Sequentially Coupled HoleâElectron Transfer ... - ACS Publications

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Sequentially Coupled Hole−Electron Transfer Pathways for BridgeMediated Triplet Excitation Energy Transfer Tsutomu Kawatsu†,‡ and Jun-ya Hasegawa*,†,§,∥,⊥ †

Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano-nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan Institute for Molecular Science, National Institute of Natural Science, 38 Nishigo-Naka, Myodaiji, Okazaki 444-8585, Japan § Quantum Chemical Research Institute (QCRI), Kyodai Katsura Venture Plaza, North Building 106, 1-36 Goryo-Oohara, Nishikyo-ku, Kyoto 615-8245, Japan ∥ Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto University, Kyoto-Daigaku-Katsura, Nishikyo-ku, Kyoto 615-8510, Japan ‡

ABSTRACT: The donor−acceptor electronic coupling for a bridge-mediated triplet excitation energy transfer (EET) was analyzed to determine the tunneling pathway using intergroup tunneling configuration fluxes. In the singlet EET, the electronic coupling is primarily composed of direct coupling between the donor and acceptor with a secondary contribution from bridge-mediated single-step through-exciton pathways. In contrast, the triplet EET is dominated by superexchange interactions due to the Förster-type interaction becoming forbidden. The triplet EET tunneling pathways are characterized as a sequentially coupled hole and electron transfer (CHET) for both direct and bridgemediated EETs. This is the first report concerning the difference between the triplet and singlet EETs of the electronic mechanism of bridge-mediated superexchange mechanisms. extended Huckel level.20,22,23 In recent development, the analysis has been extended to the Hartree−Fock,17,24−26 density functional theory,27,28 and ZINDO27,28 levels. In our recent development, we have extended the method for EET using CI wave functions.13−15 We have developed theoretical methods to calculate the superexchange electronic coupling for EET and to determine the electronic tunneling pathways.13−15 These methods were applied to singlet EETs in various model systems.13−15 The result showed that the direct coupling from the Förster term was the most important in many cases. The superexchange coupling may become the dominant term when the direct coupling decreases due to unfavorable dipole−dipole orientations.29−35 The main component of the superexchange coupling was single-step through-exciton tunneling pathways because the interactions with the virtual states arose from a long-range Förster-type pseudo-Coulombic interaction. In the triplet EET, the Förster-type interaction becomes forbidden, and the Dexter-type interaction contributes to the electronic coupling. Therefore, we seek to clarify how the triplet excitation is transferred via virtual states in molecules and to determine how the triplet and singlet cases differ. Thus, far, superexchange electronic coupling in the triplet EET has been interpreted only with direct charge-transfer (CT) interactions between the donor and acceptor,36−38 and the role of the bridging fragments has been proposed based on the experimental results.36,38 In the present study, we have

1. INTRODUCTION Excitation energy transfer (EET) is a fundamental energy conversion process in biology and material science. EETs in photosynthetic light harvesting,1−3 luminescent jellyfish aequorea Victoria,4,5 and fluorescent proteins used in imaging technology6,7 are well-known examples of singlet EET. Triplet EET also plays important roles. In the photosynthetic system, the triplet EET from the chlorophyll to the carotenoid is necessary to quench the excess energy in the triplet chlorophyll.1−3 In the light-emitting diode, a combination of an electron and a hole produces singlet and triplet excited states, and the diffusion of these states is driven by an EET mechanism until a light is emitted or quenched.8,9 Clarifying the difference between the triplet and singlet EETs is an important step for rational material design. Electronic coupling in EET is classified into direct and indirect (superexchange) couplings. The direct one is the coupling between the initial and final states of the EET and includes the Förster and Dexter terms.10 The Förster term, which is called the pseudo-Coulombic interaction, is often approximated using the dipole−dipole interaction as the lowest order of the multiple expansion.10 The Dexter term11 originates from electronic exchange interaction, and quantum chemical methods are necessary to properly evaluate this contribution. The superexchange coupling is mediated by virtual electronic states,12−16 and the tunneling pathways defined using the configuration fluxes are useful for understanding the origin of the coupling.13−16 The configuration flux originally called as tunneling current has been developed for the electron transfer.17−21 The technique has been applied to determine the tunneling pathway in various protein systems in the © 2012 American Chemical Society

Received: July 28, 2012 Revised: October 7, 2012 Published: October 18, 2012 23252

dx.doi.org/10.1021/jp307482e | J. Phys. Chem. C 2012, 116, 23252−23256

The Journal of Physical Chemistry C

Article

LMO r belongs to fragment s; otherwise, ϑsr = 0. MOs were localized in one of the fragments as described below. For convenience, JNM is normalized as

developed methods to calculate the electronic coupling for triplet EET and to determine the tunneling pathways. As shown below, there is a clear difference in the tunneling pathway between the triplet and singlet EETs. In the next section, we describe our methods and models for calculations. In the third section, the result for the triplet EET is compared with that for the singlet EET, and clear differences in the electronic coupling are explained. A brief summary is given in the fourth section.

KN → M(E) ≡

∑ C̅pI(E)(E1 − H)pq Cq̅ F(E) pq

(1)

The wave functions of the initial and final states are ΨI =

∑ C̅pI(E)Φp p∉A

C̅pI(E)

= −C̅ DI0(E)

∑

H D0pGpq(E)

p ∉ A , p ≠ D0

ΨF =

∑ C̅pF(E)Φp p∉D

C̅pF(E) = −C̅ AF0(E)

∑

Gqp(E)H pA

0

p∉D,p≠A0

(2)

where Φp is a Slater determinant with localized molecular orbitals (LMOs). D0 and A0 are the primary donor and acceptor states, respectively. The other Slater determinants are treated as perturbation terms to describe the initial and final states. Gpq(E) ≡ (1/(H − E1))pq is the Green’s function of the perturbation part. The configuration-interaction (CI) coefficients of the D0 and A0 terms are determined by normalization of the initial and final states, respectively. From eq 2, it is assumed that the wave functions of the initial and final states are not populated on the acceptor and donor, respectively. The tunneling pathways are defined as the connection between the tunneling configuration fluxes from the donor state to the acceptor state. The interdeterminant tunneling flux is13,18,19,22,26,46,47 Jpq (E) =

1 I (C̅p(E)Cq̅ F(E) − C̅pF(E)Cq̅ I(E))Hpq ℏ

∑ p∈N ,q∈M

(5)

Figure 1. GFPc-Tyr-CFPc model system. CFPc and GFPc are the donor and acceptor, respectively. The border between the fragments are separated by white broken lines. The numbers in parentheses are fragment indices.

(3)

Next, the tunneling pathways were coarse-grained and represented in the molecular fragment base.13 We introduced a group of excitations, which had been labeled N and M. The intergroup tunneling configuration was defined as JNM (E) =

TIF(E)

KN→M constructs a network of the density flux, which are termed the tunneling pathways. Here, we briefly mention a generalization of the wave function. These formulas for the tunneling pathway analysis are not limited within single excitations and can be generalized to include higher-order excitations in the initial and final wave functions because the present definition of the tunneling flux, eq 3, is represented using general determinants. However, the definition of the “group” in the intergroup tunneling configuration has to be extended. In the present study, we have developed a computational program for the triplet EET, and we have applied it to a GFPcX-CFPc model for comparison with the results from the singlet EET.14 Herein, GFPc and CFPc refer to green and cyan fluorescent protein chromophores, respectively. In this study, GFPc was in the deprotonated form, and X denotes an amino acid. We chose X = Tyr because Tyr has the highest contribution to the total TIF via the through-X pathway in our singlet EET calculations. The structure in the singlet state was optimized at the B3LYP48,49/6-31G*50 level for the X = Ala model, and an additional optimization was performed only for the Tyr portion. To compare the results for the singlet and triplet states, we used the optimized singlet-state structure for triplet state. We note that a realistic calculation should adopt a geometry in which the EET occurs. The GFPc-X-CFPc model was divided into five fragments, GFPc-pep1-Tyr-pep2-CFPc, as shown in Figure 1. The MOs were localized on each fragment

2. THEORETICAL AND COMPUTATIONAL DETAILS Our methods are briefly described below. The electronic coupling between the initial and final states is written as13,39−45 TIF(E) = ⟨Ψ|I E − Ĥ |ΨF⟩ =

ℏJNM (E)

using a hybrid localization scheme.46 LMOs for GFPc, Tyr, and CFPc were calculated using the (minimum-orbital deformation) MOD method.46,47 The reference MOs (RMOs) were calculated for isolated fragments using the Hartree−Fock (HF) method. A hydrogen atom was supplied for the link atoms. D95 basis sets51 were employed for all of the atoms. The STO-6G52 basis set was employed for the link atoms. LMOs for pep1 and pep2 were localized using the Pepek−Mezay (PM)53 method. For the tunneling energy (E), we used the average value of the first excitation energies for the GFPc and CFPc fragments (0.1515 and 0.0724 au for singlet and triplet states, respectively). All of the calculations were performed using the Gaussian03 program54 (modified for the present purpose).

Jpq (E)PpN PqM (4)

The excited determinants, which had been labeled p and q, were classified into one of the groups. The assignment was determined by PNp and PM q , which are the populations of the Slater determinant p and q in groups N and M, respectively. The population was defined by PpN = ϑanϑim. Here, the determinant p describes the excitation from MO i to MO a, and the excitation group N corresponds to an excitation from fragment n to fragment m. ϑsr is a step function: ϑsr = 1 when 23253



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3. RESULTS AND DISCUSSION In Figure 2, we show the intergroup tunneling configuration fluxes, KN→M (eq 5), in a two-dimensional matrix. The reddish

is illustrated in Figure 3a. The K7→13 and K13→1 connection in Figure 2a is interpreted as a singlet EET via an exciton state at

Figure 3. Examples of the EET tunneling pathways. (a) Excitonmediated superexchange mechanism in the singlet EET. (b) The superexchange mechanism mediated by the coupled hole and electron transfers (CHET) in the triplet EET. Fragment 4 was discarded for simplicity.

fragment 3. This result agrees with the results from our previous studies,13−15 in which we determined that the direct pathway is the most important pathway and that the single-step through-exciton superexchange pathways are secondary pathways for the singlet EET. In contrast, the KN→M map for the triplet EET is completely different from the singlet one, as shown in Figure 2b. The Hamiltonian interaction between excited determinantsΦi→a and Φj→b are written as

Figure 2. Maps of the intergroup tunneling configuration flux. The reddish and bluish colors indicate positive and negative KN→M values. The fluxes with |KN→M| ≥ 10−5 are shown on a log scale. (a) Singlet EET. The pink squares correspond to exciton transfer groups. (b) Triplet EET. The purple and green squares correspond to the electron and hole transfer regions, respectively. (c) List of groups and corresponding types of excited states. N: n → m means that group N is an excitation from fragment n to fragment m. The fragment number is shown in Figure 1.

⟨Φi → a|Ĥ |Φj → b⟩ = δi , jFa , b − δa , bFi , j + ⟨aj|ib⟩ − ⟨aj|bi⟩

(6)

where occupied indices (i, j) and unoccupied indices (a, b) are the spin orbitals. Fxy is a Fock matrix element. In the triplet EET, the third term of eq 6 is zero because spin orbitals i and a have different spins. In other words, the Förster term, which is the origin of the singlet EET, becomes spin forbidden. The total TIF (2.3 × 10−8 au) becomes much smaller than that of the singlet EET (TIF = 7.2 × 10−4 au). Therefore, alternative tunneling pathways dominate the electronic coupling for the triplet EET. The purple and green squares in Figure 2b indicate areas of electron transfers (ET) and hole transfers (HT), respectively. Inside a purple square, an electron in an unoccupied orbital moves another unoccupied orbital in another fragment and a hole in an occupied orbital stays in the same fragment. In contrast, each element in the green square shows that only a hole moves and an electron stays in a certain fragment. These areas became much more prominent in the KN→M map. The large KN→M of the triplet EET primarily belongs to either the ET or HT in Figure 2b. On the basis of the EET pathway, we determined that sequentially coupled hole and electron transfers (CHET) were the dominant pathways. The strongest pathway was a combination of K7→2 → K2→1, which corresponds to a direct HT from fragment 2 (donor) to fragment 1 (acceptor), followed by a direct ET from fragment 2 to fragment 1. The large KN→M values for groups 7 and 1, which are the local excitations in the donor and acceptor, respectively, are due to these groups having particularly large CI coefficients.

and bluish colors indicate positive and negative KN→M values. Because of the character of the flux, the KN→M matrix is antisymmetric. By connecting KN→M in a sequential manner, we define the tunneling pathway from the donor to the acceptor via the bridge fragments. The vertical and horizontal axes are groups of excited configurations. In Figure 2c, we show how an index for a group corresponds to an excitation from fragment n to fragment m. A group with n = m refers to an exciton state because an electron excitation occurs in the local fragment, n. If n ≠ m, a group is referred to a CT state. To understand the difference between the singlet and triplet EETs, we first explain the KN→M map for the singlet EET shown in Figure 2a. The KN→M distribution exhibits a particular pattern. To illustrate the specificity, we show the groups of exciton states as pink squares. A crossing point between two squares indicates an exciton transfer between groups N and M. The strongest case was found for K7→1, which is the direct excitation transfer from donor (7) to acceptor (1). This result indicates that the singlet EET of the model system is driven by the fluorescent resonance energy transfer (FRET) mechanism. Visible KN→M occurs only on the K7→M and KN→1, which indicates that the primary tunneling pathways use only one other bridge group than do the donor and acceptor. One of the prominent examples of exciton-mediated singlet EET pathways 23254



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optimized in the HF calculation, the MOs of the higher energy unoccupied MOs are typically more widely distributed than the occupied MOs.

This direct CT contribution was discussed by Harcourt et al.12,55,56 However, the triplet EET pathways are actually composed of multiple CHET; an example of this type of pathway is shown in Figure 3b. Sequential HT to fragment 5 and then to fragment 1 is followed by sequential ET to fragment 3 and then to fragment 1. This result can be understood by examining the form of the exchange integral shown in the fourth term of eq 6. The integral ⟨aj|bi⟩ becomes large when a = b or i = j. Therefore, it is favorable to maintain the electron/hole in a fixed orbital and to let the hole/electron move forward. A comparison of Figures 3a and 3b reveals that the triplet EET pathways involve more steps than the singlet one and that a number of combination patterns exist. We note that the same pathways observed in the triplet EET exist in the singlet EET, but the absolute contribution to TIF is very small. In addition, the total TIF (2.3 × 10−8 au) of the triplet EET is much smaller than the indirect term (3.2 × 10−5 au) of singlet EET. Therefore, even though the direct pathway of singlet EET becomes forbidden by the specific conformation between the donor and acceptor, the triplet EET is much slower than the singlet EET. Therefore, the strong pathways, such as the one shown in Figure 3a, dominate the weak CHET pathways. The CHET mechanism includes many tunneling pathways. The number of spare pathways may keep the size of the electronic coupling under nuclear fluctuations. On the other hand, the electronic coupling might be affected by an external electronic field comparing with the singlet EET case because the electronic coupling of the triplet EET in CHET mechanism is influenced by many charge transfer states in the bridge. As shown in Figure 3b for the triplet EET, the electrons and holes are transferred not only to a neighboring fragment but also to distant fragments. We have classified KN→M for ET and HT by the transferring distances. The |KN→M| values for ET and HT were accumulated for each transferring distance, as shown in Figure 4. To do this, we employed the number of fragments

4. CONCLUSIONS In conclusion, we compared the tunneling pathways between the triplet and singlet EETs and clarified the difference between the superexchange mechanisms in these EETs. The triplet EET is driven by an exchange interaction, while the singlet EET is driven by a Fö rster-type pseudo-Coulombic interaction. Therefore, the superexchange coupling in the singlet EET is dominated by single-step through-exciton pathways, and the triplet EET pathways are dominated by sequential CHET pathways. In the present model system, the HT distances were shorter than the ET distances due to the radial distributions of the occupied and unoccupied orbitals.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], Tel +81-11-706-9120, Fax +81-11-706-9120. Present Address ⊥

Catalysis Research Center, Hokkaido University Kita 21 Nishi 10, Kita-ku, Sapporo 001-0021, Japan.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by KAKENHI (21685002, 24350008) from the Japan Society for the Promotion of Science (JSPS), JST-CREST, and Strategic Programs for Innovative Research (SPIRE). A portion of the computations were performed at RCCS (Okazaki, Japan) and ACCMS (Kyoto University).

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REFERENCES

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Figure 4. Sum of |KN→M| for each transferring distance in the ET and HT steps of the triplet EET. The transferring distance was measured in terms of the number of fragments between the ET and HT steps.

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