A better understanding of the formation of polycyclic aromatic hydrocarbons (PAH) is of great practical interest because of their potential hazardous health effects and their role as intermediates in soot and fullerene formation. The potential surfaces of the reactions C6H5 + C2H2 and 1-C10H7 + C2H2 were explored by density-functional theory using BLYP and B3LYP functionals. Vibrational analysis allowed the determination of thermodynamic data and deduction of high-pressure-limit rate constants via transition state theory. The pressure and temperature dependences of these chemically activated reactions were computed using the modified strong collision approximation. The comparison of the predictions for the C6H5 + C2H2 system with experimental data showed good agreement in particular at high temperatures relevant for a combustion environment. The dominant product from acetylene addition to I-naphthyl at low pressures is the five-membered ring species acenaphthylene, consistent with the more pronounced formation of fullerenes under such conditions. High pressure favors formation of stabilized initial adducts, i.e., phenylvinyl and 1-naphthylvinyl. Some products not considered previously, such as 1-acenaphthenyl, 1-naphthylacetylene, 2-vinylphenyl, and 1-vinyl-2-phenyl, are found to be important under some pressure and temperature conditions. All of our results are consistent with known free-radical chemistry. Rate constants describing the formation of phenylacetylene, phenylvinyl, -vinyl-2-phenyl, 1-naphthylvinyl, 1-vinyl-8-naphthyl, 1-napthylacetylene, acenaphthylene, and 1-acenaphthenyl are given at 20 and 40 Ton as well as at 1 and 10 atm for the temperature range from 300 to 2100 K.