PIXEL analysis of interactions in organic and inorganic systems
Maloney, Andrew Gerrard Patrick
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The PIXEL method has been used for several years to analyse intermolecular interactions in organic crystals. The simplicity and speed of the calculations, along with the breakdown of intermolecular energies into physical contributing terms, mean that it has had a massive influence on the way organic crystal structures are interpreted. In the work done to date, the parameters required to perform a PIXEL calculation have been established for 1st, 2nd and 3rd row transition metals. Using these parameters, lattice energies of several transition metal complexes containing various chemical environments have been calculated and compared to experimental sublimation enthalpies. Straight line parameters for these results have been comparable to work by Gavezzotti, the author of the program, in testing the method for organic crystal structures. In addition to lattice energies, PIXEL gives dimer interaction energies of molecules in a crystal structure. The values of these interactions have been compared to single point DFT energy calculations. PIXEL has shown good agreement with a range of different intermolecular interactions, along with a significant saving in computer time over the higher level calculations. Aside from four empirical parameters, PIXEL requires only fundamental atomic properties such as ionisation potentials, electronegativities and van der Waals radii. For the most part, these values are obtained from standard reference tables and texts with the exception of atomic polarizabilities. This parameter is of great importance as it is used during the calculation of the dispersion term, an interaction which has a major influence on crystal packing. In previous work, atomic polarizabilities have been calculated using either the Slater-Kirkwood approximation or the Clausius-Mossotti relation. Both of these methods are rather simple, and do not account for possible changes in atomic polarizability resulting from differences in chemical environment. The Atoms in Molecules (AIM) approach has been used to attempt to obtain a range of polarizability values for atoms common to organic chemistry. It is observed that in the series of straight chained primary monoamines, Cn-H2n+3N, an alternation in melting points occurs between odd and even values of n. This alternation could be traced to differences in hydrogen-bonding and chain-packing that occur between odd and even-membered amines. Molecular interaction energy calculations were carried out using the PIXEL method, enabling quantitative energetic analysis of the packing differences. In this work, the crystal structures of the primary amines from ethylamine to decylamine were solved for the first time. All of these compounds are liquids at room temperature, so crystals were grown in situ by laser-assisted zone refinement at 10 K below their melting points. Diffraction data were then collected at 150 K. From propylamine to decylamine, all crystal structures are orthorhombic (or pseudo-orthorhomic) with the unit cell dimensions ~5 Ǻ x ~7 Ǻ x c Ǻ, where c increases with chain length. In the case of ethylamine, a phase characterised by single crystal diffraction at 180 K underwent a transition to a different phase on cooling to 150 K. The low-temperature phase was investigated using powder methods.