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In this thesis, we consider the problem of constructing G₂-instantons on two types of asymptotically conical manifolds, namely the Bryant-Salamon S³xR⁴ and the infinite collection of manifolds Mm,n constructed by Foscolo, Haskins and Nordström. Some progress has been made with the former example by Clarke, Lotay and Oliveira, while nothing was known about the existence of such instantons on the manifolds Mm,n. We firstly construct a 1-parameter family of instantons on the Bryant-Salamon S³xR⁴, and hence complete the picture of all invariant instantons on this manifold. Secondly, we construct a 1-parameter family of instantons on M₁,₁ via a dynamical systems argument. Further, we consider an existence question of G₂-instantons on S³xR⁴ with an asymptotically locally conical metric, known as the BGGG metric. Again, some progress has been made in understanding the existence of such instantons on this manifold by Lotay and Oliveira, but there is still a region of initial conditions for which the existence of global solutions was previously unknown. We prove the existence of a boundary of initial conditions running through this unknown region and hence fully characterise the asymptotic behaviour of all complete bounded G₂-instantons on a specific bundle over this manifold.

The work in this thesis considers the effect of solvation on both electronic and vibrational spectroscopy. It examines the accurate modelling of solvation effects in the prediction of chemical properties and the influence of solvation when conducting ultrafast spectroscopy. In the first presented paper, the molecule alizarin is observed to have a secondary species in solution when dissolved in methanol. We identify this species first by conducting pump-dependent/pH-dependent transient electronic absorption spectroscopy (TEAS) and then by predicting the UV-Vis of different candidate species with explicit-solvent time-dependent density functional theory (TDDFT). This paper showed the three main considerations for UV-Vis prediction in solution are electrostatic effects, non-electrostatic effects (eg. hydrogen bonding), and possible photoactive equilibrium species in solution. In the second presented paper catechol was examined in acetonitrile. Catechol is a key building block of the natural photoprotecting molecule eumelanin and hence is often used in a bottom-up approach to understand its photochemical properties. In this paper, we find that, contrary to previous work, catechol does not exist in two different conformers in polar and non-polar solvents. Rather, the differences in excited state lifetime in acetonitrile versus cyclohexane is due to hydrogen bonding to the solvent coupled with a higher propensity to aggregate in the former. This was studied using concentration-dependent TEAS and frequency prediction with explicitly modelled solvent. The third presented paper considers the sunscreen component homosalate. Homosalate undergoes ultrafast intramolecular proton transfer to form a \keto" form when photoexcited. Following this, the keto-S1 form decays non-radiatively, similarly to catechol, to the ground-state via a conical intersection. A small population of the keto-S1 state decays radiatively via uflorescence. In the solution phase, alongside these two processes, there is evidence that inter-system crossing also takes place to form a triplet state, this decays via phosphorescence. While this molecule behaves favourably as a sunscreen, the formation of a potentially reactive triplet state warrants further investigation. These conclusions were the result of gas and solution phase ultrafast spectroscopy as well as implicit-solvent TDDFT.

The Ab peptide is a key molecule in the development of Alzheimer’s Disease - Ab peptides form toxic aggregates in the brain. Density functional theory (DFT), Parametric Model 7 (PM7) and ligand-Field Molecular Mechanics (LFMM) methods have been used to model the interactions of a series of potential therapeutic PtII(ligand) complexes with various fragments of the Ab peptide. LFMM calculations with the AMBER forcefield were used to generate conformations of PtII-Ab6-14 via LowMode MD and results validated against BHandH. While LFMM showed insufficient agreement with DFT, the semi-empirical PM7 method displayed strong geometric and energetic agreement and was used to predict coordination preference and stable conformations of PtII(bipy) and PtII(phen) complexes. These species are shown to restrict the conformational freedom of Ab and the coordination of PtII(phen) is shown to be in agreement with experimental data. Studies of additional PtII(ligand) complexes in this manner revealed distinct preferences in metal binding mode for each of the complexes studied, with varied His Nd and His Ne coordination observed. Analysis of peptide conformations using Ramachandran plots and the STRIDE algorithm indicate that coordination of the PtII(ligand) complexes disrupts existing peptide structure in a ligand-specific fashion, interrupting or translating the turn structure, suggesting that controlling peptide structure and behaviour may be achieved via ligand design. Ligand-field molecular dynamics (LFMD) simulations of PtII(phen) -Ab16 and -Ab42 are compared to those of the metal-free peptides to investigate the influence of the PtII complex on the structure and properties of the peptide. Simulations of Ab16 and PtII(phen)-Ab16 revealed that PtII coordination does not drastically alter peptide size, but increases the occurrence of 3,10-helical conformations while disrupting hydrogen bond and salt bridge networks. Simulation data also highlights the prevalence of p-p stacking interactions between residues Phe4 and His13 with the phenanthroline ligand. Similarly, microsecond timescale simulations of PtII(phen)-Ab42 and Ab42 illustrate profound effects of PtII coordination on peptide structure; while Ab is shown to adopt collapsed conformations, PtII-Ab42 systems assume extended structures. PtII coordination also induces large changes in peptide secondary structure, particularly an increase in helical character throughout the central hydrophobic region of the peptide, considered a potential route to preventing formation of Ab fibrils. The results detailed here provide insight into the coordination of these complexes to the peptide and present a new understanding of the effects of PtII complexes on Ab.

Exhaled breath is a rich and complex matrix containing many hundreds of compounds. Every breath offers the potential of a non-invasive measurement of the biochemical processes occurring in the human body and it is this notion that has led to the application of breath analysis for the detection of disease. With the majority of research in the field being focused on the detection of biomarkers, little has been presented on how the seemingly homeostatic matrix of breath varies during the course of normal life events. The research in this thesis describes how a subject's emotional state, physical state, and daily activities can alter the composition of exhaled breath.