J. Phys. Chem. 1995, 99, 12301-12304
12301
Photoinduced Charge Transfer in Excited Ca G. P. Zhang,*Jy$ygR. T. Fu,+*gX. Sun,+,*and X. F. Zong' T. D. Lee Laboratory and Department of Physics and Department of Material Science, Fudan University, Shanghai 200433, China, and National Laboratory of Infrared Physics, Academic Sinica, Shanghai 200083, China
K. H. Lee and T. Y. Park Departments of Chemistry and Physics Education, Won Kwang University, Iri 570-749, Korea Received: March 22, 1995@
Based on the original inequality, I$ - AA - U, < 0, a generalized mechanism for photoinduced charge transfer (PCT) in the excited Cm is proposed. Using the single configuration interaction approximation, we find that the increase of the electron affinity in the excited Cm, which has been experimentally confirmed, plays a critical role in the photoinduced charge transfer. This role becomes more significant when the donor is not excited. We discover that the increase of the electron-phonon coupling a can improve the electron affinity significantly, whereas the electron-electron interaction slightly affects the electron affinity.
I. Introduction Photoinduced charge transfer (PCT) in Cm, due to its potential application, has been extensively studied. Sension et al.' first studied the process of photoinduced charge transfer in a C& N,N,-dimethylaniline (CflMA) complex. Though their initial experiments are rather rough and the fraction of charge transferred is not clear, the main feature of the charge transfer is well-resolved in the ultrafast absorption spectrum. This primary work spurred many experimental investigations. Wang2 discovered several potential applications, such as photodetection and electrostatic imaging. Sariciftci et ale3 conducted PCT research in detail and presented direct evidence for the photoinduced electron transfer from a conducting polymer to buckminsterfullerene. Recently, they fabricated the photodiode from a C~poly[2-methoxy-5-((2'-ethylhexyl)oxy)-p-phenylene]( C d MEH-PPV) complex, which overwhelmingly attracted many researcher^.^-^ Although experimental studies of PCT have been carried out extensively, the theoretical understanding is very limited. The traditional electron transfer theory, which was proposed by Marcus? could phenomenalistically explain some parts of PCT chemically, but this explanation is not satisfying physically. Sariciftci et aL3 employed one novel mechanism; that is, PCT depends on the ionization potential (I;) of the excited donor, the electron affinity (AA) (EA) of the acceptors, the Coulombic energy (U,) of the separate ions (including polarization effects, Le., dielectric relaxation of the molecular environment to stabilize the charge separation), and structural relaxation of the polymer backbone due to electronlattice coupling. Photoinduced electron transfer cannot occur unless these quantities satisfy the following inequality: Ig Aa - U, < 0. Charge separation can be stabilized by carrier delocalization and by structural relaxation. This clear picture strongly motivates us to propose a detailed theoretical understanding. From the inequality, one can easily understand why the PCT process occurs if the photon energy h is larger than 2.0 eV. Since from the linear absorption spectrum when hw =2.0 eV the donor is excited, electrons are excited to higher
' T. D. Lee Laboratory and Department of Physics. Department of Material Science. 5 National Laboratory of Infrared Physics. @
Abstract published in Advance ACS Abstracts, June 15, 1995.
energy levels, the ionization energy is lowered and it is much easier to ionize these electrons. If the lowest unoccupied molecular orbital (LUMO) of the acceptor is lower than the excited state of the donor, electrons can be transferred from the donor to the acceptor. From the photoconductivity spectrum one may notice that the photoconductive response of MEHPPVICm increases sharply at about 1.3 eV$ which is lower than the photoconductivity onset of the components alone and reflects that PCT occurs. In Sension's experiments,' excitation is performed on the buckminsterfullerene, but PCT is observed too. However, for the region with the photon energy between 1.3 and 2.0eV the PCT process is hard to understand from the above inequality since in this region the donor is not excited. From our calculation we find that one should consider another important factor, namely, the affinity of the EXCITED acceptor Cm. Of course, a complete understanding of PCT is very difficult, but here we simplify the process and just answer whether, once Cm is excited, the electron affinity of Cm can be raised or not. The increase of EA favors the above inequality; thus, it is much easier for the excited Cm (hereafter we abbreviate the excited Cm as Cm*) to accept electrons, and PCT occurs. We find that the electron affinity of Cm is raised in Cm*, and the increase of the affinity of c60* plays a significant role in the charge transfer; this process is much promoted especially in the region with the donor unexcited. Actually, experiments'O already predicted that the photoexcited Cm* was a stronger acceptor than Cm in the ground state, and our results are consistent with their experimental outcomes. We discover that the increase of electron-phonon coupling can effectively improve the electron affinity, Le., the efficiency of charge transfer. Lastly, an important implication of the PCT relaxation process is discussed. This paper is arranged as follows. In section I1 we outline the theoretical scheme, and main results and discussions appear in section 111.
11. Scheme When Cm is photoexcited, an electron is excited to excited states. Naturally, the lowest excited states (LES) are most important. One complete configuration interaction (CI) approach'] to Cm* and another study,'* which is limited to LES,
0022-3654/95/2099-12301$09.00/00 1995 American Chemical Society
Zhang et al.
12302 J. Phys. Chem., Vol. 99, No. 32, 1995 clearly conclude that LES can reflect main characteristic of Cm*. Here we only consider the single electron excitation process while leaving double excitation for forthcoming research. The LES space is constructed from five h, and three tl, states, namely,
+ + G , + H,,
/EX) = t,, x h, = TI, T,,
(1)
Once an electron is excited to the excited states, due to the electron-phonon interaction (EPI), the original configuration cannot be held any longer and the lattice begins to relax. This relaxation process is actually experimentally observable, as photoinduced absorption, and one can determine the relaxation time from the spectra. Our previous studyI3 discovered that the relaxation time of the excited state is about 100 fs and the pristine configuration is distorted with the symmetry reduction from I h to D5d.I4 With the new equilibrium configuration one can easily calculate the affinity of Cm. However, it is worthwhile to recall the definition of the affinity, that is, in the one-electron-charged molecule the minimum energy needed to ionize an electron. Thus for this reason, the affinity is often called the zero ionization energy. Here we are only interested in the relative value of the affinity rather than its absolute value. Since in the one-electron-charged Cm the transferred electron occupies one of the LUMO states, the energy one needs to ionize this transferred electron is equal to the absolute value of the LUMO; that is, the LUMO level can measure the affinity. In this sense we regard the absolute value of the LUMO level just as the affinity. Thus in the unexcited state, the initial affinity Ai of c 6 0 is simply the LUMO energy, and after the relaxation the final affinity Af is the new LUMO level. Since in the experiments4the MEH-PPV/Cm composite films are not as uniform as the films of the pure conducting polymer due to segregation of the less soluble Cm component, one may anticipate that the Cm’s are separated. Therefore, the main feature of the composite films can be well characterized by a single Cm. We can write the following Hami1tonian:l5
(2) where
e:s creates a rc electron at site i with spin s and ni,s =
els~i,s.is the hopping integral between the nearest neighbor tu
(NN) atoms sitting at -;i and Tj. tu = to - a(Fi - 7j1 - Do), where to is the average hopping constant and a is the electronphonon interaction. U is the on-site electronic repulsion. V(ru) is the Ohno potential,
-4
1
(3)
V(r) =
The last term in (2) is the elastic energy with the elastic constant K. Our previous work has provided the values of the above parameters, to = 1.8 eV, a = 3.5 eV/& and K = 15.0 eV/A2, through fitting the optical energy gap and two kinds of bond lengths. We choose U = 5.0 eV and V = 2.0 eV, as before.I6 Here DOis taken as 1.54 A. Following the standard procedure, we write the matrix elements for the excited states as
where H’ = H - HHF, HHFis the Hartree-Fock-approximated Hamiltonian, and Efl is the single particle energy in HartreeFock space. IpA) = C,,oCA,rlg)is the single-electron-hole excitation, where p represents an unoccupied state and 2. an occupied state and 18) is the Hartree-Fock ground state. (8) - ~ ~ : o c c u p i e d ~ ~ , + ~ :6s, , ~=~ )1. or 6s = o refers to spin singlet or triplet, respectively, and
J@’,A’;p,4 = ~ ~ ~ , j c U ’ l i ) ( A ’ l ~ } ~ l ~ ) ~ l A )( 5 ) iJ
K@’,A’;p,A) = ~ ~ , , j ~ ’ ~ } ( A ’ l i ) ~ l p ) ( i l A ) (6) iJ
where Wi,i = U and Wi,j = V(ri,,) for i f j . Thus, one can obtain the energy spectra simply by diagonializing the above matrix. Therefore, the total energy for LES is
E((7-,)) = E, i-E,
(7) where E, is the electron total energy and El is the elastic energy. To get a relaxed excited state, we employ a dynamical technique, which previously has been reiterated several and whose effectiveness has been checked. Thus, we describe it briefly here. Mainly solving the following dynamical equations for the atoms of Cm,
gi = -dE({Ti})/d7i
-V, = d T j d t
(8) (9)
where Fi and ?i are the force and the velocity of the atom i, respectively, one can get the new equilibrium state, which is a self-trapping exciton state, from which one can uniquely determine the EA of the excited Cm.
111. Main Results and Discussion Before we offer the main results of our calculations, let’s look at the main characteristic of donor MEH-PPV. Firstly, MEH-PPV exhibits a high quantum efficiency of the photoluminescence3 with a small Stokes shift, thereby demonstrating that the effects of structural relaxation are relatively small compared to those in trans-polyacetylene (where the ground state is degenerate). From the absorption spectrum, Sariciftci et aL4have shown the energy band scheme (see Figure 1). It is very clear that in the ground state (GS) the valence band (VB) of the conducting polymer is slightly lower than the LUMO of Cm; thus, electron transfer from MEH-PPV to Cm in the ground state is unlikely, which is what the GS absorption spectrum reveals (see Figure 1 of ref 19). To observe the PCT process, the photoconductive spectrum is a direct tool. Figure 2 (Le. Figure 25 of ref 4,for convenience shown here) illustrates a very interesting story. The photoconductive spectral response of MEH-PPV shows a sharp onset at about 2.0 eV, which coincides with the optical absorption edge across the energy gap. One can easily explain this feature due to the inequality (see above). Since MEH-PPV is photoexcited, its ionization energy is decreased sharply and PCT occurs from MEH-PPV to Cm. However, with the concentration of c 6 0 about 1%, the photoconductivity of the MEH-PPV/Cm complex increases sharply at about 1.3 eV, which is lower than the photoconductivity onset of the components a10ne.I~ Since MEH-PPV has no absorption peak at 1.3 eV, due to its large energy gap (2.5 eV), MEH-PPV is unlikely to be excited. Furthermore, the small Stokes shift rules out possible phonon-
Photoinduced Charge Transfer in Excited Cm
J. Phys. Chem., Vol. 99, No. 32, 1995 12303
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ELECTRON-PHONON COUPLING (eV/A ) Figure 3. Affinity of the excited Cm via the electron-phonon coupling a. The solid line is for the affinity of the excited Cm, while the dashed line is for that of the unexcited Cm,
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Figure 1. Schematic energy band diagram for the photoinduced electron transfer from semiconducting polymers onto Cm. Reprinted with permission from ref 4. Copyright 1994 World Scientific Publishing Co. Re. Ltd.
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o 50 ~k c, in r+m-PPv n 5%C,hhEH-PPV 0 I k, C io MEH-PPV 0 0
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assisted transitions in MEH-PPV. Thus, Cm must account for the sharp increase of photoconductivity. Differently in Cm bulk material, the ab initio calculation20 showed the energy gap was about 1.5 eV with the bandwidth around 0.4 eV, while the photoinduced absorption of a thin film of c 6 0 clearly showed a new peak around 1.3 eV.21 Therefore, one can conclude that at 1.3 eV c 6 0 can be excited. It should be noted that the spectral response of the photoconductivity of pure Cm closely follows the optical absorption spectrum of Cm,** with PC onset at 1.5 eV, and the sharply increased photoconductivity shows that PCT does occur. From the inequality 1; - AA - U, -= 0, one can easily understand why PCT occurs when MEH-PPV is excited, but for the unexcited MEH-PPV it is very hard to understand why PCT still occurs. From our calculation, we find that when Cm is excited, the lattice begins to relax and the atoms come to new equilibrium positions. This
new structure of Cm is distorted, due to Jahn-Tellar effects and forms a self-trapping exciton with a symmetry reduction from I h to D5d. With this newly built structure one can easily calculate the new electron affinity. We find that after the relaxation of the excited state, the new EA of Cm is raised. In a single-cluster Cm the new EA is about 0.15 eV higher than the old EA of unexcited Cm, and we anticipate that in bulk material this amount is about 0.3 eV. With the increased EA of C a , it is much easier for the excited Cm to take up electrons from the donor MEH-PPV; namely, PCT occurs, though at this moment the donor is not excited. We find that the increase of EA strongly depends on electron-phonon (e-ph) coupling a (see Figure 3). From Figure 3 it is very clear that for the same e-ph coupling a,the EA of the excited state is higher than that of the unexcited state Cm. The difference between these two EAs becomes more obvious as a increases, which indicates that the electron-phonon coupling plays an important role in it. However, the increase of affinity in the excited Cm is less dependent on the electron-electron (e-e) interaction V (see Figure 4). Carefully comparing Figure 3 with Figure 4, one may discover that the dependences on e-e interaction and e-ph interaction of the electron affinity are different, Le., for the different electron interactions, EA almost gaining the same amount, about 0.1 eV. This increased EA plays a critical role in PCT. At 1.3 eV with the increasing concentration of Cm from 1% to 50%, the photoconductivity has been improved many orders of magnitude. It can be understood that the higher
12304 J. Phys. Chem., Vol. 99,No. 32, 1995 the concentration of Cm, due to the higher EA, the more the fullerenes can get electrons; thus, the photoconductivity increases sharply at 1.3 eV. It is noticeable with the concentration 50% of Cm that the conductivity has increased so much that the improvement of conductivity, which is driven by the increasing donor ionization Ig in the region with ho > 2.0 eV, plays an unimportant role, i.e., only a small modification to the original photoconductivity (see Figure 2). This is manifested that one should consider the increasing EA of the acceptor at the excited states. Hence, one may conclude that the inequality should be generalized as I; - AX - U, 0. Although superficially the change is slight, the main physics are different. With the new inequality we can explain the whole region of the photoconductivity spectrum convincingly, especially when the donor is unexcited. Based on this work and our previous workI3 about the relaxation process of the excited state in Cm, a possible physical picture about PCT may be obtained: When Cm is photoexcited, the excited state will relax to a stable state within 100 fs; thus, the possible charge transfer occurs only after 100 fs. However, to form a stable charge-transferred state, it needs about 0.4 ps.” We suggest that a time-resolved ultrafast spectrum experiment may show this two-component relaxation; namely, one is fast, while the other is slow. Based on the original inequality, which could determine whether PCT occurs or not, a generalized mechanism is proposed. From our calculation, we find that the increased EA of the acceptor plays an significant role in PCT, although a direct picture may emphasize the increasing of the ionization energy of the donor at the excited states. As PCT is a chief process in photodiode devices and improving its quantum efficiency is experimentally meaningful, we appeal that experimentalists should notice that the acceptor’s affinity plays a critical role in PCT and, hence, affects its quantum efficiency. For an effective way to improve the quantum efficiency, one should pay more attentions to e-ph interactions of materials. Lastly, we would like to mention that the experiments’.l0 have confirmed that photoexcited Cm is a stronger acceptor than Cm in the ground state, which again reflects the increasing EA and is fully consistent with our theoretical results.
Zhang et al.
Acknowledgment. The authors thank Mr. Wei Chang for providing them with the Supercomputer and for his hospitality. This work is supported by the National Natural Science Foundation of China, Advanced Material Committee of China, and Korea Ministry of Education BSRI 943438. References and Notes (1) Sension, R. J.; Szarka, A. Z.; Smith, G. R.; Hochstrasser, R. M. Chem. Phys. Lett. 1991, 185, 179. (2) Wang, Y. Nature 1992, 356, 585. (3) Sariciftci, N. S.; Smilowitz, L.; Heeger, A. H.; Wudl, F. Science 1992, 258, 1474. (4) Sariciftci, N. S.; Heeger, A. J. Int. J . Mod. Phys. 1994, 8 8 , 237. (5) Watanabe, A.; Ito, 0. J. Phys. Chem. 1994, 98, 7736. (6) Guldi, D. M.; Neta, P.; Asmus, K.-D. J. Phys. Chem. 1994, 98, 4617. (7) Gneskowiak, K. N.; Smimov, S. N.; Braun, C. L. J. Phys. Chem. 1994, 98, 5661. ( 8 ) Micheali, S.; Meiklyar, V.; Schulz, M.; Mobius, K.; Levanon, H. J. Phys. Chem. 1994, 98, 7444. (9) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985,1985,265. (10) Abogast, J. W.; Darmanyan, A. P.; Foote, C. S.; Rubin, Y.; Diederich, F. N.; Alvarez, M. M.; Anz, S. J.; Whetten, R. L. J . Phys. Chem. 1991, 95, 1 1 . (11) Fagerstram, J.; Stafstrom, S. Phys. Rev. 1993, 848, 11367. (12) Suzuki, S.; Inomata, D.; Sashide, N.; Nakao, K. Phys. Rev. 1993, 848, 14615. (13) Fu, R. L.; Ye, H. J.; Fu, R. T.; Yu, 2.G.; Sun, X. Acta Phys. Sin. 1994, 43, 1336. (14) Fu, R. L.; Fu, R. T.; Sun, X . Phys. Rev. 1993, 848, 17615. (15) Harigaya, K.; Abe, S. Phys. Rev. 1994, 849, 16746. (16) Huang, Q.-F.; Fu, R. T.; Sun, X.; Fu, R. L. Acta Phys. Sin. 1994, 43, 1834. (17) Zhang, G. P.; Fu, R. T.; Sun, X.; Lin, D. L.; George, T. F. Phys. Rev. 1994, 850, 11976. (18) Fu, R. T.; Lee, K. H.; Park, T. Y.; Sun, X.; Yu, Z. G. Bull. Korean Chem. Soc. 1994, 15, 112. (19) Lee, C. H.; Yu, G.; Moses, D.; Pakbaz, F.; Zhang, C.; Sariciftci, N. S . ; Heeger, A. J.; Wudl, F. Phys. Rev. 1993, 848, 15425. (20) Saito, S.; Oshiyama, A. Phys. Rev. Lett. 1991, 66, 2637. (21) Pichler, K.; Graham, S.; Gelsen, 0. M.; Friend, R. H.; Romanow, W. J.; McCaoley, J. P.; Coustel, N.; Fischer, J. E.; Smith, A. B., 111. J. Phys. Condens. Matter 1991, 3, 9259. (22) Mort, J.; Okumura, K.; Machonkin, M.; Ziolo, R.; Huffman, D. R.; Ferguson, M. I. Chem. Phys. Lett. 1991, 186, 281.
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