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COVER ARTICLE Jacquemin et al. Spectral properties of self-assembled squaraine–tetralactam: a theoretical assessment
PERSPECTIVE Miller et al. Detailed balance in multiple-well chemical reactions
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Spectral properties of self-assembled squaraine–tetralactam: a theoretical assessment Denis Jacquemin,w*a Eric A. Perpe`te,wa Ade`le D. Laurent,b Xavier Assfeldb and Carlo Adamo*c Received 8th October 2008, Accepted 19th November 2008 First published as an Advance Article on the web 12th January 2009 DOI: 10.1039/b817720a Using several theoretical approaches relying on the time-dependent density functional theory, we have computed the electronic spectrum in the visible range of a squaraine dye, either isolated or embedded into a tetralactam macrocycle. The amplitude of the bathochromic displacement induced by the complexation is well-reproduced by the most accurate models. This total shift is split into speciﬁc components, allowing us to unravel the most-important contributions (geometry modiﬁcations, polarisations. . .). This study constitutes a further step in the investigation of environmental eﬀects on dyes’ absorption spectra.
1. Introduction Squaraines constitute a primary class of near-IR dyes, that is, they absorb at very long wavelengths (typically around 650 nm), an uncommon feature for relatively compact compounds. Though squaraines are easy to substitute and relatively cheap to synthesise, they suﬀer two major drawbacks for practical applications: they are sensitive to (bio)chemical attacks and, in some special conditions, they may form aggregates. Smith and coworkers1–3 have set up an eﬃcient strategy to circumvent these two limitations: they propose to encapsulate the dye (see Fig. 1) into a macrocyclic host (see Fig. 2). As summarised in their successive contributions, such a scheme paves the way towards applications in various ﬁelds, e.g. ﬂuorescence resonance energy transfer, bio-imaging and rotaxane-related technologies. Our focus in this contribution is to model the impact of the guest–host self-assembly interactions on the spectral signature of the dye. To hit this target, our main tool is timedependent density functional theory (TD-DFT), as it clearly emerges as the best modelling scheme, in terms of the accuracy/computational eﬀort ratio, for simulating UV/visible spectra.4–12 For such a large system (see Fig. 2), the electroncorrelated wavefunction approaches (CAS-PT2, EOM-CC, MR-CI. . .) are not applicable without cumbersome modiﬁcations, while the semi-empirical schemes, such as ZINDO, are not adequate to grasp such reﬁned complexation eﬀects.
The ability of TD-DFT to reproduce the absorption and ﬂuorescence spectra of solvated organic dyes has recently been assessed by us (see ref. 13–16 and references therein) and it turned out that TD-DFT often correctly foresees auxochromic shifts. Additionally, once combined to a continuum solvation model,17,18 it reproduces the solvatochromic or acidochromic shifts induced by most solvents. More speciﬁcally, for substituted squaraines, an extensive study performed by Srinivas and coworkers19 demonstrates TD-DFT’s aptitude for this class of dyes. While the inﬂuence of a liquid environment on the visible spectrum are now well-mastered by quantum chemists, investigations of the changes resulting from solidstate eﬀects (pigments) or complexation (self-assembled molecules) have, to our knowledge, been the subject of much less investigations. There are works on hydrogen-bonded DNA bases20,21 that are suited for ‘‘full’’ TD-DFT calculations, whereas calculations with hybrid quantum mechanical (QM)/molecular mechanics (MM) schemes, similar to the one used here, have been performed by Elstner22–27 and by us28 previously. One should also point out the works of Cammi and Curutchet in which the surrounding protein is modelled by a dielectric continuum.29–31 Therefore, this work aims, on the one hand, to provide insights explaining the spectral variations provoked by the squaraine-tetralactam complexation (Fig. 2), and, on the other hand, to assess the ability of TD-DFT to reproduce the impact of non-trivial self-assembly on the absorption wavelengths of compounds of practical interest.
Laboratoire de Chimie The´orique Applique´e, Groupe de Chimie Physique The´orique et Structurale, Faculte´s Universitaires Notre-Dame de la Paix, rue de Bruxelles, 61, B-5000 Namur, Belgium. E-mail: [email protected]
b Equipe de Chimie et Biochimie The´oriques, UMR CNRS-UHP 7565, Institut Jean Barriol (FR CNRS 2843), Faculte´ des Sciences et Techniques, Nancy-Universite´, BP 239, 54506 Vandoeuvre-le`s-Nancy Cedex, France c Ecole Nationale Supe´rieure de Chimie de Paris, Laboratoire Electrochimie et Chimie Analytique, UMR CNRS-ENSCP no. 7575, 11, rue Pierre et Marie Curie, F-75321 Paris Cedex 05, France. E-mail: [email protected]
w 1 Research Associate of the Belgian National Fund for Scientiﬁc Research.
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Fig. 1 Sketch of the squaraine dyes, with naming conventions for the bonds.
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Fig. 2 Sketch of the DFT-optimised self-assembled system with the central dye of Fig. 1 displayed as a transparent material.
2. Methodological approaches The DFT and TD-DFT calculations have been performed with the Gaussian03 suite of programs,32 with a tighten selfconsistent ﬁeld convergence threshold (108 a.u.). We have followed a well-established approach based on the parameterfree PBE0 functional,33,34 which is particularly suited for investigating electronic transitions.14,16,35 First, starting with the crystal structure reported in ref. 2, the ground-state geometry (Ci point group) has been fully optimised until the residual mean force was smaller than 1.0 105 a.u. This force-minimisation procedure has been carried out with the 6-31G(d,p) atomic basis set, which yields accurate groundstate parameters at a limited computational cost (see section 3). Secondly, the vertical transition energies to the ﬁrst ﬁve valence excited states have been computed with TD-DFT. For this part, we have selected the 6-31++G(d,p) atomic basis set, as it is well known that diﬀuse functions are mandatory to attain a balanced description of excited states. These calculations have been repeated, individually considering the two elements (dye and cage) in order to gain further insights to the complexation eﬀects. Due to the large size of the investigated case (41800 basis functions, 4130 atoms), we could not aﬀord to perform a direct modelling of the liquid environment (chloroform is used experimentally), except when noted. It is likely that the inclusion of the solvent in our protocol would lead to a bathochromic displacement of the computed spectra for both the isolated molecule and the self-assembled system. Nevertheless, this should not signiﬁcantly modify the inclusion eﬀect. In order to resolve the various eﬀects due to the cage on the absorption spectrum of the dye, we have also performed hybrid calculations, in which the dye is studied at the QM level whereas the cage is treated by means of a MM force ﬁeld. All computations are run with the above-mentioned PBE0/ 6-31G(d,p) geometry. Amongst all the interactions between This journal is
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the dye and the cage, one can certainly consider the electrostatic one the most important for the absorption spectrum. The dispersion, though necessary to get accurate total interaction energy and geometry, does not noticeably modify the ground nor the excited electronic state charge distributions. To correctly model the electrostatic interaction between the dye and the cage, we have chosen an iterative procedure to determine the atomic point charges (APCs) plugged in the MM force ﬁeld. First, we performed a QM calculation on the isolated squaraine, and the dye’s APCs were tuned to reproduce the electrostatic potential given by the MSK scheme.36 In a second step, a QM calculation of the tetralactam has been carried out, taking into account the dye’s previously determined APCs that polarised the cage’s wavefunction. The APCs are then consistently determined for the atoms constituting the cage, and are consequently used in a third-step calculation performed on the squaraine surrounded by the cage’s APCs. This procedure is applied until convergence is reached, that is when the APCs of both host and guest change by less than 104|e|. The ﬁnal set of cage’s APCs is called the self-consistent point charges (SCPCs). Within this procedure, it is safe to state that the electrostatic interaction between the dye ground-state and the cage is accurate, and as a consequence, that the wavefunction of the guest is also accurately polarised by the host. The Franck–Condon principle37 implies that the nuclear conﬁguration of both the dye and the cage can be frozen during the electronic transition. However, the electronic cloud of the cage is able to instantaneously readapt to the new electronic distribution of the dye. We then modelled this electronic response of the tetralactam’s electronic density by means of a polarizable dielectric continuum characterized by the dielectric constant at inﬁnite frequency.18 The squaraine is placed inside a cavity created in the continuum including MM point charges of the cage. Computations using this methodology are denoted ERS, for electronic response of the surroundings.
3. Results and discussion First, we compare the DFT-optimised structure of Fig. 2 to its X-ray counterpart obtained from ref. 2. As can be seen in Table 1, the geometric parameters within the dye are wellreproduced at the PBE0/6-31G(d,p) level. For instance, the computed CQO [C–N(Me)2] distance in the squaraine is 1.238 [1.363] A˚, in almost perfect agreement with the measured data 1.241 [1.362] A˚. The bond lengths inside the four-member cycles of the central dye are also completely similar: 1.459 A˚ and 1.465 A˚ (theory) versus 1.458 A˚ and 1.468 A˚ (X-ray). Additionally, the squaric–phenyl inter-ring distance is 1.408 A˚ (theory) and 1.409 A˚ (X-ray). The same conclusion holds for the geometry of the macrocycle. For instance, the CN distance in the pyridine rings is 1.334 A˚ theoretically and 1.338 A˚ experimentally, whereas the spacing between the two parallel anthracene units, 6.8 A˚,2 is overestimated by 3% only (7.0 A˚) with our computational scheme. In fact, the only signiﬁcant diﬀerence originates in the conformation of the macrocycle, which is predicted to be chair-like, although the solid-state structure is more levelled. Nevertheless, as pointed out by the experimental group, the ﬂattening probably originates in the Phys. Chem. Chem. Phys., 2009, 11, 1258–1262 | 1259
Table 1 Comparison between the geometrical parameters of the dye obtained by diﬀerent approaches. All values are in A˚. See Fig. 1 for naming conventions Parameter
a b, b 0 c d, d 0 e, e 0 f, f 0 g h, h 0
1.225 1.470 1.408 1.414 1.376 1.419 1.365 1.446
1.238 1.459, 1.408 1.415, 1.375, 1.419, 1.363 1.447,
1.242 1.458, 1.409 1.412, 1.374, 1.417, 1.362 1.458,
crystal packing eﬀects.2 This assumption is conﬁrmed by other X-ray investigations performed on (very) similar squaraine/ macrocycle structures that actually yield chair conformers in the majority of cases.1,3 Of course, to correctly reproduce the caging eﬀects it is more important to properly describe the intramolecular hydrogen bonds than the individual structures of both units. Our calculations deliver N–H OQC distances of 1.945 A˚ and 1.937 A˚, that are not directly comparable to experiment as the hydrogen atoms have been constrained during the X-ray data analysis. The computed NH bond lengths attain 1.021 A˚. A straightforward confrontation of the experimental to the theoretical hydrogen bond is possible by investigating the N O distance, for which theory foresees smaller and more-symmetric values (2.937 A˚ and 2.931 A˚) than experiment (3.005 A˚ and 2.942 A˚). This discrepancy probably originates in the above-mentioned packing eﬀects that induce a ﬂattening. Indeed for the two similar chairlike self-assembled structures described in ref. 1, the average N O distances are shorter: 2.840 A˚ and 2.904 A˚, respectively. In short, PBE0/6-31G(d,p) gives accurate geometrical parameters. The geometric variations induced by the complexation are signiﬁcant. For the squaraine dye, the carbonyl bond length is elongated by 0.015 A˚ due to interaction with the tetralactam. The bond lengths of the now symmetric four-membered rings are slightly longer in the isolated dye (1.470 A˚ isolated, 1.459 A˚ and 1.465 A˚ for the complete system), while the other parameters are almost unchanged, e.g. the C–N(Me)2 bond length [inter-ring distance] is 1.365 A˚ [1.408 A˚] for the isolated squaraine, totally comparable to the values computed for the whole system. Therefore, the geometric alternations induced by the molecular container are located on the region directly involved with the hydrogen bonds, as expected. This is conﬁrmed by a geometry optimisation performed on the empty macrocycle, that delivers a NH bond shorter (1.009 A˚) than in the complex (1.021 A˚). This 1.009 A˚ value is, not surprisingly, close to the one computed in N-methylacetamide (1.01 A˚).38 We have subsequently performed TD-DFT calculations to evaluate the spectra of all the components (Fig. 3). For the isolated dye, we found a strong absorption (oscillator strength, f = 1.5) at 2.45 eV, corresponding to the expected HOMO–LUMO transition in this type of structures. This absorption wavelength is strongly underestimated compared to the experiment (1.97 eV in ref. 2). This error is partly due to the lack of the solvent eﬀects (chloroform) in our model. Indeed, an investigation on the same dye with the polarizable continuum model (PCM18) switched on during both the 1260 | Phys. Chem. Chem. Phys., 2009, 11, 1258–1262
1.465 1.413 1.374 1.419 1.446
1.468 1.414 1.374 1.422 1.452
Fig. 3 Evolution of the TD-DFT absorption spectra upon complexation. The (intensity normalised) theoretical peaks have been obtained by using a broadening Gaussian with FWHM of 25 nm.
geometry optimisation and the spectra calculations provides a transition energy of 2.30 eV. The residual theory/experiment discrepancy (0.33 eV) is sizable but not unexpected with TD-DFT, as blue-shifted theoretical values are quite common for squaraine dyes.19,39 In fact, as our focus is to analyse the eﬀects of complexation, such an absolute error is without repercussions for the present work. For the isolated cage, the ﬁrst signiﬁcant absorption is located at 3.14 eV (f = 0.3) and is to be assigned to the fused aromatic moiety of the tetralactam structure. Indeed, anthracene absorbs in the very same region of the spectrum (3.31 eV in hexane40), and a small experimental absorption band presenting the typical vibronic signature of fused acenes appears in that region for the complex.2 For the self-assembled architecture, the corresponding dipole-allowed TD-DFT transition takes place at 2.38 eV, that is, we compute a bathochromic complexation shift of 0.07 eV compared to the isolated dye. This value is in perfect agreement with the experimental displacement of 0.06 eV (the experimental absorption of the complexed dye is located at 1.91 eV). In Fig. 4, the topology of the occupied and unoccupied orbitals implied in the lmax transition are sketched. It clearly appears that both are fully delocalised on the dye part and present no contribution on the cage, as expected. It is interesting to note that the HOMO-2 has a much larger contribution on the oxygen atoms than the LUMO. This is consistent with the relative stabilisation of the frontier orbitals upon complexation: 0.39 eV for the relevant occupied orbital but 0.27 eV for the LUMO. These values also imply that the electronic gap deduced from the This journal is
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measurements. This clearly demonstrates that including only the polarisation of the ground-state, as done in some conventional QM/MM models, is inappropriate to correctly reproduce the reﬁned spectroscopic eﬀects.
4. Concluding remarks
Fig. 4 Topology of the orbitals involved in the lmax transition. The occupied orbital (HOMO-2) lies on the bottom, whereas the virtual orbital (LUMO) is depicted at the top (contour threshold = 0.035 a.u.).
orbital energies is larger for the whole system than for the isolated dye, i.e. that a simple look at the softness evolution, within the conceptual DFT framework, would incorrectly predict an hypsochromic shift. In other words, the electronic reorganisation eﬀects that are accurately accounted for within the TD-DFT framework are essential in the present case. We have also investigated the origin of the shift by decomposing the total eﬀects into major contributions. Such a splitting procedure was applied, on the one hand, to determine the ratio between electronic and geometric eﬀects, and, on the other hand, to evaluate the relative importance of ground and excited-state polarisations. By performing a calculation on the isolated squaraine, but using the in-complex geometry, we compute a 2.41 eV absorption, which is bracketed by the responses of the optimised-isolated (0.04 eV) and selfassembled (+0.03 eV) structures. Consequently, we can state that about half of the shift noted upon complexation originates in the geometric deformations implied by the self-assembly process. To gain further insight QM/MM results are required. Indeed, using the SCPC (see section 2) approximation for modelling tetralactam leads to a transition energy of 2.55 eV, i.e. an incorrect hypsochromic displacement upon self-assembly is foreseen. In other words, the ground-state caging (polarisation) of the dye is not responsible for the bathochromic shift. If one turns towards the SCPC + ERS scheme, which correctly accounts for the electronic reorganization of the cage due to excitation of the dye, one obtains a peak located at 2.36 eV. This corresponds to a bathochromic shift of 0.09 eV with respect to the isolated dye, a value in good agreement with both the ‘‘full’’ TD-DFT results and the This journal is
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The impact of self-assembly on the geometry and visible absorption spectrum of a squaraine–tetralactam structure has been assessed using DFT, TD-DFT and QM/MM approaches. It turns out that DFT provides an accurate description of the complex’s geometry for both the dye and its container. TD-DFT is also able to accurately deliver the experimental bathochromic shift induced by self-assembly, whereas simpler models, such as an investigation of the frontier orbital energies or the modelling of the sole groundstate polarisation, could lead to qualitatively and quantitatively incorrect trends. We have demonstrated that half of the experimental shift is brought on by geometrical deformations, while the modiﬁcation of the polarisation of the cage upon photon absorption by the central dye is essential to explain the bathochromic eﬀect. As this investigation paves the way towards TD-DFT simulations in complex media, we are currently investigating the colouring changes implied by solid-state eﬀects.
Acknowledgements DJ and EAP thank the Belgian National Fund for Scientiﬁc Research for their research associate positions. Three authors (DJ, EAP and CA) thank the Commissariat Ge´ne´ral aux Relations Internationales (CGRI) and the Egide agency for supporting this work within the framework of the Tournesol Scientiﬁc cooperation between the Communaute´ Franc¸aise de Belgique and France. Several calculations have been 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.
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