Density-operator description of excitons in molecular aggregates. II. Optical line-shape selection rules of "one-dimensional" excitons and excitation localization in finite molecular chains

In a previous paper, a method based on superoperators techniques suggested by Fano and on the stochastic exciton Hamiltonian proposed by Haken et al., has been proposed for the calculation of optical line shapes and macroscopic dynamics of exciton states of an assembly of oriented dimers in a nonresonant matrix. This method is now extended to the calculation in a very simple manner for larger systems: analytical expressions are obtained for optical line shapes of exciton states in finite chains where the Born-von Kármán boundary conditions are relaxed in the nearest-neighbor constant coupling scheme. Edge effects (asymmetrical nondefinite positive contributions to the absorption) appear to be negligible only for large chains ($N\gtrsim 20$) and also depend on the prepared state. Numerous line shapes are presented; molecular chains possessing simple geometrical configurations (parallel, alternate, and helix) exhibit specific optical selection rules, shown to be very sensitive to the conformation (for instance, to the angular step in helix chains). The mathematics of the selection rules are worked out extensively. The selection rules are related to the concept of collective excitations in a homogeneous photon field and with analogy to an interference experiment. For large chains the selection rules relax to those predicted for "one-dimensional" crystals. Using an entropylike function from information theory, we have investigated the expectation value of the degree of localization of an electronic excitation in an aggregate by direct optical absorption. The localization is discussed quantitatively: for instance, it is shown that, in the absence of traps, drastic conditions are required for the material system and the exciting light (polarization, energy, and coherence) to obtain localization on a site.