Excitonic coupling in covalently linked multiporphyrin systems by matrix diagonalization

During the last decade, a variety of multidimensional chromophore arrays have been prepared to mimic the photosynthetic processes in natural light-harvesting complexes. At the same time, ultrafast spectroscopy has proven to be a good tool for elucidating their photophysical properties, including excitation energy transfer processes. Recently, ultrafast exciton dynamics in multiporphyrin arrays have been extensively investigated by time-resolved spectroscopic techniques such as time-correlated single photon counting and femtosecond transient absorption. The depolarization and exciton-exciton annihilation times could be obtained by time-resolved spectroscopic measurements using Förster-type incoherent energy transfer theory based on dipole-dipole coupling. In this article, the coupling energies of H- and J-type porphyrin aggregates were calculated by matrix diagonalization whose elements are the transition dipole coupling energies, including information on the relative orientation of transition dipoles, distances, and solvents. Analyzing the eigenvalues and eigenvectors obtained by matrix diagonalization, we were able to determine electronically allowed or forbidden transitions. The relationship between molecular structures and transition dipolar interactions exhibited in the steady-state absorption spectra was reexamined and compared with the experimentally observed incoherent energy hopping times in view of exciton coupling.