On the Absorption Spectra of Recently Synthesized Carbonyl Dyes

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On the Absorption Spectra of Recently Synthesized Carbonyl Dyes: TD-DFT Insights Denis Jacquemin,*,†,¶ Cyril Peltier,‡ and Ilaria Ciofini*,‡ Laboratoire CEISAM, UMR 6230, 2 Rue de la Houssinie´re, BP 92208, 44322 Nantes Cedex 3, France, and 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 ReceiVed: June 24, 2010; ReVised Manuscript ReceiVed: July 22, 2010

The development of theoretical schemes allowing for efficient reproduction of the features of electronically excited states remains a challenging task. In that framework, time-dependent density functional theory (TDDFT) has emerged as an efficient approach for reproducing and understanding the UV/visible spectra of large solvated molecules. In this paper, we investigate the ground and excited-state properties of two carbonyl dyes presenting very similar structures but possessing absorption peaks differing by both their transition energies and their band shapes. Using a global (PBE0) and a range-separated hybrid (CAM-B3LYP), we obtain consistent conclusions demonstrating, for this couple of dyes, the necessity to go beyond the vertical TD-DFT approximation even for a qualitative interpretation. These simulations are striking examples of the interest of using more refined theoretical schemes for correctly evaluating the transition energies of specific carbonyl dyes. Introduction An accurate simulation of the properties of electronically excited states remains a major challenge for theoretical chemists. In that framework, wavefunction based approaches that simultaneously account for the static and the dynamic correlations, e.g. CAS-PT2 or MR-CI, are certainly approaches of choice but are limited to relatively small systems due to their computational cost. As an illustration, Thiel’s group has recently calculated state-of-the-art CAS-PT2 vertical transitions energies for a set of molecules,1 and the largest compounds treated were naphthalene and the DNA bases. An alternative scheme to these CPU-intensive methods, namely, time-dependent density functional theory (TD-DFT),2,3 appears quite successful for most low-lying states of solvated organic and inorganic derivatives,4-7 but certainly suffers a series of limitations. In practice, a portion of the problems of TD-DFT when used in conjunction with “standard” functionals, is related to states corresponding to an electronic transfer from a donor group to an acceptor moiety8 or to twisted intramolecular charge-transfer situations,9 and might be resolved by using range-separated hybrids, such as CAM-B3LYP.10 These range-separated functionals rely on a growing fraction of exact exchange when the interelectronic distance increases, subsequently providing a more physically sound model for long-range phenomena. Another notable improvement, that has recently received increased attention, is the possibility to compute vibrationally resolved absorption and emission spectra for both gas-phase and solvated compounds,11,12 thanks to the developments of analytic gradients of excited states using TD-DFT. Indeed, these gradients allow to numerically calculate excited-state vibrational patterns, and subsequently vibronic couplings, although the associated computational cost * To whom correspondence should be addressed. E-mail: [email protected] (D. J.); [email protected] (I. C.). † CEISAM. ‡ ENSCP. ¶ Previous address: 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.

SCHEME 1: Representation of the Two Investigated Dyes

of such a procedure is large, especially when no point group symmetry could be used. Such scheme delivers not only the position of the absorption band, but also its shape and paves thewaytowardmoreaccuratetheory/experimentconfrontations.11,12 Recently, we have shown that this procedure was successful for naphthazarin, an important naphthoquinone derivative,13 although none of the tested functionals could provide very accurate transition energies and band shapes simultaneously. In this contribution, we investigate two relatively large (43 atoms) carbonyl dyes that have been recently synthesized by the group of P. J. Coelho through the reaction of 1-hydroxy2-acetonaphthone with 2-fluorobenzophenone.14,15 These two dyes (represented in Scheme 1) are isomers differing only by the s-trans or s-cis character of the double bond connecting the two sides of the molecules. However, their absorption spectra is significantly different with a broad absorption band presenting two maxima at 538 and 577 nm (and two shoulders at 504 and 630 nm) for I14 and a first structureless absorption peak at 394 nm for II.15 These differences are reflected in their color: I is blue and II appears yellow in dichloromethane. Method All our calculations have been performed with Gaussian09,16 using the PBE017 and the CAM-B3LYP10 hybrid functionals. These two functionals have been shown to efficiently reproduce the absorption spectra of medium-sized organic dyes.5,7,18 As

10.1021/jp105824x  2010 American Chemical Society Published on Web 08/12/2010

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Jacquemin et al. TABLE 1: Computed Vertical Absorption for the Singlet States of I and II dye I PBE0 state λ (nm) S1 S2 S3 S4 S5 S6 S7 S8

Figure 1. CAM-B3LYP HOMO (bottom) and LUMO (top) of the ground-state of I (left) and II (right). The orientation of the molecules is the same as in Scheme 1. A contour threshold of 0.04 au has been used.

atomic basis set, we have chosen 6-31++G(d,p) as the inclusion of both polarization and diffuse orbitals is often necessary to model the excited-state properties. The ground-state (excitedstates) geometries have first been optimized with DFT (TDDFT) until the residual mean square forces are smaller than 1 × 10-5 au. For all ground-state structures, we have analytically computed the Hessian to obtain the vibrational frequencies and intensities. The same procedure was performed numerically for the first excited state of I in order to evaluate the vibronic couplings (see below). This step required extreme resources at this level of theory (∼1 year of CPU-time for each functional as the system possess 43 atoms, 609 basis functions, and no symmetry), so it was restricted to the case for which the experimental band presents an obvious structure. The vertical TD-DFT values, obtained on the ground-state geometries, have been obtained in a third step using the same functionals and basis set as in the two first phases. At all stages, we have included bulk solvent effects by using the integral equation formalism of the polarizable continuum model (PCM)19,20 and defaults parameters of Gaussian09. Dichloromethane has been chosen as the medium, consistently with experiment. The values reported in Figure 3 have been obtained through a fully relaxed scan of the S0 state using a step size of 10°. This scan was followed by vertical TD-DFT calculations on each optimized geometry, that is, we did not performed a fully relaxed S1 scan as a qualitative picture was sufficient for our purposes. Vibrationally resolved spectra within the harmonic approximation were computed using the FCclasses program of F. Santoro (see http://village.ipcf.cnr.it).12,21,22 The reported spectra have been simulated at 300 K and convoluted using Gaussian functions with a full width at half-maximum (fwhm) of 0.08 eV. A maximal number of 24 overtones for each mode and 19 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. Results and Discussion For the two compounds, the optimizations of the groundstate geometries lead to nearly coplanar aromatic cycles (see Figure 1). Indeed, the CAM-B3LYP (PBE0) dihedral angles,

522 403 354 337 325 318 307 301

dye II

CAM-B3LYP

PBE0

CAM-B3LYP

f

λ (nm)

f

λ (nm)

f

λ (nm)

f

0.65 0.00 0.36 0.02 0.14 0.02 0.03 0.06

460 351 312 294 284 276 263 260

0.85 0.00 0.19 0.04 0.19 0.21 0.14 0.18

501 417 350 340 318 313 296 296

0.60 0.00 0.25 0.29 0.12 0.08 0.20 0.02

439 364 309 293 281 276 255 254

0.84 0.00 0.08 0.39 0.24 0.11 0.17 0.17

measured between these two sides of the dyes, are 180.0 (179.8) and 0.7 (1.5)° for I and II, respectively. For these dyes, the respective DFT estimates for the central bond length are 1.395 (1.403) and 1.396 (1.404) Å, at the CAM-B3LYP (PBE0) level. In other words, both the range-separated and global hybrids provide similar predictions with a relatively flat core and an inter-ring bond distance typical of an aromatic system. I is more stable than II by ∼4.2 kcal. mol-1 in terms of Gibbs free energies since the stabilizing inter-ring O · · · H interactions of I are replaced by less favorable O · · · O interactions in II.15 However, this effect remains too limited to induce a significant deviation from planarity. The vertical absorption data have been computed using a standard TD-DFT approach and are collected in Table 1. For the first dye, TD-DFT foresees a strong absorption close to 500 nm. The vertical wavelength predicted by PBE0 (522 nm) is in better agreement with the experimental λmax (538 nm) than the CAM-B3LYP estimates (460 nm), which is the expected behavior for π f π* transitions.18 The next dipole-allowed absorption is due to the S3 state, located at 354 nm by PBE0, which is again in reasonable agreement with the experimental spectra.14 In short, although the vibronic shape of the visible band is, of course, not reproduced (see below), the vertical TD-DFT scheme is successful for I. For II, both functionals yield a strong absorption above 400 nm. If one could argue that the 439 nm λmax of CAM-B3LYP could potentially fit the experimental value (394 nm, that is a 0.3 eV error), such assignment would be problematic. Indeed, the evolution with respect to I would be completely unrealistic, as both functionals provide -21 nm hypsochromic shift and an almost unmodified transition probability, in sharp contrast with experimental findings. A possible explanation of this discrepancy between the TDDFT description of two very similar structures could be that the excited-state nature of S1 differs for the two dyes, so that PBE0 would be more adequate for I and CAM-B3LYP for II. For this reason, we have analyzed the frontier orbitals in Figure 1. This comparison is meaningful as TD-DFT indicates that the S1 excited states mainly correspond to a promotion from the HOMO to the LUMO in all cases (functionals and structures). As can be seen, photon absorption of S1 corresponds to a partial electron transfer from one side of the molecule to the other, with a significant (trifling) density on the central double bond for the HOMO (LUMO). More importantly, the orbitals are completely similar for I and II and cannot account for different descriptions at the TD-DFT level. In addition, let us underline that there is a nonzero overlap between the occupied and virtual orbitals, so that a global hybrid such as PBE0 are expected to be adequate according to Tozer’s criterion.5 Following the previous inconclusive attempts, we have optimized the excited-state geometries of the Sn states of the two dyes to gain more insights. The results are graphically

Absorption Spectra of Synthesized Carbonyl Dyes

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Figure 3. Scan around the central dihedral angle (see Method section). The blue (green) lines correspond to the S0 (S1) state, whereas the continuous (broken) lines indicate the CAM-B3LYP (PBE0) values. In all cases, the energy of the ground-state of I is selected as reference.

Figure 2. CAM-B3LYP optimized geometries obtained for I (left) and II (right). The relative total energies (in eV) selecting the S0 state of I as reference are also given.

summarized in Figure 2 for CAM-B3LYP. PBE0 provides completely similar patterns, and this agreement between two significantly different hybrid functionals supports the validity of TD-DFT predictions for these dyes.9 For I, the first three excited states are nearly planar, and this is consistent with the relative efficiency of the vertical approach. The CAM-B3LYP (PBE0) 0-0 total energies obtained for S1, S2, and S3 correspond to 539 (620), 377 (445), and 332 (379) nm, respectively (see Table 2). As these values have been obtained with an equilibrium, rather than a nonequilibrium solvent model,19 we have to correct them for this effect,23 and the 0-0 nonequilibium estimates are 510 (588), 377 (445), and 328 (375) nm, for the same set of transitions as above. Of course, one finds the expected bathochromic shift when comparing the vertical and 0-0 values, but no qualitatively new conclusion emerges. The first experimental absorption maxima at 577 nm now stands in between the PBE0 and CAM-B3LYP estimates, but is closer to the former. In the S1 state of I, the bridging bond length

attains 1.455 (1.466) Å at the CAM-B3LYP (PBE0) level: this large extension compared to the ground-state is consistent with the orbital topologies of Figure 1. For II, after optimization, the first excited state becomes nearly perpendicular (dihedral angles of -87 and -88° with CAM-B3LYP and PBE0, respectively). As a consequence, the transition energy of the S1 state significantly decreases and the associated oscillator strength tends to zero. In other words, the vertical approximation becomes ineffective for this specific case. This is further illustrated in Figure 3 where a scan around the central dihedral angles is presented.24 It is clear that on the S1 surface, the planar II corresponds to a transition state between the two possible perpendicular structures. The optimization of the S2 state of II yields a nearly planar geometry, but with a null transition probability as in Table 1. In fact, the first state providing a large oscillator strength is S3, which is only slightly twisted (∼10°). For this state, the 0-0 energy corrected for nonequilibrium effects corresponds to 325 nm (CAM-B3LYP) and 372 nm (PBE0) in quite good agreement with the first experimental transition at 394 nm, at least with PBE0. Eventually, we have computed the vibronic spectrum corresponding to the S0 f S1 absorption of I. The results of the two functionals are compared in Figure 4. As can be seen, they provide consistent pictures with two maxima and a shoulder at smaller wavelength. As already noted above, the smaller transition energies of Figure 4 with respect to Table 1 partly illustrates the approximation related to the (much faster) vertical approach. Compared to the experimental spectra, the present models are unable to reproduce the shoulder appearing above 600 nm, but nevertheless deliver a valuable approximation of

TABLE 2: Transition Wavelength (nm) Computed with Different Models for the First Three Excited-States of Both Dyesa dye I PBE0

dye II CAM-B3LYP

PBE0

CAM-B3LYP

state

vertical

0-0

vertical

0-0

vertical

0-0

vertical

0-0

S1 S2 S3

522 (548) 403 (404) 354 (358)

588 (620) 445 (445) 375 (379)

460 (485) 351 (351) 312 (316)

510 (539) 377 (377) 328 (332)

501 (523) 417 (417) 350 (354)

947 (878) 466 (466) 372 (376)

439 (459) 364 (364) 309 (312)

596 (632) 396 (396) 325 (329)

a

The values between brackets have been obtained within the equilibrium (rather than nonequilibrium) PCM model. See text for more details.

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Jacquemin et al. discussions and a careful reading of the manuscript, as well as the Belgian National Fund for Scientific Research for his research associate position. This research used resources of the Interuniversity Scientific Computing Facility located at the University of Namur, Belgium, which is supported by the F.R.S.-FNRS under convention No. 2.4617.07. The collaboration between the Belgian and French group is supported by the Wallonie-Bruxelles International, the Fonds de la Recherche Scientifique, the Ministere Franc¸ais des Affaires e´trangeres et europe´ennes, the Ministere de l’Enseignement supe´rieur et de la Recherche in the framework of Hubert Curien Partnership. I. C. and C. P. thank the French National Agency for Research (ANR) program blanc (nexus project, No. BLAN07-1_196405). References and Notes

Figure 4. Vibrationally resolved spectra for the first absorption band of I. The position of the two maxima (in nm) are indicated for the PBE0 (blue) and the CAM-B3LYP (red) curves. Equilibium PCM solutions have been used.

the band shape. Indeed, both functionals give a difference between the two maxima of ca. 0.12 eV instead of 0.15 eV experimentally. Once the values are corrected for nonequilibrium solvent effects, the position of the CAM-B3LYP (PBE0) peaks are 508 and 482 (582 and 551) nm. For the global hybrid, the agreement with the experimental positions is really astonishing, with an absolute average error of 0.04 eV only. CAM-B3LYP yields a large error (0.28 eV) but is still in the usual range of TD-DFT.5,7,18 Similarly to naphthazarin,13 relative intensities are more accurate with CAM-B3LYP, with the short-wavelength peak being the strongest, exactly as in the experiment.14 To account for the band shape of Figure 4, the most important vibrational mode corresponds to simultaneous variations of the relative orientations of the three entities of I (the two nearly planar fused rings and the side phenyl group). For the excited state, this mode appears at 60 cm-1 with both functionals. Conclusions With the help of a TD-DFT model systematically accounting for bulk solvent effects, we have computed the spectra of two carbonyl dyes recently synthesized by Coelho and co-workers. For I, the ground and first excited states present similar structural parameters, and the vertical TD-DFT approximation is able to reasonably reproduce the λmax. In addition, for the same dye, a full vibronic study provides a band shape consistent with the experimental measurements, especially when the CAM-B3LYP functional is used. For II, the molecular structures goes from a nearly planar ground state to an almost perpendicular excited state, making the vertical approach qualitatively inadequate. Indeed, in the vertical scheme, the first electronic transition artificially presents a large oscillator strength. The present contribution also illustrates that, although a global hybrid containing 25% of exact exchange (PBE0) is optimal within the (fast) vertical approach, functionals including a larger share of exact exchange (e.g., CAM-B3LYP) might be more satisfactory to mimic the (physically sound) vibrationally resolved spectra. Though the extend of the validity of this statement remains to be ascertained, this work clearly supports recent TD-DFT benchmarks performed on large dyes with both approaches.7,18 Acknowledgment. The authors are deeply indebted to Prof. P. J. Coelho (Portugal) for providing the absorption spectra of II prior to publication. D. J. thanks Dr. Y. Caudano for fruitful

(1) Schreiber, M.; Silva-Junior, M. R.; Sauer, S. P. A.; Thiel, W. J. Chem. Phys. 2008, 128, 134110. (2) 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. (3) Dreuw, A.; Head-Gordon, M. Chem. ReV. 2005, 105, 4009–4037. (4) Barone, V.; Polimeno, A. Chem. Soc. ReV. 2007, 36, 1724–1731. (5) Peach, M. J. G.; Benfield, P.; Helgaker, T.; Tozer, D. J. J. Chem. Phys. 2008, 128, 044118. (6) Jacquemin, D.; Perpe´te, E. A.; Ciofini, I.; Adamo, C. Acc. Chem. Res. 2009, 42, 326–334. (7) Goerigk, L.; Grimme, S. J. Chem. Phys. 2010, 132, 184103. (8) Dreuw, A.; Head-Gordon, M. J. Am. Chem. Soc. 2004, 126, 4007– 4016. (9) Wiggins, P.; Gareth Williams, J. A.; Tozer, D. J. J. Chem. Phys. 2009, 131, 091101. (10) Yanai, T.; Tew, D. P.; Handy, N. C. Chem. Phys. Lett. 2004, 393, 51–56. (11) Dierksen, M.; Grimme, S. J. Phys. Chem. A 2004, 108, 10225– 10237. (12) Santoro, F.; Improta, R.; Lami, A.; Bloino, J.; Barone, V. J. Chem. Phys. 2007, 126, 084509. (13) Jacquemin, D.; Peltier, C.; Ciofini, I. Chem. Phys. Lett. 2010, 493, 67–71. (14) Coelho, P. J.; Carvalho, L. M. Dyes Pigm. 2008, 78, 173–176. (15) Coelho, P. J.; Fernandes, I. C.; Carvalho, L. M. J. Heterocyclic Chem. 2010, DOI: 10.1002/jhet.434. (16) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (17) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158–6170. (18) Jacquemin, D.; Wathelet, V.; Perpe´te, E. A.; Adamo, C. J. Chem. Theory Comput. 2009, 5, 2420–2435. (19) Cossi, M.; Barone, V. J. Chem. Phys. 2001, 115, 4708–4717. (20) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. ReV. 2005, 105, 2999– 3094. (21) Santoro, F.; Improta, R.; Lami, A.; Bloino, J.; Barone, V. J. Chem. Phys. 2007, 126, 184102. (22) Santoro, F.; Lami, A.; Improta, R.; Bloino, J.; Barone, V. J. Chem. Phys. 2008, 128, 224311. (23) We have performed equilibrium vertical calculations and compared the results to the nonequilibrium one (see Table 2). The CAM-B3LYP (PBE0) shifts for S1 and S3 amount to +0.13 (+0.11) and +0.04 (+0.03) eV, respectively. The effect is completely negligible for the S2 state. These variations have been applied to the equilibrium 0-0 values to correct them. (24) We are well aware that the discontinuity computed at the GS (S0) for a dihedral angle of ( 90° is related to the multi-determinantal character of the TS corresponding to the breaking of a double bond, which cannot be reproduced by mono-determinantal DFT-based approaches.

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