Impact of Vibronic Couplings on Perceived Colors: Two

Letter pubs.acs.org/JPCL

Impact of Vibronic Couplings on Perceived Colors: Two Anthraquinones as a Working Example Denis Jacquemin,*,† Eric Brémond,‡ Ilaria Ciofini,‡ and Carlo Adamo*,‡,¶ †

Laboratoire CEISAM - UMR CNR 6230, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France Laboratoire LECIME, CNRS UMR-7575, Chimie-ParisTech, 11 rue P. et M. Curie, F-75231 Paris Cedex 05, France ¶ Institut Universitaire de France, 103 bd Saint-Michel, F-75005 Paris Cedex 05, France ‡

ABSTRACT: The accurate simulation of the dye colors remains a significant challenge for theoreticians, notably due to the sensitivity of the human eyes that are able to distinguish variations of hues corresponding to trifling energetic shifts. Using time-dependent density functional theory and two hybrid functionals, we have simulated vibrationally resolved absorption spectra of two anthraquinone derivatives (solvent blue 35 and solvent green 3) solvated in cyclohexane. Comparisons with recent experiments demonstrate the efficiency of the ωB97XD/6-31++G(d,p) approach for these structures. The impact of microscopic vibronic couplings on the macroscopic chromatic coordinates of the dyes is quantified. This work unravels the key role of these couplings and is consequently a step further in the modeling of human-perceived colors from purely ab initio models. SECTION: Electron Transport, Optical and Electronic Devices, Hard Matter

A

Scheme 1. Representation of the Two Dyes under Study, As Well As the Reference Disperse Violet 1 (Right)

nthraquinodic derivatives (AQs) represent about onethird of the world production of organic dyes. This success originates not only in the limited fabrication costs and straightforward synthetic routes, both characteristic of AQ dyes, but also in the vivid panel of blue and green colors obtained once hydrogen bond donors are grafted on the chromophore.1−3 In the panel of possible substitutions, the 1,4 symmetric pattern relying on powerful amino groups is certainly one of the most successful. Indeed, it yields intense, broad, and structured absorption bands, typically in the 500− 650 nm domain.1−3 The industrial impact of AQs has stimulated a series of theoretical works. Specifically, several investigations relying on time-dependent density functional theory (TD-DFT) have been performed in order to predict and rationalize the absorption spectra of these dyes.4−7 However, most of these works have been performed within a vertical TDDFT model, which may be relevant for structureless bands but becomes inadequate if a multipeak band is investigated,8,9 or for studying complex photoexcited phenomena.10−12 Therefore, more complex theoretical schemes have to be applied for the most interesting AQ compounds. In a recent TD-DFT benchmark investigation devoted to small hydroxy- and amino- substituted AQs,13 we have shown that the hallmark shape of the visible absorption band originates in vibronic couplings for the prototype DV-1 (see Scheme 1). The topology of the experimental peaks is specifically well reproduced with Head-Gordon’s ωB97X-D range-separated hybrid functional,14 though it overshoots the transition energy significantly, as expected.15 In this Letter, we extend this recent work in two directions. On the one hand, we consider significantly larger dyes than before, solvent blue 35, SB35, and © 2012 American Chemical Society

solvent green 3, SG3 (see Scheme 1), for which recent experimental measurements are available,16 and show that the shape of the vibronic envelope is different despite the obvious structural similarity of these two compounds. On the other hand, we aim to go from a microscopic to a macroscopic description by quantifying the impact of vibronic couplings on the perceived color. Both goals are necessary to reach a rational in silico design of novel dyes. Before discussing the optical properties, let us briefly review the main structural parameters of SB35 and SG3. The most significant data are collected in Table 1. For both structures, photon absorption induces an elongation of the carbonyl groups and a significant contraction of the hydrogen bonds, as foreseen. Indeed, from a qualitative point of view, the absorption induces a transition from a CO to a C+−O− Received: November 24, 2011 Accepted: January 24, 2012 Published: January 24, 2012 468

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Table 1. Selected Geometrical Parameters for the Ground and Excited States of the Two Dyesa dye SB35

functional B3LYP ωB97X-D

SG3

B3LYP ωB97X-D

a

state

dCO

dC−N

dN−H

dHbond

αN−H···O

VTW

S0 S1 S0 S1 S0 S1 S0 S1

1.258 1.261 1.244 1.255 1.254 1.261 1.242 1.256

1.360 1.359 1.357 1.348 1.369 1.382 1.365 1.359

1.020 1.028 1.015 1.027 1.025 1.032 1.019 1.033

1.747 1.708 1.773 1.700 1.727 1.682 1.753 1.664

137.2 140.7 135.2 140.7 138.1 142.5 136.0 142.7

590 513 621 509

Distances are in Å, and valence angles are in degrees. At the right of the table, the vertical transition wavelengths (VTW, in nm) are also listed.

form, a transformation assisted by the presence of a nearby acidic proton. The S1 state is therefore more ionic, which in turn might explain the decrease of the H-bond lengths when going from S0 to S1. This shortening is predicted to be significantly larger with ωB97X-D than with B3LYP, which is perfectly in the line of results previously obtained for DV-1.13 However, the absolute hydrogen bond distances are about 0.1 Å shorter in the two dyes investigated in the present Letter than those in their di-NH2 counterpart, which is consistent with a stronger auxochromic effect and hence a longer λmax for SB35 and SG3 than that for DV-1. Indeed, stronger hydrogen bonds imply more polarized carbonyl bonds and hence more similar ground and excited states. After superimposition of S0 and S1 structures, the geometric root-mean square (rms) deviations were computed, and we obtained 0.063 and 0.293 Å for SB35 and SG3, respectively. This hints to a significant difference of vibronic patterns (see below). Within the PCM-TD-DFT scheme, the computed vertical energies of SB35 (SG3) correspond to wavelengths of 590 (621) and 513 (509) nm with B3LYP and ωB97X-D, respectively. Although we are well aware of the limits of the vertical approximation,8,9,17 we compare these estimates with an experiment that provides 639 (646) nm in the same medium.16 It is obvious that the absolute values provided by B3LYP are in reasonable agreement with that from experiment (errors below the 0.2 eV threshold for both compounds), though this hybrid functional significantly overestimates the auxochormic shift. On the contrary, in this model, the ωB97X-D functional is significantly less satisfying for both absolute values and auxochromic shifts (incorrect sign). In fact, neither of the two hybrid functionals is very satisfying for this latter criterion. For both dyes, TD-DFT predicts that this first strongly dipoleallowed transition mainly corresponds to the promotion of an electron from the HOMO to the LUMO. The differences of total electronic density induced by this transitions can be seen in Figure 1 and are alike for the two dyes. Indeed, the major variations are mainly centered on the two substituted rings of the AQ core, with a significant increase (decrease) of density for the oxygen (nitrogen) atoms and no significant contributions from the butyl of phenyl side groups. The PCM-ωB97X-D vibrationally resolved absorption bands are displayed in Figure 2, and the differences between the two dyes are obvious. For SB35, theory predicts two clear-cut maxima at 565 and 524 nm, as well as a shoulder at 490 nm. The relative intensities of these three characteristic points are 1.00, 0.73, and 0.26, respectively. They can be straightforwardly compared to their experimental counterparts of 639 (1.00), 599 (0.91), and 565 nm (0.47).16 ωB97X-D still underrates the transition energies significantly but to a smaller extent than within the vertical scheme. More importantly, the energetic

Figure 1. Density difference plots for SB35 (left) and SG3 (right). The red (blue) zones indicate an increase (decrease) of electron density as a result of electronic transition. The countours have been computed at the PCM-ωB97X-D level of theory with a threshold of 0.001 au.

separations between the different bands, as well as their heights, are correctly reproduced. The vibronic analysis indicates that two (S1) vibrational modes are principally responsible for the band shape of SB35, a wagging mode of the NBu groups at 214 cm−1 and a breathing mode of the quinoidic core at 372 cm−1, both inducing variations of the hydrogen bond distances. For SG3, TD-DFT yields a less-structured envelope for the visible absorption band (Figure 2), with two peaks centered at 557 (1.00) and 539 nm (0.79). This is again in line with experimental findings; a less-resolved band is obtained in SG3 than that in SB35, with maxima at 646 (1.00) and 599 nm (0.95) for the former.16 Nevertheless, it is obvious that the qualitative agreement between theory and experiment is less satisfying for SG3 as the envelope is too tight with theory. For SG3, the vibronic analysis yields a quite complex picture. Nevertheless, TD-DFT predicts that the modes with the phenyl side chains start to play a role in the shape of the band, which was not the case for SB35. With B3LYP, the agreement between theoretical and experimental vibronic shapes is significantly less satisfying (though still qualitatively correct for SB35), and we will not discuss further this already documented finding.13 To move toward a more anthropocentric description, we have transformed the computed spectra of Figure 2 into colors by using the “natural light” D65 illuminant and the CIE 10° standard observer. We have considered a relatively small concentration, 5 × 10−3 mol·L−1, as these two AQs are known to be efficient dyes. The results are summarized in Table 2 for the well-known CIE Lab colorimetric space. By comparing the colors computed with vibronic couplings with a one-peak (vertical-like) approximation, it is evident that the latter approach is inadequate to provide physically sound results; 469

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Figure 2. Stick and convoluted spectra of the visible band of SB35 (left) and SG3 (right). These data have been obtained at the PCM-ωB97X-D level. The black lines are the (shifted) experimental curves taken from ref 16, the offset is 0.33 and 0.35 eV for SB35 and SG3, respectively.

functional restores the measured topologies of visible spectra for both molecules, though it overshoots the transition energies. Transforming our theoretical data into colorimetric parameters, we were able to demonstrate that the perceived hues are, in the present case, strongly dependent on the vibronic couplings. The proposed methodology could still be useful when there is no access to measured spectra. Indeed, the distances between two CIE Lab coordinates is (nearly) linearly proportional to differences in colors perceived by the human eye. Therefore, even if absolute colors may be difficult to predict without experimental reference, it remains possible to quantify the impact of vibronic couplings (as well as other chemical effects).

Table 2. Colorimetric CIE Lab Coordinates and Predicted Colors Using Different Modelsa

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METHOD All our calculations have been performed with the Gaussian0918 program, using default thresholds and algorithms except when noted. Following our previous benchmark work performed on AQs,13 we have selected the 6-31++G(d,p) basis set and two functionals, namely, B3LYP19,20 and ωB97X-D,14 to perform our simulations. Indeed, this basis set leads to converged structural and spectroscopic parameters, whereas the chosen functionals yield accurate estimates for transition energies (B3LYP) and vibronic shapes (ωB97X-D). We redirect the reader to ref 13 for more details. The ground-state (excitedstate) geometries were first optimized with DFT (TD-DFT) until the residual mean square forces were smaller than 1 × 10−5 au (tight threshold). The vibrational frequencies were then computed analytically (numerically) for the S0 (S1) state, a C2 point group symmetry being systematically imposed. During all calculation steps, we included bulk solvent effects by using the Polarizable Continuum Model (PCM)21 that correctly models the major solvent effects, as long as no specific solute−solvent interactions are implied. This condition is fulfilled by using the cyclohexane, an apolar aprotic solvent used in the reference experiments.16 Vibrationally resolved spectra within the harmonic approximation were computed using the FCclasses program.9,22,23 The reported spectra were simulated at 298.15 K using a convoluting Gaussian function presenting a full width at halfmaximum (fwhm) of 0.04 eV for both SB35 and SG3. A maximum number of 25 overtones for each mode and 20 combination bands on each pair of modes were included in the calculation. The maximum number of integrals to be computed for each class was set to 106. The transformation of the absorption spectra in colorimetric data was made with a homebrewed program, following the protocol proposed by Beck.24

a

Experimental values have been obtained from the experimental spectra of ref 16. All theoretical values are computed using ωB97X-D as the starting data. “raw” corresponds to the spectra of Figure 2, “1peak” stands for the same results but switching off the vibronic couplings, and “corr.” values have been obtained by shifting the theoretical bands so that the first maximum matches experimental λmax. L, a, and b are the standard coordinates in the CIE colorimetric sphere.

the structure of the bands of Figure 2 has a macroscopic impact. Nevertheless, the colors computed from the raw theoretical results (burgundy for SB35 and purple for SG3) do not match those from experiment. This effect is in fact related to the overestimation of the transition energies by ωB97X-D. By conserving the theoretical topology of the absorption bands but positioning the first maximum on the experimental value, one obtains more realistic values, blue for SB35 and greenish-blue for SG3. For the latter, there is nevertheless a significant discrepancy with the experiment (see also Figure 2). For the record, using the B3LYP vertical values to correct the position of the first ωB97X-D absorption peak would also be successful, while using a broader single-peak Gaussian does not allow one to restore a satisfactory color compared to experiment, for example, it yields a light green color for SB35. In other words, it is not only the global width of the visible band but its structure that may account for the perceived color. Eventually, let us note that using B3LYP vibronic shapes to predict the color systematically yields disappointing results, at least for these two dyes. We have used a PCM-TD-DFT approach to simulate the absorption bands and colors of two large quinodic dyes of industrial interest. It turns out that the range-separated ωB97X-D 470

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Letter

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (D.J.); [email protected] (C.A.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.J. is indebted to the Région des Pays de la Loire for financial support in the framework of a recrutement sur poste stratégique. D.J. thanks the ERC StG program (Grant: Marches-278845) for financial support. The Parisian group thanks Sanofi for financial support. The authors are indebted to the COST program CODECS and its members for support and many helpful discussions, respectively. This research used resources of (1) the GENCI-CINES/IDRIS (Grant c2011085117) and (2) the CCIPL (Centre de Calcul Intensif des Pays de Loire).

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REFERENCES

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