ARTICLE pubs.acs.org/JPCC
Two Different Lifetimes of Charge Separated States: a Porphyrin Quinone System in Artificial Photosynthesis Ryota Jono* and Koichi Yamashita* Department of Chemical System Engineering, School of Engineering, The University of Tokyo 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
bS Supporting Information ABSTRACT: We investigated the charge separation process of an artificial photosynthesis molecule, zinc porphyrin benzoquinone (ZnP BQ) using the ab initio symmetry adapted cluster configuration interaction method and density functional theory. The energy of the charge separated (CS) state of the monomer indicates that electron transfer “via through bond” is inhibited. We used a dimer model of ZnP BQ as an example for electron transfer “via through space” and qualitatively reproduced the experimentally determined energy relation. The calculated oscillator strengths show a difference in lifetimes between the CSLOW and CSHIGH states.
1. INTRODUCTION Photoinduced charge separation between a donor and an acceptor is a key process for photoenergy conversion systems such as photosynthesis1 and solar cells.2 It is important to elucidate the properties of the charge separated (CS) state and the mechanism of the charge separation process because any photoenergy conversion system goes through the CS state and to obtain a clue for improving a lifetime of the CS state. A chlorophyll and a quinone are the principal actors in photosynthesis, performing as electron donor and acceptor, respectively.1 A porphyrin is a basic structure of the chlorophyll and a benzoquinone is one of the simplest quinones. A chemical compound ZnP BQ dyad that consists of the zinc porphyrin (ZnP) and the benzoquinone (BQ) moieties is known as an artificial photosynthesis molecule.3,4 The ZnP and the BQ moieties are linked by one peptide and two phenyl groups, each of which is a common component in the biochemical systems. Electron conjugation in this compound is split because the ZnP plane is perpendicular to that of the phenyl group. It was observed that the CS state of the ZnP BQ is generated from the relaxation of the Q state5 of the ZnP moiety by time-resolved transient absorption spectra in benzene solvent. The energies of the CS state and the Q state of this system in benzene solvent were about 1.5 and 2.1 eV, respectively.3 Some ZnP BQ type chemical species have been reported, and the experimental energies of the CS state and the Q state were almost the same, although some ligands of the porphyrin improve the quantum yield of the CS states.6 To investigate theoretically the CS state of experimentally known systems is important to provide an atomic and electronic picture to understand the CS state and the charge separation process. Theoretical studies of some dyad and triad molecules designed as artificial photosynthesis systems have been reported.7 However, many of these calculations were limited in the orbital energy-based discussion on the excited r 2011 American Chemical Society
states. In particular, there are no reports investigating properties of the CS state. In this work, we applied the ab initio symmetry adapted cluster configuration interaction (SAC CI) method to obtain properties of the excited-states and propose a mechanism of the charge separation process.
2. METHODS All quantum chemical calculations were performed using the Gaussian 09 software package.8 The ground-state structure of ZnP BQ in the gas phase was optimized at the B3LYP/6-31G* level of theory. The excited state of monomer was calculated by using the SAC CI/LANL2DZ level of theory with 73 occupied and 242 unoccupied orbitals for the active space and levelone criterion. The orbitals in this active space were consistent with the orbitals that are actually used in the frozen-core CIS/LANL2DZ level of theory. All calculations were performed in the gas phase because the experimentally used benzene solvent is known as a nonpolar solution, and we also evaluated this hypothesis below. The time-dependent density functional theory (TD-DFT) calculations were performed using 16 functionals with the 6-31G* and the LANL2DZ basis sets. 3. RESULTS AND DISCUSSION 3.1. Monomer. We used a common structure of the ZnP-BQ as shown in Figure 1.3 The lowest unoccupied molecular orbital (LUMO) is localized around the BQ moiety, and the another four frontier orbitals, such as the highest occupied molecular orbital (HOMO), HOMO 1, LUMO + 1, and LUMO + 2, are the Gouterman orbitals.9 The main excited-state energies of the optimized structure for the ground state are illustrated in Figure 2 Received: August 5, 2011 Revised: November 20, 2011 Published: November 22, 2011 1445
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Table 2. Excited-State Energies of ZnP BQ Monomer Calculated by SAC CI, CIS, and DFTs basis set
Figure 1. Common structure of zinc porphyrin benzoquinone, artificial photosynthesis molecules. The porphyrin plane and phenyl group are perpendicular to each other.
Figure 2. Ground- and excited-state energies of optimized ZnP BQ at the B3LYP/6-31G* level of theory.
Table 1. Excited-State Energies and Main Contributions of ZnP BQ Monomera excitation energy/eV oscillator strength 2.45
0.0023
2.47
0.0002
2.96
0.0000
characterb,c (|c| > 0.25) 0.66 [H f L + 1] 0.65 [H 0.65 [H
1 f L + 2] 1 f L + 1]
Q Q
0.65 [H f L + 2]
3.25
0.0001
3.84
2.2272
0.63 [H
18 f L]
0.49 [H
17 f L
0.83 [H
21 f L]
0.59 [H f L + 2] 0.57 [H
LEBQ LEBQ B
1 f L + 1]
0.58 [H f L + 1] 0.58 [H 1 f L + 2]
3.87
1.6269
4.47
0.0000
0.92 [H f L]
4.49
0.0001
0.92 [H
1 f L]
B CS CS
a
This table shows excited states calculated by using the SAC CI/ LANL2DZ level of theory with 73 occupied and 242 unoccupied orbitals for the active space. b The H and L in the character column denote the HOMO and LUMO, respectively. c Q, B, and CS denote Q and B state of ZnP moiety and charge separated state of the system. LEBQ denotes locally excited state of BenzoQuinone moiety.
with oscillator strengths between the ground and the excited states and between the excited states. All of the main contributions to the excited states considered in this study were composed of LUMO and Gouterman orbitals. The main contributions of the excited states were listed in Table 1. The excitation energy dependencies with respect to basis set and that from timedependent density functional theory (DFT) are listed in Table 2. It should be noted that all density functionals, such as LDA, GGA, hybrid, and LC DFT, can describe the energy of local excitation correctly, although the orbital energies calculated by these methods differed from each other. The energies of the Q states
LANL2DZ
method
Q state/eV
CS state/eV
SAC CIa
2.45, 2.47
4.47, 4.49
CISa
2.65, 2.65
5.13, 5.31
CISb LC-BLYPb
2.59, 2.60 2.15, 2.16
LC-wPBEb CAM-B3LYPb
6-31G* Q state/eV
CS state/eV
5.13, 5.30 4.71, 4.83
2.53, 2.53 2.10, 2.11
5.13, 5.65 4.90, 5.02
2.18, 2.19
4.57, 4.75
2.13, 2.14
4.81, 4.86
2.38, 2.39
2.97, 3.15
2.36, 2.37
3.20, 3.20
BH and HLYPb
2.45, 2.46
2.67, 2.79
2.42, 2.42
2.81, 2.90
PBEh1PBEb
2.45, 2.45
1.44, 1.66
2.44, 2.44
1.63, 1.69
PBE1PBEb,c
2.45, 2.45
1.44, 1.66
2.44, 2.44
1.63, 1.70
mPW1PW91b
2.45, 2.45
1.43, 1.65
2.43, 2.43
1.62, 1.68
B3LYPb mPW3PBEb
2.41, 2.41 2.42, 2.42
1.16, 1.38 1.18, 1.41
2.40, 2.40 2.41, 2.42
1.35, 1.42 1.36, 1.45
HSEh1PBEb,d
2.45, 2.45
0.96, 1.17
2.43, 2.43
1.14, 1.20
tHCTHhybb
2.33, 2.39
0.93, 1.16
2.38, 2.39
1.10, 1.20
PBEhPBEb
2.27, 2.27
0.23, 0.49
2.27, 2.28
0.40, 0.54
BP86b
2.27, 2.27
0.23, 0.49
2.27, 2.28
0.39, 0.53
HCTHb
2.28, 2.28
0.20, 0.46
2.26, 2.27
0.38, 0.51
BLYPb
2.25, 2.26
0.21, 0.45
2.26, 2.26
0.37, 0.51
SVWNb experiment
2.28, 2.28 2.08
0.19, 0.46 1.53
2.28, 2.28
0.35, 0.51
a
These calculations were performed with active space for 73 occupied and 242 unoccupied orbitals. b These calculations were performed with active space for frozen-core orbital approximation. c PBE0. d HSE06.
of the ZnP moiety calculated by the SAC CI method were 2.5 eV and in qualitative agreement with the experimentally observed value of 2.08 eV.3 However, the energies of the CS states of the system were 4.5 eV and were higher than those of the Q states of the ZnP moiety. Four benzene molecules were explicitly placed around the zinc atom and the oxygen atoms of the BQ moiety, which were charged in the CS states, to examine the effect of solvent. The stabilization energy should be large if solvent effect is dominant, as explicit placements around charged moiety can be regarded as first-order perturbation for solvent effects. However, the CS states of the optimized structure under the loose criteria in Gaussian 09 were only slightly stabilized by 0.2 eV. The excitation energies from the ground state to the Q states were 2.48 eV and those to the CS states were 4.30 and 4.33 eV, respectively. This indicates that the influence of the benzene solvent is insignificant, and the generation of the CS states of the system by relaxation from the Q states of the ZnP moiety is impossible in this optimized structure. Furthermore, the potential energy curves with respect to the rotation of the dihedral angles in the linkage part were tested. Four dihedral angles were selected to investigate the effect of conformational changes for the energy of CS state. The green bonds in the structures in Figure 3 indicate the selected dihedral angles for the reaction coordinate. The excitation energy calculations were performed by using LC-ωPBE/6-31G* level of theory, because it gives the nearest results for excitation energies with respect to SAC CI/LANL2DZ calculation at the optimized structure with B3LYP/6-31G* level of theory at the ground state as shown in Table 2. However, any conformational changes cannot achieve the situation that the CS states are more stable than the Q states of the ZnP moiety. In fact, the lower limit of the 1446
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Figure 3. Potential energy surface against four dihedral angles in the linkage part of ZnP BQ. The green bonds show the reaction coordinate. All calculations were performed by using LC-ωPBE/6-31G* level of theory.
energy of the CS states can be estimated to be about 4 eV using the ionization potential of porphin (6.9 eV),10 the electronic affinity of p-benzoquinone (1.9 eV),11 and the Coulomb interaction estimated from the edge-to-edge distance (1.1 eV) and is 2 eV higher than the energy of the Q states. Therefore, the electron transfer from the Q states to the CS states “via through bond” seems to be inhibited, and some artifices are needed. 3.2. Dimer. At the site of the reaction center of the photosynthesis system, a chlorophyll forms a special pair conformation with another chlorophyll molecule.1 It is also known that porphyrins tend to be aggregated together.5 Hence, we considered the extreme situation, a highly symmetric dimer ZnP BQ molecule as an example for the electron transfer “via through space”. The distance between the zinc and one oxygen of the BQ moiety, r(Zn O), was 2.25 Å in the optimized structure (Figure 4). In this situation, the lower two energies of the CS state of the system, calculated using the SAC CI/6-31G* level of theory with 10 frontier orbitals for the active space and levelthree criterion, was more stable than the Q state of the ZnP moiety. Although it is noted that each orbital for the ZnP BQ was degenerated due to the assumption of highly symmetric structure, the lower two CS energies were newly observed in the dimer calculation, thus, these two states and the remaining ones can be regarded to be generated “via through space“ and “via through bond”, respectively. Therefore, access of the acceptor
moiety to the donor moiety is important to create the energy level allowing electron transfer. The frozen core SAC CI/ LANL2DZ calculation for the complex ZnP molecule and BQ molecule without linkage part was also performed using optimized structure at the B3LYP/6-31G* level of theory. The r(Zn O) is 2.29 Å at the optimized structure, and the energies of CS and Q states of the complex were 2.0 and 2.45 eV, respectively. It indicates that large active space is needed to reproduce the experimental results quantitatively. The potential energy curves against r(Zn O) are shown in Figure 4. The formation energy of the dimer is 0.66 eV (15 kcal mol 1 ) and supports the accessibility of the donor and the acceptor. The experimental results can now be explained as follows from the viewpoint of the energy landscape (Figure 4). First, the ZnP moiety absorbs a photon that has the corresponding energy of the Q state to produce the locally excited state ZnP* BQ. Next, this Q state of the ZnP BQ molecule forms a complex because the complexes are more stable than the monomer for both the Q state and the ground state of the ZnP BQ molecules (green and black line in Figure 4). Around the most stable structure of the ground state and the Q state, the potential energy curves of the Q state and the CS state are very close. Finally, a nonadiabatic transition occurs and the CS states of the system are achieved. Furthermore, a slightly more stable structure is obtained by descending the energy curve (red line in Figure 4) 1447
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the Qx and the CSLOW states are smaller than 0.0003 and can be neglected. The transition dipole moments at the r(Zn O) = 2.10 and 2.35 Å structures are spiked because the energies of CS and Q state are very close and these wave functions have both ZnP and BQ characters in adiabatic representation. The oscillator strengths between the Qy and the CSLOW states (dark green line in Figure 5) and that between the CSLOW and the ground states (red line in Figure 5) are correlated while that between the Qx and the CSHIGH states (light green line in Figure 5) and that between the CSHIGH and the ground states (orange line in Figure 5) are anticorrelated in the energy region where the CS state is more stable than the Q state. It indicates that the lifetime of the CSHIGH state generated from the Qx state is longer than that of the CSLOW state generated from the Qy state. Hence, it is useful for extending the lifetime of the CS state to excite into the Qx state and to stabilize the CSHIGH state. Figure 4. Potential energy surface against the distance in the ZnP BQ dimer. The definition of the distance between the dimer components r (Zn O) is also shown with the optimized dimer structure using the B3LYP/6-31G* level of theory. SAC CI/6-31G* with 10 frontier orbitals for the active space was used to calculate the energy of the excited states.
4. CONCLUSION We qualitatively reproduced the experimentally determined energy of the CS state using a dimer model and show the properties of the CS state. The lifetimes of the CSLOW and the CSHIGH states were explained using the relation of the oscillator strengths. ’ ASSOCIATED CONTENT
bS
Supporting Information. Complete list of authors for ref 8. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Authors
*E-mail: (R.J.)
[email protected], (K.Y.) yamasita@chemsys. t.u-tokyo.ac.jp. Figure 5. Oscillator strengths of the dimer model between the ground state and the excited state and between the excited states calculated using the SAC CI/6-31G* level of theory with 10 frontier orbitals for the active space.
and the CS state remains with a finite lifetime. The energy levels around B states were not concerned because the picosecond 530 or 590 nm laser pulses were used in experiments. 3.3. Properties of Excited States. Figure 5 shows the oscillator strengths between the ground state and the excited state and between the excited states with respect to the reaction coordinate r(Zn O). We considered only lower two CS states in Figure 4 and named CSLOW state and CSHIGH state, which are the lower and higher states of the CS states. According to generalized Mulliken Hush theory,12 the oscillator strength between the CS state and the Q state is a main factor in the diabatic coupling matrix element between the corresponding states. The properties of the 13 Å distance structure is regarded as being of the “via through bond” type. The oscillator strength “via through bond” was inhibited while that “via through space” shows a dependence on the distance between the molecules. The CSLOW state and the CSHIGH state are generated from only the Qy and the Qx states, respectively, because the oscillator strengths between the Qy and the CSHIGH states and between
’ ACKNOWLEDGMENT This research was supported by a grant from KAKENHI (no. 21245004) and the Global COE Program “Chemical Innovation” from the Ministry of Education, Cluture, Sports, Science, and Technology of Japan. The authors thank the Research Center for Computational Science, Okazaki, for the use of supercomputers. ’ REFERENCES (1) Alberts, B.; Johnson, A; Lewis, J.; Raff, M.; Roberts, K.;Walter, P. Molecular Biology of the Cell, 4th ed.; Garland Science: New York, 2002; Ch. 14, pp 767 829. (2) Gr€atzel, M. Acc. Chem. Res. 2009, 42, 1788–1798. (3) (a) Asahi, T.; Ohkohchi, M.; Matsusaka, R.; Mataga, N.; Zhang, R. P.; Osuka, A.; Maruyama, K. J. Am. Chem. Soc. 1993, 115, 5665–5674. (b) Imahori, H.; Hagiwara, K.; Akiyama, T.; Aoki, M.; Taniguchi, S.; Okada, T.; Shirakawa, M.; Sakata, Y. Chem. Phys. Lett. 1996, 263, 545–550. (4) (a) Lendzian, F.; Schl€upmann, J. Angew. Chem., Int. Ed. Engl. 1991, 30, 1461–1463. (b) Kurreck, H.; Huber, M. Angew. Chem., Int. Ed. Engl. 1995, 34, 849–866. (c) Liu, J.-y.; Bolton, J. R. J. Phys. Chem. 1992, 96, 1718–1725. (d) Okamoto, K.; Fukuzumi, S. J. Phys. Chem. B 2005, 109, 7713–7723. (5) Kadish, K. M.; Smith, K. M.; Guilard, R. The Porphyrin Handbook; Elsevier Science: New York, 2003, Vol. 18, Ch. 113, pp 63 250. 1448
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