The rate constants for intramolecular reactions in polymer chains, obtained through a simulation method in the previous paper, are compared with the predictions of the theory of Friedman and O＇Shaughnessy, based on the renormalization group formalism. The theory describes a novel behavior of the cyclization process in certain conditions, predicting that it may be controlled by the equilibrium distribution of distances and not by the diffusion of the chain units. This prediction is confirmed by our simulation results, through the calculation of scaling laws of the rate constants with the length of the chain fragment between the reactive groups. Some quantitative theoretical predictions of the constants themselves are also checked against the simulation results. The effects of the theoretical treatment of relaxation times for internal fragments in the quantitative estimations of the rate constants is briefly discussed.