Benjamin
Lasorne
*a,
Arnaud
Fihey
b,
David
Mendive-Tapia
a and
Denis
Jacquemin
*bc
aInstitut Charles Gerhardt Montpellier, UMR 5253, CNRS-UM, CTMM, Université Montpellier, CC 1501, Place Eugène Bataillon, 34095 Montpellier, France. E-mail: david.mendive-tapia@univ-montp2.fr
bChimie Et Interdisciplinarité, Synthèse, Analyse, Modélisation (CEISAM), UMR CNRS no. 6230, BP 92208, Université de Nantes, 2, Rue de la Houssinière, 44322 Nantes Cedex 3, France. E-mail: denis.jacquemin@univ-nantes.fr
cInstitut Universitaire de France, 103 bd St. Michel, 75005 Paris Cedex 5, France
First published on 29th June 2015
Going from photochromic compounds presenting a single switchable function to multi-addressable photochromic multimers remains an extremely difficult task notably because the interactions of several photochromic units through a linker generally result in a substantial loss of photoactivity. Due to their size and the intrinsic complexity of their electronic structure, coupled photochromes also constitute a fundamental challenge for theoretical chemistry. We present here an effective curve-crossing model that, used in connection with easily accessible ab initio data, allows a first understanding of the difficulty to obtain efficient multiphotochromes. Indeed, we demonstrate that extra crossing points, specific to multiphotochromes, have to be passed to ensure reactivity. In addition, the proposed approach allows the definition of an intuitive tilt criterion that can be used to screen a large number of substitution patterns and hence help in the design of new compounds, an aspect that is also developed here. The compatibility of this tilt criterion with previously proposed static Franck–Condon parameters is discussed as well.
Fig. 1 Top: representation of a typical DAE with the o (left) and c (right) isomers. Bottom: experimental evolution for the DAE dyad studied in ref. 6: the second cyclization is not observed. |
To go further, molecules encompassing several switchable units have been proposed, notably DAE dyads.7 The experimental outcomes were however rather frustrating. On the one hand, in systems in which the DAE subunits are almost non-interacting, e.g., when a non-conjugated linker is used to bind the two DAEs, photochromism tends to be conserved but the visible absorption bands of the mixed closed–open (co) and fully-closed (cc) isomers peak at nearly the same wavelength, making it difficult to distinguish the two isomers with cheap spectroscopic techniques.8–12 On the other hand, strongly-coupled DAE dyads tend to present partial photochromism only: one can go from the oo to the co isomer but prolonged irradiation does not yield the expected cc structure.13 This is illustrated at the bottom of Fig. 1 for one specific dyad, but this holds for many other derivatives.6,13–17 In these situations, the DAE multimer behaves like a new partially reactive monomer and is thus a rather unexciting system.
To explain this loss of photochromism, energy transfer (ET) between the different subunits was invoked.13,18,19 The idea is that the irradiation of the open form in the hybrid co isomer yields a co* state that is rapidly deactivated by ET leading to c*o. While this interpretation is convenient and chemically intuitive, there is, to the best of our knowledge, no theoretical background supporting that interpretation. It is indeed possible to apply refined multi-reference wavefunction theories to explore the photochromism of isolated DAEs,20–26 but they are in practice not applicable to DAE dyads. For this reason, the present theoretical state-of-the-art is to use Time-Dependent Density Functional Theory (TD-DFT) to determine the nature of the excited-state in the Franck–Condon (FC) region for all isomers.27 Such a crude and static procedure was able to explain several experimental outcomes,28–30 but as it is completely blind in the actual photochemical region, it incorrectly predicts several experimental events.28,31 For instance, Staykov and collaborators explored the properties of two DAE separated by a sexithiophene linker,32 and by considering several charged states, they indicated an orbital control of the photochromism. We have recently used a similar approach to investigate a large series of dimers,33 and could define optimal substitution patterns providing an (FC) excited-state with the ideal topology, but no proper assessment on how the photoreactivity takes place after the vertical transition could be performed. To try to bypass this limitation, we provide here the first model allowing a direct rationalisation of the photoreactivity of DAE dyads. This model is based on electronic-state correlation diagrams built from the energy profiles of the isolated DAE units and considers the weak-coupling regime (spectator bridge). We focus on the occurrence of curve crossings along ring-closing/opening pathways, which could decrease the yield of some of the products by inducing branching in the transfer of population. Despite its limits (weak-coupling), this model allows a fundamental understanding of the difficulty of designing efficient DAE dyads and provides hints at the most adequate substitution patterns. In that sense, it is complementary to the previously proposed “orbital TD-DFT” approach.
Fig. 2 Simplified correlation diagram for a single DAE unit A (red: state C; green: state O). xA is the dimensionless reaction coordinate linking the open (xA = 1, rhs on the Figure) and closed (xA = 0, lhs on the Figure) isomers, hA defines the relative energies (in eV). The energy parameters, corresponding to an isolated DAE displayed on top of the Figure, have been taken in ref. 33. |
H0 (xA, xB) = hA (xA) + hB (xB) | (1) |
Of course, in practice the isolated DAE units are in fact the hydrogen-capped moieties, A–H and H–B, so to obtain closed-shell species rather than radical fragments. As we focus our description on the electronic π-system, we can ignore this subtlety for the time being. Each reaction coordinate, xA or xB, will be defined as a dimensionless and scaled parameter so that it is respectively 0 for the closed form and 1 at the open form (see Fig. 2). In addition, we assume that the reaction coordinates are curved in such a way that the reaction path goes through the S1/S0 CI along a direction that lifts degeneracy. In other words, we assume that xA or xB present large enough components along the branching-plane vectors in the vicinity of the CI. Using the states C and O defined above as a basis set, the diagonal entries of the one-unit Hamiltonian can be expressed as quadratic functions of the reaction coordinate,
(2) |
The E-parameters correspond to the absolute energies, whereas the T-parameters are the vertical transition energies (see Fig. 2). By construction, at both points xA = 0 (closed) and xA = 1 (open), they respectively satisfy
(3) |
(4) |
For simplicity, we set EOA = 0, that is, we use the ground-state energy of the most stable open isomer as reference. We also introduce DCOA = ECA − EOA, the difference between the ground state energies of the two isomers. This term is positive for all systems investigated here. The three preceding equations now read,
(5) |
(6) |
(7) |
Now, from this simple additive description, we can build four singlet “direct-product states” based on the states C and O of the fragments: CC, CO, OC, and OO, where the first (second) label indicates the VBT state of the A (B) DAE unit. When such states occur to be excited states, according to the geometry of the dyad, they are characterised by excitations localized on either or both of the two fragments. Here, we assume that these four states are dominated by electronic transitions between photochromic orbitals that is the orbitals involved in the photoreaction (see ref. 27 for a definition of such orbitals). However, they can be embedded in a set of other low-lying excited states ignored in this work. In other words, CC, CO, OC, and OO are not necessarily zero-order approximations of S0, S1, S2, and S3 but rather of the states that are expected to play the most significant role in the photochromic activity of DAE dyads.37
The zero-order electronic Hamiltonian matrix of the dyad, H0 (xA, xB) is diagonal, as we neglect direct coupling, and its diagonal elements read:
H0CC(xA, xB) = DCOA + DCOB + (TOA − DCOA)xA2 + (TOB − DCOB)xB2, | (8) |
H0CO(xA, xB) = DCOA + (TOA − DCOA)xA2 + (TCB + DCOB)(xB − 1)2, | (9) |
H0OC(xA, xB) = DCOB + (TCA + DCOA)(xA − 1)2 + (TOB − DCOB)xB2, | (10) |
H0OO(xA, xB) = (TCA + DCOA)(xA − 1)2 + (TCB + DCOB)(xB − 1)2. | (11) |
Fig. 3 Simplified cyclic reaction path from (o-A)–X–(o-B) to (c-A)–X–(o-B) to (c-A)–X–(c-B) to (o-A)–X–(c-B) and back to (o-A)–X–(o-B). Blue curve: OO state; purple curve: CO state; orange curve: CC state; green curve: OC state. The energy parameters correspond to a symmetric dyad made of the two DAEs displayed in Fig. 2. The x-coordinate corresponds to a cyclic “square path” relating the four possible minimal structures corresponding to all open/closed combinations.43x was chosen so that one goes from the fully open structure at x = 0 to the fully closed structure at x = 2 (and hence its sign is different from that of xA of Fig. 2).43 Note that x = 0 and x = 4 correspond to the same point, namely the fully open dyad, whereas x = 1 and x = 3 correspond to mixed closed/open structures. |
Fig. 4 Comparison between the formation of (o-A)–X–(o-B) from (c-A)*–X–(o-B) through a single crossing (grey square) and the formation of (c-A)–X–(c-B) from (c-A)–X–(o-B)* through a sequence of two crossings (black circle and grey square). The energy parameters are the same as in Fig. 3. The full (dashed) arrows indicate reactive (unreactive) photochemical pathways. On this Figure, the doubly open dyad is at the left hand-side (x = 0). |
Other energy parameters may also influence the outcome and more systematic indicators are required. To this end, let us consider the extra crossing between CC and OO, the two states correlating the oo and cc isomers in the ground-state, over the interval displayed in Fig. 4. The possible values of xB for which H0OO(0, xB) = H0CC(0, xB) are given by,
(12) |
(13) |
A positive value at the crossing point indicates an average force pointing toward xB = 0. Increasing its magnitude should thus favour formation of the closed–closed dyad (c-A)–X–(c-B) by enhancing the ballistic behaviour of the system as it passes through the extra crossing.
Let us start by considering homo-dyads (B–X–B). The results are listed in Table 1. For all studied systems, xec−B fall in the quite narrow 0.7–0.9 range, e.g., it is 0.76 for the seminal DAE dimer (a–X–a). By contrast, the tilt criterion is much more sensitive to the chemical nature of the DAE, it ranges from 0.86 to 2.66 eV (it is 2.13 eV for the reference a–X–a dyad). A general trend emerges: adding substituents on the reactive carbon atoms (l–p series) yields a smaller tilt criterion, which should induce a less efficient reaction to the extra crossing. This contrasts with the study of the topology of the orbitals at the FC point that indicated that this substitution of the reactive carbon atoms can be very useful (but in a strong coupling case),33 illustrating the difficulty to simultaneously optimize all parameters. We underline that the tilt criterion focuses on the reactivity at the crossing region, whereas orbital topology criteria focus on the nature of the FC point, and these two criteria are therefore complementary (see next Section). Keeping constant the perfluorocyclopentene bridge, the replacement of the thiophene rings by a thieno-thiophene group (g) or by a furan cycles (q) appear as the most effective options to increase the tilt, though the effect is rather moderate compared to the standard a–X–a dimer (+7% and +15%, respectively). To the very best of our knowledge, the use of furan rings in DAE multimers was never assessed experimentally, but furan-based DAE monomers present large cyclization quantum yields, similar to the one obtained with thiophene-DAEs.45–47 The largest tilt are reached for w and u. However, the former is not a chemically interesting option. Monomers of DAE using the latter cyclohexene bridge have been synthesized, but were found to be less effective that the corresponding perfluororcyclopentene structures.48,49 On balance, the maleimide group (r) is probably the most pertinent “bridge” option to increase the tilt. In DAE monomer, this maleimide bridge yields however less efficient cyclization than the well-known perfluorocyclopentene bridge, especially in polar environments.50–52
Compound | D COB | T CB | T OB | x ec−B | Tilt |
---|---|---|---|---|---|
a | 0.65 | 2.68 | 4.51 | 0.76 | 2.13 |
b | 0.97 | 3.19 | 4.08 | 0.86 | 2.09 |
c | 0.79 | 2.93 | 4.30 | 0.81 | 2.10 |
d | 0.59 | 2.52 | 4.33 | 0.75 | 2.05 |
e | 0.72 | 2.48 | 4.53 | 0.72 | 1.87 |
f | 0.56 | 2.50 | 4.23 | 0.76 | 2.06 |
g | 0.45 | 2.61 | 4.25 | 0.78 | 2.28 |
h | 0.55 | 2.46 | 4.22 | 0.75 | 2.03 |
i | 0.53 | 2.66 | 4.32 | 0.78 | 2.24 |
j | 0.65 | 2.50 | 4.42 | 0.74 | 1.97 |
k | 0.62 | 2.40 | 4.11 | 0.75 | 1.87 |
l | 1.19 | 2.78 | 4.17 | 0.77 | 1.42 |
m | 0.70 | 2.58 | 4.24 | 0.76 | 1.92 |
n | 1.36 | 2.56 | 4.21 | 0.72 | 0.99 |
o | 1.35 | 2.59 | 4.12 | 0.74 | 1.01 |
p | 1.35 | 2.47 | 3.88 | 0.74 | 0.86 |
q | 0.58 | 2.98 | 4.49 | 0.81 | 2.46 |
r | 0.35 | 2.73 | 3.48 | 0.88 | 2.38 |
s | 0.56 | 2.97 | 4.25 | 0.83 | 2.43 |
t | 1.11 | 2.62 | 4.61 | 0.72 | 1.46 |
u | 0.35 | 2.83 | 4.37 | 0.80 | 2.61 |
v | 0.58 | 2.59 | 3.53 | 0.84 | 1.98 |
w | 0.44 | 2.93 | 4.79 | 0.78 | 2.66 |
Given these results, we have also evaluated the qr case (maleimide bridge, furan rings). Such a qr–X–qr dyad presents a tilt of 2.68 eV, the largest of the series (+26% improvement compared to a–X–a). As we show in the following section, the topologies of the associated molecular orbitals also indicate a possible second cyclization, and this system might be worth an experimental try. Nevertheless, we note that in the specific case of a symmetric qr dyad presenting an ethynyl linker (see next Section), the S1 and S2 states of the closed–open isomer are energetically close (2.62 eV and 3.33 eV, a difference of 0.71 eV to be compared to ca. 2.0 eV in most dyads) indicating that the extra crossing takes place close to FC point, which may be detrimental for the cyclization process.
The general trends noted above correlate to a large extent with the value of DCOB. Increasing the stability difference seems unfavourable to forming the closed–closed isomer. The extra crossing is less tilted, which implies more branching between the two channels. This also affects the normal crossing in a similar way and both effects tend to play in the same direction. A good solution to favour formation of cc seems to stabilise the closed form.
After this discussion of symmetric dyads in which TCB = TCA, we analyse the impact of using two different DAEs. Of course, the synthesis of asymmetric dyads is more challenging, but examples exist in the literature.15,53 We have investigated the tilt for all A/B combinations and the results are given in Table S-2† in the ESI.† In that Table, we consider that the A DAE is the first to react, so that the closed–open isomer contains a closed A and an open B DAE. Increasing TCA − TCB favours the formation of the cc structure. Interestingly, if B is the standard DAE structure, a, the best candidate is to select an inverse DAE (b) as second photochrome, with a tilt criterion of 2.62 eV. From the data of Table S-2,† it is clear that significantly exceeding this value of tilt is difficult [the largest figure, 2.95 eV, is obtained with (c-b)–X–(o-u)], but many substitution patterns yield small tilts, close or even below 1 eV. As for the homo-dyads of Table 1, this is the case for hetero-dyads of DAEs substituted at the reactive carbon atoms. Often, but not always, improving the yield of formation of (c-A)–X–(c-B) from (c-A)–X–(o-B)* often hinders that from (o-A)*–X–(c-B), as both pathways are no longer equivalent. For instance, the 2.62 eV value noted above goes down to 1.52 eV is one considers a dyad with an open b and a closed a, rather than the reverse. Clearly, it is therefore of prime importance to determine which DAE cyclizes the first in such asymmetric dimers.
As seen in Fig. 6, we have considered a symmetric dimer built with two qr photochromes, as well as all asymmetric combinations of normal (a), inverse (b) and hybrid (c) DAEs. For these asymmetric dyads, we have first determined the unit undergoing the first cyclization in the fully-open isomer. Therefore the closed–open structures shown in Fig. 6 are the results of this first analysis (see the ESI† for optical properties and relevant orbitals of the open–open forms). The tilt criterion for these structures are large: 2.68 eV for (c-qr)–E–(o-qr), 2.62 eV for (c-b)–E–(o-a), 2.37 eV for (c-c)–E–(o-a) and 2.36 eV (c-b)–E−(o-c).
The symmetric (c-qr)–E–(o-qr) dyad presents a LUMO showing a clear bonding interaction between the reactive carbon atoms (see Fig. 7). This orbital is strongly involved (72% overall, see the ESI†) in the rather intense S0 → S2 transition peaking at 373 nm and relevant for ring-closure. Following the orbital criterion, this dyad is therefore expected to yield the fully closed form. Using the qr monomers, we have also tested other conjugated linkers and similar results were obtained (see the ESI†).
All three asymmetric dyads present a LUMO+1 as the first virtual orbital with a photochromic topology (see Fig. 7), a typical outcome.27 TD-DFT reveals that this orbital is not accessed by the same kind of transitions for the three compounds. In (c-b)–E–(o-a), it is populated (17% of the total) by the very intense S0 → S2 transition (f = 0.81) at 310 nm. In both (c–c)–E–(o-a) and (c-b)–E–(o-c) the LUMO+1 is only involved in transitions below 300 nm, but the efficiency of the transition is larger for the latter system (see the ESI†). In short, (c-qr)–E–(o-qr), (c-b)–E–(o-a) and (c-b)–E–(o-c) could be retained as potential candidates for full-closure using the orbital analysis. The first is quite “exotic” (w.r.t. synthesis of DAEs), but the latter two are built with well-known monomers and they successfully passed the FC orbital topology test in the coupled limit and the curve-crossing test in the weak coupling limit.
Due to the intrinsic complexity of the investigated problem, the present theoretical effort is certainly not the terminus. Our short-term plans include (i) designing a more sophisticated model accounting for the explicit effect of the bridge in the form of an electronic coupling that could alter conjugation between the fragments; (ii) assessing the ET nature and efficiency using alternative models.54–56 Later, we also plan to account for the possible electronic excitations partly-localised on the bridge.
Footnote |
† Electronic supplementary information (ESI) available: Analytic expression for the energies of Fig. 3, complete table of tilt values for the hetero-dyads, orbital considerations for selected systems. See DOI: 10.1039/c5sc01960e |
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