Exciton migration dynamics in a dendritic molecular aggregate

Optimized excitonic transport mediated by local energy defects: Survival of optimization laws in the presence of dephasing

In an extended star with peripheral defects and a core occupied by a trap, it has been shown that exciton-mediated energy transport from the periphery to the core can be optimized [S. Yalouz et al., Phys. Rev. E 106, 064313 (2022)2470-004510.1103/PhysRevE.106.064313]. If the defects are judiciously chosen, then the exciton dynamics is isomorphic to that of an asymmetric chain and a speedup of the excitonic propagation is observed. Here we extend this previous work by considering that the exciton in both an extended star and an asymmetric chain is perturbed by the presence of a dephasing environment. Simulating the dynamics using a Lindblad master equation, two questions are addressed: How does the environment affect the energy transport on these two networks? and Do the two systems still behave equivalently in the presence of dephasing? Our results reveal that the timescale for the exciton dynamics strongly depends on the nature of the network. But quite surprisingly, the two networks behave similarly regarding the survival of their optimization law. In both cases, the energy transport can be improved using the same original optimal tuning of energy defects as long as the dephasing remains weak. However, for moderate or strong dephasing, the optimization law is lost due to quantum Zeno effect.

Extended star graph as a light-harvesting-complex prototype: Excitonic absorption speedup by peripheral energy defect tuning

We study the quantum dynamics of a photoexcitation uniformly distributed at the periphery of an extended star network (with N_{B} branches of length L_{B}). More specifically, we address here the question of the energy absorption at the core of the network and how this process can be improved (or not) by the inclusion of peripheral defects with a tunable energy amplitude Δ. Our numerical simulations reveal the existence of optimal value of energy defect Δ^{*} which depends on the network architecture. Around this value, the absorption process presents a strong speedup (i.e., reduction of the absorption time) provided that L_{B}≤L_{B}^{*} with L_{B}^{*}≈12.5/ln(N_{B}). Analytical and numerical developments are then conducted to interpret this feature. We show that the origin of this speedup takes place in the hybridization of two upper-band excitonic eigenstates. This hybridization is important when L_{B}≤L_{B}^{*} and vanishes almost totally when L_{B}>L_{B}^{*}. These structural rules we draw here could represent a potential guide for the practical design of molecular nanonetwork dedicated to the realization of efficient photoexcitation absorption.

Continuous-time quantum walk on an extended star graph: Disorder-enhanced trapping process

Using a tight binding model, we investigate the dynamics of an exciton on a disordered extended star graph whose central site acts as an energy trap. When compared with what happens in an ordered network, our results reveal that the disorder drastically improves the excitonic absorption that becomes complete. Moreover, we show the occurrence of an optimal disorder for which the absorption time is strongly minimized, a surprising effect that originates in a disorder-induced restructuring process of the exciton eigenstates. Finally, we also show the existence of an optimal value of the absorption rate that reduces even more the absorption time. The resulting superoptimized trapping process is interpreted as a positive interplay between both the disorder and the so-called superradiance transition.

Continuous-time quantum walk on an extended star graph: Trapping and superradiance transition

A tight-binding model is introduced for describing the dynamics of an exciton on an extended star graph whose central node is occupied by a trap. On this graph, the exciton dynamics is governed by two kinds of eigenstates: many eigenstates are associated with degenerate real eigenvalues insensitive to the trap, whereas three decaying eigenstates characterized by complex energies contribute to the trapping process. It is shown that the excitonic population absorbed by the trap depends on the size of the graph, only. By contrast, both the size parameters and the absorption rate control the dynamics of the trapping. When these parameters are judiciously chosen, the efficiency of the transfer is optimized resulting in the minimization of the absorption time. Analysis of the eigenstates reveals that such a feature arises around the superradiance transition. Moreover, depending on the size of the network, two situations are highlighted where the transport efficiency is either superoptimized or suboptimized.

A theoretical investigation of symmetry-origin unidirectional energy gradient in light-harvesting dendrimers

We theoretically investigate a possibility that the symmetry of the repetitively branched structure of light-harvesting dendrimers creates the energy gradient descending toward inner generations (layers of pigment molecules) of the dendrimers. In the first half of this paper, we define a model system using the Frenkel exciton Hamiltonian that focuses only on the topology of dendrimers and numerically show that excitation energy tends to gather at inner generations of the model system at a thermal equilibrium state. This indicates that an energy gradient is formed in the model system. In the last half, we attribute this result to the symmetry of the model system and propose two symmetry-origin mechanisms creating the energy gradient. The present analysis and proposition are based on the theory of the linear chain (LC) decomposition [S. Koda, J. Chem. Phys. 142, 204112 (2015)], which equivalently transforms the model system into a set of one-dimensional systems on the basis of the symmetry of dendrimers. In the picture of the LC decomposition, we find that energy gradient is formed both in each linear chain and among linear chains, and these two mechanisms explain the numerical results well.

Equivalence between a generalized dendritic network and a set of one-dimensional networks as a ground of linear dynamics

It has been shown by some existing studies that some linear dynamical systems defined on a dendritic network are equivalent to those defined on a set of one-dimensional networks in special cases and this transformation to the simple picture, which we call linear chain (LC) decomposition, has a significant advantage in understanding properties of dendrimers. In this paper, we expand the class of LC decomposable system with some generalizations. In addition, we propose two general sufficient conditions for LC decomposability with a procedure to systematically realize the LC decomposition. Some examples of LC decomposable linear dynamical systems are also presented with their graphs. The generalization of the LC decomposition is implemented in the following three aspects: (i) the type of linear operators; (ii) the shape of dendritic networks on which linear operators are defined; and (iii) the type of symmetry operations representing the symmetry of the systems. In the generalization (iii), symmetry groups that represent the symmetry of dendritic systems are defined. The LC decomposition is realized by changing the basis of a linear operator defined on a dendritic network into bases of irreducible representations of the symmetry group. The achievement of this paper makes it easier to utilize the LC decomposition in various cases. This may lead to a further understanding of the relation between structure and functions of dendrimers in future studies.

Disorder-enhanced exciton delocalization in an extended dendrimer

The exciton dynamics in a disordered extended dendrimer is investigated numerically. Because a homogeneous dendrimer exhibits few highly degenerate energy levels, a dynamical localization arises when the exciton is initially located on the periphery. However, it is shown that the disorder lifts the degeneracy and favors a delocalization-relocalization transition. Weak disorder enhances the delocalized nature of the exciton and improves any quantum communication, whereas strong disorder prevents the exciton from propagating in accordance with the well-known Anderson theory.

EXCITON MIGRATION IN DENDRITIC AGGREGATE SYSTEMS USING THE QUANTUM MASTER EQUATION APPROACH INVOLVING WEAK EXCITON-PHONON COUPLING

The quantum master equation approach involving a weak exciton-phonon coupling is applied to the exciton migration dynamics of dendritic molecular aggregates modeled after a phenylacetylene dendrimer, D25, which exhibits an efficient light-harvesting property. The mechanism of efficient exciton migration from the periphery to the core is studied by analyzing relaxation terms among the exciton states originating in weak exciton-phonon coupling. Partial overlaps of exciton distributions between neighboring exciton states are found to be important for realizing the unique migration behavior by step-by-step transfer from the periphery to the core via multi-step exciton states. The same calculation method is applied to the exciton dynamics of a larger dendritic aggregate model, D127, modeled after the largest synthesized phenylacetylene dendrimer D127 in order to examine the dependencies of the exciton migration on the strength of the intermolecular interaction and the temperature of phonon bath. In the case of the relatively weak dipole-dipole coupling, exciton is not observed to migrate efficiently from the periphery to the core, while the largest exciton population is found to remain in the intermediate generations. This is ascribed to the fact that the thermal excitation to the higher exciton states significantly contributes to the exciton distribution in the equilibrium state when the weak intermolecular interaction reduces the energy difference between exciton states. This indicates that the intermolecular interaction is important not only for the overlaps of the exciton distributions between the exciton states, but also the relation between the exciton energy differences and thermal excitations, which spoil the distinct concentration of exciton distribution in the core generation. In the case of a low temperature, even if the intermolecular interaction is weak, the exciton population in the core region is found to be the largest in all the generations. This suggests that exciton tends to efficiently migrate from the periphery to the core when the temperature is sufficiently low. Implications of these theoretical results are discussed in relation to design of magneto-optical materials and other technological applications.

Mechanistic principles and applications of resonance energy transfer

Resonance energy transfer is the primary mechanism for the migration of electronic excitation in the condensed phase. Well-known in the particular context of molecular photochemistry, it is a phenomenon whose much wider prevalence in both natural and synthetic materials has only slowly been appreciated, and for which the fundamental theory and understanding have witnessed major advances in recent years. With the growing to maturity of a robust theoretical foundation, the latest developments have led to a more complete and thorough identification of key principles. The present review first describes the context and general features of energy transfer, then focusing on its electrodynamic, optical, and photophysical characteristics. The particular role the mechanism plays in photosynthetic materials and synthetic analogue polymers is then discussed, followed by a summary of its primarily biological structure determination applications. Lastly, several possible methods are described, by the means of which all-optical switching might be effected through the control and application of resonance energy transfer in suitably fabricated nanostructures.Key words: FRET, Förster energy transfer, photophysics, fluorescence, laser.

Excited-State Structure and Dynamics of 1,3,5-Tris(phenylethynyl)benzene as Studied by Raman and Time-Resolved Fluorescence Spectroscopy

Excited-state structure and dynamics of 1,3,5-tris(phenylethynyl)benzene (TPB) have been studied in n-hexane and n-heptane solutions. Time-resolved fluorescence spectra, fluorescence anisotropy, and lifetime of TPB were recorded with femtosecond to nanosecond time resolution. Raman depolarization ratio was also measured to elucidate a nonplanar structure of the ground state. Two fluorescence components, the short-lived component with 150 fs lifetime and the long-lived component with 10 ns lifetime, were observed. The analysis of the fluorescence anisotropy values combined with the Raman depolarization data has led to a conclusion that TPB is primarily excited to a short-lived excited singlet state with a nonplanar structure, and then it relaxes to a long-lived excited singlet state with a 3-fold axis. A rapid structural change from a nonplanar to a planar structure is suggested to take place in the process of relaxation.

Exciton recurrence motion in aggregate systems in the presence of quantized optical fields

The exciton dynamics of model aggregate systems, dimer, trimer, and pentamer, composed of two-state monomers is computationally investigated in the presence of three types of quantized optical fields, i.e., coherent, amplitude-squeezed, and phase-squeezed fields, in comparison with the case of classical laser fields. The constituent monomers are assumed to interact with each other by the dipole-dipole interaction, and the two-exciton model, which takes into account both the one- and two-exciton generations, is employed. As shown in previous studies, near-degenerate exciton states in the presence of a (near) resonant classical laser field create quantum superposition states and thus cause the spatial exciton recurrence motion after cutting the applied field. In contrast, continuously applied quantized optical fields turn out to induce similar exciton recurrence motions in the quiescent region between the collapse and revival behaviors of Rabi oscillation. The spatial features of exciton recurrence motions are shown to depend on the architecture of aggregates. It is also found that the coherent and amplitude-squeezed fields tend to induce longer-term exciton recurrence behavior than the phase-squeezed field. These features have a possibility for opening up a novel creation and control scheme of exciton recurrence motions in aggregate systems under the quantized optical fields.

Light-harvesting function through one-by-one electron and hole transfer in a methane-lithium system

Carrying out a semiclassical molecular dynamics simulation of a CH4-Li2 system by using the time-dependent local density approximation of the time-dependent density functional theory, we find that one-by-one electron and hole transfer takes place from CH4 to Li2 when an electron is excited in CH4. Probability of the transfer is low when the molecules are fixed, but it increases when the molecules are freely relaxed or Li2 has 1 eV of initial velocity.

Quantum Master Equation Approach to the Second Hyperpolarizability of Nanostar Dendritic Systems

We investigate the dynamic second hyperpolarizability (gamma) of nanostar dendritic systems using the quantum master equation approach. In the nanostar dendritic systems composed of three-state monomers, the multistep exciton states are obtained by the dipole-dipole interactions, and the directional energy transport, i.e., exciton migration, from the periphery to the core is predicted to occur by the relaxation between exciton states originating in the exciton-phonon coupling. The effects of the intermolcecular interaction and the exciton migration, i.e., exciton relaxation, on the gamma in the third-harmonic generation (THG) are examined in the three-photon off- and on- resonance regions using the two-exciton model. Furthermore, the method for analysis of spatial contributions of excitons to gamma is presented by partitioning the total gamma into the one- and two-exciton contributions. It turns out that the exciton relaxation between exciton states causes significant broadening of the spectra of gamma and their mutual overlap as well as the relative increase of two-exciton contributions in the nanostar dendritic system.

Exciton migration dynamics in a dendritic molecule: Quantum master equation approach usingab initiomolecular orbital configuration interaction method

We investigate the exciton migration dynamics in a dendritic molecular model composed of pi-conjugation linear-leg units (acetylenes and diacetylene) and a benzene ring (branching point) using the quantum master equation approach with the ab initio molecular orbital (MO) configuration interaction (CI) method. The efficient migration of exciton from short-length linear legs (acetylenes) to long-length linear leg (diacetylene) via a benzene ring is observed. As predicted in previous studies, the exciton (electron and hole) distributions are relatively well localized in each generation segmented by the meta-branching point (meta-substituted benzene ring) though the electron and hole distributions are delocalized and are somewhat spatially different from each other within each generation. It is found that the excitons localized in the generation composed of short linear legs occupy in higher-lying exciton states, while those in the generation composed of long linear legs do in lower-lying ones. These features suggest the decoupling of pi-conjugation at the meta-branching point. On the other hand, the relaxation effect between exciton states is found to be caused by the exciton-phonon coupling, in which the existence of common configurations (electron-hole pairs) in CI wave functions between adjacent exciton states (having primary distributions on short and long linear-leg regions, respectively) is important for the relaxation between their exciton states. This feature indicates the importance of partial penetration of pi-conjugation through the meta-substituted benzene ring in excited states for such exciton migration.

THEORETICAL STUDY OF EXCITON–EXCITON CORRELATION EFFECT ON EXCITON MIGRATION IN MOLECULAR AGGREGATE

Two-exciton migration dynamics of a molecular aggregate is performed using the density matrix approach. Exciton–exciton correlation is shown to cause an oscillatory behavior in the one-exciton population dynamics. Such a feature is found to be well explained by the bypass transition from the ground to a one-exciton forbidden state via a two-exciton state.

Theoretical study on second hyperpolarizabilities of phenylacetylene dendrimer: toward an understanding of structure-property relation in NLO responses of fractal antenna dendrimers

This contribution explores the relation between molecular second hyperpolarizabilities (gamma) and molecular architecture in phenylacetylene dendrimers using the semiempirical molecular orbital method, that is, INDO/S method. The orientationally averaged gamma of a large-size phenylacetylene dendrimer, which is composed of 24 units of phenylacetylenes and is referred to as D25, is found to be about 50 times as large as that of the diphenylacetylene monomer. In contrast, the gamma(s)() value of D25 is found to be about 6 times as small as that of the para-substituted phenylacetylene oligomer (L25) composed of 24 units of phenylacetylenes. To investigate the structure-property relation in gamma for D25 and L25, we examine the spatial contributions of electrons to gamma values using gamma density analysis. The present analysis reveals that the dominant contributions of electrons to gamma of D25 are localized in the linear-leg regions parallel to the applied electric field and the contributions are also well segmented at the meta-connected points (benzene rings), while the spatial distribution of the gamma density of L25 is extended over the whole region of the chain, and the dominant contribution stems from the both-end regions. It is found for D25 that the magnitude of contributions to gamma in the internal region is more enhanced than that in the outer region. We further found that the magnitudes of contributions in internal linear-leg regions of D25 are somewhat larger than those of the same-size isolated linear-leg molecules. This suggests that the slightly remaining pi-conjugations via the meta-branching points still enhance the contributions to gamma localized in the linear-leg regions. These features of spatial contributions to gamma of D25 are found to originate in the fractal architecture, in which pi-conjugation lengths in the linear-leg region increase on going from the periphery to the core. Finally, fractal antenna dendrimers are expected to be promising novel nonlinear optical (NLO) substances with a controllability of the magnitude and spatial contribution of the third-order NLO properties.