<p>The prediction and characterisation of chemical and biochemical processes are fundamental tasks in computational chemistry. Small chemical systems can be characterised by the stationary points on potential energy surface and reaction paths linking them. For large biological systems, statistical sampling is required to characterising their average properties.</p> <p>This thesis presents my Ph.D. work on developing new methods to predict and characterise chemical and biological processes. Two path-finding methods for finding the minimum energy reaction path and alternative reaction paths for small gas-phase reactions have been elucidated with examples, and molecular dynamic simulations have been used to characterise the binding affinity of protein-ligand complex and the free energy of protonation processes in a protein.</p> <p>Specifically, the fast marching method (FMM) has been used to find the minimum energy path (MEP) on the potential energy surface (PES) for small gas-phase reactions. In this thesis, FMM is shown to be one of the most general and reliable surface-walking algorithms for finding the MEP. However, it is an expensive method. Some improvements have been illustrated in chapter 2 and chapter 3.</p> <p>I also proposed a new method (called QSM-NT) for finding all stationary points, accordingly all alternative reaction paths on the PES. Unlike other path-finding methods, QSM-NT overcomes the need of an initial guess of the path, and it can find all stationary points on the PES. QSM-NT has been proven to be efficient and reliable through applications on analytical PES and real chemical reaction. The difficulties and pitfalls associated with QSM-NT have been elucidated with examples.</p> <p>Molecular dynamic (MD) simulation and associated postprocessing procedures have been used to study the binding properties of caffeine-A_2A complex. The binding affinities of different binding modes have been calculated using MM/PBSA method. The binding pocket has been characterised with MM/GBSA energy decomposition. Our computational work provides significant insight to the targeted drug design of the adenosine A_2A receptor.</p> <p>The pH-dependent properties of a protein play important roles in the fundamental biological processes. The protonation states, namely, the pK_a values of ionisable residues, especially active-site residues are the prerequisites to understanding of the mechanisms of many biological processes. In this thesis, acetoacetate decarboxylase (AADase) is used as a test case for studying different types of pK_a prediction methods. Our computational results have shown that the site-site interactions from other ionisable residues are crucial to the pK_a prediction of the target residue.</p> <p>This thesis covers the range from small gas phase reaction prediction to large complex biological systems characterisation using quantum mechanical and molecular mechanical methods.</p> / Doctor of Philosophy (PhD)