Extensive ab initio Gaussian-3-type calculations of potential energy surfaces (PES), which are expected to be accurate within 1-2 kcal/mol, combined with statistical theory calculations of reaction rate constants have been applied to study various possible pathways in the hydrogen abstraction acetylene addition (HACA) mechanism of naphthalene and acenaphthalene formation as well as Diels-Alder pathways to acenaphthalene, phenanthrene, and pyrene. The barrier heights; reaction energies; and molecular parameters of the reactants, products, intermediates, and transition states have been generated for all types of reactions involved in the HACA and Diels-Alder mechanisms, including H abstraction from various aromatic intermediates, acetylene addition to radical sites, ring closures leading to the formation of additional aromatic rings, elimination of hydrogen atoms, H disproportionation, C2H2 cycloaddition, and H2 loss. The reactions participating in various HACA sequences (e.g., Frenklach's, alternative Frenklach's, and Bittner and Howard's routes) are demonstrated to have relatively low barriers and high rate constants under combustion conditions. A comparison of the significance of different HACA mechanisms in PAH growth can be made in the future using PES and molecular parameters obtained in the present work. The results show that the Diels-Alder mechanism cannot compete with the HACA pathways even at high combustion temperatures, because of high barriers and consequently low reaction rate constants. The calculated energetic parameters and rate constants have been compared with experimental and theoretical data available in the literature.