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Effects of Structural Fluctuations on Two-Photon Absorption Activity of Interacting Dipolar Chromophores Ke Zhao,*,†,‡ Peng-Wei Liu,† Chuan-Kui Wang,† and Yi Luo‡ College of Physics and Electronics, Shandong Normal UniVersity, 250014 Jinan, Shandong, China, and Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, S-106 91 Stockholm, Sweden ReceiVed: April 27, 2010; ReVised Manuscript ReceiVed: July 17, 2010
One- and two-photon absorption properties of organic chromophores consisting of interacting dipolar branches have been studied using density functional response theory in combination with molecular dynamics simulation. Effects of dipole interaction on optical absorptions have been examined. The importance of solvent effects on optical properties of charge-transfer states is explored by means of polarizable continuum model. It is found that for the interacting dipolar molecule with flexible conformations in solutions, the structural fluctuations can result in new spectral features or significant broadening of one-photon absorption spectrum. Our study highlights again the usefulness of the combined quantum chemical and molecular dynamics approach for modeling two-photon absorption materials in solutions. I. Introduction Quantum chemical (QC) methods have been successfully applied to study nonlinear optical (NLO) properties, in particular two-photon absorption (TPA) of organic conjugated molecules, in the past two decades. These studies have provided useful structure-to-property relationships for many different charge transfer systems, which have been adopted as guidelines for the design and synthesis of nonlinear materials.1-10 However, certain rules obtained for a single isolated molecule are often found to be inapplicable to real materials in condensed phases. In these cases, intermolecular interactions become very important, which can have, for instance, significant effects on TPA of molecules in solutions as clearly demonstrated by both experimental and theoretical studies.11-22 The interaction between solute and solvent molecules can lead to the changes of geometric and electric structures in comparison with that in the gas phase. Moreover, the solute-solute interaction can induce molecular aggregation in highly concentrated solutions. One of the simplest theoretical models to describe effects of the intermolecular interaction on optical absorptions is the famous Frenkel excition model, in which the dipole-dipole interaction plays the dominate role. Recently, Terenziani et al.23 used an advanced Davydov-Frenkel exciton model to examine optical absorptions of a series of well-designed interacting dipolar molecules. With proper parameters, the simulated one- and twophoton absorption spectra have reproduced the corresponding experimental results. The supramolecular structures they designed (see Figure 1) seem to be really good model systems for studying molecular dimerization or aggregations. It would be interesting to see how good conventional density functionals can be for these systems. We have thus applied time-dependent density functional theory in combination with polarizable continuum model to calculate one-photon absorption (OPA) and TPA properties of these * To whom correspondence should be addressed. E-mail: zhaoke@ sdnu.edu.cn. † Shandong Normal University. ‡ Royal Institute of Technology.
Figure 1. Molecular structures of studied compounds.
interacting dipolar molecules. The performance of two wellknown hybrid functionals has been examined. For the interacting dipolar chromophores, the interplay and the coupling among the branches have significant effects on nonlinear optical response. Cooperative enhancement or linear correlation of TPA in multibranched structures have been observed in experiments.7,8 Cho and his co-workers have investigated the NLO properties for series of octupolar molecules both experimentally and theoretically.24-26 The effects of the conjugation length and the substituted electron donor or acceptor strength on TPA cross section were studied in detail. It has been found that the TPA cross section increases as the donor or acceptor strength and conjugation length increase.24 On the basis of the four-state model, the design strategy to maximize the TPA cross section of the octupolar molecule was established.25 A comparative study of the TPA properties of octupolar compounds and their dipolar one-dimensional counterparts was performed by Beljonne et al.27 The roles of dimensionality and symmetry were discussed on the basis of the exciton model. The correlated quantum chemical calculations suggested that a much larger TPA cross section can be achieved through proper design of chromophores with strong interarm couplings.
10.1021/jp103791s 2010 American Chemical Society Published on Web 08/03/2010
Absorption Properties of Organic Chromophores
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In general, temperature effects are not considered in QC calculations. For a molecule in the solution at room temperature, the structural fluctuation becomes possible. In some cases, the structural fluctuation can only lead to a simple broadening of the spectra, which can be simply recovered by a lifetime broadening factor. But the effect of the structural fluctuation is not always uniform and it can result in new spectral features. In this case, specific structural information has to be obtained. This can be of course done by molecular dynamics (MD) simulations. Actually, MD simulation techniques have been already applied to the study of NLO properties of organic solutions, for instance, the electric field poling effects,28-34 the linear and nonlinear hyperpolarizability,33,35-37 and two-photon absorption.20,38 As can be seen, only a couple of studies on TPA are available. Paterson et al.38 gave a test study on solvent effects of formaldehyde and water molecules using hybrid coupledcluster/molecular mechanics (CC/MM) response theory. Prior to the CC/MM calculations, MD simulations were performed on the systems and many configurations were generated. The statistically averaged excitation energies and TPA cross sections were obtained, which gave a better agreement with the experimental data. Liu et al.20 calculated the TPA cross sections of clusters formed by octupolar molecules employing density functional quadratic response theory and explored the role of molecular aggregates on TPA property. The structures of clusters including dimers, trimers, and tetramers were taken from snapshots of MD simulations.29 All of these model studies are very encouraging and more studies along this line are highly desirable, which is also the intention of this study. II. Computational Methods The transition intensity for one-photon absorption (OPA) is determined by oscillator strength39
δop )
2ωf 3
∑ |〈0|µR|f〉|2
(1)
R
where ωf is the excitation energy from the ground, |0〉, to the excited, |f〉, states. µR is the electric dipole moment operator and the summation is performed over the molecular x, y, and z axes. The TPA cross sections of randomly oriented systems can be directly related to the imaginary part of the third susceptibility. Alternatively, in the vicinity of two-photon resonance TPA cross section can be obtained by computing the individual TP transition matrix elements SRβ defined as40,41,11
SRβ )
∑ s
(
〈0|µR |s〉〈s|µβ |f〉 〈0|µβ |s〉〈s|µR |f〉 + ωsi - ω ωsi - ω
)
The TPA cross section that can be directly compared with experiment is defined as41,11,12
σtp )
(4)
Here a0 is the Bohr radius, c0 is the speed of light, R is the fine structure constant, L is the Lorentz field factor, g(ω) represents the spectral line profile, n is the refractive index, and the level broadening Γf of final state is assumed to have the commonly used value Γf ) 0.1 eV. This choice of damping factor is consistent with the width of the TPA spectra in a number of conjugated molecules. TPA cross section is the unit of GM, 1 GM ) 10-50 cm4 s/photon. A straightforward application of eq 2 for calculating TP transition matrix elements is limited since it requires the knowledge of all excited states. The conventional approach to overcome this difficulty is to employ so-called “few-states” model,3,12,43 in which only the dominating terms in eq 2 are accounted for. It is known that for one-dimensional charge transfer molecules the two- or three-state models can provide essential features of TPA process. In spite of simplifications, the few-states model is greatly beneficial for interpreting the spectra and understanding so-called structure-to-property relations. Another, more rigorous method to calculate the TP transition matrix elements is by the response theory:44 in this framework the summation over excited states is substituted by the solution of a set of coupled linear equations. The TP transition matrix elements can be identified from the residue of the quadratic response function. Nowadays, the linear and nonlinear response formalisms have been implemented in the Dalton45 quantum chemistry program. In this study, the geometries of molecules are optimized at hybrid B3LYP level with 6-31G(d) basis set using the Gaussian 03 program.46 At the same level, TD-DFT has been employed to obtain excitation energies and oscillator strengths of the optimized structures. The linear response function in the Dalton program45 has also been used to describe linear absorption process but with coulomb-attenuated CAM-B3LYP functional.47,48 The solvent effects on linear absorption are explored by using polarizable continuum model (PCM).49 The TPA cross sections, as well as the transition dipole momentums between excited states, are calculated through a residue of quadratic response function using the Dalton program.45 MD simulations are used to investigate the conformation of the molecule 2s (see Figure 1) in chloroform solution. The intraand intermolecular interactions are modeled by a classical molecular mechanical force field with the following form:
(2) E)
∑ kr(r - req)2 + ∑ kθ(θ - θeq)2 +
bonds
where R,β ∈ (x,y,z), ω is the fundamental frequency of the laser beam, and we assume it is equal to half of the excited state |f〉, i.e., 2ω ) ωf. The summation here includes all intermediate, initial, and final states, and ωsi represents the excited energy of intermediate state |s〉. The microscopic TPA cross section of molecules excited by a linear polarized monochromatic beam can be calculated by42
δtp ) 6(Sxx + Syy + Szz)2 + 8(Sxy2 + Sxz2 + Syz2 SxxSyy - SxxSzz - SyySzz)
4π2a50R ω2 L4 g(ω)δtp 15c0 Γf n2
(3)
angles
νn [1 + cos(nφ - γ)] + 2 dihedrals
∑
∑ i 1.49 eV, in gas phase), its TPA probability is expected to be lower even though it has another transition channel. In 2s, the S0 f S2 f S2 excitation channel has the main contribution to TPA transition matrix. We can then compare it with 1r. It is found that their energy differences are almost the same, 1.49 v.s. 1.47 eV. However, its transition dipole moments are much larger than that of 1r, which makes 2s possess the strongest TPA cross section in this energy region. B. Molecular Dynamics Simulations. It is evident that QC calculations have been able to explain experimental observations for 1r and 2a. However, they are not so successful in providing good descriptions for 2s in terms of the relative position of OPA maximum and the reduction of the TPA cross section. By closely inspecting the structures of these chromophores, one can immediately realize that the dimer 2s has a very flexible structure, in which the mutual orientation of two subchromophores could be changed in solutions. To verify this hypothesis, we have carried out MD simulations for dimer 2s in solutions. The evolution of the N-N distance between N1 and N2 atoms (see Figure 2) during 1-5 ns simulations is plotted in Figure 6, and the optimized N-N distance of 21.24 Å from QC calculations is marked with a line. As expected, this distance experiences large changes in the range of 9-24 Å under the solvent interactions and thermal motions. It is clear to see that the N-N distance stays more of the time shorter than the equilibrium distance, implying that the two dipolar subunits are often with a smaller angle than that in the optimized gas geometry. We have then carried out constrained geometry optimizations for a set of geometries with different ∠CNO (as defined in Figure 2), and the corresponding geometries are also illustrated in Figure 6. It is found that with respect to the relaxed geometry (125°), the energy difference is very small for conformations with angles of 160, 130, and 100°, which has a value of only 1.48, 0.027, and 1.46 kcal/mol, respectively. When the angle becomes 70°, the energy barrier is only increased to 5.68 kcal/ mol. The largest conformational energy increase in these geometries is 10.9 kcal/mol, which corresponds to the structure with an angle of 50° and the N-N distance of 12.5 Å. This high energy structure could be found in CHCl3 solution according to MD simulations. All of these indicate that the change of the mutual orientation between two dipolar chromophores is highly possible in the solution from the thermodynamic point of view. In order to demonstrate the effects of such structural fluctuations, the calculated OPA spectra for conformations with the angles of 160° and 70° are given in Figure 7 together with the result for the relaxed geometry. It can be seen that the excitation energies of two CT states are almost the same in all three cases, but the intensity of the one at shorter wavelength increases with the decrease of the angle. This produces a broader spectral profile and a blue-shifted absorption maximum. From MD simulations, we know that the two dipolar branches of dimer 2s tend to orientate at small angles in most of the simulation time. Therefore, the resulted OPA spectrum of 2s in solutions can have a blue-shifted and broader absorption band with respect to 1r, in good agreement with the experimental observations.23 From the exciton model, it is known that for interacting dipoles with nearly antiparallel orientation, the TPA cross section is often decreased.23 Since the dimer 2s often stays with the antiparallel fashion in the solution, its maximal TPA cross section should be much reduced, which explains the observed large reduction in experiments.23
J. Phys. Chem. B, Vol. 114, No. 33, 2010 10819
Figure 6. N-N distance during 1-5 ns simulations and optimized constrained geometries with different ∠CNO angles.
Figure 7. Calculated OPA spectra for 2s in constrained conformations with angles of 160° (black) and 70° (red), as well as in the relaxed conformation (blue).
IV. Summary We have employed time-dependent density functional theory in combination with molecular dynamics simulations to inves-
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tigate the linear and nonlinear optical absorptions of interacting dipolar chromophores. The obtained results are compared with those from experiments. The underlying structure-to-property relation for TPA cross section of different molecules has been revealed by a few-states model. Our calculated results are in excellent agreement with their experimental counterparts when the conformation fluctuations from MD simulations are taken into account. Our calculations indicate that the interacting dipolar dimers under investigations are not good TPA materials since the dipolar interaction can significantly reduce their maximal TPA cross section in comparison with the corresponding monomer. It shows that caution must be exerted in practical applications when a high concentration of TPA materials is required simply because of the possible molecular aggregations. Acknowledgment. We acknowledge support from Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 10904085) and National Natural Science Foundation of China (Grant Nos. 10974121 and 20925311). References and Notes (1) Albota, M.; Beljonne, D.; Bredas, J. L.; Ehrlich, J. E.; Fu, J.; Heikal, A. A.; Hess, S. E.; Kogej, T.; Levin, M. D.; Marder, S. R.; Maughon, D. M.; Perry, J. W.; Ro¨ckel, H.; Rumi, M.; Subramaniam, G.; Webb, W. W.; Wu, X.; Xu, C. Science 1998, 281, 1653. (2) Macak, P.; Luo, Y.; Norman, P.; Ågren, H. J. Chem. Phys. 2000, 113, 7055. (3) Wang, C. K.; Macak, P.; Luo, Y.; Ågren, H. J. Chem. Phys. 2001, 114, 9813. (4) Nguyen, K. A.; Rogers, J. E.; Slagle, J. E.; Day, P. N.; Kannan, R.; Tan, L.-S.; Fleitz, P. A.; Pachter, R. J. Phys. Chem. A 2006, 110, 13172. (5) Nguyen, K. A.; Day, P. N.; Pachter, R. J. Phys. Chem. A 2009, 113, 13943. (6) Day, P. N.; Nguyen, K. A.; Pachter, R. J. Phys. Chem. B 2005, 109, 1803. (7) Chung, S.-J.; Kim, K.-S.; Lin, T.-C.; He, G. S.; Swiatkiewicz, J.; Prasad, P. N. J. Phys. Chem. B 1999, 103, 10741. (8) Adronov, A.; Fre´chet, J. M. J.; He, G. S.; Kim, K.-S.; Chung, S.J.; Swiatkiewicz, J.; Prasad, P. N. Chem. Mater. 2000, 12, 2838. (9) Chung, S.-J.; Lin, T.-C.; Kim, K.-S.; He, G. S.; Swiatkiewicz, J.; Prasad, P. N.; Baker, G. A.; Bright, F. V. Chem. Mater. 2001, 13, 4071. (10) Drobizhev, M.; Karotki, A.; Dzenis, Y.; Rebane, A.; Suo, Z.; Spangler, C. W. J. Phys. Chem. B 2003, 107, 7540. (11) Luo, Y.; Norman, P.; Macak, P.; Ågren, H. J. Phys. Chem. A 2000, 104, 4718. (12) Wang, C. K.; Zhao, K.; Su, Y.; Yan, R.; Zhao, X.; Luo, Y. J. Chem. Phys. 2003, 119, 1208. (13) Frediani, L.; Rinkevicius, Z.; Ågren, H. J. Chem. Phys. 2005, 122, 244104. (14) Woo, H. Y.; Liu, B.; Kohler, B.; Korystov, D.; Mikhailovsky, A.; Bazan, G. C. J. Am. Chem. Soc. 2005, 127, 14721. (15) Zhao, K.; Ferrighi, L.; Frediani, L.; Wang, C. W.; Luo, Y. J. Chem. Phys. 2007, 126, 204509. (16) Kim, S.; Zheng, Q. D.; He, G. S.; Bharali, D. J.; Pudavar, H. E.; Baev, A.; Prasad, P. N. AdV. Funct. Mater. 2006, 16, 2317. (17) Park, J. S.; Kim, R. H.; Cho, N. S.; Shim, H.-K.; Lee, K.-S. J. Nanosci. Nanotechnol. 2008, 8, 4793. (18) Collini, E.; Ferrante, C.; Bozio, R. J. Phys. Chem. B 2005, 109, 2. (19) Ray, P. C.; Sainudeen, Z. J. Phys. Chem. A 2006, 110, 12342. (20) Liu, K.; Wang, Y. H.; Tu, Y. Q.; Ågren, H.; Luo, Y. J. Phys. Chem. B 2008, 112, 4387. (21) Ray, P. C.; Leszczynski, J. J. Phys. Chem. A 2005, 109, 6689. (22) Drobizhev, M.; Stepanenko, Y.; Dzenis, Y.; Karotki, A.; Rebane, A.; Taylor, P. N.; Anderson, H. L. J. Phys. Chem. B 2005, 109, 7223. (23) Terenziani, F.; Morone, M.; Gmouh, S.; Blanchard-Desce, M. ChemPhysChem. 2006, 7, 685. (24) Cho, B. R.; Son, K. H.; Lee, S. H.; Song, Y.-S.; Lee, Y.-K.; Jeon, S.-J.; Choi, J. H.; Lee, H.; Cho, M. J. Am. Chem. Soc. 2001, 123, 10039. (25) Lee, W.-H.; Lee, H.; Kim, J.-A.; Choi, J. H.; Cho, M.; Jeon, S.-J.; Cho, B. R. J. Am. Chem. Soc. 2001, 123, 10658. (26) Cho, B. R.; Piao, M. J.; Son, K. H.; Lee, S. H.; Yoon, S. J.; Jeon, S.-J.; Cho, M. Chem.sEur. J. 2002, 8, 3907. (27) Beljonne, D.; Wenseleers, W.; Zojer, E.; Shuai, Z.; Vogel, H.; Pond, S. J. K.; Perry, J. W.; Marder, S. R.; Bre´das, J.-L. AdV. Funct. Mater. 2002, 12, 631.
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JP103791S
