Doubly Closing or Not? Theoretical Analysis for ... - ACS Publications

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J. Phys. Chem. C 2010, 114, 9489–9497

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Doubly Closing or Not? Theoretical Analysis for Coupled Photochromes Denis Jacquemin,*,† Eric A. Perpe`te,† Franc¸ois Maurel,‡ and Aure´lie Perrier*,‡ Unite´ de Chimie Physique The´orique et Structurale (UCPTS), Faculte´s UniVersitaires Notre-Dame de la Paix, rue de Bruxelles, 61, B-5000 Namur, Belgium, and Laboratoire Interfaces, Traitements, Organisation et Dynamique des Syste`mes (ITODYS), CNRS UMR 7086, UniVersite´ Paris 7 - Paris Diderot, Baˆtiment LaVoisier, 15 rue Jean Antoine de Baı¨f, 75205 Paris Cedex 13, France ReceiVed: March 9, 2010; ReVised Manuscript ReceiVed: April 20, 2010

In the course of developing elaborate molecular switches allowing logic operations more evolved than the “on/off” effect, multiply addressable structures containing several dithienylethenes have been recently proposed. Using an ab initio spectroscopic tool, we investigate the structural and electronic properties of two dithienylethenes connected with four types of bridging units (phenyl, silyl, covalent, and ethynylene links). In each case, doubly closed, doubly open, and mixed open/closed structures have been considered. Combining a range-separated hybrid functional (CAM-B3LYP) to an extended basis set and a well-known solvent model, we accurately reproduced the position of the measured optical transitions of the different photochromes. This level of theory also allows to understand the presence or the absence of the fully closed form in most cases. Indeed, for three out of the four bridging units, a careful analysis of the molecular orbitals implied in the low-wavelength bands of the mixed open/closed compounds helps in predicting the photochromic properties of the coupled switches. Introduction In the course of developing electronic devices on a molecular scale, dithienylethenes (also referred to as diarylethenes, DA) constitute promising candidates for optoelectronic applications such as memories and switches.1 These molecules show photochromic activity as a reversible transformation between two isomers presenting different optical and electronic properties that can be induced by irradiation with light of appropriate wavelengths.2,3 The nearly insulating open form of DA undergoes a ring-closure reaction under UV irradiation, while the ringopening of the strongly delocalized closed form occurs under visible light irradiation. The cyclization and cycloreversion reactions between the two thermally stable isomers can be achieved a huge number of times and offer both large quantum yields and short response times. The high thermal- and photostabilities of DA as well as their reversible cyclization have led to the elaboration of refined applications based on the modulation of electric currents,4 magnetic interactions,5 or surface plasmon resonances of metallic nanoparticles,6 explaining the great interest in elaborating multiaddressable photochromes. These multicomponent molecular systems, based on the covalent connection of several DA photochromic units, can display several different colors depending on their electronic state and produce higher density data storage systems. Recently, the photochromic behavior of dimeric DA has been studied by different groups.7–13 Owing to the existence of three different states, open-open (oo), closed-open (co), and closed-closed (cc), these systems can store more information and lead to more complex logic operations than a single DA. Nonetheless, these experimental studies have shown that, in most cases, only one of the DA can convert to the closed-ring form upon UV * To whom correspondence should be addressed. E-mail: denis. [email protected] (D.J.); [email protected] (A.P.). † UCPTS, Namur. ‡ ITODYS, Paris.

excitations. The preservation of the photochemical reactivity of the individual units seems in fact highly sensitive to the nature of the bridging moiety between the two DA. For instance, for dimers connected with a single bond,10 an acetylene,11 a bis(phenylethynyl)-anthracene,12 or a diyne,14 the second ringclosing reaction is prohibited, while DA coupled by a sexithiophene wire,13 a silyl bridge,9 or a phenyl linker8 show full photochromism. Consequently, there is a great challenge to understand the influence of the bridging moiety on the electronic properties of the multicomponent systems. In that framework, theoretical tools complete the experimental studies aiming at designing more efficient multiaddressable molecular architectures. Previously, we have studied the structural and electronic properties of meta- and para-coupled DA connected with an acetylene-phenyl-acetylene linker15 with time-dependent density functional theory (TD-DFT). We have shown that it is necessary to go beyond the simple frontier molecular orbital (FMO) picture because the HOMO and the LUMO do not contain the relevant information to explain the nonoccurrence of the second ring closure. More recently, we have used a similar TD-DFT strategy, based on the analysis of the relevant orbitals (beyond the FMO scope), to investigate the full photochromism of two DA coupled with a molecular wire16 and the structures and the electronic properties of star-shaped DA trimers coupled through delocalized ethynyl-containing bridge.17 The present paper aims at modeling the electronic features of coupled DA relying on a panel of bridges. We have selected four series of coupled dithienylethenes depicted in Figure 1: on the one hand, I and II8,9 that show full photochromism, and on the other hand, III and IV10,11 that only present a partial photochromic activity. The objective is to evaluate the coupling between the different units and to get insights into the key parameters for the design of bridges allowing for doubly closed forms. As we will demonstrate, a careful yet simple analysis of the molecular orbitals implied in the different absorption bands can often hint the presence or absence of doubly closed isomers.

10.1021/jp102118w  2010 American Chemical Society Published on Web 05/04/2010

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Figure 1. Representation of the four coupled switches under investigation. Fully closed forms are sketched. The undesired side product, V, formed experimentally by the irradiation of the mixed closed/open IV, is also presented.

Method Given the number and size of the investigated systems, we have selected density functional theory (DFT) and its timedependent variation (TD-DFT)18,19 for simulating the structural and electronic properties of the coupled photochromes. Indeed, TD-DFT is a method of choice in terms of accuracy/ computational effort ratio, and it also allows to take into account environmental effects. In the present work, the bulk solvent effects have been included at all computational steps by means of the polarizable continuum model (PCM).20 For TD-DFT, the PCM calculations have been performed in the linear-response nonequilibrium model21 that is adequate for evaluating absorption spectra. We systematically perform comparisons with experiments carried out in aprotic solvents so to ensure that the PCM approach that neglects specific solute-solvent interactions can be straightforwardly applied. For all compounds, we have applied a recently reviewed22 threestep approach that is specifically optimized for simulating the UV/ vis spectra of organic23–26 and inorganic27–30 dyes. Our calculations, performed with the Gaussian0331 and Gaussian0932 packages, start with a full optimization of the ground-state geometries. These optimizations have been performed until the residual mean square force is smaller than 1 × 10-5 a.u. without imposing any symmetry constraint. In a second stage, the vibrational frequencies have been computed analytically to ensure that we consider only true minima on the potential energy surface. These two first steps have been performed at the PBE0/6-311G(d,p) level of theory33,34 as this approach yields accurate structural parameters for most conjugated molecules.22,35 In the last leg, the first 10-20 low-lying electronic excited states have been computed using the vertical TD-DFT approximation, which is clearly the most widely applied ab initio approach for medium and large molecules.36 This phase has been performed with the 6-311+G(2d,p) basis set that yields converged transition energies for the present class of photochromes.37,38 We

have selected both the CAM-B3LYP functional,39 that is particularly suited for delocalized and charge-transfer cases40,41 and closedring diarylethenes,35,42 and the PBE0 hybrid33,34 to perform the TDDFT calculations. In the former functional the percentage of exact exchange smoothly increases from 19 to 65% as a function of the interelectronic distance, whereas in the latter hybrid, a constant fraction of exact exchange (25%) is selected. To plot the different molecular orbitals, we systematically used a contour threshold of 0.03 a.u. Results and Discussion Fully Closing Compounds. For the two systems showing full photochromism, the results of the TD-DFT calculations performed with the PBE0 and CAM-B3LYP functionals are summarized in Table 1. For the three forms of I, the geometry optimizations have led to two conformers presenting different relative orientations of the DA. In conformer A, the thiophene rings of one DA point down the plane constituted by the Si and the two sulfur atoms of the other DA, whereas for conformer B the two sulfur atoms point up the same plane (see Figure S1 in Supporting Information). The conformer A is found to be slightly more favorable with a PBE0/6-311+G(2d,p) internal energy difference amounting to +0.8 kcal · mol-1 for both the I(cc) and I(oo) structures. For the I(co) system, this difference is completely negligible (+0.04 kcal · mol-1). It is likely that the two conformers coexist in solution and that both should be considered when simulating the absorption spectra. However, the transition energies computed with TD-DFT are extremely similar for conformers A and B, for example, for I(cc), the CAM-B3LYP λmax is 518 nm for conformer A and 520 nm for conformer B. Consequently, we only report (Table 1) the results obtained for the most stable conformer A. As can be seen in Table 1 and Figure 2,9,43 the CAM-B3LYP functional provides UV/vis data on the experimental spot for I(cc), whereas the

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TABLE 1: Vertical Transitions Obtained with the PBE0 and CAM-B3LYP Functionals for the Two Compounds Experimentally Showing Full Photochromisma PBE0

CAM-B3LYP

experiment

structure

solvent

form

λ

∆E

f

λ

∆E

f

I

heptane

cc

578

2.15

0.62

co

565

2.20

0.43

314

3.95

0.23

314 312 289 283 282 281 746 391 346

3.94 3.97 4.29 4.38 4.39 4.40 1.66 3.35 3.58

0.22 0.20 0.21 0.24 0.29 0.31 1.35 0.32 0.95

co

651 403 384 378

1.91 3.07 3.23 3.28

0.74 0.41 0.31 0.24

oo

348 296

3.56 4.19

1.79 0.46

518 500 328 509 328 292 267 292 290 268 268 247 232 631 370 311 296 279 587 354 337 324 283 276 324 308 286 277 275

2.39 2.48 3.78 2.44 3.78 4.25 4.64 4.25 4.28 4.62 4.63 5.02 5.12 1.96 3.35 3.98 4.19 4.45 2.11 3.50 3.68 3.82 4.39 4.49 3.82 4.03 4.34 4.48 4.51

0.66 0.21 0.26 0.46 0.27 0.43 0.32 0.44 0.41 0.36 0.38 0.31 0.23 1.32 0.65 0.38 0.60 0.45 0.72 0.66 0.26 0.57 0.25 0.67 1.52 0.34 0.27 0.49 0.49

oo

II

hexane

cc

ε

ref.

518

21900

9

345

15600

9

270

45000

9

233

44000

9

588 ∼375

25000

8

569 342

13500

8

42700

8

λ

265 ∼310 271

a Wavelengths (λ, in nm), transition energies (∆E, in eV), oscillator strengths (f), and molar absorption coefficients (ε) in L · cm-1 · mol-1 are given. Only transitions with f g 0.2 are listed in this table. Values with a tilde are estimated from graphical data.

Figure 2. Comparison between experimental9,43 and CAM-B3LYP spectra for I in doubly open (left) and doubly closed (right) forms. The continuous (dashed) lines correspond to the CAM-B3LYP (experimental) data. The theoretical curves are obtained using a convolution Gaussian with a FWHM of 0.45 eV.

deviations are larger with PBE0. This finding was expected as it has been previously reported that, for (uncoupled) closedring DA presenting a delocalized nature, CAM-B3LYP provides transition wavelengths in better agreement with experimental data than PBE0,35,42 at least within the vertical TDDFT approach. Though for I(oo), the experimental presence of a very large absorption band implying several excitations makes completely unambiguous assignment impossible, the qualitative agreement is satisfying in Figure 2. For I(co), the comparison between experiments and theory can not be achieved because the singly and doubly closed forms, which are both known to be present in the reacting mixture, could not be separated by HPLC.9 From

I(co) to I(cc), CAM-B3LYP predicts only a small bathochromic shift (+9 nm) for the λmax. For II, the trends upon successive ring closure are clearly well-reproduced by our calculation scheme (Figure 3). Especially, the evolution of the absorption bands around 600 nm fits the measurements and the bathochromic shift observed for the λmax from II(co) to II(cc) is qualitatively reproduced by theory. Note that the agreement observed in Figure 3 is confirmed by examining the data of Table 1. Indeed, the measured first absorption band of II(cc) is centered around 588 nm,8 and this value is well reproduced by CAM-B3LYP (631 nm that is a 0.14 eV error) but not by PBE0 that predicts

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Figure 3. CAM-B3LYP calculated spectra for the three possible isomers of II, using a convolution Gaussian with a FWHM of 0.45 eV. The upper panel is the corresponding experimental plot reprinted with permission from Kobatake, S.; Irie, M. Synthesis and photochromic reactivity of a diarylethene dimer linked by a phenyl group. Tetrahedron 2008, 59, 8359-8364. Copyright 2003, Elsevier.

a significantly too large λmax (746 nm or a 0.47 eV error). The same conclusion holds for II(co) with a signed (experimental theory) error of +0.07 eV for CAM-B3LYP and +0.27 eV for PBE0. While in both II(cc) and II(co) cases, the assignment of the absorption bands is pretty easy, difficulties occur for II(oo). Indeed, a rough comparison between the theoretical and the experimental λmax leads to very large errors for both CAMB3LYP (0.75 eV) and PBE0 (1.01 eV). Such extreme discrep-

Jacquemin et al. ancies probably arise from a shoulder at ∼310 nm in the experimental spectrum.8 By assigning this shoulder to the 324 nm absorption band computed with the CAM-B3LYP functional, we reach a deviation of 0.17 eV, in the line of the expected accuracy of TD-DFT.35 The band experimentally peaking at 271 nm is subsequently identified to the 275 and 277 nm excitation wavelengths, leading to a 0.08 eV error. In that framework, CAM-B3LYP yields excitation wavelengths in very good agreement with experimental features (mean absolute deviation of 0.13 eV) but unsatisfying estimates of the relative intensities of the maximum absorption band and its shoulder (see Figure 3). The weaker ability of TD-DFT to reproduce oscillator strengths than transition energies is a recognized fact.44–46 Calculations of the vibronic couplings47,48 would be needed to definitively clarify the residual discordance. Nevertheless, such intense computational work is far beyond the scope of the present study that aims at gaining insights for the ring closure rather than reproducing accurately all band shapes. To understand the photochromic behavior of systems I and II, we have analyzed the orbital features of the oo, co, and cc derivatives. For I, the inspection of the orbitals of the I(oo) and I(co) structures shows that there is no significant electronic communication between the two DA systems. For instance, for I(oo), the HOMO-1 and HOMO (LUMO and LUMO+1) present similar shape, except that the former orbital is centered on one DA, the latter on the second one (see Figure S2 in Supporting Informtion (SI)), which leads to a negligible energy difference of 0.05 eV (0.08 eV) between the two orbital levels. In fact, we found no overlap with the Si atom orbitals, the last occupied (first unoccupied) orbital involving the central silicon atom corresponding to the HOMO-4 (LUMO+3). The 292 nm transition in Table 1 arises from a HOMO-1 to LUMO electronic excitation centered on one DA, whereas the quasi-degenerated

Figure 4. Topology of frontier orbitals of the mixed open/closed I obtained at the PCM-CAM-B3LYP/6-311+G(2d,p) level using a contour threshold of 0.03 a.u.

Theoretical Analysis for Coupled Photochromes 290 nm peak implies an electron promotion from the HOMO to the LUMO+1 that are both localized on the second DA. Therefore, the absorption spectrum of I(oo) is a superposition of the absorption bands of two independent photochromes. Similarly for I(co), the 518 nm (328 nm) transition mainly corresponds to an electron promotion from the HOMO to the LUMO (from the HOMO-2 to the LUMO). All these orbitals are centered on the closed-ring side, as shown by Figure 4, and are therefore unhelpful for inducing the electro-cyclization of the open DA.49 On the contrary, the dominating orbital contribution in the 292 nm absorption is a HOMO-1 to LUMO+1 transition with both orbitals localized on the open-ring DA (Figure 4). We can identify the absorption band characteristic of the doubly open DA and the relevant virtual orbital (which is almost unmodified by the presence of the other closed-ring isomer) presents the desired topology for initiating the ringclosure reaction.50,51 Indeed, there is a significant contribution on one of the reactive carbon atom, and it has been checked that there is a bonding character with respect to the other reactive carbon atom. For I(cc), the strong absorption band at 518 nm and the smaller peak at 500 nm are related to important contributions of both HOMO-1 f LUMO and HOMO f LUMO+1 excitations. As shown in Figure S3, the HOMO-1 and LUMO are centered on one DA core, the HOMO and LUMO+1 on the other one, but there is a modest interdependence of the two closed-ring DA since we do not have perfectly degenerated absorption bands. In summary, the inspection of the orbitals of system I corroborates the findings of Areephong et al. who have demonstrated, with the help of 1H NMR spectroscopy and a ring-closure kinetic study, that the two DA do not show conjugation interaction. In other words, the fully closed structure is obtained because the two photochromes are essentially independent, so that continuous irradiation of the system with the same excitation wavelength induces sequential electro-cyclizations of the two DA. For the system II, the features of the frontier orbitals involved in the absorption band transitions are drastically different. As expected, the phenyl linker allows for an efficient π-electronic delocalization over the complete molecule (see, for instance, the HOMO and LUMO of II(oo) and II(cc) in Figures S4 and S5, respectively). To understand the presence of the II(cc) structure, we have focused on the II(co) system, which should undergo ring-closure to deliver the fully closed derivative. The 588 nm transition is related to an electron promotion from the HOMO to the LUMO (see Figure 5) with both orbitals centered on the closed switch and the phenyl bridge. Compared to a single DA linked to two phenyl moieties, the λmax is almost unchanged. Indeed, the “monomer” presents a vertical absorption maximum at 575 nm, and the calculated bathochromic displacement (+13 nm), in the line of the measured red-shift (+7 nm8), can be ascribed to the extension of the π-conjugation toward the thiophene ring of the second DA. Because the topology of the virtual orbitals is a key factor guiding the photochromic activity,15–17,50,51 an electronic excitation to the LUMO is unlikely to lead to the ring-closure reaction on the second DA. To initiate such a reaction, one should promote the electron toward the LUMO+2, LUMO+4, or the LUMO+1, which all present the required topology, especially the latter. Indeed, these three orbitals present a significant electronic density on at least one of the reactive carbon atoms of the open-ring DA51 and a bonding character allowing to form the new σ bond.50 As can be seen in Figure 6, the strong absorption band at about 340 nm encompasses a large share of these key orbitals, and this is consistent with the observed ring-closure reaction upon irradia-

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Figure 5. Topology of the relevant orbitals of the mixed open/closed II. See Figure 4 for more details.

Figure 6. CAM-B3LYP spectrum of II(co) obtained with a convoluting Gaussian (FWHM ) 0.3 eV). The stick spectrum and virtual orbital compositions for the two main bands are reported.

tion at 313 nm.8 Note that this inspection of the topology of the relevant virtual MO relies on static considerations and does not provide insights into the complete photochemical reaction paths nor the dynamics of the reaction, so that the obtained results should always be analyzed with a critical eye. However, this first-order approach seems to often provide a handy explanation of the photochromic behavior of coupled DA. As a matter of fact, such explanation is not limited to I and II. As for an acetylene-phenyl-acetylene linker,15 the virtual molecular orbitals implied in the different absorption bands do not present the correct shape, subsequently preventing the second ring closure reaction, as experimentally concluded.12,52 On the

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TABLE 2: Vertical Transitions Obtained with the PBE0 and CAM-B3LYP Functionals for III, IV, and Va PBE0 structure III

solvent hexane

cyclohexane

λ

∆E

f

λ

∆E

f

cc

777 338

1.60 3.67

0.90 0.35

666 378

1.86 3.28

0.88 0.50

co

639 383 371 314 289 677 323 554 316

1.94 3.24 3.34 3.94 4.29 1.83 3.83 2.24 3.92

0.50 0.43 0.38 0.22 0.22 0.96 0.27 0.54 0.34

oo

341 293

3.64 4.23

0.46 0.29

co

561 324 316 289

2.21 3.83 3.92 4.29

0.34 0.23 0.25 0.20

581 366 335 337 255 586 328 505 327 277 322 272 247 510 316 288 275 250 240

2.13 3.39 3.70 3.68 4.86 2.07 3.78 2.45 3.80 4.48 3.85 4.55 5.03 2.43 3.92 4.30 4.51 4.96 5.18

0.51 0.53 0.55 1.18 0.28 0.97 0.56 0.57 0.32 0.37 0.55 0.45 0.57 0.35 0.38 0.24 0.39 0.30 0.20

cc co

V

a

cyclohexane

experiment

form

oo IV

CAM-B3LYP λ

ε

584 ∼365

ref.

11

320 ∼270

23000

11

505 302 ∼238 324 ∼270 (sh) 240 501 299

18180

10

18500

10

10520

55 10 55

237

55

See Table 1 footnote for more details.

contrary, for the DA bridged through an oligothiophene wire,16 the orbital components of the low-wavelength peaks, similar to these of the phenyl system II, account for the fully active photochromism experimentally detected.53,54 Partially Photochromic Systems. Results obtained for systems showing partial photochromism are given in Table 2. For the ethylene-bridged structure III, the agreement between CAM-B3LYP and experimental data is again very satisfactory. Indeed, for III(oo), an average error of 0.24 eV is obtained, whereas for III(co), the deviation is as small as 0.01 eV. The ring closure of the second DA, that remains unseen experimentally,11 leads to a bathochromic shift of +85 nm for the CAMB3LYP λmax. This displacement is larger than the corresponding shift observed for II8 or for the sexithiophene wire13 (+19 nm experimentally in both cases). For the fully open III, the maximum absorption band corresponds to a HOMO f LUMO transition with the HOMO mainly localized on the multiple bonds of the central conjugated moiety and the LUMO’s density centered on single bonds (Figure S6): there is a clear conjugation between the two DA through the ethylene bridge. The LUMO presents significant electron density on only one side of each DA but with a bonding character, which is consistent with the observed ring-closure of the first DA. To account for the experimental absence of second ring closure, we have examined the energetics as well as the geometrical and orbital features of III(co). As a matter of fact, the limited photochromism can not be explained by simple energetic considerations, such as a destabilization of the doubly closed isomer because at the CAMB3LYP/6-311+G(2d,p) level, the first and second ring-closure reactions have similar costs of +11.7 kcal · mol-1 and +13.0 kcal · mol-1, respectively. For the records, for the system showing full photochromism I (II), the relative energies of the mixed open/closed and the closed/closed structures, respectively, attain +14.5 kcal · mol-1 (15.0 kcal · mol-1) and 30.3 kcal · mol-1 (29.3 kcal · mol-1). There is a small variation of the distance between the two reactive carbons in the open-ring DA, with a value of 3.763 Å for III(co) instead of 3.752 Å for III(oo), but this small bond stretching of +0.011 Å can not explain the loss of photochromic properties. However, it is worth noting that

Figure 7. Topology of the relevant virtual orbitals of the mixed open/ closed III. See Figure 4 for more details. Figure S7 presents the same information with a smaller contour threshold.

this bond distance is appreciably larger in III(oo) than in other systems [3.526 Å for I(oo), 3.560 Å for II(oo), and 3.522 Å for IV(oo)]. We have then examined the virtual orbitals of III(co) and it turns out that only the LUMO+1 could allow ring closure. Indeed, both the LUMO and LUMO+2, which are involved in the 581, 366, and 335 nm transitions listed in Table 2, present an antibonding character between the two reactive carbons, which prevents the photochromic bond formation (see Figure 7 and Figure S7). The relevant LUMO+1 orbital can only be populated with small-wavelength excitations (302, 297, and 272 nm), but these absorption bands present very weak

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Figure 8. Comparison between experimental10,55 and convoluted (FWHM ) 0.3 eV) CAM-B3LYP spectra for IV (left) and V (right) in their mixed open/closed forms. The continuous (dashed) lines correspond to the CAM-B3LYP (experimental) data.

oscillator strength (0.01-0.05) and are therefore inefficient. Additionally, in the experiment of Kaieda et al.,11 the irradiation is performed with a 320 nm light that is probably not sufficiently energetic to induce electronic excitations toward the LUMO+1. In fact, this analysis backs the experimental conclusions: because the excitation on the open-ring unit is unhelpful for ring closure, a nonphotochromic desexcitation pathway occurs.11 Dynamical aspects would thus complete our static model to investigate the competition between the two possible photochemical paths, namely, intramolecular energy transfer and ring-closure reaction. For the system IV(oo) with two open-ring DA covalently linked, several conformers presenting different relative orientations of the rings are obtained. In conformers A and B, the dihedral angle between the central thiophene rings presents a deviation from planarity of about 32°, whereas in conformer C (optimized starting with the symmetric crystallographic structure from ref 10), the two central rings are perfectly coplanar. In addition, in conformer A, the two open DA lie on the same side of the plane formed by the central thiophene rings, whereas in conformers B and C, the reverse situation is found. For all structures, the distance between the two reactive carbons is close to 3.52 Å, in agreement with XRD measurements (3.53 Å).10 Conformer B is slightly more stable than the two other structures because A and C relative PCM-PBE0/6-311G(d,p) Gibbs free energies are 0.5 kcal · mol-1 and 1.5 kcal · mol-1, respectively. As these differences are extremely small at this level of theory, the three conformers might coexist in solution and contribute to the absorption spectra. Because the transition energies computed with TD-DFT are extremely similar for the three structures with a CAM-B3LYP λmax of 323 nm (A), 322 nm (B), and 332 nm (C), we only report the results obtained for the most stable conformer B. The conclusions presented below are indeed independent of the selected conformer. From a geometrical point of view, the IV(oo) XRD structure shows a near coplanarity of the two central thiophene rings is observed (dihedral angle of 1.4°), whereas a larger twist appears for the conformer B geometry. Such discrepancy is, however, not necessarily due to a theoretical inaccuracy as relative orientations of rings in oligothiophenes are known to differ in solid and solvent environments.53,54 As can be seen in Table 2, the agreement between CAMB3LYP calculations and experiment is very good, with a mean absolute deviation of 0.03 eV for IV(oo), and 0.02 eV for the two low-lying transitions of IV(co). The concordance is not as impressive for the lower wavelength transition of the mixed isomer, but Figure 8,10,55 nevertheless, demonstrates the accuracy

Figure 9. Topology of the relevant virtual orbitals of the mixed open/ closed IV. See Figure 4 for more details.

of the selected approach. As expected for DA switches,1,50 the IV(oo) isomer is more stable than the partially and fully closed structures, and the energy costs for successive ring-closure reactions are found to be nearly additive. Indeed the relative CAM-B3LYP/6-311+G(2d,p) internal energies of IV(co) and IV(cc) with respect to the fully open isomer are, respectively, +7.1 kcal · mol-1 and +14.4 kcal · mol-1, smaller than for the two fully photochromic cases (see above). One can therefore conclude that for IV, the nonclosing of the second DA can not be explained by simple energetic considerations. In the same way, the partial photochromic activity can not be rationalized by geometrical constraints. For IV(co), the distance between the two reactive carbons of the open DA is 3.519 Å, a trifling difference with the IV(oo) structure (3.522 Å). We have then examined the orbitals of the mixed IV(co) system. The inspection of the topology of the virtual orbitals shows that the LUMO and especially the LUMO+1 are relevant for ring-closure reaction (Figure 9). The LUMO dominates the absorption band at 505 nm, while the electronic excitations at 327 and 277 nm largely involve these two key orbitals. The orbital analysis indicates that the electro-cyclization of the second DA should occur. However, experimental attempts failed

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to ring-close the second DA with an irradiation in the range 254-365 nm and produced the parasitic product V depicted in Figure 1. This system results from a diatropic rearrangement of the closed-ring moiety, while the geometry of the open-ring isomer is not modified. In particular, the distance between the two reactive carbons is unchanged when going from IV(co) to V. The relative CAM-B3LYP/6-311+G(2d,p) internal energy of V with respect to IV(oo) is actually identical to the fully closed isomer value (14.9 kcal · mol-1). For the undesired side product, the ring closure of the second DA was not observed.10,55 For the record, the TD-DFT transition energies of V(co) are given in Table 2, with an error limited to 0.11 eV. On Figure 8 we can notice a strong similarity between the absorption bands of IV(co) and V(co), though the intensity corresponding to the λmax is significantly smaller for the latter compound. In short, for IV, a simple TD-DFT/orbital analysis can not rationalize the nonformation of the fully closed isomer. A dynamic investigation of the photochemical reaction path after the first ring-closure reaction would help explain the diatropic rearrangement and the photochromic inactivity of this system, and we redirect the interested reader to the literature for a quantum mechanical study of side photochromic products.56 Concerning the possible approaches to predict relative quantum yields of competitive processes, a combined quantum chemical and molecular dynamics study has been recently applied to investigate the photoisomerization reaction of a fluorene-based molecular rotary motor.57 However, due to the size of our dimer system, the application of this methodology is not straightforward and requires further investigation. Conclusions and Outlook The structure and the electronic properties of two dithienylethenes coupled by a panel of chemical bridges (phenyl, silyl, covalent and ethynylene links) have been investigated using an ab initio spectroscopic tool, namely, time-dependent density functional theory. It turned out that the CAM-B3LYP functional predicts the experimentally observed optical transitions of the different systems with a remarkable accuracy. Additionally, this level of theory generally allows to explain why the totally closed form is observed or not. For the silyl bridge, the two dithienylethenes remain mainly unconjugated and the absorption spectrum is a simple superposition of the absorption bands of two independent photochromes. Irradiation at low wavelength, therefore, induces a simultaneous ring closure of both switches. On the contrary, a strong electronic delocalization over the two photochromic units is observed for both phenyl and acetylene bridges. The analysis of the virtual orbitals playing a key role in the electronic transition corresponding to the UV absorption bands explains why ring closure occurs for the phenyl bridge but not for the acetylene moiety. Indeed, in the former, the virtual orbitals present the required photochromic topology, whereas for the latter, they possess an antibonding character for the to-be-formed σ bond. The TDDFT/orbital analysis, which is a simple first-order approach, proved to be a fast and powerful tool for these three coupled photochromic systems but it fails for the covalently link compound due to the formation of a nonphotochromic side product. Such a drawback cannot be crystal-balled by our first-order approach, and we are currently investigating the excited-state properties of IV(co) with more refined theoretical tools. In short, in the majority of the systems, a careful investigation of the orbital features of the low-wavelength bands actually helps

Jacquemin et al. in predicting the photochromic properties of DA connected by different bridging units. Acknowledgment. The authors are deeply indebted to W.R. Browne and N. Branda for providing their experimental data, as well as for fruitful discussions. D.J. and E.A.P. thank the Belgian National Fund for Scientific Research for their research associate and senior research associate positions, respectively. The calculations have been partially performed on the Interuniversity Scientific Computing Facility (ISCF), installed at the Faculte´s Universitaires Notre-Dame de la Paix (Namur, Belgium), for which the authors gratefully acknowledge the financial support of the FNRS-FRFC and the “Loterie Nationale” for the convention number 2.4578.02 and of the FUNDP. The collaboration between the Belgian and French groups is supported by Wallonie-Bruxelles International, the Belgian Fonds de la Recherche Scientifique, the Ministère Franc¸ais des Affaires e´trangeres et europe´ennes, and the French Ministère de l’Enseignement supe´rieur et de la Recherche in the framework of Hubert Curien Partnership. Supporting Information Available: Conformers of doubly closed I, conformers of fully open IV, and figures with frontier orbitals for the doubly closed and doubly open forms. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Irie, M. Chem. ReV. 2000, 100, 1685–1716. (2) Du¨rr, H.; Bouas-Laurent, H. Photochromism: Molecules and Systems; Elsevier: New York, 2003. (3) Balzani, V.; Credi, A.; Venturi, M. Molecular DeVices and MachinessA Journey into Nano World; Wiley-VCH: Weinheim, 2004. (4) Guirado, G.; Coudret, C.; Launay, J.-P. J. Phys. Chem. C 2007, 111, 2770–2776. (5) Matsuda, K.; Irie, M. Chem.sEur. J. 2001, 7, 3466–3473. (6) Masson, J. F.; Liddell, P. A.; Banerji, S.; Battaglia, T. M.; Gust, D.; Booksh, K. Langmuir 2005, 21, 7413–7420. (7) Matsuda, K.; Irie, M. J. Am. Chem. Soc. 2001, 123, 9896–9897. (8) Kobatake, S.; Irie, M. Tetrahedron 2003, 59, 8359–8364. (9) Areephong, J.; Browne, W. R.; Feringa, B. L. Org. Biomol. Chem. 2007, 5, 1170–1174. (10) Peters, A.; Branda, N. R. AdV. Mater. Opt. Electron. 2000, 10, 245– 249. (11) Kaieda, T.; Kobatake, S.; Miyasaka, H.; Murakami, M.; Iwai, N.; Nagata, Y.; Itaya, A.; Irie, M. J. Am. Chem. Soc. 2002, 124, 2015–2024. (12) Kawai, S. H.; Sasaki, T.; Irie, M. Chem. Commun. 2001, 711–712. (13) Areephong, J.; Hurenkamp, J. H.; Milder, M. T. W.; Meetsma, A.; Herek, J. L.; Browne, W. R.; Feringa, B. L. Org. Lett. 2009, 11, 721–724. (14) Yagi, K.; Irie, M. Chem. Lett. 2003, 32, 848–849. (15) Jacquemin, D.; Perpe`te, E. A.; Maurel, F.; Perrier, A. J. Phys. Chem. Lett. 2010, 1, 434–438. (16) Jacquemin, D.; Michaux, C.; Perpète, E. A.; Maurel, F.; Perrier, A. Chem. Phys. Lett. 2010, 488, 193–197. (17) Jacquemin, D.; Perpe`te, E. A.; Maurel, F.; Perrier, A. Phys. Chem. Chem. Phys. 2010, DOI: 10.1039/B927323A. (18) Runge, E.; Gross, E. K. U. Phys. ReV. Lett. 1984, 52, 997–1000. (19) Casida, M. E. In Time-Dependent Density-Functional Response Theory for Molecules.; Chong, D. P., Ed.; World Scientific: Singapore, 1995; Vol. 1, pp 155-192. (20) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. ReV. 2005, 105, 2999– 3094. (21) Cossi, M.; Barone, V. J. Chem. Phys. 2001, 115, 4708–4717. (22) Jacquemin, D.; Perpe`te, E. A.; Ciofini, I.; Adamo, C. Acc. Chem. Res. 2009, 42, 326–334. (23) Preat, J.; Michaux, C.; Lewalle, A.; Perpe`te, E. A.; Jacquemin, D. Chem. Phys. Lett. 2008, 451, 37–42. (24) Jacquemin, D.; Perpe`te, E. A.; Scuseria, G. E.; Ciofini, I.; Adamo, C. Chem. Phys. Lett. 2008, 465, 226–229. (25) Jacquemin, D.; Perpe`te, E. A.; Ciofini, I.; Adamo, C. Theor. Chem. Acc. 2008, 120, 405–410. (26) Le Bahers, T.; Pauporte´, T.; Scalmani, G.; Adamo, C.; Ciofini, I. Phys. Chem. Chem. Phys. 2010, 11, 11276–11284. (27) Guillemoles, J.-F.; Barone, V.; Joubert, L.; Adamo, C. J. Phys. Chem. A 2002, 106, 11354–11360.

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