A simulation is presented that microscopically accounts for the role of incoherent excitation transfer in immobile, nonrandom pendent group aromatic polymers (single chain limit). By using a Monte-Carlo standard routine and master equation simulation software, accurate statistical mechanical averages of the relaxing optical excitation have been calculated for self-avoiding random chains of length N = 50 and N = 100(50 and 100 sites). Both the frequency-regime solution and its time-domain analog, i.e. the eigenvalues spectrum [Phi(omega(i))] and the excitation survival propability (p(t), respectively, have been computed. The focus of the simulations has been the study of excitation trapping as a function of varying D-D intersite coupling (i) for different trap locations (end-tagged vs random) and dimensionality, (ii) in presence of a radiative cutoff (fluorescence), and (iii) for reversible D-T events (detrapping) due to thermal release. We show that, in particular, the frequency spectrum of hopping modes [Phi(omega(i))] represents a powerful tool for extracting dynamical information that is usually concealed in phenomenological (nonexponential) kinetic models. The importance of reconstructing [Phi(omega(i))] from fluorescence convolution data by means of unbiased, numerical inversion in future measurements has been addressed.