Suppression or reduction of soot emissions is an important goal in the development of automotive engines for environmental and human health purposes. A better understanding at the molecular level of the formation process of soot particles resulting from collision and aggregation of smaller particles made of Polycyclic Aromatic Hydrocarbon (PAH) is needed. In addition to experiments, computational methods are efficient and valuable tools for this purpose. As a first step in our detailed computational chemistry study, we applied Ultra-Accelerated Molecular Dynamics (UAQCMD) and Canonical Monte-Carlo (CMC) methods to investigate the nucleation process. The UA-QCMD can calculate chemical reaction dynamics 107 times faster than conventional first principle molecular dynamics methods, while CMC can calculate equilibrium properties at various temperatures, pressures, and chemical compositions. We first calculated the dimerization dynamics (or stacking dynamics) of Polycyclic Aromatic Hydrocarbon (PAH) with different numbers of aromatic rings and taken as soot core for various practical automotive engine conditions. We found that PAH having 4-10 rings can stack under various combustion conditions by transferring efficiently collision energy to internal vibration energy (i.e., sliding motion among molecules) in agreement with previous studies. Such behavior was confirmed by CMC calculations of PAH stacking for various temperatures and pressures. Calculation of the collision dynamics of PAH in the presence of H or PAH radical species confirmed the formation of strong C-C chemical bonds stabilizing dimer structures even at high temperatures. These results were compared with previous computational and experimental results.