This thesis investigates the optical, kinetic, and thermodynamic properties of soot precursor molecules, namely polyaromatic hydrocarbons (PAHs), by applying \textit{ab initio} quantum chemical methods. In particular, density functional theory (DFT) is applied to study the properties of several different types of PAHs, including curved PAHs, localized $\pi$-radical PAHs, and cross-linked PAHs. These studies help model the gas phase chemistry that leads to the formation of these different types of PAHs, and also help assess their relevance to the formation of soot.

The optical band gaps (OBGs) of curved, cross-linked, and radical PAHs are computed using a DFT method corroborated with UV/Visible spectroscopy measurements. Curved PAHs are shown to increase the OBG due to hybridisation changes. In contrast, $\pi$-radical character was found to decrease the band gap. Crosslinks are observed to minimally impact the OBG of the monomers. The effect of $\sigma$-radicals on the OBG was also shown to be negligible. The results suggest that curved and $\pi$-radical PAHs of moderate size can also explain the optical properties of flames.

The persistence of the polarity of curved aromatics in flame conditions is investigated by using DFT to calculate their barriers and rates of inversion. Curved PAHs above 11--15 ($\approx$ 0.8 nm) rings in size were seen to be unable to invert at flame temperatures. This is seen to be a function of the number of pentagons, and hence curvature. \textit{Ab initio} quantum molecular dynamics of a 1 nm curved PAH and C\textsubscript{3}H\textsubscript{3}\textsuperscript{+} chemi-ion suggest molecular dipole fluctuations of 10--20%, with the chemi-ion and PAH being bound for the entire simulation. This suggests curved PAHs are persistently polar at 1500~K and can bind substantially to ions in flames.

The kinetics of seven-member ring formation in PAHs containing a five-member ring is investigated. Seven-member ring formation by the hydrogen-abstraction-acetylene-addition (HACA) mechanism is studied for two different PAHs, one closed shell and one resonance-stabilised-radical (RSR) PAH. The seven-member ring forms more quickly for the RSR PAH. Seven-member ring formation by four different bay closure processes is also studied. The rate constants determined for the pathways are then used in kinetic simulations in 0D homogeneous reactors. The hydrogen abstraction based pathway is seen to dominate until higher temperatures, where the carbene pathway takes over. The results suggest that seven-member ring formation in PAHs containing a five-member ring is possible at flame temperatures.

The impact of localized $\pi$-radicals on soot formation is explored by developing a simple mechanism for their formation and computing their relative concentrations under flame conditions using 0D homogeneous reactor simulations. It is seen that flame temperatures at the onset of nucleation (1400--1500~K) promote the formation of localized $\pi$-radicals on rim-based pentagonal rings, whilst lower temperatures favor fully saturated rings, and higher temperatures favor the $\sigma$-radical. A kinetic Monte Carlo study indicates that multiple localized $\pi$-radicals can form on a single PAH suggesting localized $\pi$-radicals on rim-based pentagonal rings could be important to understanding the mechanism of soot formation.

The rate and equilibrium constants of cross-linking reactions between PAHs of various reactive edge types is computed. The forward rate constants confirms that reactions involving aryl $\sigma$-radicals are generally fast, but the reactions between aryl $\sigma$-radicals and localized $\pi$-radicals were notably faster than others. Computed equilibrium constants showed that reactions involving $\sigma$ and $\pi$-radical PAHs are the most favorable at flame temperatures. Calculations for larger PAHs showed that the formation of bonded-and-stacked structures results in substantially enhanced equilibrium constants for the reaction of two large localized $\pi$-radicals. This suggests that combined physical and chemical interactions between larger $\pi$-radical PAHs could be important in flame environments.