Dielectric and lattice dynamical properties of molecular crystals via density functional perturbation theory: implementation within a first principles code

Abstract

Organic molecular crystals form a condensed solid phase offering a rich vein of physical phenomena which are open to investigation. The desire to harness these properties for technological and biological purposes has led to extensive experimental and theoretical investigations. The naturally occurring ɑ-amino acids form molecular crystals in the solid state; to date there have been very few studies of these systems. The work in this thesis is concerned with attempting to understand the relationship between the properties of the molecular crystal, and how these relate to the properties of the constituent molecules in isolation. To this end, density functional calculations of the structural and electronic properties of amino acids in both the crystalline and gaseous states are performed, and the results reported. The bonding mechanisms responsible for the crystal being stable are elucidated, and used to explain the zwitterionisation of the molecules upon formation of the solid state. In order to investigate the lattice dynamical and dielectric properties, the implementation of a variational density functional perturbation theory (DFPT) scheme within the plane wave pseudopotential formalism is described in detail. This scheme is fully self-consistent, and its computational cost is comparable to that of a single-point self-consistent total energy calculation. The long wave method is used to alleviate well-known problems associated with the application of homogeneous fields to crystal systems, viz. that such fields break the crystal symmetry, and the adequate treatment of electronic screening. Calculation of the first order perturbed wavefunctions and the second order change in the Kohn-Sham functional allows properties such as the polarisability, dielectric matrix, dynamical matrix and Born effective charge tensors to be determined. The treatment of crystalline symmetries is described in detail. The DFPT formalism is extended to allow IR absorption spectra to be obtained. The lattice dynamical and dielectric behaviour of the isolated molecules and the molecular crystals are obtained; calculation of the IR spectra facilitates an insight into the effects of the crystalline environment and zwitterionisation upon the lattice dynamics. Results indicate the importance of the molecular shape and structure upon the intermolecular interactions, and hence the crystal structure formed. It is these intermolecular interactions that are found to play the major part in modification of the lattice dynamical and dielectric behaviour.