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

Abstract

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.

Time-Evolving Quantum Superpositions in Open Systems and the Rich Content of Coherence Maps

“…One of the most notable examples is the B850 ring of the LH2 complex, where the arrangement of the bacteriochlorophyll units leads to H-type nearest-neighbor coupling terms . Besides flipping the signs of the eigenstates, positive coupling values were recently found to give rise to intriguing dynamical effects in excitonic Hamiltonians with a dendrimer topology, which were attributed to electronic frustration . Here we examine the time evolution of coherence maps for a 10-site chain weakly coupled to a low-temperature bath with parameters to those in Figure , but with J nn = prefix+ 1 .…”

“…30 Besides flipping the signs of the eigenstates, positive coupling values were recently found to give rise to intriguing dynamical effects in excitonic Hamiltonians with a dendrimer topology, which were attributed to electronic frustration. 41 Here we examine the time evolution of coherence maps for a 10-site chain weakly coupled to a lowtemperature bath with parameters to those in Figure 5, but with = + J 1 nn . In this frustration-free system, the population evolution is very similar to that shown in the middle panel of Figure 4.…”

Path Integral over Equivalence Classes for Quantum Dynamics with Static Disorder

“…If exciton−vibration coupling is neglected, the dynamics of excitation energy transfer does not depend on the sign of the electronic coupling. However, recent work 47,48 found that the time evolution of electronic populations is much slower in the case of a trimer with J > 0. This finding was explained 48 by the presence of a conical intersection between the ground and excited adiabatic states of this trimer, which leads to geometric phases that can significantly affect the dynamics.…”

“…This finding was explained 48 by the presence of a conical intersection between the ground and excited adiabatic states of this trimer, which leads to geometric phases that can significantly affect the dynamics. 49−51 The appearance of a conical intersection that involves the ground state is the consequence of electronic frustration, 47 the formation of a pair of degenerate states which are created because it is not possible to accommodate alternating signs in the wave function of a system with an odd number of units. The Figure 4 also investigates the effects of static disorder in model trimers with opposite signs of J.…”

Quantum Coherent Phenomena in Energy Harvesting and Storage

“…Recent breakthroughs have also come from advances in theoretical and computational methods, such as the ability to accurately simulate complex spectra from complex and heterogeneous chemical systems, as well as to model interactions between chromophores, polymers, and donor−acceptor complexes. This includes accurate evaluation of exciton-vibration coupling, 24 identification of intermolecular charge-transfer couplings leading to excimer formation, 25 quantification of interchain contacts in donor−acceptor polymers, 12 consideration of vibrations as an energy buffer, 26 and modeling of Herzberg−Teller vibronic coupling in hexacene. 27 Overall, this VSI highlights a few of the many exciting directions possible when considering the role of quantum coherences in energy conversion pathways.…”