4142
J. Phys. Chem. C 2010, 114, 4142–4148
Photodimerization of Crystalline 9-Anthracenecarboxylic Acid: A Nontopotactic Autocatalytic Transformation Rene´ More´,† Gerhard Busse,† Jo¨rg Hallmann,† Carsten Paulmann,‡ Mirko Scholz,† and Simone Techert*,† Max-Planck-Institut fu¨r Biophysikalische Chemie, IFG Strukturdynamik (bio)chemischer Systeme, Am Fassberg 11, 37070 Go¨ttingen, Germany, Hasylab, Notkestr. 85, 22607 Hamburg, Germany, and Mineralogisches Institut, UniVersita¨t Hamburg, Grindelallee 48, 20146 Hamburg, Germany ReceiVed: October 4, 2009; ReVised Manuscript ReceiVed: January 22, 2010
This work discusses the photoreaction of crystalline β-9-anthracenecarboxylic acid (C15H10O2, 9AC). The thermally reversible [4 + 4] photodimerization of crystalline 9AC was investigated with electronic and vibrational spectroscopy and with photocrystallographic techniques. The photocrystallographic studies and their interpretation lead to a complex picture of the mechanism of this photoreaction. The increase of the peak widths during photoreaction is interpreted as a disorder increase in the crystalline lattice. Quantum chemical calculations suggest that this disorder is caused by the formation of various product configurations during photoreaction. At least three possible configurations have been found. Different tautomeric sites lead to an additional disorder parameter adding another complexity in the observed photodimerization reaction. For the overall photodimerization a maximum conversion rate of 75% has been determined. Application of the Johnson, Mehl, Avrami, and Kolmogorov (JMAK) model leads to an extraordinary Avrami parameter suggesting unusual transformation kinetics of the bulk during photoreaction. The unusual Avrami parameter is discussed as an autocatalytic step during photoreaction through an excimer state. It is created by one photoexcited 9AC molecule and a ground state 9AC molecule. Taking into account this additional kinetical pathway, out of statistical reasons additional lattice disordering mechanisms are possible. Introduction In solid-state chemistry, the crystal lattice acts as a template, which allows efficient regio- and stereoselectivity in the reaction. Photoinduced solid-state reactive processes can be separated into two categories: reversible and irreversible reactions. A system that undergoes a reversible single-crystal to single-crystal photoinduced reaction is an ideal candidate for a molecular switch or motor.1–3 For these reasons, photoinduced transformations in organic crystals have been studied for a long time.2–11 In particular, [4 + 4] photodimerization of anthracene derivates in the solid state plays a key role as a model system for this kind of transformation. These photodimerizations are often of heterogeneous character.10,12,13 Some anthracene derivates are known for their quite unusual reaction behavior in the solid state, for example the photodimerization of 9-cyanoanthracene, which crystallizes in a head-to-head “cis” arrangement also known as β-type packing.14 By taking into account the packing symmetry of 9-cyanoanthracene and applying the topochemical principle, a cis-photodimer for the [4 + 4] photodimerization is expected. However, photolysis experiments in the solid state yield only the trans-product.10 In order to shed light on this unusual chemical behavior, it is of interest to understand, in more detail, the mechanism of [4 + 4] photodimerization of these compounds. 9-Anthracenecarboxlyic acid (C15H10O2, 9AC, see Chart 1) crystallizes like 9-cyanoanthracene in a β-type packing.14,15 However, various studies7,12 on the photodimerization of several anthracene derivates in the solid state have shown that 9AC is photostable. * To whom correspondence should be addressed. † Max-Planck-Institut fu¨r Biophysikalische Chemie. ‡ Hasylab and Mineralogisches Institut.
CHART 1: Chemical Structure of 9-Anthracenecarboxylic Acid (9AC)
Nonetheless, the work of Ito et al.16 shows that isolation of the thermally unstable head-head photodimer of 9AC after illumination at low temperature (2 °C) and its characterization by NMR spectroscopy are possible. In this study, only the head-head photodimer was found. A reversible photoinduced change of the shape of crystalline 9AC nanorods, grown on Al2O3 templates, has been observed by Bardeen et al.8 The studies on the nanorods imply a single-crystal to single-crystal transformation. The crystal structure of a 9AC photodimer has not been reported in the literature so far. The aim of the present investigations is to add more puzzle parts to the understanding and characterization of the reaction mechanism of 9AC photodimerization. 9AC dimerizes by the absorption of an optical photon through an excimer-state to the photodimer, as sketched in Figure 1. In the present work, we describe a combined spectroscopic and X-ray analysis of the [4 + 4] photodimerization of 9AC by irradiation at the rededge of S1 r S0 absorption band. Using optical spectroscopy, it is possible to monitor the photoreaction on a molecular level, which offers direct access to its reaction kinetics. The photocrystallographic techniques allow us to study the evolution of the whole crystal lattice over time.17 Combining these methods, we are able to monitor the local-to-global changes of disorder in crystalline 9AC systems4 as well as their effects on the
10.1021/jp909513v 2010 American Chemical Society Published on Web 02/12/2010
Crystalline 9-Anthracenecarboxylic Acid
J. Phys. Chem. C, Vol. 114, No. 9, 2010 4143
Figure 1. Reaction scheme of the [4 + 4] photodimerization of β-9anthracenecarboxylic acid (C15H10O2, 9AC) leading to the head-head photoproduct and its thermal back-reaction.
periodic lattice. Kinetic analysis allows the determination of a mechanistic picture of 9AC photodimerization. The experimental results are interpreted by including simulations based on quantum chemical density functional theory (DFT). Experimental Section 9AC was purchased from Sigma-Aldrich. Monomer single crystals suitable for photodimerization and X-ray diffraction studies were obtained by recrystallization from toluene. They belong to the monoclinic space-group P21/n, with the cell parameters of a ) 3.89 Å, b ) 9.27 Å, c ) 29.06 Å, and β ) 90.64°.15 For FTIR and UV-vis spectroscopy, 9AC was dispersed in KBr pellets with 0.9 mm thickness and 13 mm diameter size. In the studies of the dimerization with X-ray diffraction, the samples were irradiated with a 150 W Xe arc lamp, which was equipped with a glass filter combination to transmit between 375 and 425 nm. The longer infrared wavelengths were blocked with a water filter. The light was transported to the sample via a fiberoptic light guide (LINOS Photonics) and focused down to a spot diameter of 1-2 mm with a Schwarzschild objective (Newport). In the optical spectroscopy studies of the dimerization, the samples were irradiated with a 200 W high-pressure Hg lamp. The 405 nm emission from the mercury spectrum was selected with an interference filter and attenuated with neutral glass filters (Schott). During the spectroscopic experiments the KBr pellet was placed in a home-built temperaturecontrolled cell. The sample is cooled down by circulation of a water-glycol mixture (4 °C). The illumination power was about 4-5 mW/cm2. The FTIR spectra were recorded with a Bruker IFD 25 FTIR spectrometer. The fluorescence spectra were obtained with a Jobin-Yvon Fluorolog spectrofluorometer and the UV-vis spectra with a Cary-5E absorption spectrometer. A detailed description of the experimental setups and the determination of the fluorescence quantum yield can be found elsewhere.18,19 Single-crystal X-ray diffraction studies have been performed at the beamline F1 at the DORIS storage ring at HASYLAB/ DESY. The crystals were mounted on a 4 circle κ-diffractometer, and the measurements have been performed for the diffraction angles 2θ ) 0°, ω ) 0°, χ ) 10° under full 180° φ-rotation in steps of ∆φ ) 1°. The X-ray diffraction data were collected at 270 K by using a two-dimensional detector (MarCCD165) at a wavelength of 0.6 Å. After completing the first data set, the illumination was started and the following data sets were recorded under constant illumination conditions. Further details about the used setups have been published elsewhere.20 Computational Details The density functional theory (DFT) calculations of the 9AC monomer and the photodimer have been performed by using the computer program Gaussian03.21 For our simulations the B3LYP DFT approach, which includes the interchange hybrid functional from Becke22 in combination with the three-parameter correlation functional by Lee-Yang-Parr,23 was employed with
Figure 2. (a) UV-vis absorption spectra of 9AC recorded for different illumination times from 0 to 180 min (405 nm, 4.5mW/cm2). (b) Dimerization rate of the 9AC photoreaction (405 nm excitation wavelength, 4.5 mW/cm2). The experimental data points are based on the integrated absorption intensity of the S1 r S0 transition band. The fit according to the JMAK model (eq 1) is assigned as solid line [parameters: n ) 0.55 ( 0.08 and k ) (0.17 ( 0.06) min-1]. The dashed line assigns a fit based on the autoinhibition model (eq 3) with k ) (0.18 ( 0.01) min-1 and kcat ) (0.26 ( 0.02) min-1.
the 6-31G (d, p) basis set for geometry optimization and vibrational frequency calculation. The simulations have been performed for the monomer and various head-head photodimer configurations as they have been predicted in the geometry optimization. The same theoretical approach has already been demonstrated to work successfully for analogue compounds.24 The DFT calculations have been performed in order to rationalize the experimental findings in the IR spectra and to predict possible structures of the photodimer. Results and Discussion Kinetic Investigation Based on Optical Spectroscopy. The UV-vis spectroscopic experiments characterize the optical properties of 9AC monomer and photodimer and monitor the local molecular responses of the photochemical reaction (Figure 2a). In the wavelength range from 300 to 420 nm, the UV-vis spectra show vibronic substructures (fingerlike absorption bands), which are typical for an anthracene monomer and its derivatives. During illumination, the integral absorption in this absorption band decreases without any significant changes of the typical structure of these vibronic transitions. The timedependent analysis of these spectroscopic results reveals that the photochemical reaction stops after a (75 ( 5)% conversion from the monomer to the photodimer. Since the photoreaction observed is in the solid state, fundamental kinetic schemes can be applied as derived for nucleation kinetics. The kinetic rate dependence (Figure 2a) has been fitted with a modified Johnson,25 Mehl, Avrami,26–28 and Kolmogorov29 model. In this model the transformation kinetics is described as
[9AC] ) [9AC]t)∞ + ([9AC]t)0 [9AC]t)∞) · exp(-(kJMAK · t)n)
(1)
where [9AC]0 is the starting monomer concentration at the beginning of the reaction t ) 0, [9AC]∞ is the monomer end
4144
J. Phys. Chem. C, Vol. 114, No. 9, 2010
More´ et al.
Figure 3. Fluorescence spectra of β-9AC excimer emission (KBr pellet, T ) 5 °C. excitation wavelength ) 380 nm) showing a fluorescence quantum yield of 7 ( 1%.
concentration for infinity time t ) ∞, kJMAK is the transformation rate constant, and n is the Avrami exponent. The Avrami exponent n relates to the dimensionality dim of the growth of the dimer phase according to
dim ) n - 1
(2)
A homogeneous transformation, which probably can occur in any region of the crystal for a given time interval, has zero dimensionality.26–28 The JMAK-model has already been applied to the kinetic analysis of photodimerization for various systems with zero dimensionality in phototransformation kinetics.9,30 JMAK analysis of the spectroscopic investigations of 9AC dimerization leads to the kinetic description as shown in Figure 2b. Here, an Avrami exponent of n ) 0.55 ( 0.08 has been determined with a dimerization rate constant of k ) (0.17 ( 0.06) min-1 (Figure 2b, solid line fit). The dimensionality of the reaction is determined as dim ) -0.45 ( 0.08, which is a negative value. The negative sign of the dimensionality can be explained by a negative autocatalytic step within the reaction, also termed as autoinhibition.31 As a consequence, the photochemical rate additionally needs to be fitted on the basis of a model which includes this autocatalytic effect. This relates to the kinetics description as:
[9AC] ) [9AC]t)0 ·
(
k - kcat k exp[(k - kcat)t] - kcat
Figure 4. Comparison of the different B3LYP/6-31G(d,p) simulated 9AC photodimer conformers and their predicted energy differences. The difference in the dihedral angles of carboxylic acid groups is shown in the Newman projection of the three conformers.
)
(3)
In eq 3, [9AC]t)0 is the starting concentration at t ) 0, and k is the rate constant of the original reaction while kcat denotes the rate constant of the catalyzed reaction. Our data yields an original rate constant k ) (0.18 ( 0.01) min-1 and a catalyzed rate constant kcat ) (0.26 ( 0.02) min-1. The quality of the fit of the experimental data is shown in Figure 2b (dashed line). Note that this model does not require a negative dimensionality to describe the reactions kinetics. It is suited just as eq 1 with negative dimensionality. The comparison of the rate constant kJMAK from the JMAK model and the original rate constant k from the autoinhibition model is in very good agreement, leading to the fair conclusion that an autocatalytic effect is present. Such a negative autocatalytic effect also explains the incomplete conversion at a photodimerization rate of 75%. Steady-state fluorescence spectroscopy was performed to characterize the excited state properties of β-9AC. The fluorescence spectrum (Figure 3) was recorded after excitation at 380 nm at a temperature of 5 °C. The fluorescence spectrum is characterized through an unstructured, broad, and strongly redshifted emission band (λmax ) 504 nm, full width of halfmaximum Γ ) 89 nm), which is typical for an excimer
Figure 5. Mechanism of the 9AC photodimerization reaction. The reaction proceeds via an excimer intermediate and yields various product conformers which can be investigated in the infrared and photocrystallographic studies as molecular disorder. The different possible product configurations have been predicted by DFT quantum chemical calculations of the photoproducts.
fluorescence of anthracene but not for the fingerlike structured emission band of the locally excited state of the anthracene monomer. From our measurement we determined the fluorescence quantum yield to be ΦF ) 7 ( 1% at a temperature of 278 K. The excimer state is formed from a photoexcited 9AC* molecule and 9AC ground state molecule. From this excimer state, the photodimerization reaction can proceed through a pericyclic transition state to the head-head photodimer. This kinetic analysis suggests that one photon leads to the formation of one photodimer molecule, which is beyond the typical Woodward-Hoffmann photodimerization behavior.32 In a photodimerization, which follows the Woodward-Hoffmann rules, two photons absorbed by two monomer molecules are necessary to form one photodimer molecule. The excimer formation has essential input on the kinetic scheme of the [4 + 4] photodimerization as is revealed in the description of the reaction scheme later on. Molecular Mechanism of the [4 + 4] Photodimerization. The geometry optimizations for the photodimer suggest three stable conformers which differ in the dihedral angles of the carboxylic acid groups as defined in the Newman projection of Figure 4. For conformer 1 (2, 3), dihedral angles of 147.8° and 147.5° (47.3° and 152.1°, 43.8° and 43.8°) have been found. The calculations predict an energetic difference between conformer 1 and conformer 2 of 49 cm-1, and between conformer 1 and conformer 3 of 230 cm-1. We propose that during the bulk photoreaction these three conformers are all formed as a mixture. Their formation leads to an increase in disorder during the photoreaction of the β-9AC crystal, with the structural consequences as explained in the following paragraph. Figure 5 summarizes the mechanism of the [4 + 4] photodimerization on a molecular level as supported by our experimental findings. It shows the formation of the three photodimer configurations mentioned before through the formation of an
Crystalline 9-Anthracenecarboxylic Acid
J. Phys. Chem. C, Vol. 114, No. 9, 2010 4145
Figure 6. FTIR spectra of 9AC showing the most intense band at 1681.5 cm-1 assigned to the CO stretching mode νCO.
intermediate excimer state. After excitation of a 9AC monomer molecule (with the characteristic rate constant k0) the population of the excimer state can be described as a reaction of pseudofirst-order with the rate constant k1 for the first reaction step, followed by the excimer forming the photodimer with the rate constants k21, k22, and k23. The kinetic analysis of our measurements suggests that the autoinhibition process of the [4 + 4] photodimerization of β-9AC (with the rate constant kcat) occurs on the way to excimer formation. However, the analysis cannot exclude that kcat alternatively catalyzes the step from the excimer to the dimer product. Therefore, we have assigned the catalytic rate constant to both reaction steps in Figure 5 where it could be potentially involved. Further investigations are currently performed to clear this point. Kinetic Investigations Based on Structural Studies. The optical kinetic analysis has been completed by time-resolved structural studies based on infrared and photocrystallographic investigations which are again supported by DFT calculations. Before writing about the time-resolved studies, we present the static IR spectra of 9AC before illumination and their transition band assignment (Figure 6). FTIR spectroscopy is ideal to reveal the influence of hydrogen bonding in a structure. According to Figure 6 in the FTIR spectrum the most intense band at 1681.5 cm-1 can be assigned to the typical CO stretching vibration of 9AC. The DFT calculations yield a frequency of 1736.8 cm-1 for this vibration. The discrepancy between experiment and theory can be explained by the strong hydrogen bonding in β-9AC, which causes a red shift for CO stretching vibration. Besides this red shift there is a second piece of evidence for strong hydrogen bonding in 9AC crystals. In the region from 2500 to 3650 cm-1 a broad transition band system is visible, which can be assigned to CH and OH stretching vibrations. The broadening of the OH stretching mode transitions, in particular, is typical for strong hydrogen bonding in solid-state organic systems.33 For monitoring the real time structural dynamics of the photodimerization with IR spectroscopy, the method of difference spectra has been applied. Figure 7 shows the difference map of the IR spectra at various times after illumination minus the IR spectrum before illumination for various vibrational transition band areas. During the photodimerization, a bleaching of the IR absorption band in the wavenumber region between 1225 and 1320 cm-1 has been observed (Figure 7a). In this area, the transition band of the phenyl ring deformation is found. In the area of the CO stretching vibration the transition band shifts from 1681 to 1707 cm-1 during illumination (Figure 7b). In the wavenumber region between 2275 and 2325 cm-1 three new absorption bands appear at 2327, 2338, and 2362 cm-1 (Figure 7c). These three bands can be assigned to a CH stretching and the OH stretching vibration of the photodimer. As clearly seen, the IR spectra also show clear evidence for the proceeding photochemical reaction. The bleaching in the ring deformation
Figure 7. FTIR difference spectra after irradiation with 405 nm excitation wavelength and 4.1 mW/cm2 power: (a) bleaching in the region of ring deformation vibration δring, (b) blue shift of the CO stretching vibration νCO, (c) appearance of new absorption bands near the OH stretching region νOH.
region supports the proposed photochemical reaction in Figure 5, which confirms the results from Ito et al.16 The blue shift of the CO stretching vibration during phototransformation indicates a cleavage of the hydrogen bonds. This cleavage is a necessary step in phototransformation, which can easily be seen in the crystal structure in Figure 8, described later. The assignments of the bands are confirmed by the results of our computational studies already described. Indeed, the DFT calculations reveal the CO stretching mode to be located at νCO ) 1688 cm-1 with νCO,calc ) 1736 cm-1. The reflections of the single crystal X-ray diffraction experiments before and after 77.8 h illumination were indexed and integrated with the program package XDS.34 The refinement with SHELXTL35 of the crystal structures before illumination has an R1-value of 0.0504 based on 2151 unique reflections, wR2 is 0.1088, and the GooF-value amounts to 1.044. The crystal structure of the 9AC monomer before illumination is shown along the crystallographic b-axis in Figure 8 (space group: P21/n). The refinement of the monomer yields another disorder step in β-9AC which makes the description of the mechanism of the [4 + 4] photodimerization more complex. The refined disorder effect has been located in the acidic proton yielding a tautomeric equilibrium. This disorder is caused by strong hydrogen bonding between two carboxylic groups. Hydrogen bonds between carboxylic acid groups in the solid state are usually described by an asymmetric double-well potential36,37 resulting in two different tautomers. We interpret the formation of the tautomers as another cause for lattice disorder in this system. Consequently, the occupancies for both possible proton sites of the tautomers can be refined via a disorder model35,38 where the site occupation factors are free variables. The site occupation factors represent the molar fraction of both tautomeric sites. The equilibrium constant Ka for the proton along the hydrogen bond has been calculated using the site occupation factors (0.63 and 0.37). According to ∆G ) -RT ln(Ka), the Gibbs energy of this double-well potential is ∆G ) (106 ( 10) cm-1. This value for the Gibbs energy of tautomerism is approximately 2 times higher than the Gibbs energy for the proton transfer in benzoic acid36 crystals. Independent of the excitation conditions and of illumination time, it was (in contrast to the spectroscopic investigations) not
4146
J. Phys. Chem. C, Vol. 114, No. 9, 2010
More´ et al.
Figure 9. Difference map before and after 77.8 h of illumination of the selected Bragg reflections with the Miller indices (a) (023) and (b) (101) (irradiation conditions: 375-425 nm wavelength range, 17 mW/ cm2 power).
TABLE 1: Unit Cell Parameters of β-9AC from Single Crystal X-ray Diffraction before and after 77.8 h Illumination (375-425 nm, 17 mW/cm2) a/Å b/Å c/Å β/deg V/Å3 Z space group
Figure 8. Crystal structure of β-9AC viewed along the [010] axis. The analysis is based on a single crystal X-ray diffraction experiment. The unit cell parameters (space group P21/n) have been determined to be a ) 3.89 Å, b ) 9.37 Å, c ) 29.06 Å, and β ) 90.64°.
possible to refine a periodically ordered dimer structure in the single crystals of β-9AC during the photocrystallographic experiment. Instead of the formation of a regular dimer phase giving rise to additional new Bragg diffraction features, the photodimerization only leads to a decrease of the refinement quality of the monomer structure. After 77.8 h of illumination, still only the monomer structure in the single crystal could be refined with an R1-value of 0.0608 based on 2204 unique reflections, and a wR2 of 0.1355, and the GooF-value of 1.105. The unit-cell parameters varied only slightly after illumination (Table 1). More detailed investigations on the monomer Bragg reflections allowed us to determine in more detail the mechanism of bulk structural changes which are caused by the [4 + 4] dimerization reaction (Figure 9) but not of periodic character. For this, the Bragg reflections have been cut azimuthally by means of the computer program Fit2D.39 The cuts have been fitted with a pseudo-Voigt profile. During photodimerization,
before illumination
after illumination
3.8900(8) 9.3700(19) 29.060(6) 90.64(3) 1059.2(4) 4 P21/n
3.9000(8) 9.3700(19) 29.070(6) 90.64(3) 1062.2(4) 4 P21/n
the azimuthal peak width of the Bragg reflection increases. A growth of the azimuthal peak width coincides with a shrinking of the transverse coherence length.40 This behavior reflects the decrease of the orientational order parameter in the crystalline lattice. However, the investigated variations of the full width of half-maximum (fwhm) of the azimuthal cuts through the Bragg reflections have been determined to be quite small, varying only from 5% to 10% during photoillumination. These small changes do not allow determination of further parameters which characterize the disorder-inducing dimerization. Instead, a more pronounced shift of the Bragg reflection toward a higher diffraction angle has been observed (Figure 10). The time dependence of this position change could be fitted by a single exponential time law. For the presented system the time constants have been found to be around 12 h (Figure 11) which coincides with the expected photodimerization time for the given photoillumination conditions. Bulk Structural Mechanism of [4 + 4] Photodimerization. Contrary to the spectroscopic investigations, the photocrystallographic studies do not give unique evidence of the photochemical reaction. The coincidence of the rate constant of the increase of the structural disorder with respect to the expected transformation rate for the given number of monomer molecules to the number of absorbed photons ratio, no.(molecules)/ no.(absorbed photons), is the only evidence for the phototransformation. Nonetheless, the photocrystallographic studies explain in a unique way why it is not possible to solve a structure of a pure dimer crystal formed during the photoreaction. On one hand, the spectroscopic experiments and their interpretation suggest that on a molecular level the formation
Crystalline 9-Anthracenecarboxylic Acid
J. Phys. Chem. C, Vol. 114, No. 9, 2010 4147
Figure 12. Disorder mechanism of 9AC photodimerization on the bulk lattice level. Possible disorder effects caused by the phototransformation are viewed along the c-axis. The gray boxes indicate possible dimerization sites which are statistically chosen. Figure 10. Time dependence of the peak position and azimuthal peak width of (101) Bragg reflection during illumination with optical light (irradiation conditions: 375-425 nm wavelength range, 17 mW/cm2 power). Top graph shows fit based on monoexponential model with a lifetime of 12 ( 2 h for the peak shift; bottom graph shows fit based on monoexponetial model with a growing time of 16 ( 3 h for the peak width.
Figure 11. Comparison of the lifetime from the temporal evolution of the peak position and the peak width during illumination for different Bragg reflections.
of different product configurations (Figure 8), which only differ in the dihedral angle of the carboxylic acid group, induces disorder. Furthermore, the tautomerisms of the carboxylic groups add additional possibilities for disorder. These molecular disorder schemes allow point defects in the lattice during the photoreaction. On the other hand, the crystal structure of β-9AC reflects evidently how the lattice disorder increases during phototransformation: According to the crystal structure and the stacking of the 9AC molecules (Figure 8), each 9AC monomer has two potential partners in a distance of 3.88 Å with which it can react during photodimerization. Additionally, the 9AC monomers can also find further potential reaction partners in the neighboring unit cells. This local variety of reaction partners in the lattice will be a first guide to various dimer nucleation sites in different orientations. The time evolution of this lattice disorder process and the different product orientations during the photoreaction are visualized in Figure 12 with a schematic view along the crystallographic c-axis. The dashed boxes represent the unit cell, the black bars are 9AC monomer molecules, and the gray boxes are possible dimerization sites. In Figure 12, three possible product orientations formed during photodimerization are selected. Similar variations and disorder sites can be expected for the crystallographic b-axis. A comparable behavior is known for the dimerization of pure anthracene.13 Because of this variety of different potential orientations of the product, the photodimer is only formed as a
solid solution in the parent crystal, which renders still the possibility to refine the monomer structure during the illumination but not the dimer product. The disorder induced by the lattice site and configurational variety of the photoproducts also allows us to draw the conclusion that, in the present case, the 9AC photodimerization is no topotactical single-crystal to singlecrystal transformation. In contrast to our results, Bardeen et al.8 recently published a photoinduced change of the shape of crystalline 9AC nanorods which can only be explained as a topotactical single-crystal to single-crystal transformation. Since the precise crystal structure of these nanorods is unknown, it is possible that 9AC forms another polymorph in these nanorods which allows single-crystal to single-crystal transformation. Furthermore, it is possible that the 9AC photodimerization is underpinned by a size effect. Finally, we would like to give an explanation of how the found autoinhibition process could also be influenced by the reported lattice order and disorder processes beyond the local molecular picture. In 9AC the π-stacking is not the only influence on the structure: the hydrogen bonding of carboxylic acid groups is as well. Photodimerization now leads to an increase of the dislocation sites of the photodimer in the monomer lattice which then disturbs the electronic structure of 9AC. The increase of the photodimer dislocation could lead to a restructuring of the 9AC lattice away from the equilibrium structure created by hydrogen bonding and π-π interactions. This restructuring decreases the long-range order of 9AC and moves the remaining monomer molecules into less reactive positions: the process is autoinhibitive. Conclusion We showed that during the illumination of the red-edge absorption band of 9AC a [4 + 4] photodimerization occurs which has autoinhibition character. Kinetic analysis of the spectroscopic results on a molecular level based on the JMAK model renders a negative dimensionality of the investigated solid-state reaction. This unusual effect can be explained by a negative autocatalysis within the 9AC reaction scheme. Detailed kinetic analysis of this negative autocatalysis leads to an autoinhibition model. Compared to the ordinary JMAK model the autoinhibition model fits more accurately the experimental data and does not lead to a negative dimensionality of the photoreaction. The negative autocatalysis can be caused either by structural features or by energetic effects. In combination with photocrystallographic studies we have revealed that the photochemical reaction in β-9AC does not yield in a singlecrystal to single-crystal transformation for crystals bigger than 50 µm. For these systems we could only observe an increase of disorder in β-9AC during the phototransformation in crystal-
4148
J. Phys. Chem. C, Vol. 114, No. 9, 2010
lography. The increase of the bulk disorder is associated with the negative autocatalysis through the formation of an excimer intermediate which is formed along the photodimerization reaction coordinate. The excimer has been observed via fluorescence spectroscopy. It is formed by a reaction of one photoexcited and one ground-state 9AC molecule. The fact that each molecule has two possible reaction partners leads to different possible polymorphs for the photodimer. Additionally, quantum chemical calculations based on density functional theory (DFT) methods predict three different photodimer configurations which can be formed. These three product configurations can further one cause or enhance the lattice disorder during the photoreaction. Different tautomeric sites leading to additional disorder effects add another level of complexity in the observed photodimerization reaction. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft (DFG) via SFB 602. The authors thank Ju¨rgen Bienert for his assistance with the FTIR measurements, Karl-Heinz Kahlmeyer for his assistance in the design of the cooling cell, and Sissi Sonnenkalb for her assistance with the crystal growth. Supporting Information Available: CIF files of β-9anthracenecarboxylic acid (C15H10O2, 9AC) before and after illumination. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Garcia-Garibay, M. A. Angew. Chem. 2007, 119, 9103. (2) Irie, M.; Kobatake, S.; Horichi, M. Science 2001, 291, 1769. (3) Irie, M. Bull. Chem. Soc. Jpn. 2008, 81, 917. (4) Davaasambuu, J.; Busse, G.; Techert, S. J Phys Chem A 2006, 110, 3261. (5) Davaasambuu, J.; Durand, P.; Techert, S. J. Synchrotron Radiat. 2004, 11, 483. (6) Schmidt, G. M. J. Pure Appl. Chem. 1971, 647. (7) Heller, E.; Schmidt, G. M. J. Isr. J. Chem. 1971, 9, 449. (8) Al-Kaysi, R. O.; Bardeen, C. J. AdV. Mater. 2007, 19, 1276. (9) Benedict, J. B.; Coppens, P. J. Phys. Chem. A 2009, 113, 3116. (10) Cohen, M. D. Angew. Chem. 1975, 87, 439. (11) Hallmann, J.; Morgenroth, W.; Paulmann, C.; Davaasambuu, J.; Kong, Q. Y.; Wulff, M.; Techert, S. J. Am. Chem. Soc. 2009, 131, 15018. (12) Kaupp, G. Angew. Chem., Int. Ed. Engl. 1992, 31, 595. (13) Julian, M. M. Acta Crystallogr., Sect. A 1973, A 29, 116. (14) Cohen, M. D.; Ludmer, Z.; Yakhot, V. Phys. Status Solidi B 1975, 67, 51.
More´ et al. (15) Fitzgerald, L. J.; Gerkin, R. E. Acta Crystallogr., Sect. C 1997, 53, 71. (16) Ito, Y.; Fujita, H. J. Org. Chem. 1996, 61, 5677. (17) Cole, J. M. Z. Kristallogr. 2008, 223, 363. (18) Ramos, A. S. F.; Techert, S. Phys. Chem. Chem. Phys. 2003, 5, 5176. (19) Techert, S.; Wiessner, A.; Schmatz, S.; Staerk, H. J. Phys. Chem. B 2001, 105, 7579. (20) Grabowsky, S.; Pfeuffer, T.; Morgenroth, W.; Paulmann, C.; Schirmeister, T.; Luger, P. Org. Biomol. Chem. 2008, 6, 2295. (21) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E. Rob, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C. Millam, J. M.; Iyengar, S. S.; Tomasi, J. Barone, V.; Mennucci, B. Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K. Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T. Honda, Y. Kitao, O. Nakai, H.; Klene, M. Li, X. Knox, J. E. Hratchian, H. P.; Cross, J. B. Bakken, V. Adamo, C. Jaramillo, J.; Gomperts, R. Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K. Voth, G. A.; Salvador, P.; Dannenberg, J. J. Zakrzewski, V. G.; Dapprich, S. Daniels, A. D. Strain, M. C. Farkas, O. Malick, D. K. Rabuck, A. D.; Raghavachari, K. Foresman, J. B. Ortiz, J. V.; Cui, Q.; Baboul, A. G. Clifford, S.; Cioslowski, J. Stefanov, B. B.; Liu, G. Liashenko, A. Piskorz, P.; Komaromi, I. Martin, R. L. Fox, D. J.; Keith, T. Al-Laham, M. A. Peng, C. Y. Nanayakkara, A. Challacombe, M. Gill, P. M.W.; Johnson, B. Chen, W.; Wong, M. W.; Gonzalez, C. Pople, J. A. In Gaussian03; Gaussian, Inc.: Wallingford, CT, 2003. (22) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (23) Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (24) Barraza-Jimenez, D.; Flores-Hidalgo, A.; Glossman-Mitnik, D. THEOCHEM 2009, 894, 64. (25) Johnson, W. A.; Mehl, R. F. Trans. Am. Inst. Min. Metall. Eng. 1939, 135, 416. (26) Avrami, M. J. Chem. Phys. 1941, 9, 177. (27) Avrami, M. J. Chem. Phys. 1940, 8, 212. (28) Avrami, M. J. Chem. Phys. 1939, 7, 1103. (29) Kolmogorov, A. N. Bull. Acad. Sci. USSR, Phys. Ser. 1937, 1, 335. (30) Bertmer, M.; Nieuwendaal, R. C.; Barnes, A. B.; Hayes, S. E. J. Phys. Chem. B 2006, 110, 6270. (31) Kohout, J. J. Mater. Sci. 2008, 43, 1334. (32) Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87, 395. (33) Flakus, H. T.; Chelmecki, M. J. Mol. Struct. 2003, 659, 103. (34) Kabsch, W. J. Appl. Crystallogr. 1993, 26, 795. (35) Sheldrick, G. M. Acta Crystallogr., Sect. A 2008, 64, 112. (36) Fillaux, F. Int. ReV. Phys. Chem. 2000, 19, 553. (37) Fillaux, F. J. Mol. Struct. 2007, 844-845, 308. (38) Mu¨ller, P.; Herbst-Irmer, R.; Spek, A. L.; Schneider, T. R.; Sawaya, M. R. Crystal Structure Refinement: A Crystallographer’s Guide to SHELXL; IUCr/Oxford University Press: Oxford, U.K., 2006. (39) Hammersley, A. P. Fit2D Program package V5.18 Reference Manual (see also www.esrf.eu) V1.6; 1995. (40) Forster, S.; Timmann, A.; Schellbach, C.; Fromsdorf, A.; Kornowski, A.; Weller, H.; Roth, S. V.; Lindner, P. Nat. Mater. 2007, 6, 888.
JP909513V
