J. Phys. Chem. B 2007, 111, 12053-12058
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ARTICLES Chromophore Localization in Conjugated Polymers: Molecular Dynamics Simulation S. Grimm, D. Tabatabai, A. Scherer, J. Michaelis, and I. Frank* Department of Chemistry and Biochemistry, Center for Nanoscience and Nanosystems InitiatiVe Munich, Ludwig Maximilians UniVersity Munich, 81337 Munich, Germany ReceiVed: March 13, 2007; In Final Form: July 23, 2007
Quantum chemical calculations of undistorted poly(phenylene vinylene) chains at zero temperature exhibit chromophores which are delocalized over the whole polymer. We demonstrate with molecular dynamics simulations that chromophore localization in agreement with experiment can be obtained if the system is simulated at finite temperature. The dependence of the chromophore localization on the temperature is investigated.
I. Introduction Conjugated polymers1 have earned much interest because of their optical, electrical, and mechanical properties. Possible applications of these novel materials lie in the area of organic semiconductor devices, such as organic LEDs and displays,2 photovoltaic cells,2 or FETs.3 A prototype substance is PPV, poly(1,4-phenylene vinylene), and its derivatives such as MEH-PPV, poly[2-methoxy-5-(2′ethylhexyloxy)-1,4-phenylene vinylene], which is better soluble in organic solvents. The electronic structure and the resulting photochemical properties of these polymers have been subject to many theoretical4-10,14,15 and experimental14-29 studies. From a theoretical point of view, the conjugated polymer can be approximated by an infinite system and the electronic structure can be interpreted within the band theory framework. The photoexcited states are considered as excitons.1 Alternatively, conjugated systems of finite size (oligomers or short polymer chains) can be described with molecular orbital theory. The full systems are described as single large molecules. The electronic structure is interpreted in terms of individual molecular orbitals (MOs), and photoexcitation can be seen as the transition of an electron from an occupied to an unoccupied MO. In this picture, the strongly allowed 1Bu transition between the two frontier orbitals, i.e., from the highest occupied (HOMO) to the lowest unoccupied MO (LUMO), corresponds to the lowest excited singlet state of PPV, being responsible for absorption as well as emission processes.4 Particularly in longer chains, however, configuration interaction (CI) has to be taken into account, whereby the excitation is described by a linear combination of transitions between different orbitals (more precisely between the corresponding spin-adapted functions).4 From the molecular orbital theory of π systems, one might expect that the chromophore is delocalized over the whole chain. However, it is known from absorption spectroscopy that the conjugated system separates in several segments with a conjugation length of 10 to 17 monomer units.14,16 According to this finding, one single PPV chain consists of hundreds or more separate chromophores. The conjugation of the chain can be
broken by static defects such as saturated groups or cis-vinylene groups, as has been shown in theoretical5,15 and experimental17 studies. The static defects also include tetrahedral kinks of the chain, resulting in defect-coil or defect-cylinder structures29 of the polymer in solution. The geometry relaxation of PPV oligomers in the 11Bu state has been examined by semiempirical excited-state methods.6-8 Only a few monomer units in the middle of the chain showed significant bond-length relaxation, suggesting an excited state (exciton) confined in a very short chain segment. Exciton selftrapping and intrachain migration are discussed in this context;9 the exciton binding energy is expected to lie between 0.2 and 0.45 eV,9-11 but also values as high as 1.0 eV have been suggested.11-13 Exciton diffusion and energy transfer in MEH-PPV has been measured by site-selective fluorescence spectroscopy,18 single molecule spectroscopy,19 and femtosecond pump-probe experiments.20,21 Efficient energy transfer was observed. Single molecule studies of MEH-PPV at low temperature22,23 show that emission occurs from only a few sites of the multichromophore chain. Emission from a few single chromophores was also observed in correlation spectroscopy experiments24 under bad solvent conditions, where strong interchain interactions are expected. In contrast, for isolated rodlike chains, multichromophore emission was found.25 The relative amount of interchain versus intrachain interactions strongly depends on the solvent conditions26-28 and on the defect concentrations.29 The present study examines the dynamic chromophore separation of PPV oligomers with up to 60 phenylene rings at finite temperatures. The time evolution of the ground state geometries at different temperatures is simulated via molecular mechanics methods. For the resulting trajectories semiempirical MO calculations are carried out. II. Methods The investigated systems are phenylene endcapped oligomers and are named after the number of aromatic rings (i.e., stilbene will be called dimer).
10.1021/jp072032f CCC: $37.00 © 2007 American Chemical Society Published on Web 10/04/2007
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The GAUSSIAN 03 package31 has been used for all quantum chemical calculations. Geometries of PPV oligomers with up to 60 aromatic rings have been optimized with the semiempirical AM132 and the PM333 methods, which are parametrized to yield realistic geometries for organic molecules. To assess the accuracy of the semiempirical methods, for the smaller systems (dimer to pentamer) geometry optimizations have been carried out at the density functional theory (DFT) level with use of the BLYP34,35 functional, which is based on the Generalized Gradient Approximation (GGA). A 6-31G* basis set was used for all DFT calculations. The electronic spectra have been calculated with the semiempirical ZINDO method (Zerner’s Intermediate Neglect of Differential Overlap, also called INDO/S)36 and with the ab initio method CIS (configuration interaction, singles). Both methods represent the excited-state wavefunction as a linear combination of the singly excited electronic configurations whereby in the much faster ZINDO method part of the twoelectron integrals is either neglected or approximated by using empirical parameters. Furthermore, excitation energies have been calculated with time dependent density functional theory in the linear response approximation as implemented in the GAUSSIAN program package (TDDFT37-41). For the TDDFT calculations we employed the BLYP functional and the hybrid B3LYP42 functional, which includes a more accurate description of the exchange part of the electron-electron interaction through admixture of Hartree-Fock exchange. Classical molecular dynamics simulations at 298 K with a time step of 1 fs have been carried out with the MM3 forcefield43 as implemented in the TINKER44 package. In case of the shorter chains, the bond alternation in the vinylene units was described by using the π system formalism of the force field. For the longer chains, the vinylene carbon atoms have been reparametrized to reproduce the results of DFT calculations. For the resulting trajectories, semiempirical single point calculations have been carried out. The ground state molecular orbitals have been calculated with the INDO method, and excited states have been calculated with ZINDO. III. Results and Discussion A. Ideal Geometry. PM3 geometry optimization yields planar ground state geometries for all systems examined. The same result is found with DFT geometry optimization of the pentamer (five aromatic rings). In contrast, AM1 geometry optimization leads to an dihedral angle of 22° between the phenylene and the vinylene plane. This different result obtained with AM1 has been discussed in the literature.5,14 Neutron scattering experiments suggest dihedral angles near 8° in the solid state.46 However, a direct comparison to the theoretical data is not possible, since in experiment packing effects are expected to dominate. 1. Frontier Orbitals. The orbital localization has been examined by Mulliken population analysis of the INDO orbitals. The sum of the squared orbital coefficients Ci2 in a certain π MO has been calculated for each monomer unit i in the chain: p-AOs in i
Ci2 )
∑j
cj2
(1)
This quantity represents a measure of the contribution of the monomer unit to the electronic density corresponding to the considered MO. The four highest occupied and lowest unoccupied orbitals of the decamer are shown in Figure 1. A characteristic pattern is
Figure 1. Isosurfaces of the four highest occupied and lowest unoccupied orbitals of the decamer as obtained with INDO. Arrows indicate the most important allowed transitions.
observed, which is known from Hu¨ckel theory of the linear polyenes.45 HOMO and LUMO each exhibit one maximum of the squared MO coefficients in the center of the chain, the next pair (HOMO-1 and LUMO+1) has two maxima, and so on. We verified for chains with up to 60 rings that the extent of the MOs is linearly correlated to the chain length (i.e., the full width at half-maximum of the HOMOs and LUMOs equals about half the number of monomer units in the chain). The enveloping curves of the squared MO coefficients are very similar for HOMO and LUMO concerning their shapes and extensions, likewise for other pairs (HOMO-1/LUMO+1, HOMO-2/LUMO+2, etc.). This means that an electronic transition between such pairs of orbitals in the ideal chain is not connected with a major transfer of charge. 2. Electronic Transitions. The question if the light absorbing units are localized or not cannot necessarily be decided from the shape of the frontier orbitals only. Instead the nature of the electronic excitation, which eventually must be described as linear combination of several excited configurations, has to be investigated. The lowest lying electronic excitation as computed with ZINDO for chains with up to 23 monomer units is strongly allowed and dominated by the HOMO-LUMO transition. As the HOMO and LUMO density distributions exhibit a single maximum, this finding might, at first glance, be interpreted as chromophore localization in the middle of the chain.6 However, for the longer chains significant admixture of the transitions from HOMO-n to LUMO+n (n ) 1, 2, ...) is observed (ZINDO, Table 1, see arrows in Figure 1). The corresponding orbitals contribute more significantly to the density toward the ends of the chain. The ab initio method CIS shows a similar behavior as the semiempirical ZINDO method, while the admixture of energetically higher lying transitions is found to be less pronounced when employing TDDFT using the B3LYP functional, and almost vanishes if the BLYP functional is used. In the eicosamer the BLYP CI coefficient for the HOMO-LUMO transition CLH still amounts to more than 0.6 (Table 1) corresponding to a clear dominance of the HOMO-LUMO excitation. Generally, this is in line with the fact that in density functional methods, correlation is to some degree included via the correlation term of the homogeneous electron gas.
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TABLE 1: Vertical Singlet Excitation Energies for the Lowest Electronic Transition of the Dimer (Stilbene) and the Eicosamer (20 Rings) in eV As Obtained with ZINDO, CIS, and TDDFT (BLYP and B3LYP Functionals)a dimer ZINDO energy CLH L+1 CH-1 L+2 CH-2 L+3 CH-3 L+4 CH-4
3.8 0.68 < 0.1 < 0.1 < 0.1 < 0.1
CIS 4.7 0.66 < 0.1 < 0.1 < 0.1 < 0.1
eicosamer B3LYP
BLYP
ZINDO
CIS
B3LYP
BLYP
4.0 0.63 < 0.1 < 0.1 < 0.1 < 0.1
3.7 0.61 < 0.1 < 0.1 < 0.1 < 0.1
2.8 0.34 0.26 0.24 0.21 0.19
3.3 0.34 0.26 0.23 0.21 0.19
2.2 0.55 0.30 0.19 0.12 < 0.1
1.5 0.67 0.16 0.10 < 0.1 < 0.1
polymer exp. 2.48
a The contributions of the most important electronic configurations to the CI expansion are also given (CLH stands for the pure HOMO-LUMO excitation). The HOMO-LUMO excitation is clearly dominant for stilbene while the contribution of other configurations becomes significant for longer oligo- and polymers.
Figure 2. Vertical excitation energies in dependence of the number of aromatic rings (chain length) as obtained with different theoretical methods and compared to experiment.14 While ZINDO and CIS reproduce the experimental trend correctly, the TDDFT values decrease too strongly with chain length.
There is a trend in vertical excitation energies (Table 1 and Figure 2) in the columns CIS (100% Hartree-Fock exchange) to B3LYP (20% Hartree-Fock exchange) to BLYP (0% Hartree-Fock exchange). For stilbene, the B3LYP value is closest to the experimental value. The deviation of roughly 1 eV is quite typical for CIS, reflecting the neglect of the correlation resulting from higher excitations. The too low BLYP value is attributed to the lack of Hartree-Fock exchange. Also ZINDO reproduces the experimental values for short chains quite well. The ZINDO result of about 2.8 eV for the planar PM3 geometries of longer chains agrees reasonably well with the experimental value of 2.48 eV30 for the polymer, confirming that the semiempirical parametrization still works for larger systems. For longer chains (Figure 2) TDDFT yields asymptotic values of 2.1 eV with B3LYP and 1.5 eV with BLYP. The deviation of TDDFT from experiment increases with the chain length, and this increase of the deviation is most pronounced in the region between trimer and decamer. The oscillator strengths calculated with ZINDO, TDDFT/ B3LYP, and CIS increase linearly with the length of the π system. This behavior is expected for ideal conjugated oligomers.9 In the case of TDDFT/BLYP, the oscillator strength does not increase further for longer chains (see the Supporting Information, Figure 1). This deviation of the TDDFT/BLYP approach from the
experiment is attributed to the fact that in linear response theory, local GGA exchange is not equally suited as Hartree-Fock exchange for the description of large conjugated systems.41 Hereby, B3LYP which contains Hartree-Fock exchange is closer to the experiment than BLYP, which uses pure GGA exchange. In summary, ZINDO reproduces the experimental results (trend of vertical excitation energies and oscillator strengths) quite well and is an appropriate method to further investigate the chromophore localization, whereas the generally more powerful TDDFT approach shows significant shortcomings in the description of the longer chains, particularly in combination with GGA exchange-correlation functionals. B. Chromophore Localization. Before proceeding to the molecular dynamics simulations we analyze the energetic accessibility of structural deformations that lead to chromophore localization. The ground state energy profiles for the single bonds have been calculated with PM3, AM1, and DFT (BLYP and B3LYP). The PM3 and DFT curves have only one minimum at the planar structure, whereas AM1 exhibits a shallow double well behavior with a maximum of 1 kJ mol-1 at 0° (see the Supporting Information, Figure 2). The torsional barrier about the single bonds for AM1 and PM3 is 7 to 8 kJ mol-1 and does not significantly depend on the position of the bond in the oligomer. In the case of the decamer, there is an increase of 0.4 kJ mol-1 from the borders of the chain to the center. Considerably higher barriers are obtained with DFT (20 kJ mol-1 with B3LYP, 25 kJ mol-1 with BLYP), which seems plausible for single bonds in a conjugated π system. Stronger correlation of barrier height and bond position is found for the excited state. The vertical ZINDO excitation energy increases by 1 kJ mol-1 upon rotation about the terminal single bond, and by 9 kJ mol-1 if one of the central single bonds is rotated (see the Supporting Information, Figure 2). From our calculations, rotation of one single bond of the decamer (Figure 3a) does not lead to chromophore localization unless dihedral angles of 60° and above are reached, corresponding to a deformation that is unlikely to occur at room temperature. For longer oligomers, however, this is only true for bond rotation in the middle of the chain (Figure 4a). Bond rotation near the edges leads to HOMO localization in the longer fragment of the chain already at angles of 30° (Figure 4b), which corresponds to a destabilization by less than 5 kJ mol-1. In conclusion, single bond rotation induced by temperature or matrix effects may open a pathway to dynamic chromophore localization. Other possibilities are chemical modifications such as saturated groups and cis double bonds (Figure 3b,c). Saturated groups may be formed during the synthesis of the material,
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Figure 3. Defects leading to π system separation: (a) torsion, (b) saturated group, and (c) cis defect.
Figure 5. Classical molecular dynamics simulation of a 25 ring PPV chain (100 fs, 298 K). From top to bottom: vinylene single and double bond torsion angles [deg], vinylene single and double bond lengths [Å], ZINDO excitation energies of the two lowest excited states [eV], and corresponding oscillator strengths (black: first excited state; red: second excited state).
Figure 4. HOMO localization of a 40 ring PPV chain as a consequence of single bond rotation between the 10th and 11th (a) and 20th and 21th (b) monomer units. Shown are the sums of the squared MO coefficients Ci2 for each monomer unit i at different rotation angles (eq 1). In the long 40 ring chain already single bond rotations by about 30° lead to localization.
whereas cis defects can be induced photochemically. These defects lead to static π system separation. All three kinds of defects have been discussed in the literature5 and contribute to some degree to the chromophore localization observed in experiment. In the next step, we examine the effect of finite temperature on chromophore localization. C. Classical Molecular Dynamics Simulation 1. Excitation. Figure 5 shows the oscillation of the torsion angles and bond lengths of an oligomer containing 25 phenylene units at 298 K.
The excitation energies and oscillator strengths have been calculated with ZINDO for each time point of the molecular dynamics run. On the time scale of the bond vibrations, the excitation energy oscillates in a range of more than 0.5 eV (Figure 5, third row). The excitation energy decreases with shortening of the single bonds and elongation of the double bonds. This behavior is in line with the assumption that the single bonds get shorter and the double bonds get longer in the excited state as one would conclude from the nodal structure of the PPV HOMOs and LUMOs: The HOMOs exhibit binding interactions at the double bond positions while the LUMOs exhibit antibinding interactions at the double bond positions. Occupation of the LUMOs thus leads to a weakening of the double bonds. For the single bonds the situation is vice versa. Hence the excited state is stabilized (and the ground state destabilized) if the double bonds are elongated and the single bonds are shortened. To investigate how far the fluctuations in molecular structure influence the transitions we studied the temporal behavior of the electronic structure in dependence of chain length. ZINDO calculations for the geometries from the molecular dynamics runs reveal a splitting of the allowed transition in the case of chains with 15 rings or more. As shown in Figure 5 (bottom) for the 25 ring chain, the oscillator strength of the second excited state becomes large quite frequently. In the case of the planar, optimized PM3 geometry, the ZINDO oscillator strength of the lowest transition is 17. At several points in Figure 5 (for example, at 17 fs, 30 fs, 40 fs, etc.) two allowed transitions are found, each with an oscillator strength of about half the value of the ideal chromophore, corresponding to two shorter chromophores with 10 to 15 rings. The relevant pairs of orbitals (HOMO/LUMO and HOMO-1/LUMO+1, respectively) localize in different regions of the chain, and each transition can be considered as HOMO f LUMO excitation of a shorter subchromophore. 2. Orbitals. The chromophore splitting observed for the longer chains is characterized by orbital localization over a range of roughly 10 monomer units. In the following section, we investigate this phenomenon in more detail. For the geometries of each trajectory, INDO calculations were performed and the spatial extent of the orbitals was measured via Mulliken population analysis as described above. As an example, the
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Figure 7. fwhm histograms of the INDO HOMO Gaussian fits. Upper row: 40 monomer units, 298 and 598 K. Lower row: 60 monomer units, 298 and 598 K.
Figure 6. Classical molecular dynamics simulation of the 40 ring PPV chain at 298 K, plot of the Ci2 of the highest occupied and lowest unoccupied orbitals against the time. The simulation starts from the optimized PPV structure, hence the nodal structure characteristic of the ideal chain can be seen at t ) 0.
oligomer with 40 aromatic rings is considered (Figure 6). The simulation is also done at 298 K and starts from the planar, optimized geometry. In Figure 6 the Ci2 (eq 1) values of the highest occupied and lowest unoccupied orbitals are plotted against the simulation time. Since this molecular dynamics run was not started from an equilibrated structure but from an optimized geometry, the orbitals initially show the characteristic nodal behavior of the ideal structure at 0 K (see Figure 1). They localize within 20 fs, that is on the time scale of bond length oscillations. The C2 peaks of the LUMO are essentially colocalized with the corresponding peaks of the HOMO. Exceptions represent, for example, two peaks at 140 and 160 fs, which are colocalized with HOMO-1 instead (6, middle). For the other orbitals similar pairwise colocalization is found. In summary, there are several colocalized pairs of occupied and unoccupied orbitals on the oligomer chain. They can be interpreted as individual HOMOLUMO pairs of several chromophores. The spatial extent of the orbitals was determined by Gaussian fits of the orbital-localization plots. Figure 7 shows fwhm histograms of the INDO HOMOs for several molecular dynamics simulations at room temperature and 300 °C. The most frequent values are in the range between 3 and 6, corresponding to chromophore lengths of 6 to 12 monomer units. Higher temperatures lead to more localized orbitals since larger deformations of the chain become more easily accessible. Figure 8 shows localized HOMO-LUMO pairs calculated with different methods. INDO (as well as Hartree-Fock, not shown here) yields the least extended orbitals. Use of KohnSham exchange instead of Hartree-Fock exchange leads to stronger delocalization. The BLYP orbitals are relatively extended. The B3LYP orbitals with 20% Hartree-Fock ex-
Figure 8. Localized HOMO-LUMO pairs: (a) INDO [PM3 and Hartree-Fock orbitals (not shown) are similar], (b) B3LYP, and (c) BLYP.
change are quite close to the orbitals as obtained with semiempirical and ab initio methods. If we consider B3LYP as the most reliable method of the ones used, our value of 6 to 12 monomer units in a chromophore obtained on the basis of INDO orbitals is probably a bit too low. IV. Conclusion We studied the localization and extension of chromophores on PPV molecules. In case of the planar structures optimized at 0 K, the frontier orbitals are delocalized over the whole chain, resulting in a single chromophore. The seeming localization of the HOMOs and LUMOs to half the chain length is of no revelance in this context since for longer chains higher transitions are admixtured. When calculating the structure of the molecules at higher temperatures using molecular dynamics simulations we found significant deviations from the ideal structure leading to chromophore localization. This has been verified by using semiempirical MO calculations atop classical molecular dynamics simulations of the longer molecules. We find temperaturedependent orbital localization on the bond vibration time scale. This leads to dynamic separation of the π system, and to several
12058 J. Phys. Chem. B, Vol. 111, No. 42, 2007 mobile chromophores on the chain. Most frequently, the orbitals span over 6 to 12 monomer units, qualitatively confirming the estimation on the basis of experimental results.14 In addition to previously studied chromophore localization by static defects, the described dynamical localization is likely to play an important role for the chromophores of conjugated polymers. Note that in the present study we considered only ground state dynamics thus modeling photon absorption, not luminescence. The investigation of excited-state dynamics which may lead to phenomena like exciton trapping is left to future work. Acknowledgment. The authors thank John Lupton and Christoph Bra¨uchle for valuable discussions. Financial support by the Deutsche Forschungsgemeinschaft (SFB 486, “Manipulation von Materie auf der Nanometerskala”) is gratefully acknowledged. Supporting Information Available: Plot of the oscillator strengths against the number of aromatic rings for different semiempirical methods and density functionals and single-bond rotation energy profiles as calculated with semiempirical and DFT methods. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Heeger, A. Synth. Met. 2000, 125, 23. (2) Friend, R. Pure Appl. Chem. 2001, 73, 425. (3) Chua, L.; Zamuseil, J.; Chang, J.; Ou, E.; Ho, P.; Sirringhaus, H.; Friend, R. Nature 2005, 434, 194. (4) Bredas, J. L.; Cornil, J.; Beljonne, D.; Dos Santos, D.; Shuai, Z. Acc. Chem. Res. 1999, 32, 267. (5) Wong, K.; Skaf, M.; Yang, C.; Rossky, P.; Bagchi, B.; Hu, D.; Yu, J.; Barbara, P. J. Phys. Chem. B 2001, 105, 6103-6107. (6) Cornil, J.; Beljonne, D.; Friend, R.; Bredas, J. L. Chem. Phys. Lett. 1994, 223, 82 . (7) Beljonne, D.; Shuai, Z.; Friend, R.; Bredas, J. L. J. Chem. Phys. 1995, 102, 2042. (8) Cornil, J.; Beljonne, D.; Bredas, J. L. Synth. Met. 1997, 85, 1029. (9) Lavrentiev, M.; Barford, W.; Martin, S.; Day, H.; Bursill, R. Phys. ReV. B 1999, 59, 9987. (10) Gartstein, Y.; Rice, M.; Conwell, E. Phys. ReV. B 1995, 52, 1683. (11) Shuai, Z.; Pati, S. K.; Su, W. P.; Bredas, J. L.; Ramasesha, S. Phys. ReV. B 1997, 55, 15368. (12) Chandross, M.; Mazumdar, S.; Jeglinski, S.; Wei, X.; Vardeny, Z. V.; Kwock, E. W.; Miller, T. M. Phys. ReV. B 1994, 50, 14702. (13) Leng, J. M.; Jeglinski, S.; Wei, X.; Benner, R. E.; Vardeny, Z. V.; Guo, F.; Mazumdar, S. Phys. ReV. Lett. 1994, 72, 156. (14) Woo, H.; Lhost, O.; Grahem, S.; Bradley, C.; Friend, R.; Quattrocci, C.; Bredas, J. L.; Schenk, R.; Mu¨llen, K. Synth. Met. 1993, 59, 13. (15) Grage, M.; Wood, P.; Ruseckas, A.; Pullerits, T.; Mitchell, W.; Burn, P.; Samuel, I.; Sundstro¨m, V. J. Chem. Phys. 2003, 118, 7644. (16) Gettinger, C.; Heeger, A.; Drake, M.; Pine, D. J. Chem. Phys. 1994, 101, 1673. (17) Padmanaban, G.; Ramakrishnan, S. J. Phys. Chem. B 2004, 108, 14933.
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