  Although H$_{2}$ is the simplest and the most abundant molecule in the
Universe, its formation in the interstellar medium, especially in the
photodissociation regions is far from being fully understood. According to
suggestions, the formation of H$_{2}$ is catalyzed by polyaromatic hydrocarbons
(PAHs) on the surface of interstellar grains. In the present study, we have
investigated the catalytic effect of small PAHs with an imperfect aromatic
system. Quantum chemical computations were performed for the H-atom-abstraction
and H-atom-addition reactions of benzene, cyclopentadiene, cycloheptatriene,
indene, and 1H-phenalene. Heights of reaction barriers and tunneling reaction
rate constants were computed with density functional theory using the MPWB1K
functional. For each molecule, the reaction path and the \warn{rate constants}
were determined at 50 K using ring-polymer instanton theory, and the
temperature dependence of the \warn{rate constants} was investigated for
cyclopentadiene and cycloheptatriene. The computational results reveal that
defects in the aromatic system compared to benzene can increase the rate of the
catalytic H$_{2}$ formation at 50 K.
