Photochromic Diarylethenes with Heterocyclic Aromatic Rings

Aug 12, 2015 - We present a density functional theory study on the thermal bistability of a number of photochromic diarylethenes, with emphasis on the...
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Photochromic Diarylethenes with Heterocyclic Aromatic Rings: Correlation between Thermal Bistability and Geometrical Characters of Transition States Xin Li,*,† Qi Zou,*,‡ and Hans Ågren† †

Division of Theoretical Chemistry & Biology, School of Biotechnology, KTH Royal Institute of Technology, SE-10691 Stockholm, Sweden ‡ Shanghai Key Laboratory of Materials Protection and Advanced Materials in Electric Power, Shanghai University of Electric Power, Shanghai 200090, P. R. China S Supporting Information *

ABSTRACT: We present a density functional theory study on the thermal bistability of a number of photochromic diarylethenes, with emphasis on the free energy barrier of the ground-state ring-opening process. We found that the free energy barrier is correlated with the geometrical and vibrational character of the transition state, in particular the distance between the two reactive carbon atoms, the out-ofplane angles of the methyl groups at the reactive carbon atoms, and the imaginary vibrational frequency. Based on these relationships we propose a linear fitting expression for the free energy barrier in terms of the three aforementioned transitionstate quantities and obtained a correlation coefficient of R2 = 0.971. In this way quantum chemical calculations may provide insight and structure−property relationships, which can be applied in the development of novel photochromic materials.

1. INTRODUCTION Photochromic compounds are a family of optoelectronic functional materials that are able to isomerize between two different states with distinct properties.1−3 The isomerization processes usually involve chemical reactions such as ringopening/closure and cis/trans isomerization, which lead to dramatic changes in the π-conjugation and electronic structures of the two states. As such, these two states are often termed as “on” and “off” states. The accompanying change in optical, mechanical, and/or magnetic properties promises the use of photochromic materials for applications in optical switching, data storage, signal communications, logic gates, etc.4−9 In particular, organic photochromic materials with synthetic flexibility have attracted a wide research interest in the past decades, among which the diarylethene family has become a hot topic owing to its outstanding properties such as fast response, high contrast, good reversibility, and excellent thermal bistability.10−17 Among the desired properties of organic photochromic compounds, the thermal bistability in the “on” and the “off” states is a very important factor that determines the applicability of the material since the storage of information or processing of signals requires the material to be sufficiently stable in both states.18−23 To date, dithienyl-perfluorocyclopentene-based compounds have been demonstrated to possess excellent thermal stability in both the ring-open and the ring© 2015 American Chemical Society

closed states, owing not only to the favorable performance of the perfluorocyclopentene bridging unit but also due to the particular electronic character of the thiophene aryl rings.24−26 The heterocyclic thiophene rings provide π-conjugation and optical response in the ultraviolet and visible region, which serve as input and output signals in real applications. Importantly, the thiophene rings are less aromatic than the benzene rings, so that the photochromic cyclization and cycloreversion reactions of photochromic dithienylethene compounds become reversible. In the case of strongly aromatic aryl rings, the ring-closed isomers will be instable and quickly revert back to the ring-open isomer under ambient temperature.17 Researchers in this field have made great efforts to develop organic photochromic materials with desirable properties by introducing different functional groups, substituents, and/or newly designed ethene bridges into the diarylethene framework. In such efforts it is of importance to keep the bistability of the diarylethene derivative, otherwise the advantageous performance of the material would be lost. These research efforts have mainly been directed in two directions: (i) exploration of new ethene bridging units and (ii) the incorporation of new aryl Received: May 4, 2015 Revised: August 7, 2015 Published: August 12, 2015 9140

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The Journal of Physical Chemistry A Scheme 1. Chemical Structures of Perfluorocyclopentene-Based Diarylethene Compounds

rings. On one hand, Zhu and co-workers reported photochromic dithienylethene derivatives utilizing benzobisthiadiazole as ethene bridging unit to reduce the aromaticity of the central CC bridge, which led to excellent thermal bistability in various solvents.27,28 Yam and co-workers incorporated the silole moiety into the photochromic dithienylethene backbone and obtained drastic enhancement in the thermal stability of the ring-closed form due to the similar aromaticity and energy level of the open form and closed form of the dithienylethene.29 On the other hand, Pu and co-workers have reported a series of studies on the dithienyl-perfluorocyclopentene-based photochromic compounds, with focus on the modifications at the substituted aryl groups of diarylethenes.30−33 The investigated photochromic compounds are mainly unsymmetrical diarylethenes containing naphthalene, pyrrolopyridine, phenylthiophene, methoxylpyrimidine, or cyanopyrrole rings as the aryl components, which have shown various thermal stability depending on the specific aromaticity of the aryl rings. Alongside with experimental efforts, computational approaches can contribute significantly to this area by predicting the thermal bistability of the designed compounds in advance. A number of properties including the cyclization and cycloreversion reaction pathways, quantum yields, and formation of byproducts have been studied by configuration interaction with density functional theory (DFT), singlet excitations (CIS), complete active space (CAS), and multiconfiguration self-consistent (MCSCF) approaches.34−39 Timedependent (TD) DFT calculations have also been employed to investigate multiphotochromism in a single photochromic molecule.40−44 Noteworthy, Patel and Masunov have reported that DFT calculations are able to reproduce the reaction barriers of the ground-state ring-opening processes of several photochromic diarylethene compounds within a mean absolute error of around 3 kcal mol−1, provided that the diradical character of the transition state is properly described by an open-shell singlet state.45 Chu and co-workers also reported DFT and TD-DFT study on the ground-state and excited-state potential energy surfaces.46

In this work, we employ DFT calculations to investigate a number of perfluorocyclopentene-based diarylethene compounds (listed in Scheme 1) and show that (i) the thermal bistability can be reliably predicted by theoretical calculations and that (ii) the free energy barriers are correlated with geometrical characters of the transition states. These compounds contain a number of five- and six-membered aryl rings that form the photochromic diarylethene framework. Among the selected compounds, 1 and 2 are prototypical perfluorocyclopentene-based diarylethenes, the thermal stability of the latter has been studied by experimental measurements.47 Compound 3 with pyrrolopyridine and phenylthiophene aryl rings has been proven thermally stable under ambient temperature.31 Compounds 4 and 5 possess methoxylpyrimidine aryl rings,32 and the ring-closed isomers gradually undergo cycloreversion reactions under room temperature. Compounds 6−9 constitute a family of diarylethenes with cyanopyrrole rings,33 which show different thermal stability depending on the other aryl substituent.

2. COMPUTATIONAL DETAILS The geometries of the ring-open and ring-closed isomers of the photochromic diarylethene compounds were optimized by DFT calculations, using the Minnesota 06 functional48 (M06) and the double-ζ 6-31G(d,p) basis set.49 At the optimized geometries, potential energy scan was performed with respect to the distance between the two reactive carbon atoms, in order to locate the reaction pathway of the ground-state isomerization process. The approximate transition state, which corresponds to the highest energy point of the potential energy surface, was further optimized at the M06/6-31G(d,p) level of theory. The keyword Guess(Mix, Always) in the Gaussian 09 program50 was used to describe the diradical character of the transition state.45 Subsequent frequency analyses were carried out to verify that the optimized ground-state isomers are true minima on the potential energy surfaces and that the optimized transition states correspond to first-order saddle points. Thermodynamic data were calculated under 298 K and 1 atm, except for compound 2, the thermodynamic data of which 9141

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reproducing the free energy barrier of the ground-state ringopening process of compound 2. Increasing the size of the basis set from the double-ζ 6-31G(d,p) to the triple-ζ 6-311+ +G(2d,2p) leads to a decrease in the predicted barrier, and the performances of the BMK and the ωB97X-D functional are comparable to each other. Our final choice of the computational model is the combination of the M06 functional for geometry optimization and the BMK functional for refinement of self-consistent energy, namely, the BMK/6311++G(2d,2p)//M06/6-31G(d,p) level of theory. This choice of computational model, inspired by the fact that the M06 functional has been widely tested for geometry optimization and that the BMK functional is particularly developed for thermochemical kinetics, offers a free energy barrier of 143 kJ mol−1, which is comparable to the experimental value47 of 139 kJ mol−1. Further calculations also show that this computational model is able to reproduce the ground-state ring-opening free energy barrier of other diarylethene compounds. Apart from compound 2, the experimental free energy barriers for compounds 4, 5, 8, and 9 are obtained from the thermal bleaching measurements as reported in literature.32,33 In particular, the thermal bleaching rate is calculated from the first-order kinetics of the decrease in the absorption, and the corresponding free energy barrier is then obtained according to the transition state theory.62 Such experiments were conducted in solutions, using hexane for compounds 4 and 5 and ethyl acetate for compounds 8 and 9.32,33 In our calculations, the solvent effects have also been evaluated using the polarizable continuum model,56 as listed in Table S1 in the Supporting Information. The calculated energy barriers for the nine photochromic diarylethene compounds are shown in Figure 2. Here ΔE

were calculated at 423 K to keep consistency with experimental measurements.47 The harmonic approximation was used in the calculations of thermal contributions to free energy owing to its computational feasibility and efficiency.51 This approximation is known to slightly overestimate the vibrational frequencies and zero-point energies, and scaling factors are often used to account for the anharmonicity effects.52,53 For the level of theory used in frequency analyses in this work, the suggested scaling factors for the thermal contributions to free energy range from 0.96 to 0.98 in the temperature interval between 298 and 450 K, which lead to very small corrections to the free energy barrier (on the magnitude of 0.5 kJ mol−1). Therefore, it is safe to neglect the anharmonicity effects in the frequency analyses. At the optimized geometries of the ground-state isomers and the transition states, the self-consistent field energies were refined using the BMK functional54 and the triple-ζ 6-311++G(2d,2p) basis set.55 In case solvent effects are taken into account, we employed the polarizable continuum model.56 All theoretical calculations were carried out using the Gaussian 09 program package.50

3. RESULTS AND DISCUSSION The investigated photochromic diarylethene compounds are shown in Scheme 1. Among the nine photochromic compounds, we employed compound 2 as a test case to benchmark the performance several density functionals on reproducing the experimental barrier of the ground-state ringopening process. Since the ring-open isomers of the photochromic diarylethene compounds in general are stable, we are particularly interested in the free energy barrier of the groundstate ring-opening process from the ring-closed isomer. This free energy barrier is calculated as the difference between the ring-closed isomer and the corresponding transition state. As shown in Figure 1, the M06 functional underestimates the

Figure 2. Computed potential energy barrier ΔE and free energy barrier ΔG for the ground-state ring-opening process from the ringclosed isomers. TZ and DZ denote triple-ζ and double-ζ basis sets, respectively.

Figure 1. Computed free energy barriers from different density functionals and basis sets. The dashed line indicates the experimental free energy barrier47 of 139 kJ mol−1.

denotes the potential energy difference between the ring-closed isomer and the transition state, and ΔG represents the corresponding free energy difference. For all the compounds investigated, the free energy barrier is lower than the potential energy barrier, and the difference between ΔG and ΔE mainly arises from zero-point energy (ZPE) corrections and entropy contributions (Figure S1). Here the energies and free energies are evaluated using different density functionals and basis sets at the same geometries optimized at the M06/6-31G(d,p) level of

barrier by ∼10 kJ mol−1, while the M06-2X functional48 with double amount of exact exchange overestimates the barrier by approximately the same amount. The B3LYP functional57,58 predicts a similar barrier to that of M06, and the inclusion of the dispersion correction59,60 slightly improves its performance. The other two functionals, the BMK functional54 and the ωB97X-D functional,61 show much better performance in 9142

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The Journal of Physical Chemistry A theory. It turned out that calculations at the BMK/6-311+ +G(2d,2p)//M06/6-31G(d,p) level of theory predict free energy barriers that are consistent with those experimental values for compounds 2, 4, 5, 8, and 9. The data presented in Figure 2 are calculated in vacuum, and the solvent effects were found to slightly diminish the free energy barriers (within 4%) for the photochromic compounds under investigation (Table S1). The computed free energy barriers for compounds 1, 2, 3, 6, and 7 are all above 120 kJ mol−1, in agreement with their observed thermal stability under ambient temperature.31,33,47 It is interesting to mention that the potential energy predicted by the M06/6-31G(d,p) approach show reasonable agreement with the experimental free energies, presumably owing to fortunate cancellation of errors. Free energy barriers of the ground-state ring-opening processes from the ring-closed isomers, however, are systematically underestimated by the M06/6-31G(d,p) approach. We further analyzed the geometries of the transition states connecting the ground-states of the ring-open and the ringclosed isomers and found a correlation between the free energy barrier and the distance between the two reactive carbon atoms, as shown in Figure 3. Although the investigated diarylethene

Figure 4. Comparison between the potential energy surfaces of compounds 2 and 8, computed at the M06/6-31G(d,p) level of theory. The transition states are marked by stars.

Owing to the closeness between the ring-closed ground state and the transition state, the ring-closed isomer of compound 8 can easily cross the transition state on the ring-opening reaction pathway, leading to thermal bleaching of the ring-closed isomer and formation of the ring-open isomer. Previous studies have suggested that the thermal instability is connected with the strong aromaticity of the aryl rings in the photochromic diarylethene compound. Indeed, such behavior of compound 8 (in contrast to compound 2) arises from the imbalanced aromaticity of the aryl groups in the ring-open and the ring-closed states. In the case that the aryl rings in the ringopen diarylethene compound shows strong aromaticity, the energy difference between the transition state and the ringopen state is larger (e.g., compound 8 in Figure 4) since the formation of the transition state requires a large amount of energy to destroy the aromaticity of the aryl ring itself. The consequence is that, however, the resultant ring-closed isomer is less stabilized, leading to smaller energy difference between the ring-closed isomer and the transition state and hence inferior thermal bistability of the ring-closed isomer. As can be seen from Figure 4, the potential energy surface of compound 8 is more unsymmetric than that of compound 2, which is connected with the poor thermal stability of the ring-closed isomer of compound 8. The aromaticity of the aryl rings in a diarylethene compound can also be reflected by the out-of-plane angle of the methyl groups at the reactive carbon atoms. For strongly aromatic aryl rings, the energy cost to bend a methyl substituent out of the πconjugation plane is expected to be greater than that for weakly aromatic aryl rings. We thus examined the out-of-plane angles of the methyl groups (including methoxyl groups in compounds 4 and 5) in the transition states of the diarylethene compounds. As shown in Figure 5, a linear correlation is found between the free energy barrier and the transition-state out-ofplane angle of the methyl group at the reactive carbon atoms, except for compounds 4 and 5. Here the out-of-plane angle is defined as the angle between the methyl group at the reactive carbon atom and the plane of π-conjugation, averaged over the two aryl rings, as shown in the inset of Figure 5. All photochromic compounds, except for compounds 4 and 5, have methyl groups at the reactive carbon atoms and show clear criteria for assessing the thermal stability of the ring-closed

Figure 3. Correlation between the free energy barrier and the distance between the two reactive carbon atoms in the transition state geometries.

compounds contain different aryl rings, the correlation between the ground-state ring-opening barrier and the transition-state C−C distance is reasonably good. It is also noteworthy that in Figure 3 the thermally stable and instable compounds are separated by a big gap. The photochromic compounds, the ring-closed isomers of which are thermally instable, have transition-state C−C distances smaller than 1.90 Å, while the thermally bistable photochromic compounds show transitionstate C−C distances larger than 1.95 Å. This indicates that the transition state of a thermally instable diarylethene compound is located both geometrically and energetically closer to the ring-closed isomer. We show in Figure 4 the comparison between the potential energy surfaces of two representative diarylethene compounds, 2 and 8, which are thermally stable and instable, respectively. Based on the data presented in Figure 2, it is expected that the potential energy surfaces predicted by the M06/6-31G(d,p) approach resemble those in reality. 9143

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Figure 6. Correlation between the free energy barrier and the imaginary frequency of the transition state.

Figure 5. Correlation between the free energy barrier and the out-ofplane angle of the methyl group at the reactive carbon atoms.

suggests that the transition state with prominent imaginary frequency (more negative than −700 cm−1) corresponds to thermally stable ring-closed isomer. Based on such correlation, we can infer that potential energy surface at the vicinity of the transition state is more precipitous for thermally bistable diarylethenes and that changing the methyl groups at the reactive carbon atoms to methoxyl groups can significantly reduce the absolute magnitude of the imaginary frequency of the transition state. From the discussions above we have concluded that the thermal free energy barrier of the ground-state ring-opening process of a photochromic diarylethene compound is correlated with the following quantities of the transition state: (i) distance between the two reactive carbon atoms, (ii) the out-of-plane angles of the methyl/methoxyl groups at the reactive carbon atoms, and (iii) the magnitude of the imaginary frequency. We further found that the free energy barrier can be expressed as a function of the three quantities and obtained the following relation through least-squares fitting:

isomer, that is, an average out-of-plane angle larger than 44° corresponds to poor thermal bistability. As mentioned above, the aromaticity of the aryl rings in a diarylethene compound has dual effects; a stronger aromaticity not only increases the energy difference between the ring-open isomer and the transition state but also reduces the energy difference between the ring-closed isomer and the transition state. Here we show that the aromaticity is also connected with the transition-state out-of-plane angle of the methyl groups at the reactive carbon atoms. Combining the correlation shown in Figures 3 and 5, the best candidate aryl rings should offer a transition-state C−C distance larger than 2.0 Å and an out-of-plane angle smaller than 40°. The unusual out-of-plane angles of compounds 4 and 5 arise from their chemical structures, that is, the methoxyl groups at the reactive carbon atom of the pyrimidinyl rings. In the methoxyl groups of compounds 4 and 5, the oxygen atoms are evidently less bulky than the methyl groups in the other compounds, thus leading to weaker steric hindrance and smaller out-of-plane angles (between 39° and 40°). In addition, the orientation of the methoxyl group affects the potential energy of the ring-closed isomers much more than in the ringopen ones. Taking the ring-closed isomer of compound 4 as an example, we performed a potential energy scan with respect to the orientation of the two methoxyl groups, as shown in Figure S2. The rotation of either methoxyl group of the ring-closed compound 4 can lead to notable energy differences between the global minimum and local minima, up to 12.5 kJ mol−1, and the most stable geometry of 4c has a φ of around 0° and a θ of around 60°. In this geometry the methoxyl group at the reactive carbon atom of the pyrimidinyl ring points to the opposite direction of the thiophene ring, thus minimizing steric hindrance and stabilizing the ring-closed isomer. From Figure 4 we also notice that the aromaticity of the aryl rings may put an effect on the shape of the potential energy surface. We thus further examined the imaginary frequency of the transition states of the photochromic diarylethenes and found again a linear correlation between the free energy barrier and the imaginary frequency, except for compounds 4 and 5. As the imaginary frequency is represented by negative numbers, we here follow this convention. The correlation in Figure 6

ΔGfit = −0.15ω + 171.26d − 3.97α − 152.04

(1) −1

where ω is the imaginary frequency (negative, in cm ), d is the transition-state C−C distance (in Å), α is the averaged out-ofplane angle of the methyl/methoxyl groups (in degree), and ΔGfit is the fitted free energy barrier (in kJ mol−1). Figure 7 shows the performance of the above relation by comparing the theoretical free energy barrier from quantum chemical calculations and the fitted results. A correlation coefficient of R2 = 0.971 is obtained, suggesting that the fitting procedure is indeed able to reproduce the free energy barrier with reasonable accuracy. The correlation in eq 1 shows that the thermal ring-opening barrier can be estimated from the geometrical characters of the transition state. In particular, the barrier is positively correlated with the transition state C−C distance and negatively correlated with the out-of-plane-angle and the imaginary frequency. These geometrical characters describe the transition state of bond dissociation/formation between the two reactive carbon atoms, where the electronic structure changes from the tetrahedral sp3 hybridization in the closed-ring form to the planar sp2 hybridization in the open-ring form of the 9144

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Figure 8. Geometrical parameters at the transition state of photochromic compound 10 and the theoretical and fitted free energy barriers for its ground-state ring-opening process. Figure 7. Comparison between the theoretical free energy barrier and the fitted free energy barrier.

the compounds under investigation in this work, the fitting procedure based on eq 1 can save 30−50% computational time for the thermal ring-opening barriers (Table S2). Future screening of photochromic compounds based on eq 1 is under exploration.

diarylethene molecule. Based on eq 1, diarylethene molecules with larger C−C distance and smaller out-of-plane-angles of methyl/methoxyl groups at the transition state are expected to show greater thermal bistability, and in such cases, the transition state is located at a closer region to the open-ring form (Figure 4). Compared with the widely accepted argument based on aromatic stabilization energies,2 the fitting procedure provides a more direct and feasible approach to evaluate the thermal stability of diarylethene compounds consisting of novel aryl units. We have also tested the fitting procedure based on eq 1 and compared its performance with the simple linear relationship based on bond distances in Figure 3, using an additional photochromic compound 10, which contains methoxylpyrimidine and cyanopyrrole units as aryl rings. It turned out that the fitting formula eq 1 works well in reproducing the ground-state ring-opening free energy barrier of compound 10, as shown in Figure 7. The free energy barrier of compound 10 appears in a region that is not reached by the nine photochromic compounds used in deriving the parameters, confirming the validity of the linear relationships between the thermal barrier and the geometrical characters of the transition states. The geometry of the transition state of compound 10 is shown in Figure S3, and the geometrical characters are listed in Figure 8, together with a comparison among the free energy barriers from DFT calculations, eq 1, and the linear relationship in Figure 3. The theoretical barrier for compound 10 is predicted as 54.4 kJ mol−1 by DFT calculations and is estimated as 62.4 kJ mol−1 by eq 1. The linear relationship shown in Figure 3, however, suggests a free energy barrier of 73.0 kJ mol−1 based on the optimized carbon−carbon bond distance of 1.804 Å. Therefore, the fitting procedure based on eq 1 performs better than the simple linear relationship between the barrier and the distance between the two reactive carbon atoms. Equation 1 also provides the possibility of reducing computational time for the free energy barrier of each photochromic compound since only the geometry and imaginary frequency of the transition state at the M06/6-31G(d,p) level of theory are needed to estimate the barrier, whereas conventional approach requires additional single-point calculations with triple-ζ basis set for both the closed-ring isomer and the transition state. For

4. CONCLUSIONS We have presented a density functional theory study on the thermal stabilities of the ring-closed isomers of a number of photochromic diarylethenes with different aryl rings, including five- and six-membered rings. The combination of the M06 and the BMK density functionals is shown to offer a reliable prediction of the free energy barrier of the ground-state ringopening process from the ring-closed isomers, in particular for those thermally instable diarylethenes. The free energy barriers were shown to linearly correlate with the distance between the two reactive carbon atoms in the transition-state geometries. The thermally instable ring-closed isomers are therefore both geometrically and energetically closer to the transition states, rendering their likeliness to overcome the barrier and revert back to the ring-open isomers. Moreover, the free energy barrier of the ground-state ring-opening process was found to correlate not only with the out-of-plane angles of the methyl/ methoxyl groups at the reactive carbon atoms but also with the imaginary frequencies of the transition states. Based on these dependences we expressed the free energy barrier as a function of the imaginary frequency, the distance between the reactive carbons, and the out-of-plane angles of the methyl/methoxyl groups. A correlation coefficient of R2 = 0.971 was obtained, rendering the reliability of the proposed expression for estimating free energy barriers. We envisage that the analysis of the geometry and vibrational frequency of the transition states can provide insight into the thermal bistability of photochromic diarylethene compounds and in turn be useful in the development of novel photochromic materials.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b04268. Individual contributions to the thermal free energy barriers, potential energy scan with respect to the orientation of the methoxyl groups, optimized transition 9145

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state of compound 10, and solvent effects on the barriers (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (X.L.). *E-mail: [email protected] (Q.Z.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Swedish National Infrastructure for Computing (SNIC) for providing computational resources though contract SNIC 2014/11-31. Q.Z. acknowledges financial support by the National Natural Science Foundation of China (No. 21406137) and the Science and Technology Commission of Shanghai Municipality (No. 14YF1410900 and 14DZ2261000).

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