Exciton Dynamics of Molecular Aggregate Systems Composed of

J. Phys. Chem. C 2008, 112, 16675–16681

16675

Exciton Dynamics of Molecular Aggregate Systems Composed of Triangular Lattice Units: Structural Dependence of Exciton Migration and Recurrence Takuya Minami, Masayoshi Nakano,* Hitoshi Fukui, Hiroshi Nagai, Ryohei Kishi, and Hideaki Takahashi Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka UniVersity, Toyonaka, Osaka 560-8531, Japan ReceiVed: June 17, 2008; ReVised Manuscript ReceiVed: July 30, 2008

The exciton dynamics in molecular aggregate models composed of triangular lattice units have been investigated using the quantum master equation approach including relaxation terms originating in weak exciton-phonon coupling. We observe directed migration and recurrence motion of exciton after the irradiation of a laser field. It is found that the triangular lattice aggregates tend to suppress the decoherence behavior and thus to exhibit more distinguished longer-term exciton recurrence than the similar size dendritic aggregates, although the former show less efficient exciton migration, that is, light-harvesting behavior, than the latter. These dynamical features of exciton in the triangular lattice aggregate models turned out to be characterized by the strong interactions among spatially close-packed monomers through the branching points, originating in the equilateral triangular structure, as well as by the fractal, tournament-like, architecture. 1. Introduction Exciton migration and recurrence motion in dipole-coupled molecular aggregates have been intensively investigated toward a fundamental understanding of relaxation and coherent dynamics of excited states of super- and supramolecular systems.1-12 For instance, the light-harvesting behavior, which is caused by exciton migration, of phenylacetylene dendrimer with fractal architecture has been clarified to originate in the stepwise exciton relaxation among multistep exciton states with spatially wellsegmented, but a slightly overlapped, exciton distribution.13-27 Several control schemes of exciton dynamics in aggregate systems have been proposed, for example, tuning excitation energy of core monomer7 and adjusting relative configuration of dipoles.28 On the other hand, Yamazaki et al. have observed a long-term oscillatory anisotropy decay, originating in the exciton recurrence motion, in anthracene dimers, that is, dithiaanthracenophane (DTA) and dianthrylbenzene (DAB), in solution.29,30 They have suggested that rigid and fixed conformation between the chromophores plays an important role in reducing the dephasing rate. Such sensitive structure dependence of exciton dynamics suggests that there is still lots of room for improving the efficiency of exciton migration and recurrence as well as for proposing a novel control scheme of exciton dynamics by adjusting aggregate architectures. In this study, we investigate the exciton dynamics in triangular lattice aggregates, which are widely observed in partial structures of several metal complexes,31-33 graphynes, and graphydiynes,34-39 while they have not been examined from the viewpoint of exciton dynamics. The exciton dynamics after irradiation of a laser field in several aggregate models composed of equilateral triangular lattices is investigated using the quantum master equation approach including relaxation terms originating in weak exciton-phonon coupling. As a reference, the exciton dynamics in a similar size dendritic molecular aggregate model is examined. On the basis of the present results, we illuminate * Correspondingauthor.Fax:+81668506268.E-mail:[email protected].

the differences in exciton migration and recurrence motion between triangular lattice and dendritic aggregates, and thus clarify the relationship between the exciton dynamics and the structural feature of triangular lattice aggregates. This contribution will be useful for investigating a control scheme of coherent and incoherent exciton dynamics by tuning the structures of supramolecular systems. 2. Methodology 2.1. Construction of Exciton State Models of Aggregate Systems. We consider a molecular aggregate composed of twostate monomers with excitation energies {ωi} and magnitudes of transition dipole moments {µi} (i ) 1, 2, ..., N, N: the number of monomers). The Hamiltonian Hs for molecular aggregate is expressed by N

HS )

∑

ωi|i〉〈i| +

i

1 2

N

∑ Jij|i〉〈j|

(1)

i,j

where |i〉 indicates the aggregate basis, which represents the situation that monomer i is excited. We assume a dipole-dipole coupling between monomers i and j with an intermolecular distance Rij

Jij )

1 µiµj{cos(θij - θji) - 3 cos θij cos θji} Rij3

(2)

where θij(θji) is the angle between the transition moment of monomer i(j) and the vector drawn from monomer i to j. The one-exciton states {|ψk〉} with energies {ωk} obtained by a diagonalization of HS are expressed as N

|ψk 〉 )

∑ i

N

|i〉〈i|ψk 〉 ≡

∑ Cik|i〉(k ) 2, ..., M)

(3)

i

where M is equal to N + 1 in the one-exciton model, and k ) 1 indicates the ground state of the system.

10.1021/jp805328k CCC: $40.75  2008 American Chemical Society Published on Web 09/27/2008

16676 J. Phys. Chem. C, Vol. 112, No. 42, 2008

Minami et al. M dFRβ ΓRβ;mnFmn + iE ) -i(ωR - ωβ)FRβ dt m,n

∑

N

∑ (µRnFnβ n

FRnµnβ)(R * β) (8) where E represents the amplitude of the applied laser field, and the relaxation factors are given by

ΓRR;mm ) 2δRm

M

N

k

i

∑ ∑ |CiR|2|Cik|2γi(ωm - ωk) N

2

∑ |CiR|2|Cim|2γi(ωm - ωR) (9) i

and

ΓRβ;mn )

M

N

k

i

∑ ∑ [δβnCiR* |Cik|2Cimγi(ωm - ωk) + * δRmCin |Cik|2Ciβγi(ωn - ωk)] N

∑ [CiR* CimCin* Ciβ{γi(ωm - ωR) - γi(ωn - ωβ)}] (10) i

where

Figure 1. Structures of dendritic aggregate models (a), (b) and triangular lattice aggregate model (c), which are composed of identical two-state monomers with excitation energy ωi ) 38 000 cm-1 and transition moment µi ) 10 D.

2.2. Quantum Master Equation Including Relaxation Terms Originating in Weak Exciton-Phonon Coupling. In this section, we briefly explain our quantum master equation approach.9,10,40,41 An exciton on monomer i is assumed to interact with a nuclear vibration, that is, phonon state |qi〉 with a frequency {Ωqi}. The Hamiltonian HR for the phonon is given by

∑∑ i

qi

† Ωqici,q c i i,qi

(4)

where c†i,qi and ci,qi represent the creation and annihilation operators concerning a phonon state |qi〉, respectively. The interaction Hamiltonian HSR for weak exciton-phonon coupling is assumed to be

∑∑ i

qi

* † |i〉〈i|(κi,q c + κi,qicqi) i qi

H ) HS + HR + HSR

ΓRβ;Rβ ) ΓRβ + Γ′Rβ

(12)

N

∑ ∑ |CiR|2|Cik|2γi(ωR - ωk) +

1 ΓRβ ) (ΓRR + Γββ) ) 2 k(*R)

i

N

∑ ∑ |Ciβ|2|Cik|2γi(ωβ - ωk) (13)

k(*β) i

M

M

m

n

∑ ΓRR:mmFmm + iE∑ (µRnFnR - FRnµnR)

N

Γ′Rβ )

(6)

To examine the exciton migration for the molecular aggregate, we use the reduced density matrix F ) trR[χ], where χ is a density operator for the total system, and trR[ ] represents the trace over the phonon state in thermal equilibrium. The time evolution for F is examined using the quantum master equation in the Born-Markov approximation:9

and

The factor γi(ω) is taken to satisfy the thermal equilibrium condition:42 γ0i indicates the high-temperature limit of γi(ω), and kB is the Boltzmann constant. In the present study, we adopt an approximation that offdiagonal relaxation factor ΓRβ;mn is replaced by dominant diagonal term ΓRβ;Rβ, which can be partitioned into two contributions, ΓRβ (originating in the diagonal relaxation ΓRR and Γββ) and pure dephasing Γ′Rβ:41

(5)

where κi,qi represents a coupling constant between an exciton on monomer i and phonon state |qi〉. The total Hamiltonian, H, is expressed as

dFRR )dt

(11)

and

N

HSR )

2γi0 1 + exp(-ω/kBT)

where

N

HR )

γi(ω) )

(7)

∑ (|CiR|2 - |Ciβ|2)2γi(0)

(14)

i

The density matrix element in aggregate basis |i〉 is represented by

Fii(t) )

∑ 〈i|R〉〈R|F(t)|β〉〈β|i〉 ) ∑ CiRFRβ(t)Ciβ* Rβ

(15)

Rβ

3. Results and Discussion 3.1. Exciton States for Molecular Aggregate Models. We examine three kinds of molecular aggregate models (see Figure 1) composed of two-state monomers (shown by arrows) with excitation energy 38 000 cm-1 and transition moment 10 D. The adjacent monomers (with an intermonomer distance of 15 au) are assumed to interact with each other by dipole-dipole coupling. All of the models are constructed by plural self-similar building blocks: v-shaped building blocks with 120°-branching

Exciton Dynamics of Molecular Aggregate Systems

Figure 2. One-exciton state energies, ωR, and transition moments (shown by histogram), µRβ, between the ground and one-exciton states R for models (a), (b), and (c) are shown together with insets for (a) and (b): magnified views of low-lying exciton states.

for model (a), v-shaped building blocks with 60°-branching for model (b), and equilateral triangular lattices for model (c). The structures of these models are separated by generations G1-G4 as shown in Figure 1. The number of monomers in linear-leg region is different for generations: seven monomers for G1, three monomers for G2, and one monomer for G3 and G4. Model (a) is a dendritic aggregate, which mimics nanostar dendrimers widely known for their efficient light-harvesting property,14,20 whereas model (b) could be a model for another kind of dendritic system, which is composed of ortho-branching dendrons as shown in unsymmetrical branching dendrimers.21 Models (a) and (b) exhibit a difference in the branching angles, that is, 60°, 120°, and 180° for model (b) versus 120° for model (a). In contrast to models (a) and (b), model (c) is composed of equilateral triangular lattices with a tournament-like structure, which is a hypothetical model structure, although it could be built from triangular structures such as some kinds of metal complexes31-33 in real systems. Model (c) has more branches than models (a) and (b) due to the different size equilateral triangular structures involved in model (c). The dipole-dipole interaction between neighboring monomers with a branch angle of 60° is expected to be stronger than that with branch angles of 120° and 180° because the interaction is in proportion to 1/R3ij as shown in eq 2. The one-exciton states of these aggregates are obtained by diagonalizing the Hamiltonian HS [eq 1]. Figure 2 shows the exciton state energies and transition moments from the ground (vacuum) state. We observe stepwise exciton states with large energy intervals between states 3 and 4 (ω4,3 ) 461.2 cm-1),

J. Phys. Chem. C, Vol. 112, No. 42, 2008 16677 and between states 9 and 10 (ω10,9 ) 642.5 cm-1) for model (a) (Figure 2a), in contrast to models (b) and (c), which show more continuous energy gradients of exciton states: the energy differences between adjacent exciton states in low-lying state region (3 e R e 10) are 7.5 cm-1 e ωR,R-1 e 240.9 cm-1 for model (b), and 0.51 cm-1 e ωR,R-1 e 282.1 cm-1 for model (c) (see Figure 2b and c), where ωR,β indicates the energy difference between states R and β. In the low-lying exciton state region, model (c) exhibits more gentle energy gradient of exciton states with smaller energy intervals than does model (b): ω10,2 ) 603.0 cm-1 for model (c) versus ω10,2 ) 998.0 cm-1 for model (b). Figure 3 shows the spatial exciton distributions of relatively low-lying states included in exciton relaxation pathways as well as of the states in resonance with the irradiated field (21 for model (a), 46 for model (b), and 62 for model (c)) for models (a)-(c). It is found that the exciton distributions of states 2-5 for models (a) and (b) are well localized in generations, while those for model (c) are extended over adjacent generations; that is, the primary exciton distributions gradually shift from G1 to G2 as going from state 3 to 6. Such delocalization of exciton is predicted to be a result of the strong interaction between adjacent generations due to 60°-branching for model (c): states 2 and 3 show some extension of exciton distribution from G1 to G2 through 60°-branching points between G1 and G2. This is, however, still insufficient to explain the feature of state 5 for model (c), which exhibits negligible exciton distribution on the horizontal linear-leg region in G1, although the exciton in the horizontal linear-leg region of G1 should interact with 60°-branching in G2. To illuminate this feature, we evaluate the inherent exciton states of each generation (see Figure 4), which are obtained by calculating the exciton states of each generation as isolated aggregates: for instance, the inherent exciton states of G2 for model (a) (see Figure 1a) are obtained from the calculation of the two isolated v-shaped aggregates, each of which has 120°-branching and six monomers, in G2 for model (a). Figure 4 clarifies the differences in exciton states among these three models, although the original exciton states shown in Figure 2 are not completely reproduced by gathering the exciton states for each generation due to the elimination of intergeneration interactions. For all of the models, the bandwidths turn out to increase in the order G4 < G2 < G1. This reflects the fact that the length of linear-leg region (with J-aggregate type interaction) in each generation characterizes the energy level: longer linear-leg regions tend to give lower energies. Although G3 and G4 are constructed from the same size units, they give mutually different exciton states except for model (a). This is ascribed to the significant increase in the interaction between the building blocks in G4 for models (b) and (c) due to the spatially close-packed structures in contrast to the weak interaction between adjacent building blocks in G3 for model (a) due to the large interblock distances. From the comparison of the energy bandwidths of G3 among models (a)-(c), model (c) shows the largest bandwidth (1933.1 cm-1) due to the strong interaction between close-packed monomers originating in the triangular structure with 60°-branching. Similarly, model (c) also shows the largest bandwidth in G1 (4030.4 cm-1) and G2 (3613.5 cm-1) in the three models. In addition, the interbranch interaction due to close-packed structure is predicted to become weaker with increasing size of building block because of large distances between monomers on adjacent linear legs. This feature reduces the energy difference among generations with different linear-leg lengths, and thus for model (c), the lowest states 2 and 3 for G2 are close to states 3 and 4 for G1 around 36 000 cm-1 (see Figure

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Figure 3. Exciton spatial distributions of several exciton states of models (a), (b), and (c). Each circle is located on monomer, and its size represents the magnitude of exciton distribution.

4c). These four states are predicted to interact with each other and thus split the degenerate energy levels when combining G1 and G2 blocks to constitute the original architecture of model (c) (see Figure 1). Because of this interaction, these four states form the two pairs of exciton states with a little different exciton distribution for model (c): one pair (states 3 and 6) exhibits a larger split-energy interval than another pair (states 4 and 5) due to the negligible 60°-branching interaction concerning the horizontal linear-leg region in G1 for the latter pair. This feature is exemplified by the exciton distributions in the horizontal linerleg region of G1 in states 3, 4, 5, and 6 shown in Figure 3c: significant distributions for states 3 and 6, while negligible for states 4 and 5. As a result, the slight energy interval in lowlying exciton states between G1 and G2 blocks (see Figure 4c) is predicted to cause the slight energy interval between states 4

and 5 for model (c), which has exciton distribution delocalized over G1 and G2. 3.2. Exciton Migration Dynamics. The exciton dynamics of models (a), (b), and (c) are performed using eqs 7 and 8 after irradiating an external field in resonance with the exciton state having dominant distribution in G4 (G3), that is, state 21 for model (a) (37 830 cm-1), state 46 for model (b) (39 372 cm-1), and state 62 for model (c) (39 280 cm-1). The power and the irradiating cycle of applied continuous wave (cw) laser field are fixed to be 10 MW/cm2 and 100 optical cycles, respectively. We set the high-temperature-limit relaxation factor γi0 to be 10 cm-1 to reproduce the typical observed migration time of nanostar dendrimers similar to model (a),14,20 and we assume the case of nondamping from exciton state to vacuum state. After cutting off the laser field, the exciton migration is

Exciton Dynamics of Molecular Aggregate Systems

Figure 4. Exciton states inherent in individual generation for models (a), (b), and (c). Energy intervals between the highest and the lowest one-exciton states are also shown.

shown to occur depending on diagonal relaxation factor ΓRR;mm [see eqs 9 and 11]. From these expressions, the relaxation pathway is found to be determined by the overlap of exciton spatial distribution between exciton states, for example, ∑Ni |CiR|2|Cik|2, and energy differences involved in γi(ω).9 The variation in exciton population of each generation is shown in Figure 5, where t ) 0 ps indicates the cutoff time of the irradiating laser field. As seen from Figure 5, although we observe the exciton migration from G4 to G1 for all of the models, the dynamical behavior of exciton population in G2 and G3 for models (a) and (b) is significantly different from that for model (c). For models (a) and (b), exciton populations in G3 first increase, attain extrema, and then decrease followed by the similar behavior of populations in G2, the feature of which indicates a stepwise exciton migration through the neighboring generations. It is well-known in previous studies6,9 that such multistep migration occurs when the aggregate possesses an exciton funnel composed of multistep exciton states with an energy gradient from the periphery to the core, each of which has exciton distribution well segmented in each generation except for remaining slight overlap between adjacent generations. Such feature of realizing highly efficient light-harvesting property turns out to originate in the dendritic structure with 120°-branching. This result suggests that multistep exciton

J. Phys. Chem. C, Vol. 112, No. 42, 2008 16679

Figure 5. Time evolution of exciton population in each generation for models (a), (b), and (c) after irradiating a laser field with a power of 10 MW/cm2 for 100 optical cycles. The applied laser field is resonant with state 17 for model (a) (37 830 cm-1), state 46 for model (b) (39 372 cm-1), and state 62 for model (c) (39 280 cm-1), respectively.

migration occurs even for the dendritic aggregate involving 60°branching such as model (b). On the other hand, for model (c), significant stationary exciton population is shown to remain in G2 even at t ) 50 ps, which causes the incomplete migration to G1 for model (c) as compared to that for models (a) and (b): the exciton population in G1 (G2) at 50 ps is 0.054 (0.008) for model (a), 0.060 (0.0157) for model (b), and 0.0506 (0.0214) for model (c). Such inefficient light-harvesting property for model (c) is predicted to be explained by the near-degenerate low-lying states with spatially delocalized exciton distributions. Indeed, as seen from Figures 2c and 3c, there are slight energy differences between state 2 (with primary distribution in G1) and states 3-6 with delocalized exciton distribution over G1 and G2. The relaxation between exciton states driven by ΓRR;mm associated with energy difference [see eq 9] is found to reach the thermal equilibrium when the energy difference is sufficiently small. For model (c), therefore, the exciton population for states 2-6 with exciton distribution both in G1 and G2 is predicted to reach the equilibrium immediately after populating these states (feeding from higher-lying many states less than or equal to state 62), although significant population remains in G2 as compared to those of the other models. In summary, the inefficient light-harvesting property for model (c) is attributed

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to the near-degenerate states 2-6 in thermal equilibrium, which have exciton distribution delocalized over G1 and G2. 3.3. Exciton Recurrence Dynamics. As shown in previous papers,8,12,29,30 near-degenerate exciton states create a superposition state by irradiating a near-resonant laser field, and thus cause an exciton recurrence motion after cutting off the laser field. We create the superposition state by irradiating an incident field with frequency ω, which is near-resonant with states 3 and 5 (energy difference ω5,3 ) 462.3 cm-1, ω ) 35 150 cm-1) for model (a), with states 7 and 10 (ω10,7 ) 151.2 cm-1, ω ) 36 700 cm-1) for model (b), and with states 4 and 5 for model (c) (ω5,4 ) 35.9 cm-1, ω ) 35 920 cm-1). The power and the irradiating cycle of applied cw laser field are fixed to 10 MW/cm2 and 100 optical cycles, respectively. Because the cutoff time of the laser field is regarded as t ) 0 ps, the time evolution of FRβ after cutting off the field is described from eq 8 by

dFRβ ) -i(ωR - ωβ)FRβ - ΓRβ;RβFaβ dt

(16)

This is found to possess the following solution by time integration from 0 to t,

FRβ(t) ) FRβ(0)e-ΓRβ;Rβte-i(ωR-ωβ)t

(17)

and the exciton population on monomer i is represented by eq 15:

Fii(t) )

∑ CiRCiβ* FRβ(0)e-Γ

e-i(ωR-ωβ)t

Rβ;Rβt

(18)

Rβ

This implies that the exciton population on monomer i oscillates with frequency (ωR - ωβ) and takes a maximum amplitude * CiRCiβ FRβ(0) when near-resonant states R and β possess the sufficient overlap of exciton distribution, and the oscillation is exponentially decayed with the increase of time because of the off-diagonal relaxation term ΓRβ;Rβ. If there is the relationship between two monomers i and j:

CiR ) Ciβ and CjR ) -Cjβ

(19)

then the exciton populations on monomers i and j oscillate with mutually opposite phase; that is, exciton recurrence motion appears between monomers i and j.8 Distinct exciton recurrence motion between G1 and G2 is observed for models (b) and (c), while negligible recurrence motion is done for model (a) (see Figure 6). The relaxation factors ΓRβ, Γ′Rβ, and ΓRβ;Rβ (see eqs 12-14) are listed in Table 1, where R and β represent the near-resonant states: states 3 and 5 for model (a), states 7 and 10 for model (b), and states 4 and 5 for model (c). The pure dephasing factors Γ′Rβ are show to be significantly small for models (b) (0.08 cm-1) and (c) (0.04 cm-1) as compared to that for model (a) (1.73 cm-1). Sufficient overlap of exciton distributions gives a small value of Γ′Rβ and a large amplitude of recurrence oscillation as seen * from the term of (|CiR|2 - |Ciβ|2)2 (eq 14) and CiRCiβ (eq 18), respectively. Thus, it is presumable that the small value of Γ′Rβ and the occurrence of exciton recurrence oscillation are ascribed to be the abundant overlaps of exciton distributions between near-resonance states for models (b) (states 7 and 10) and (c) (states 4 and 5) (see Figure 3b and c). On the other hand, little overlap of exciton distribution (states 3 and 5 for model (a)) is also found to cause the negligible oscillation even if neardegenerate states are coherently excited to the superposition state as shown in model (a). For these reasons, small Γ′Rβ is found to be associated with distinct exciton recurrence motion. As seen from Figure 6, model (c) exhibits longer-term recurrence motion (about 9 ps) than does model (b) (about 3

Figure 6. Time evolution of exciton population in each generation for models (a), (b), and (c), after irradiating a laser field with a power of 10 MW/cm2 for 100 optical cycles. Applied laser field is in near resonance with states 3 and 5 (frequency 36 150 cm-1) for model (a), states 7 and 10 (frequency 36 700 cm-1) for model (b), and states 4 and 5 (frequency 35 920 cm-1) for model (c).

TABLE 1: Off-Diagonal Elements of Relaxation Factors [cm-1] (See Equations 12-14) model

ΓRβ

Γ′Rβ

ΓRβ;Rβ

a b c

3.02 8.94 2.72

1.73 0.08 0.04

4.75 9.02 2.76

ps) because of the smaller value of ΓRβ;Rβ, which is primarily determined by ΓRβ for models (b) and (c) (see Table 1). From eqs 11 and 13, ΓRβ is represented by the exciton population relaxation factors (ΓRR and Γββ) from near-degenerate states R and β (which create a superposition state by the near-resonant applied field) to all other lower-lying exciton states with significant exciton distribution overlap with states R and β. Although the near-degenerate states creating a superposition state for model (b) (states 7 and 10) and (c) (states 4 and 5) have relaxation pathways to the lower exciton states because of sufficient overlaps of exciton distributions (see Figure 3b and c), fewer relaxation pathways are expected for model (c) than for model (b) because the near-degenerate states for model (c) lie in states lower than those for model (b). This feature leads to the smaller value of ΓRβ for model (c) than for model (b). Similarly, model (a), although negligible oscillation is observed, shows a smaller value of ΓRβ than does model (b) (see Table 1) because of its lower near-degenerate states (states 3 and 5 for model (a) versus states 7 and 10 for model (b)).

Exciton Dynamics of Molecular Aggregate Systems From these results, it is generally predicted that ΓRβ becomes smaller when near-degenerate exciton states R and β are lowerlying states. On the basis of the above results, it turns out that the longterm exciton recurrence motion over different generations for model (c) is ascribed to the fact that the near-degenerate states 4 and 5 (creating a superposition state) are lower-lying states and possess sufficient exciton overlaps delocalized over G1 and G2. These features are realized due to the slight difference in inherent low-lying exciton states between G1 and G2 (see Figure 4c), which have transition moments due to the J-aggregate type interaction in each linear-leg region. It is found that the lowering of low-lying exciton states of G2 due to the strong interaction among 60°-branches in close-packed triangular lattice structure tends to create a superposition exciton state over different generations and to suppress the phase relaxation by decreasing the number of lower-lying exciton states that the populations of the near-degenerate states (creating the superposition state) damp into. These structure-dependent features of exciton states for model (c) are predicted to cause the long-term exciton recurrence motion between two neighboring generations G1 and G2. 4. Concluding Remarks We have investigated the exciton dynamics of triangular lattice and dendritic aggregate models using the quantum master equation approach. It is found that triangular lattice aggregate exhibits inefficient exciton migration due to the reaching of thermal equilibrium in low-lying degenerate exciton states caused by the close-packed structure. This feature alternatively leads to a long-term exciton recurrence motion, that is, suppression of decoherence, because of a superposition state composed of low-lying degenerate states with the exciton distribution delocalized over adjacent generations. On the basis of these results, inefficient exciton migration and long-term exciton recurrence motion are predicted to occur between two building blocks giving low-lying degenerate states. To realize these features of exciton states, close-packed structures such as triangular lattice building blocks are needed as well as a fractal feature in the length of linear-leg region. At the next stage, we further examine the exciton dynamics of other types of aggregate architecturestoconfirmthevalidityofthepresentstructure-property relationship as well as the effects of initially applied laser field, for example, circular polarized laser field. Acknowledgment. This work is supported by a Grant-inAid for Scientific Research (Nos. 18350007 and 20655003) from the Japan Society for the Promotion of Science (JSPS), a Grantin-Aid for Scientific Research on Priority Areas (No. 18066010) from the Ministry of Education, Science, Sports, and Culture of Japan, and the global COE (center of excellence) program “Global Education and Research Center for Bio-Environmental Chemistry” of Osaka University. References and Notes (1) (2) (3) (4)

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