Graph theoretic and electronic properties of fullerenes, &, Biasing molecular modelling simulations with experimental residual dipolar couplings : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy at Massey University, Albany, New Zealand

Abstract

In this thesis two different models, that is levels of abstraction, are used to explore specific classes of molecular structures and their properties. In part I, fullerenes and other all-carbon cages are investigated using graphs as a representation of their molecular structure. By this means the large isomer space, simple molecular properties as well as pure graph theoretical aspects of the underlying graphs are explored. Although chemical graphs are used to represent other classes of molecules, cavernous carbon molecules are particularly well suited for this level of abstraction due to their large number of isomers with only one atom type and uniform hybridisation throughout the molecule. In part II, a force field for molecular dynamics, that is the step wise propagation of a molecular structure in time using Newtonian mechanics, is complemented by an additional term that takes into account residual dipolar couplings that are experimentally measured in NMR experiments. Adding this force term leads to more accurate simulated dynamics which is especially important for proteins whose functionality in many cases crucially depends on their dynamics. Large biomolecules are an example of chemical systems that are too large for treatment with quantum chemical methods but at the same time have an electronic structure that is simple enough for accurate simulations with a forcefield.