Electronic Spectra of the Nanostar Dendrimer: Theory and Experiment

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Electronic Spectra of the Nanostar Dendrimer: Theory and Experiment† Julio L. Palma,‡,§,∇ Evrim Atas,§ Lindsay Hardison,§ Todd B. Marder,⊥ Jonathan C. Collings,⊥ Andrew Beeby,⊥ Joseph S. Melinger,# Jeffrey L. Krause,‡,§ Valeria D. Kleiman,*,§ and Adrian E. Roitberg*,‡,§ Quantum Theory Project, UniVersity of Florida, GainesVille, Florida 32611-8435, United States, Department of Chemistry, UniVersity of Florida, GainesVille, Florida 32611-7200, United States, Department of Chemistry, UniVersity of Durham, South Road, Durham DH1 3LE, U.K., and Electronics Science and Technology DiVision, NaVal Research Laboratory, Washington, D.C. 20375, United States ReceiVed: July 7, 2010; ReVised Manuscript ReceiVed: October 8, 2010

We present a sequential molecular dynamics/quantum mechanics (MD/QM) study and steady-state spectroscopy measurements of the nanostar dendrimer (a phenylene-ethynylene dendrimer attached to a ethynylperylene chromophore) to determine the temperature dependence of the electronic absorption process. We studied the nanostar as separate units and performed MD simulations for each chromophore at 10 and 300 K to study the effects of the temperature on the structures. The absorption spectrum of the nanostar, at 10 and 300 K, was computed using an ensemble of 8000 structures for each chromophore. Quantum mechanical (QM) ZINDO/S calculations were performed for each conformation in the ensemble, including 16 excited states for a total of 128 000 excitation energies, and the intensity was scaled linearly with the number of conjugated units. Our calculations and experimental spectra measured for the individual chromophores and the nanostar are in good agreement. We found that for each system, the spectral features are narrow at 10 K because the transitions are localized in wavelength and the absorption energy depends primarily on the length of the chromophore, while at 300 K, the spectra features are quite broad and blue-shifted due to conformational changes on the systems. We explain in detail the effects of temperature and their consequence for the absorption process. I. Introduction A dendrimer is a synthetic macromolecule that emanates from a central group in a regular tree-like structure.1-6 The steric limitations of the dendritic wedge length lead to relatively small sizes, but their globular shapes lead to fairly high densities. Dendrimers have two major chemical environments, the surface, which is dominated by the terminal functional groups, and the interior, which is largely protected from the exterior environments.1,2 The existence of at least two distinct chemical environments in such a molecule enables many applications, which range from adhesivesandlubricants7,8 todrug-deliverysystems,8,9 catalysts,10-12 and biomolecule mimics.4,8,13-21 Due to the large variety of potential and proven applications, dendrimers are under active study by experimental and theoretical researchers.10,22-25 One specific type of dendrimer is based on phenyleneethynylene units, which have interesting photophysical and photochemical properties. Their highly branched structure can be organized to funnel absorbed energy directionally toward a trap at the locus.16,26-28 Experimental and theoretical analysis indicates that these dendrimers have a dual role as lightharvesting antennas as well as energy collectors, allowing new forms of supramolecular photochemistry.3,4,16,27-30 When radiation interacts with a dendrimeric molecule, electronic energy is transferred among the chromophores and collected in a trap on †

Part of the “Mark A. Ratner Festschrift”. * To whom correspondence should be addressed. E-mail: [email protected] (V.D.K.); [email protected] (A.E.R.). ‡ Quantum Theory Project, University of Florida. § Department of Chemistry, University of Florida. ⊥ University of Durham. # Naval Research Laboratory. ∇ Current address: Department of Chemistry, Yale University, New Haven, Connecticut 06520-8107, United States.

a very rapid time scale, consequently preventing the energy from leaking back out. This process is enhanced by the geometry of phenylene-ethynylene dendrimers, in which the density of atoms increases rapidly with generation and the atoms at the boundary become closely packed, hindering the dynamics that lead to loss of energy to the environment. In addition, due to the precise molecular structure and chemical composition of phenylene-ethynylene dendrimers, they resist photobleaching, which enhances their longevity.3,4,27-32 The nanostar (Figure 1), the main subject of this study, is a phenylene-ethynylene dendrimer synthesized by Moore and co-workers.31,33 It has as its core an ethynylperylene group and four generations of phenylene-ethynylene units that decrease in length as the generation increases (four-, three-, and tworing chromophores). This difference in length among the chromophores leads to an energy gradient. When the peripheral groups are excited with ultraviolet radiation, the energy is transferred down the branches to the core with nearly 100% efficiency.3,25,27,31 In the absence of this gradient, the energy would be dispersed randomly throughout the molecule and lost to the environment, and the energy transfer efficiency from the terminal groups to the core would decrease considerably.27,32 Experiments show that the absorption features in the nanostar for wavelengths lower than 400 nm correspond to the dendrimeric portion and are nearly unaffected by the presence of the ethynylperylene group. However, emission from the nanostar occurs at wavelengths associated with the isolated ethynylperylene emission. This fluorescence is 3 orders of magnitude more intense than the emission obtained from isolated perylene excited at the same wavelength. These observations indicate that the nanostar acts as a high-efficiency energy funnel and

10.1021/jp1062918  2010 American Chemical Society Published on Web 10/29/2010

Electronic Spectra of the Nanostar Dendrimer

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Figure 1. Two-dimensional sketch of the nanostar dendrimer. The chromophores studied as separate units are noted.

the perylene group as an energy trap from which the energy is emitted as visible radiation.25,27,31 The mechanism and the kinetics of the energy-transfer process have been the main subject of several investigations. Using timecorrelated single-photon counting, Swallen et al.27 determined an upper limit to the ensemble-average energy-transfer time from the peripheral groups to the ethynylperylene trap of 270 and about 10 ps from the four-ring system to the perylene group. Kleiman et al.34 measured the relaxation time of the excited two-ring system within the nanostar. The results can be modeled as the sum of two exponential components, with the faster component decaying with a time constant of 3.0 ( 0.5 ps and the slower decaying with a time constant of 14 ( 2.5 ps. They also measured subpicosecond decay after excitation of the threeand four-ring systems. The experimental results have been interpreted and modeled using Fo¨rster theory, a through-space model, where energy transfer occurs via a Coulombic dipoledipole interaction.25,34 Although Fo¨rster theory has been used successfully with many systems, it must be applied carefully in dendrimeric structures due to the presence of multiple donors in different conformational environments and the relatively short distances between donor and acceptors.35,36 Ortiz et al.36 compared rate constants for energy transfer between the two- and three-ring systems obtained via the ideal dipole approximation, Fo¨rster theory, and the transition density cube method (TDC).37 The TDC method was found to give the most accurate approximation of the Coulombic coupling and to be the most sensitive method to account for the phenylene group rotation, which must be considered for prediction of the temperature dependence. This feature has not been considered in many previous investigations, although the optical properties of the nanostar do, in fact, display distinct temperature dependencies. Kopelman and co-workers showed that at room temperature, the excitation and absorption spectra of the nanostar are nearly identical, leading to energy-transfer efficiency of near 1.31 At 10 K, the spectrum changes considerably from the one measured at room temperature, as can be observed in Figure 2. Three major peaks are observed at 10 K (313, 361, and 384 nm), whereas at room temperature, only two peaks at ∼300 and ∼350 nm are observed with broad shoulders. The peak at 313 nm observed at low temperature has a small shift toward shorter

Figure 2. Experimental excitation spectrum of the nanostar at 10 K (solid red line) and the experimental absorption spectrum at room temperature (dashed black line).

wavelength at room temperature. The peaks at 361 and 384 nm seen at low temperature are not sharply defined at high temperature, and only shoulders are seen between 330 and 370 nm. At room temperature, the peak at 310 nm has been assigned to the excitation of the two-ring system, the shoulder at 333 nm has been assigned to the three-ring system, and the shoulder at 370 nm has been assigned to the four-ring system.25,27,31 Questions remain, though, regarding the nanostar absorption process. What causes the temperature dependence of the nanostar absorption spectrum? Which chromophores contribute to the absorption process? Are the experimental assignments of the peaks and shoulders correct? Mukamel and co-workers calculated the absorption spectrum and frequency-gated fluorescence spectra for the nanostar using the collective electronic oscillator approach and developed a Frenkel exciton Hamiltonian to describe energy transfer and optical properties.32,38-40 Their results are in agreement with experiments; however, they did not consider the temperature dependence of the system. Ortiz et al.36 included these effects for energy-transfer studies, and their results show that the rotation of phenylene groups is the most important aspect that

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must be considered to understand the temperature dependence observed in the absorption spectrum. Garcia-Garibay and co-workers performed semiempirical calculations for aromatic chromophores linearly conjugated by ethynylene linkages to determine the effects of the phenylene group rotation. They determined the interruption of the conjugation due to the rotation and its effects on vertical excitation using ZINDO/S,41-44 which is a semiempirical molecular orbital method parametrized at the CI-singles (CIS) level to reproduce electronic transitions.45 It is worth noting that some experiments in that work were later retracted due to impurities in the samples, but here, we are just pointing out the relevance of their semiempirical calculations.42,46 Magyar et al.47 performed a theoretical and experimental study of phenylene-ethynylene molecular wires. They studied excitation energies at different levels of theory including ZINDO/S calculations. They also considered planar molecular structures and alternating geometries at specific angles between phenyl rings. Liu et al.48 studied the absorption spectra of phenyleneethynylene oligomers and their unusual aspects due to the rotation of the phenylene rings. The absorption spectra were obtained from a set of torsional configurations where the ground state is modeled with a molecular mechanics expression and the electronic transitions are modeled with an exciton model and INDO/SCI calculations. They found that the inclusion of the torsional disorder is essential in the spectroscopy and photophysics of conjugated polymers. In this paper, we compare molecular dynamics (MD) simulations followed by quantum mechanical (QM) calculations with steady-state spectroscopy measurements to determine the temperature dependence of the absorption process in the nanostar at 10 K and room temperature. Since meta substitution suppresses π-electron conjugation, we consider the possibility of interpreting the nanostar absorption spectrum from the sum of independent units. Theoretical calculations by Mukamel et al. indicate that meta branching electronically decouples the resonant conjugation among phenylene-ethynylene units.5 As a result, the optical excitation is localized on each phenylene-ethynylene chain in compact and extended dendrimers. Chernyak and co-workers also showed, using an exciton model, that meta connection breaks molecular wires like the nanostar into linear segments in the excited state.49 Experimental evidence for this excitonic localization is observed by steady-state spectroscopy,3 leading to the prediction that the overall absorption spectrum of the nanostar can be interpreted as the sum of the individual chromophore spectra.25,27,31 In addition, strong localization of the orbital density in the segments has been found from molecular orbital calculations.50 In contrast, Martínez and co-workers have proposed that although meta substitution blocks conjugation in the ground state, this is not necessarily true in the excited state. In fact, their model calculations suggest that the excitations are not localized on the excited states of chromophores separated by meta substitution. They find that the electronic coupling is small in the absorbing geometry, while in the emitting geometry, it is large.51,52 This result should have a direct consequence on energy-transfer calculations, but our results show that this issue is not relevant for studies of the absorption process. Martínez’s calculations correspond to segments of equal legnth (and isoenergetic) for which an increased interaction can lead to stronger coupling and more delocalization. In contrast, the nanostar, with its segments of different energies (length), cannot undergo such delocalization, as shown by Mukamel and

Palma et al. co-workers39,40 and Ortiz et al.36 since chromophores with large energy differences are not likely to form delocalized excited states. In this research, we performed MD simulations at different temperatures to construct equilibrium canonical ensembles of each chromophore. These ensembles were subsequently used to performed ZINDO/S calculations, which is a method that is known to provide a good description of conjugated systems.53 A similar technique was used by Canuto and co-workers to determine solvent effects in systems such as benzene, Nmethylacetamide, and benzophenone. They calculated electronic transitions using full QM ZINDO/S calculations in clusters generated by Monte Carlo simulations.54-56 In similar research, Krueger and co-workers used MD simulations followed by a QM time-dependent evaluation of electronic transition energies for the system of oxazine-4 in methanol.57 On the basis of absorption spectra of the individual chromophores, we predict the absorption spectra of the nanostar at 10 and 300 K, which allows us to identify the contribution from each chromophore. We also present the experimental absorption spectra of the individual phenylene-ethylene chromophores and the nanostar collected at low and room temperature. Finally, we compare the results from our MD simulations and electronic spectra calculations with the experimental spectra and discuss the causes and effects of the temperature dependence in this system. II. Methods A. Theoretical Calculations. The systems that compose the nanostar were built and studied as separate units. The core was studied as an ethynylperylene unit bonded to a phenyl group; the first generation is a four-ring system, the second generation is a three-ring system, and third and fourth generations are tworing systems (Figure 1). In addition, a model of the entire nanostar was constructed and analyzed. We performed MD simulations for each system described above using TINKER (version 3.9).58 For the interatomic interactions, the MM3 force field was used, which has been parametrized to treat organic compounds.59-61 In the nanostar and its chromophores, one important feature is the presence of phenylene groups connected with ethynylene units. The rotational barrier between these groups in the MM3 force field was 0.001 kcal mol-1, whereas the experimental value was 0.6 kcal mol-1.62-64 The force field was modified by us by changing the torsion potential to obtain the experimental energy barrier value of 0.6 kcal mol-1 and a periodicity of 2. The nanostar and its separate chromophores were built as fully extended molecules and then locally minimized to a rootmean-square gradient of energy less than 0.01 kcal mol-1 Å-1. Stochastic dynamics simulations were performed at two temperatures, 10 and 300 K, with a collision frequency friction coefficient of 1.0 ps-1. For the chromophores studied, the core, and two-, three-, and four-ring systems, 50 ns of dynamics was performed, whereas for the entire nanostar, 20 ns of dynamics was obtained. The simulations were propagated using the velocity Verlet-based stochastic dynamics algorithm with a 1 fs time step.65 ZINDO/S calculations were done for each separate unit using the Gaussian 03 package.66 Two ensembles consisting of 8000 conformations obtained from the MD simulations were constructed for each system, one from the simulation at 10 K and one from the simulation at 300 K. The ZINDO/S calculations considered only singlet excited states and included 16 excited states, resulting in a total of 128 000 computed electronic



Figure 3. Snapshots of the two-, three-, and four-ring systems during 50 ns of molecular dynamics at 300 K. Rotation of the aromatic rings and bending of the molecules are observed.

transitions for each system at each temperature. From these transitions, electronic spectra for each system were synthesized. B. Experiments. The linear phenylene-ethynylene samples were obtained from different sources. 1,2 Diphenylacetylene (two-ring system) was purchased from Aldrich and used as received. 1,4 Bis(phenylethynyl) benzene (three-ring system) was purchased from Aldrich and was purified by recrystallization from toluene before attempting the experiments. 4,4′-Bis(phenylethynyl) tolane (four-ring system)67 was synthesized at Durham via Sonogashira cross-coupling reactions, as part of ongoing studies on the synthesis, structure, and properties of monodisperse arylene-ethynylene oligomers and related compounds.68-70 The nanostar sample was provided by Professor J. Moore. For steady-state room-temperature measurements, the nanostar and the phenylene-ethynylene samples were dissolved in dichloromethane (CH2Cl2). The solvent was purchased from Aldrich (UV spectroscopy grade, >99.9%) and was stored under nitrogen before being used without any further purification. To perform steady-state measurements at low temperature, a helium flow cryostat was used to control the temperature in the range from 10 to 298 K for the nanostar, and a liquid nitrogen flow cryostat was used from 77 to 298 K for the linear phenyleneethynylene samples. 2-Methyltetrahydrofuran (MeTHF), purchased from Aldrich, was used as a solvent. To obtain a glassy sample, MeTHF was further purified and distilled to be anhydrous prior to each measurement. Comparisons of sample spectra in CH2Cl2 and MeTHF at room temperature show no appreciable differences. III. Results and Discussion A. Molecular Dynamics. After local minimization of the core and the two-, three-, and four-ring systems, the optimized structures were found to be completely planar. During 50 ns of MD at 10 K, the two-, three-, and fourring systems maintain a structure close to planar. At 300 K, the structures are no longer planar, and the rings rotate, indicating that at this temperature, the rotational barrier is accessible. In addition, the molecules lose their linear conformation and bend along the long axis, which is more pronounced as the systems get larger as there is wider range of motion, as seen in Figure 3. In Figure 4, the torsion angle distributions of the phenyl rings of the two-ring system at 10 and 300 K are shown. At 10 K, the two-ring system is essentially planar; the torsion angle mean is 0.0° with a distribution width of 16.4°. Most of the conformations are near the planar structure, but there is sufficient energy to allow for small alterations from planarity. These results demonstrate that at low temperature, free rotation of the rings is not permitted.

Figure 4. Distribution of the torsion angle of the two-ring system. At 10 K (black), the torsion angle mean is 0.0° with a distribution width of 16.4°. At 300 K (blue), the rotational barrier is easily surmounted, and the rotation of the rings is essentially free.

Figure 5. Snapshots of the nanostar during 20 ns of molecular dynamics at 10 K.

In contrast to the narrow distribution at 10 K, there is a much larger distribution of angles at 300 K. At this temperature, the rotational barrier is easily surmounted, and the rotation of the rings is nearly free, as seen in Figure 4. There is no specific maximum or minimum because once the energy of the system is higher than the rotational barrier, the probability to find a conformation at any angle is nearly constant. In the case of the three- and four-ring systems, we found similar results. At 10 K, most of the conformations are near the optimized structure with low values of the torsion angle, whereas at 300 K, this barrier is surpassed, and there is free rotation of the rings, allowing a larger distribution of conformations. For the core, the results are similar. At low temperature, it maintains a structure near the optimized geometry, while at 300 K, the rotation of the single ring occurs, just as in the three previous systems, as the rotational barrier of the ring is nearly the same in all cases. For the complete nanostar, the optimized structure is nearly planar. At 10 K, there are small motions, and the structure is no longer planar due to steric effects between branches which lie in different planes. However, there is insufficient energy to surpass the rotational barrier of the rings, and free rotation of the rings is not observed (Figure 5). At 300 K, the branches of the dendrimer rotate. All of the branches are in different planes, which indicates that at higher temperature, the motion of the system is more promounced, and entanglement among different branches is more likely. The energy is sufficient to rotate every ring of the system, including the one that is bonded to the core. This behavior was not unexpected. As shown for the separate chromophores, every ring of the two-, three-, and four-ring systems rotates at 300 K.

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Palma et al. TABLE 1: Comparison of Calculated Spectral Features of the Individual Chromophores at 10 and 300 Ka spectrum peak center two-ring system three-ring system four-ring system core a

Figure 6. Snapshots of the nanostar during 20 ns of molecular dynamics at 300 K.

The rings within each generation rotate, while the rings at the branching point do not. In the three-ring system (secondgeneration), there is one ring that rotates freely, that is, the central ring, while in the four-ring system, there are two rings that rotate freely. The distance between the two central branches goes from 35.9 Å at low temperature to 16.0 Å at high temperature; this entanglement is due to bending of the linear chromophores and the noncoplanarity of the branches, as mentioned previously (Figure 6). B. ZINDO/S Calculations. As discussed above, the spectra at different temperatures for all systems were calculated using ZINDO/S. Each spectrum was calculated in vacuum and represents the sum of 128 000 electronic transitions derived from the conformations obtained via molecular dynamics. Figure 7 shows the calculated absorption spectra of the individual phenylene-ethylene components. At 10 and 300 K, the absorption spectra of the two-ring system are centered at 353 and 352 nm, respectively. At high temperature, the spectrum is broader than that at low temperature; at 300 K, the full width at half-maximum (fwhm) is 30 nm, while at 10 K, it is 7 nm (Figure 7A). This broadening reflects the conformational variability seen in Figure 4. In the three-ring system, the absorption peak at 10 K occurs at 391 nm, while at 300 K, it is blue-shifted by 11 to 380 nm

fwhm

10 K

300 K

displ.

10 K

300 K

353 391 420 481

352 380 399 479

1 11 21 2

7 8 9 12

30 47 60 48

All values are in nanometers.

(Figure 7B). In the four-ring system, the absorption peaks are at 420 and 399 nm at 10 and 300 K, respectively (Figure 7C). For both systems, the spectrum at high temperature is broader than that at low temperature. It is clear that as the length of the chromophore increases, the higher temperature induces a larger shift and increased broadening. In the case of the ethynylperylene core, at 10 K, the absorption peak is at 481 nm, and the fwhm is 12 nm, while at 300 K, the peak is at 479 nm, and the fwhm is 48 nm (Figure 7D). These results are summarized in Table 1. Figure 8 shows the experimental (top panel) and calculated (bottom panel) absorption spectra of the individual chromophores at low and high temperature. Good agreement is observed between the experimental and calculated spectra at low temperature (Figure 8A and C) and high temperature (Figure 8B and D) for the two-, three-, and four-ring systems. The experimental spectrum at 77 K displays a sharp band at the red end of the spectrum, followed by absorption to higher-lying states and vibronic contributions. As the temperature is increased, the absorption spectrum becomes broader and loses most of its structure. In addition, a blue shift of the sharp band edge is observed at high temperatures. Similar features are observed in the calculated spectra. The three bands obtained at low temperature correspond to the band edge absorption observed in the experiments. At room temperature, these sharp bands become broad and blue-shifted.

Figure 7. Calculated absorption spectra for the two-ring chromophore (A), the three-ring chromophore (B), the four-ring chromophore (C), and the core unit (D). Solid lines show the 10 K data, and dashed lines show the 300 K data.



Figure 8. Spectra of the two- (solid line), three- (dashed line), and four-ring system (dotted line). Left panels (A,C) are at low temperature, and right panels (B,D) are at room temperature. Top panels show experimental data and bottom panels the calculated ones.

Figure 9. Calculated electronic transitions for the two-ring system at 10 (A) and 300 K (B). Excitations to the first and second singlet excited states are presented in black and red, respectively. Calculated electronic transitions for the two- (black), three- (red), and four-ring (green) and core systems (blue) at 10 (C) and 300 K (D). Each dot corresponds to 1 of the 8000 structures of the ensemble.

It is clear that as the number of phenylene-ethynylene rings increases, the effect of the temperature is to induce a larger shift and to broaden the bands. As a result, the peaks are wellseparated at low temperature and not at high temperature. Vibronic structure is observed in the experiments but is not included in the calculations.71 In Figure 9A and B, the computed two lowest transition energies for the 8000 configurations of the two-ring system at 10 and 300 K are shown, respectively. At 10 K, the main transition is localized at 353 nm; interestingly, this corresponds to the second singlet excited state (S2) and not to the first (S1), in agreement with experimental results. The excitation of the two-ring system near 300 nm was explored previously by

Hirata72 and by Kleiman.34 Measurements show that at 297 nm, excitation initially populates the S2 (1B1u) manifold, which can either return to the ground state through (mainly) nonradiative relaxation or undergo internal conversion to the S1 state. Ultrafast time-resolved experiments yielded an S2 lifetime of 6.3 ps in CH2Cl234 and a lifetime less than 8 ps in hexane.72 At 300 K, the S1 as well as S2 transitions contribute to the absorption spectrum since there is symmetry breaking due to the conformational changes. The distribution of transitions is broader, ranging from 310 to 450 nm, because the number of populated conformations increases as a function of temperature, as the distributions of Figure 4 indicate.

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Figure 10. Left panels (A,C,E) are at low temperature, and right panels (B,D,F) are at room temperature. Top panel: experimental absorption spectrum of the nanostar. Middle panel: experimental absorption spectra of the individual components (black lines) and their sum (red line). Bottom panel: calculated absorption spectra for the individual components (black lines) and their sum (red line).

For the three- and four-ring systems at 10 K, the transitions are localized (Figure 9C), while at 300 K, the distribution is considerable broader (Figure 9D). For both systems, the major transitions are those to the (S1) state. For the three-ring system, the transitions are centered at 391 nm, and for the four-ring, they are centered at 420 nm. Absorption at 300 K spans from 325 to 420 nm, a range of 95 nm, for the three-ring system and from 325 to 450 nm, a range of 125 nm, for the four-ring system. The increase in the width of the distribution of the transitions affects the spectrum directly. In the spectrum of the two-ring system at 10 K, the fwhm of the peak increases, but the peak remains localized at 353 nm. For the four-ring system at 300 K, the fwhm of the peak is affected, as well as the position of the peak, which is shifted to higher energy. The MD simulations at 10 K show that the rings in the tworing system do not undergo significant rotation, while at 300 K, ring rotation is observed, and the molecule bends. At 300 K, there are many more accessible conformations, as shown in Figures 3 and 4, resulting in more accessible states and a consequential increase in the width of the absorption band. For the four-ring system, similar behavior to that in the threering system is observed. At 10 K, no ring rotation occurs, and the molecule is planar, while at 300 K, the rings rotate, and the molecule bends. The presence of four rings increases the number of conformations and states, causing the distribution and variance to increase. Thus, the width of contributing transitions is 70 nm broader than the width of the two-ring system. The displacement of absorption maximum of the four-ring system at 300 K can be rationalized by considering the conjugation length of the molecule as the energy of the electronic transition is inversely proportional to the conjugation length. At 300 K, the rings of the four-ring system rotate freely, and loss of conjugation resulting from lack of coplanarity of the rings causes, in effect, a division of the system into smaller

subsystems. Each of these subsystems has a higher excitation energy than the coplanar four-ring system, which results in a displacement of the peak toward shorter wavelengths. For the two-ring system, the results of temperature are not as pronounced as those in the four-ring system because the relative change in length is smaller. The effect of temperature on the three-ring system lies between that of the two- and fourring systems. To investigate the prediction that the absorption spectrum of the nanostar can be constructed from the absorption spectra of each of its units, we assembled the spectrum by taking into account the fact that there are 24 two-ring systems, 4 threering systems, 2 four-ring systems, and 1 core. Figure 10 (top panel) shows the experimental spectra of the nanostar at 10 K (Figure 10 A) and at room temperature (Figure 10 B). The middle panel shows the sum of the experimental spectra of the two-, three-, and four-ring systems at 77 K (Figure 10 C) and room temperature (Figure 10 D). Experimentally, the 300 and 10 K spectra of the nanostar (Figure 10, top panel) are wellreproduced by the weighted sum of the spectra of the individual chromophores (Figure 10, middle panel). A weak coupling among chromophores is observed as a consequence of a change in the chemical environment and resonance coupling as a small frequency shift (10 nm) toward lower wavelength between the nanostar absorption spectrum and the spectrum obtained as the sum of the phenylene-ethylene components. The bottom panel shows the sum of the calculated spectra of the two-, three-, and four-ring system and the ethynylperylene core. For the middle (experimental) and bottom (calculated) panels, the spectra of the subsystems are included to identify their contribution to the total absorption spectra. The calculated spectra were shifted by 40 nm along the wavelength axis to fit the main peak of the experimental spectra of the nanostar. The overall calculated spectrum at 10 K displays four main peaks



Figure 11. Oscillator strength and vertical excitation wavelength for different conformations, where the angle of one ring is scanned from 0 to 90°.

at 313, 351, 380, and 447 nm. However, at 300 K, only two peaks are clearly visible, at 309 and 438 nm; between 328 and 390 nm, there is a prominent shoulder. The calculated spectra are in good agreement with experiments, and the features in the nanostar spectrum scale linearly with the number of chromophores in the molecule. At 10 K, each of the main peaks corresponds to the absorption of one specific unit as the electronic transitions are localized in energy and homogeneous in intensity. The peaks at 313, 351, 380, and 447 nm correspond to the absorptions of the two-, three-, and four-ring systems and the core, respectively. The experimental spectrum of the nanostar at 10 K also shows four main peaks at 313, 361, 384, and 484 nm. At 300 K, while most of the contribution to the peak at 309 nm is from the two-ring system, the three- and four-ring systems also contribute to a lesser extent. The core contributes to the peak at 438 nm, and the three- and four-ring systems contribute to the shoulders between 330 and 370 nm. This is due to the fact that the transitions are heterogeneous in wavelength and intensity. The experimental spectrum of the nanostar at 300 K shows two main peaks at 310 and 472 nm, and broader peaks are observed as shoulders between 330 and 370 nm. It is important to note that the ensemble for the transitions of the individual components represents only the dynamics of the individual segments. Hence, conformations exist in which, for example, the terminal ring in the three- and four-ring systems rotate freely at 300 K. These conformations are not present in the true dynamics of the nanostar. To determine the effect that these additional conformations might have on the final spectrum, we scanned the ZINDO/S excitation energies and oscillator strengths with respect to the rotation of the terminal ring and the middle ring. We rotated the rings from 0 to 90°. Figure 11A and B shows the values of the oscillator strength and wavelengths at different values of the angles for the outer and inner ring, respectively, of the threering system. As the angle of rotation increases, both the oscillator strength and the wavelength decrease. In the case of rotation of the outer ring, the difference in wavelength between the angles of 0 and 90° is 27 nm, and the oscillator strength changes slightly. For the case of the inner ring, the effect is remarkable.

The value of the oscillator strength when the inner ring is at 90° is close to 0, with an excitation wavelength shifted by 68 nm from that of the planar conformation. When the inner ring is rotated by 90°, the oscillator strength for the three-ring system is very close to 0 as rotation of this ring divides the molecule into three small subsystems, which breaks the conjugation. As a result, the absorption intensity is minimal. When the outer ring is rotated by 90°, a subsystem similar to a planar two-ring system exists, for which the oscillator strength is not 0. For the four-ring systems, the results are qualitatively similar to those of the three-ring system. Figure 11C and D shows the values of the oscillator strength at different excitation wavelengths as a function of the rotation angle for the outer and inner rings, respectively. A decrease in the oscillator strength and an increase in the excitation energy are observed as the rotation angle increases. When the outer ring is rotated by 90°, a decrease in the oscillator strength and a shift of 15 nm toward shorter wavelength (high energies) are observed. These values are similar to those of a planar three-ring system. In contrast, a drastic blue shift is observed upon rotation of the inner ring. The minimum value is also at 90°, but this value does not fall to 0 because the rotation of one of the two inner rings does not break the conjugation completely as two consecutive rings remain in the same plane as that in the two-ring system, for which the absorption intensity is nonzero. These results indicate that the displacement of the spectra to shorter wavelength and the change in intensity are mainly due to the rotation of the inner rings, which occurs in the dynamics of both the nanostar and the individual components. We conclude that the additional conformations present in the simulation do not contribute significantly to the results. Finally, in Figure 12, we present an energy level diagram illustrating the HOMOs and LUMOs obtained from HartreeFock calculations with a 6-31G** basis set for the two- and three-ring systems and a segment of the nanostar consisting of a two-ring system linked to a three-ring system (2,3-ring system) at a meta position. Tada et al.50 performed a similar study of the molecular orbital interaction in the nanostar using the Hu¨ckel method. We find similar results; the molecular orbitals are localized in space and energy. In particular, we observe that

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Figure 12. Energy level diagram showing the HOMO and LUMO for the two-ring system (left), the three-ring system (right), and a two-ring system linked to three-ring system at the meta position (center).

the HOMO-1 of the 2,3-ring system corresponds to the HOMO of the two-ring system, the HOMO and LUMO of the 2,3-ring system correspond to the HOMO and LUMO of the three-ring system, respectively, and the LUMO+1 of the 2,3-ring system corresponds to the LUMO of the two-ring system. Although this picture does not describe the character of the excited states completely, it indicates that the allowed transitions in the 2,3ring system are HOMO f LUMO and HOMO-1 f LUMO+1. This model is in agreement with ZINDO/S calculations performed for the same systems. The main transitions in the 2,3-ring system are to S1 and to S4, which correspond to the HOMO f LUMO and HOMO-1 f LUMO+1, respectively. The transition to S1 on the 2,3-ring system has an oscillator strength of f ) 1.7 at 315 nm, which maps to the transition to S1 on the three-ring system. The transition to S4 on the 2,3-ring system has an oscillator strength of f ) 0.64 at 289 nm, mapping to the transition to S2 on the two-ring system. As expected, transitions to S2 and to S3 on the 2,3-ring system have negligible oscillator strengths and therefore do not contribute to the spectrum.

We find a slight increase in the gap between the LUMO+1 and HOMO-1 of the 2,3-ring system with respect the HOMO-LUMO gap of the two-ring system, as well as a slight decrease in the HOMO-LUMO gap of the 2,3-ring system with respect to that of the three-ring system. This is a classic behavior for a weakly coupled four-level system. Frenkel excitons in each component become weakly perturbed. IV. Conclusions In this research, the electronic absorption spectrum of the nanostar was measured by steady-state spectroscopy and calculated using sequential MD/QM ZINDO/S calculations. A temperature dependence of the electronic spectra of the nanostar has been observed and analyzed. The theoretical results obtained by this method correspond well with experimental data. We find that in the absorption process, the excitations are localized on chromophores separated by meta substitutions. As a result, the nanostar can be considered as the sum of separate phenylene-ethynylene units, which include 24 two-ring systems, 4 three-ring system, and 2 four-ring systems. The core of

Electronic Spectra of the Nanostar Dendrimer the nanostar is an independent ethynylperylene unit bonded to an aromatic ring. At 10 K, the nanostar exhibits little dynamical motion. Free rotation of the rings leading to a nonplanar structure is not observed, and the branches tend to separate from one another due to steric effects. At 300 K, the branches separate from each other, and free rotation of the phenyl rings is observed. At 10 K, each of the three main absorption peaks corresponds directly to one of the chromophores. The peak at the shortest wavelength corresponds to the two-ring system, followed by the peaks for the three- and four-ring systems at longer wavelengths. A weak peak at the longest wavelength corresponds to the core. All of the transitions are localized because there is a narrow distribution of conformations, and the absorption energy depends primarily on the length of the chromophore. At 300 K, the spectra of the individual chromophores are broader, and the three- and four-ring systems are blue-shifted (11 and 21 nm, respectively), resulting in a spectrum with one major peak and a shoulder containing contributions from all three systems. More conformations are accessible as the number of rings and the length of the molecule increase. The two-ring system has fewer conformations, and they are not different enough to cause considerable displacement of the wavelength maximum. In the case of the three- and four-ring systems, the rotations of the rings cause the molecule to behave as a union of smaller systems that absorb at higher energies. The displacements are sufficiently large to cause the formation of a shoulder in the spectrum. Due to the presence of many different conformations with different absorption wavelengths and transition intensities at 300 K, the electronic transitions are not localized. Instead, they are dispersed over a wide energy range, which causes broadening as well as displacement of the absorption band. Future work will continue to address the issue of conformational mobility and its spectroscopic signature, both experimentally and theoretically. Acknowledgment. This work was supported in part by DOE Grant DE-FG02-02ER45995 to J.L.K. and A.E.R., NSF Grant CHE-0239120 to V.D.K., and a University of Florida Alumni Fellowship to J.L.P. Computer resources were provided by the Large Allocations Resource Committee through Grant TGMCA05S010 to A.E.R. and by the University of Florida HighPerformance Computing Center. We wish to thank Prof. J. Moore (University of Illinois) for providing us with the nanostar sample. A.B. and T.B.M. thank One North East for support via the UIC Nanotechnology programme. J.L.P. gratefully acknowledges the help of Dr. Marcelo Videa and the Chemistry Department of ITESM Campus Monterrey. Supporting Information Available: Complete ref 66. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Newkome, G. R.; Moorfield, C. N.; Vo¨gtle, F.; Dendrimers and Dendrons; Wiley-VCH: Weinheim, Germany, 2001. (2) Frećhet, J. M. J., Tomalia, D. A., Eds. Dendrimers and Other Dendritic Polymers; John Wiley & Sons: New York, 2002. (3) Kopelman, R.; Shortreed, M.; Shi, Z.-Y.; Tan, W.; Xu, Z.; Moore, J. S.; Bar-Haim, A.; Klafter, J. Phys. ReV. Lett. 1997, 78, 1239. (4) Mukamel, S. Nature 1997, 388, 425. (5) Tretiak, S.; Chernyak, V.; Mukamel, S. J. Chem. Phys. B 1998, 102, 3310. (6) Inoue, K. Prog. Polym. Sci. 2000, 25, 453. (7) Tsukruk, V. V. AdV. Mater. 2001, 13, 95.

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Electronic Spectra of the Nanostar Dendrimer: Theory and Experiment

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