A reaction pathway is explored in which two cyclopenta groups combine on the zigzag edge of a graphene layer. The process is initiated by H addition to a five-membered ring, followed by opening of that ring and the formation of a six-membered ring adjacent to another five-membered ring. The elementary steps of the migration pathway are analyzed using density functional theory to examine the region of the potential energy surface associated with the pathway. The calculations are performed on a substrate modeled by the zigzag edge of tetracene. Based on the obtained energetics, the dynamics of the system are analyzed by solving the energy transfer master equations. The results indicate energetic and reaction-rate similarity between the cyclopenta combination and migration reactions. Also examined in the present study are desorption rates of migrating cyclopenta rings which are found to be comparable to cyclopenta ring migration
