Finally details of ab initio calculations are outlined. The amount of experimental data available for the electrostatic properties of the two molecules under consideration is relatively small and the experimental data which is available is supplemented by values obtained from these calculations.
