Excitation Energy Transfer in Bias-Free Dendrimers: Eigenstate Structure, Thermodynamics, and Quantum Evolution

We use matrix diagonalization in combination with real-time path integral methods to investigate the electronic eigenstates and exciton-vibration dynamics of model dendrimers with Frenkel exciton interactions between adjacent segments, which characterize structures composed of conjugated molecules. Even in the absence of an explicit energetic gradient in the electronic Hamiltonian, exciton couplings create a funnel through the eigenstate hierarchy that pulls the excitation energy away from the periphery. The competition between eigenstate structure and entropic considerations dictates the equilibrium distribution, which in small dendrimers at low temperatures tends to favor the core, shifting outward with increasing dendrimer size and thermal energy, although this distribution can be skewed back toward the core by increasing the exciton coupling between segments of the same generation. At high temperatures the distribution becomes classical, with all excited segments having the same population. Strong exciton-vibration coupling also shifts the equilibrium distribution in the classical direction. We find that the dynamics of excitation energy transfer is highly nontrivial and strongly affected by quantum mechanical effects. A positive value of the intrageneration coupling (regardless of the sign of the intergeneration coupling parameter) introduces a very slow component to the dynamics, which we attribute to electronic frustration. With exciton coupling, vibrational reorganization energy and thermal energy of approximately the same magnitude, the energy transfer dynamics is characterized by time scales that span 2 orders of magnitude. The rich dynamics that results from a single-parameter electronic Hamiltonian suggests a multitude of design possibilities for dendrimeric structures with a desirable function.