Electrolytic solutions contain mobile ions that can pass current, and are essential components of any solution-phase electrochemical system. The Nernst–Planck–Poisson equations describe the electrodynamics and transport dynamics of electrolytic solutions. This thesis applies modern numerical and mathematical techniques in order to solve these equations, and hence determine the behaviour of electrochemical systems involving charge transport. The following systems are studied: a liquid junction where a concentration gradient causes charge transport; an ideally polarisable electrode where an applied potential difference causes charge transport; and an electrochemical cell where electrolysis causes charge transport. The nanometre Debye length and nanosecond Debye time scales are shown to control charge separation in electrolytic solutions. At equilibrium, charge separation is confined to within a Debye length scale of a charged electrode surface. Non-equilibrium charge separation is compensated in solution on a Debye time scale following a perturbation, whereafter electroneutrality dictates charge transport. The mechanism for the recovery of electroneutrality involves both migration and diffusion, and is non-linear for larger electrical potentials. Charge separation is an extremely important consideration on length scales comparable to the Debye length. The predicted features of capacitive charging and electrolysis at nanoelectrodes are shown to differ qualitatively from the behaviour of larger electrodes. Nanoscale charge separation can influence the behaviour of a larger system if it limits the overall rate of mass transport or electron transfer. This thesis advocates the use of numerical methods to solve the Nernst–Planck–Poisson equations, in order to avoid the simplifying approximations required by traditional analytical methods. As this thesis demonstrates, this methodology can reveal the behaviour of increasingly elaborate electrochemical systems, while illustrating the self-consistency and generality of fundamental theories concerning charge transport.

For the first time, successful synthesis and characterisation of the missing (Z)-isomer of thallium(I) methanediazotate has been accomplished, utilising low-temperature NMR monitoring analysis. The title compound was synthesised from N-methyl-N-nitrosourea and thallium(I) propoxide, under sub-ambient temperature conditions, as a highly moisture sensitive entity. Quantum chemical calculations, performed at the CCSD(T) level, depict excellent conformity to experimental results. Indeed, compared to its (E) counterpart, the formation of the title compound is thermodynamically less favoured, but preferred by means of kinetic control owing to a hindered isomerisation.

For the first time, successful synthesis and characterisation of the missing (Z)-isomer of thallium(I) methanediazotate has been accomplished, utilising low-temperature NMR monitoring analysis. The title compound was synthesised from N-methyl-N-nitrosourea and thallium(I) propoxide, under sub-ambient temperature conditions, as a highly moisture sensitive entity. Quantum chemical calculations, performed at the CCSD(T) level, depict excellent conformity to experimental results. Indeed, compared to its (E) counterpart, the formation of the title compound is thermodynamically less favoured, but preferred by means of kinetic control owing to a hindered isomerisation.

This thesis covers a range of methodologies to provide an account of the current (2010-2014) state of the art and to develop new methods for solubility prediction. We focus on predictions of intrinsic aqueous solubility, as this is a measure commonly used in many important industries including the pharmaceutical and agrochemical industries. These industries require fast and accurate methods, two objectives which are rarely complementary. We apply machine learning in chapters 4 and 5 suggesting methodologies to meet these objectives. In chapter 4 we look to combine machine learning, cheminformatics and chemical theory. Whilst in chapter 5 we look to predict related properties to solubility and apply them to a previously derived empirical equation. We also look at ab initio (from first principles) methods of solubility prediction. This is shown in chapter 3. In this chapter we present a proof of concept work that shows intrinsic aqueous solubility predictions, of sufficient accuracy to be used in industry, are now possible from theoretical chemistry using a small but diverse dataset. Chapter 6 provides a summary of our most recent research. We have begun to investigate predictions of sublimation thermodynamics. We apply quantum chemical, lattice minimisation and machine learning techniques in this chapter. In summary, this body of work concludes that currently, QSPR/QSAR methods remain the current state of the art for solubility prediction, although it is becoming possible for purely theoretical methods to achieve useful predictions of solubility. Theoretical chemistry can offer little useful additional input to informatics models for solubility predictions. However, theoretical chemistry will be crucial for enriching our understanding of the solvation process, and can have a beneficial impact when applied to informatics predictions of properties related to solubility.

The knowledge of the packing behaviour of small organic compounds in crystal lattices is of great importance for industries dealing with solid state materials. The properties of materials depend on how the molecules arrange themselves in a crystalline environment. Crystal structure prediction provides a theoretical approach through the application of computational strategies to seek possible crystal packing arrangements (or polymorphs) a compound may adopt. Based on the chemical diagrams, this thesis investigates polymorphism of several small organic compounds. Plausible crystal packings of those compounds are generated, and their lattice energies are minimised using molecular mechanics and/or quantum mechanics methods. Most of the work presented here is conducted using two software packages commercially available in this field, Polymorph Predictor of Materials Studio 4.0 and GRACE 1.0. In general, the computational techniques implemented in GRACE are very good at reproducing the geometries of the crystal structures corresponding to the experimental observations of the compounds, in addition to describing their solid state energetics correctly. Complementing the CSP results obtained using GRACE with isostructurality offers a route by which new potential polymorphs of the targeted compounds might be crystallised using the existing experimental data. Based on all calculations in this thesis, four new potential polymorphs for four different compounds, which have not yet been determined experimentally, are predicted to exist and may be obtained under the right crystallisation conditions. One polymorph is expected to crystallise under pressure. The remaining three polymorphs might be obtained by using a seeding technique or the utilisation of suitable tailor made additives.

A summary of research conducted since September 2007 at the University of Toronto in the laboratory of Professor Robert A. Batey is presented in this thesis, which is divided into four chapters. The first chapter contains a two-part introduction, where aryl- and aliphatic-Claisen rearrangements are discussed in part 1, and the nucleophilic addition of organoboron reagents to unsaturated C–N functionalities is described in part 2. Chapter 2 contains research involving synthetic and theoretical studies of aryl-Claisen rearrangements and other sigmatropic reactions. The work towards developing the lanthanide-catalyzed domino aryl-Claisen rearrangement for the synthesis of contiguous aryl–C(sp³) moieties is presented first. This is followed by computational studies involving E/Z-selectivity differences for the aryl-Claisen rearrangement, which was an issue noted for the domino aryl-Claisen reaction of a linear substrate. The mechanistic origins of E/Z-selectivity differences for the mono aryl-Claisen rearrangement, which was experimentally ambiguous for over 40 years, is resolved through computational methods. A theoretical analysis of selectivity differences for the allylic azide rearrangement is also described. The third section contains a discussion of Eu(fod)3-catalyzed aryl-Claisen rearrangements on vinyl bromide systems and preliminary studies involving application of the substrates in cross-coupling reactions, and other attempted mono- and domino sigmatropic rearrangements are presented in the fourth section. In chapter 3, the search for computational methods that can accurately predict experimental free energy of activation barriers for the aliphatic-Claisen rearrangement through benchmarking studies with a priori kinetic barrier and kinetic isotope effect data is described. Methods were found to predict new valid transition states and predict ΔG‡ values with a mean unsigned error of 0.3 kcal/mol relative to experimental values. In chapter 4, the development of new allylboration reaction is outlined, involving the double allylboration of nitriles and anhydrides, and initial studies towards the first aminoallylboration reactions of N-aluminoaldimines to form 1,2-diamines.

The rationalisation of drug potency using three-dimensional structures of protein-ligand complexes is a central paradigm in medicinal research. For over two decades, a major goal has been to find the rules that accurately relate the structure of any protein-ligand complex to its affinity. Addressing this problem is of great concern to the pharmaceutical industry, which uses virtual screens to computationally assay up to many millions of compounds against a protein target. A fast and trustworthy affinity estimator could potentially streamline the drug discovery process, reducing reliance on expensive wet lab experiments, speeding up the discovery of new hits and aiding lead optimization. Water plays a critical role in drug-protein interactions. To address the often ambiguous nature of water in binding sites, a water placement method was developed and found to be in good agreement with X-ray crystallography, neutron diffraction data and molecular dynamics simulations. The method is fast and has facilitated a large scale study of the statistics of water in ligand binding sites, as well as the creation of models pertaining to water binding free energies and displacement propensities, which are of particular interest to medicinal chemistry. Structure-based scoring functions employing the explicit water models were developed. Surprisingly, these attempts were no more accurate than the current state of the art, and the models suffered from the same inadequacies which have plagued all previous scoring functions. This suggests a unifying cause behind scoring function inaccuracy. Accordingly, mathematical analyses on the fundamental uncertainties in structure-based modelling were conducted. Using statistical learning theory and information theory, the existence of inherent errors in empirical scoring functions was proven. Among other results, it was found that even the very best generalised structure-based model is significantly limited in its accuracy, and protein-specific models are always likely to be better. The theoretical framework developed herein hints at modelling strategies that operate at the leading edge of achievable accuracy.

This thesis presents algorithm development in computational chemistry, and applies new computer science concepts to voltammetric simulation. To begin, this thesis discusses why algorithm development is necessary, and inherent problems found in commercial simulation solvers. As a result of this discussion, this thesis describes the need for simulators to keep abreast of recent computational developments. Algorithm development in this thesis is taken through stages. Chapter 3 applies known theory relating to the stripping voltammetry at a macroelectrode to the diffusional model of a microdisk, using finite difference and alternating direction implicit simulation techniques. Chapter 4 introduces the concept of parallel computing, and how computational hardware has developed recently to take advantage of out-of-order calculations, by processing them in parallel to reduce simulation time. The novel area of graphics card simulation for highly parallel algorithms is also explained in detail. Chapter 5 discusses the adaptation of voltammetric finite difference algorithms to a purely parallel format for simulation by explicit solution. Through explicit solution, finite difference algorithms are applied to electrode geometries which necessitate a three-dimensional solution – elliptical electrodes; square, rectangular, and microband electrodes; and dual microdisk electrodes in collector-generator mode. Chapter 6 introduces 'Random Walk' simulations, whereby individual particles in the simulation are modelled and their trajectories over time are calculated. The random walk technique in this thesis is improved for pure three-dimensional diffusion, and adapted to graphics cards, allowing up to a factor 4000 increase in speed over previous computational methods. This method is adapted to various systems of low concentration confined voltammetry (chapter 6.4) and single molecule detection, ultra low concentration cyclic voltammetry (chapter 6.5), and underpotential deposition of thallium on mobile silver nanoparticles (chapter 6.6). Overall, this thesis presents, and applies, a series of algorithm development concepts in computational electrochemistry.

The processes by which anisotropic colloidal and nanoscale particles may come together to form ordered monodisperse structures are not well understood. The canonical example of such a system is provided by the assembly of virus capsids, in which tens to thousands of particles of one or a few types assemble efficiently into ordered, highly symmetrical shells. Other examples include a wide variety of protein oligomers, and there is interest in producing analogous systems of synthetic particles. In this thesis I study the self-assembly of simple model particles, consisting of spheres decorated with attractive patches. I consider in detail the assembly of clusters of particles corresponding to the Platonic solids. For the majority of these structures assembly is found to be efficient over a wide range of parameter space. The optimal conditions represent a compromise between thermodynamic stability and kinetic accessibility. We consider two versions of the model, with and without constraints on the torsion angle of bound particles. In both cases the structures with triangular faces are found to assemble most easily. In the absence of torsional constraints dodecahedra will not assemble under any set of parameters as a result of the preferential formation of disordered aggregates. With torsional constraints included all of the Platonic solids assemble successfully and the behaviour of the model is considerably changed. In particular disordered aggregates become far less favourable. I explore possible methods of assembling larger structures, either via “hierarchical” assembly where small clusters are first assembled and then used as building blocks in another stage of assembly, or by a templating method in which an inner cluster acts as a template for a larger outer cluster. These approaches are studied using the “Virtual Move Monte Carlo” cluster move algorithm, the behaviour of which we examine in some detail.

This thesis describes the synthesis, characterisation and reactivity of diamide-amine and bis(cyclopentadienyl) supported Group 4 hydrazido(2-) compounds towards unsaturated molecules. The mechanisms of these transformations are probed using a range of structural, kinetic and computational methods.