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Solvent Effects on Cyanine Derivatives: A PCM Investigation Denis Jacquemin, Siwar Chibani, Boris Le Guennic, and Benedetta Mennucci J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp504591t • Publication Date (Web): 24 Jun 2014 Downloaded from http://pubs.acs.org on June 29, 2014

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The Journal of Physical Chemistry

Solvent Effects on Cyanine Derivatives: a PCM Investigation Denis Jacquemin,∗,†,‡ Siwar Chibani,† Boris Le Guennic,¶ and Benedetta Mennucci∗,§ Laboratoire CEISAM - UMR CNRS 6230, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France, Institut Universitaire de France, 103, bd Saint-Michel, F-75005 Paris Cedex 05, France., Institut des Sciences Chimiques de Rennes, CNRS-Université de Rennes 1, 1 Av. du General Leclerc, 35042 Rennes Cedex, France, and Department of Chemistry, University of Pisa, Via Risorgimento 35, 56126 Pisa, Italy. E-mail: [email protected]; [email protected]

∗

To whom correspondence should be addressed CEISAM, Nantes ‡ IUF, Paris ¶ ISCR, Rennes § DC, Pisa †

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Abstract In this work, we present Time-Dependent Density Functional Theory calculations of the excited-state geometries and electronic properties of both model cyanines and BODIPY derivatives which are particularly challenging dyes for theoretical chemistry. In particular, we focus on environmental effects, using a panel of approaches derived from the Polarizable Continuum Model, including full corrected linear-response values determined through a very recently developed approach. It turns out that in idealized quasi-linear cyanines, all approaches provide very similar excited-state geometries though linear-response and corrected linear-reponse models yield very different transition energies. For the fluoroborate derivatives, LR apparently overestimates the planarity of the excited-state geometries, and cLR optimizations yield slightly smaller fluorescence energies than LR, making these values closer to experimental references. The computed corrections are however too small to explain (taken alone) the significant theory/experiment discrepancies.

Keywords: Time-Dependent Density Functional Theory, Polarizable Continuum Model, Corrected Linear-Response, Emission Spectra, Cyanine Dyes, BODIPY


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Introduction The prediction of excited-state properties remains an important challenge for theoretical chemists, especially when quantitative, or at least, semi-quantitative agreement, between experiment and theory is looked for. If one considers the two widely available experimental data, namely absorption and fluorescence spectra, one could state that physically well-grounded comparisons between experiment and theory can be made by determining, on the one hand, vibrationally resolved band shapes, 1–3 and, on the other hand, 0-0 energies. 4–7 The latter energies correspond to the crossing point between absorption and emission curves. However, the simulations of these two properties imply the optimizations of both the ground-state (GS) and excited-state (ES) geometries, as well as the more complicated determination of the vibrational frequencies of the electronic excited state(s). For the ES, this is a very demanding task which drastically limits the panel of theoretical methods applicable for non-trivial systems. Several approaches have been developed to go beyond the vertical approximation (frozen geometry) by providing analytic excited-state gradients (and sometimes Hessian) and this includes Configuration Interaction Singles (CIS), Complete Active Space Self-Consistent Field (CAS-SCF), second-order approximated Coupled-Cluster (CC2) and Time-Dependent Density Functional Theory (TD-DFT). TD-DFT 8,9 certainly occupies a favorable spot in this short list, due to its computational efficiency. As other methods, TD-DFT can be coupled with a variety of environmental models, e.g., the Polarizable Continuum Model (PCM), 10 to mimic solvated absorption and emission spectra, and TD-DFT has consequently been widely used to design new organic and inorganic dyes. 11 However, TD-DFT is far from flawless and while the emergence of range-separated hybrids has provided a pragmatic answer to the well-known TD-DFT underestimation of the transition energies of charge-transfer states, 12–15 another class of excited-states, those presenting a cyanine nature, remains very challenging for TD-DFT that tends to largely overshoot the transition energies. 15–19 During the recent years, there have been significant efforts to extend the TD-DFT’s applicability area to cyanines typically through the design of more 3 ACS Paragon Plus Environment


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advanced exchange-correlation functionals, 20–22 so to reach an accuracy comparable to the one obtained with highly-correlated wavefunction approaches. 18,19 This has been motivated not only by the academic interest of rationalizing a difficulty of a very popular theory, but also by the industrial importance of these dyes. Indeed BODIPY and other fluoroborates that can be viewed as cis-constrained cyanines, are probably the most effective and versatile fluorophores developed to date with applications in countless fields, e.g., ion sensing, bioimaging and emitting diodes. 23,24 In a series of recent works, devoted to aza-BODIPY, 25 BODIPY (boron-dipyrromethene), 26 boranil 27 and dioxaborine 28 fluoroborate derivatives (see Scheme 1), our groups have shown that very accurate evolutions of the 0-0 energies with chemical substitution can be obtained for all series of compounds. In addition, two main methodological conclusions have emerged: i) despite the inclusion of vibrational effects, the transition energies are systematically overestimated with PCM-TD-DFT, a fact directly related to the cyanine nature of these compounds; ii) the selected solvent model for the excited-state calculations has a dramatic impact on the obtained results. This latter point, that motivates the present study, should be explained in more details. Indeed, there exist several PCM approaches allowing to account for the modification of the solvent polarization induced by the solute electronic transition. 29–33 With the most simple scheme, the so-called linear response (LR) model, 29,30 only the transition densities are used to determine the changes of the PCM charges located on the surface of the cavity whereas in the more complex corrected linear response (cLR), 31 state specific (SS) 32 and vertical excitation models (VEM) 33 the actual density of the excited-state is accounted for, improving the physical description of the processes. For the above-mentioned fluoroborates, 25–28,34 the absorption, emission and 0-0 energies obtained with these variants of the PCM model significantly differ (variations of ca. 0.3 eV between LR and cLR/SS are not uncommon). 25–28 Additional puzzling facts were found: i) though the corrections beyond LR are large, they tend to deteriorate the absolute match with experiment (that is cLR or SS yield larger mean deviations than LR); 25–28 ii) going beyond LR


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might even lead to incorrect chemical rankings (e.g., smaller linear determination coefficient, R2 , with SS than with LR) in several cases. 27,28 However, it should be mentioned that these previous works used cLR or SS to correct the total excited-state energies, the corresponding geometries being optimized at the LR level, the only implemented approach in commercial quantum chemistry packages. This blend cannot be considered as satisfying as it is clearly inconsistent for this class of molecules: if LR is not sufficient for total energies, why should it be accurate for geometries ? Very recently, we have performed the first cLR excited-state geometry optimizations for model compounds, 35 allowing to obtain “full” cLR results. We showed that the LR method often exaggerates the solvent-induced geometrical changes. The present contribution therefore aims to provide a consistent approach for cyanine derivatives, including both model streptocyanines and realistic cores representative of aza-BODIPY, BODIPY, boranil and dioxaborine derivatives (see Scheme 1), as these dyes are known to yield very large LR–cLR transition energy differences. N RM6

H 2N

4

5

CN3

1 2

H 2N

B

F

1 6 2

N

3

CN5 RM8

BF1

NH 2

H 2N

3 4

7

H 2N

CN9

H 2N

BF2

3

1

5

F

NH 2

H 2N

CN7

N

N

NH 2

2

B

F

N F

O NH 2

CN11 H N 2

N

BF3

F

NH 2

CN13 H N 2

NH 2

BF4

O F

B

O

B

F

O F

Scheme 1: Representation of the models of the retinal (RMx), streptocyanines (CNx) and fluoroborates (BFx) derivatives investigated herein.



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Methods All calculations have been performed with the latest version of Gaussian09 program 36 that was modified to allow cLR optimization of the excited-state geometries. 35 We have applied an improved energy convergence threshold (at least 10−10 a.u.), a tight geometry optimization criterion (10−5 a.u. on the residual root mean square force) 37 and a high-level DFT integration grid (so-called ultrafine grid) in order to ensure the numerical stability of the presented data. Default parameters have been used for the PCM cavity and we have considered dichloromethane (DCM) as medium, as this solvent is commonly used for both cyanine and BODIPY derivatives. TD-DFT optimizations in gas phase have been performed with the analytical gradients implemented in Gaussian09, and the same holds for the LR-PCM excited-state calculations. For the BFx compounds, it was checked that the obtained structures correspond to true minima of the potential energy surface by numerically differentiating the LR-PCM-TD-DFT forces. cLR optimizations of the excited-state structures have been performed following Ref. 35. These geometry calculations were performed with the M06-2X/6-31G(d) approach. Indeed, M06-2X has been shown to be an adequate exchangecorrelation functional for investigating excited-state energies and structures of many classes of molecules, 3,6,15,38–41 and this general statement holds for cyanine derivatives as well. 21,26,27 The choice of 6-31G(d) is justified by previous works on similar derivatives that have shown that this atomic basis set is sufficient for geometries of both the ground and excited states. 25,42 This selection of functional and basis sets is further assessed in the following Section. The transition energies between the two states have been computed with the same functional but with a more extended atomic basis set, namely 6-311+G(2d,p). In this work, the geometry optimizations have been performed in the equilibrium PCM limit whereas the reported emission wavelengths are computed in the non-equilibrium PCM limit, except for the LR model for which non-equilibrium emission values are ill-defined.


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Results Methodological Tests As we are interested in phenomena related to ES geometries, it is important to assess the accuracy of the M06-2X approach in the framework of cyanine-like compounds. To the best of our knowledge, experimental ES bond lengths and valence angles are not available for compounds shown in Scheme 1, and we have decided to use the CAS-PT2/cc-pVDZ geometries obtained by Valsson and Filippi for two models of the retinal chromophores, RM6 and RM8, 43 in order to appraise the quality of M06-2X geometries. The performances of TD-DFT for these molecules was already assessed, 44 but this previous benchmark did not include the M06-2X exchange-correlation functional. The results are collected in Table 1. The mean absolute deviations for the bond lengths (valence angles) are 0.013 ˚ A (0.5 o ) and 0.012 ˚ A (0.6 o ) for RM6 and RM8, respectively. This confirms that M06-2X is a method of choice for our purposes. We redirect the interest readers to previous benchmarks for a more general discussion of the accuracy of TD-DFT ES geometries. 44–47 Table 1: Comparison between gas phase TD-M06-2X/cc-pVDZ and CASPT2/cc-pVDZ ES geometries for RM6 and RM8. Cs point group is systematically enforced. Bond lengths (valence angles) are in ˚ A (degrees). The atomic numbering is shown in Scheme 1. CAS-PT2 values are taken from Ref. 43. Parameter NC1 C1 C2 C2 C3 C3 C4 C4 C5 C5 C6 C6 C7 NC1 C2 C1 C2 C3 C2 C3 C4 C3 C4 C5 C4 C5 C6 C5 C6 C7

RM6 M06-2X CAS-PT2 1.341 1.367 1.448 1.447 1.408 1.432 1.429 1.430 1.384 1.396

116.2 131.1 127.4 121.9

115.9 130.9 126.8 121.1

RM8 M06-2X CAS-PT2 1.330 1.352 1.409 1.422 1.405 1.419 1.445 1.455 1.398 1.408 1.429 1.432 1.369 1.382 122.8 121.9 126.2 126.8 114.9 114.4 131.5 131.4 129.1 128.3 121.0 120.5



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A further aspect to be evaluated is atomic basis set effects. Indeed, in this work, we go for a 6-311+G(2d,p)//6-31G(d), implying that the structures are optimized with a rather compact atomic basis set. For this reason, we have optimized the geometry of a medium-size system, CN7, with 6-311G(d,p) and 6-311+G(2d,p) in gas-phase but also with the LR and cLR-PCM models. Bond lengths are collected in Table 2 and the variations induced by changing the basis set are, at most, 0.003 ˚ A considering a given environmental model. The 6-311+G(2d,p) emission energies computed on 6-31G(d), 6-311G(d,p) and 6-311++G(d,p) structures are 3.860 eV, 3.868 eV and 3.868 eV, respectively. 48 In other words, the deviations are smaller than 0.010 eV. This demonstrates that 6-31G(d) provides sufficiently accurate geometries. ˚) computed for CN7 using different environmental Table 2: Bond lengths (A approaches and atomic basis sets. Parameter NC1 C1 C2 C2 C3

Gas 1.335 1.408 1.411

6-31G(d) LR cLR 1.334 1.333 1.408 1.408 1.409 1.411

6-311G(d,p) Gas LR cLR 1.334 1.333 1.331 1.406 1.407 1.407 1.409 1.407 1.409

6-311++G(d,p) Gas LR cLR 1.334 1.334 1.333 1.407 1.407 1.408 1.408 1.406 1.408

Quasi-Linear Cyanines We have first considered the prototypical cyanine derivatives, CNx, that have been extensively investigated with a wide panel of theoretical methods, 16,18–22,42 though the majority of these works have been focussed on gas phase absorption energies. We have imposed the C2v point group during all calculations. We are well aware that these cyanine dyes present a twisted excited-state geometry, 18 and that C2v structures constitute true minima of the potential energy surface only for the ground-state, but this specificity of these compounds is not relevant as most industrially relevant cyanine dyes are constrained and cannot undergo significant twist in the excited-state (see next Section). For the shortest and longest chain considered, the cLR (LR) vertical absorption energies are 7.482 (7.330) eV and 2.602 (2.297) eV, respectively. This confirms that the cLR corrections are non negligible for this class of 8 ACS Paragon Plus Environment

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molecules and that they tend to increase the transition energies computed with LR. The main results obtained for emission are collected in Table 3. If one considers a given geometry and investigates the evolution of ωfluo as a function of the environmental model selected, one notices a strong positive solvatochromism, that is a large decrease of the emission energies compared to gas phase when LR is used. For the longest chain investigated, the LR correction exceeds 0.5 eV, which is a very large change for quite compact molecules. However, much smaller solvatochromic effects are predicted by cLR. Indeed, the gas and cLR values are extremely close for each geometries, which hints that the LR solvatochromic effects are too large. We underline that this LR–cLR discrepancy is not related to (non)equilibrium effects, as the cLR equilibrium values are very close to their non-equilibrium counterparts (typical variations smaller than 0.01 eV). Table 3: Relative cLR energies (∆E, in eV) and cLR fluorescence transition energies (ωfluo , in eV) obtained for the CNx dyes considering three different optimal C2v geometries. Calculations at the cLR-PCM(DCM)-M062X/6-311+G(2d,p)//PCM(DCM)-M06-2X/6-31G(d) level considering equilibrium (∆E, LR ωfluo ) or non-equilibrium (cLR ωfluo ) limits of the PCM model. For ∆E, the optimized cLR structure is used as reference.

Compound CN3 CN5 CN7 CN9 CN11 CN13

∆E +0.001 +0.000 +0.000 +0.001 +0.002 +0.003

Gas geometry ωfluo Gas LR 6.082 5.799 4.734 4.267 3.855 3.300 3.262 2.668 2.843 2.232 2.528 1.916

cLR 6.047 4.720 3.853 3.265 2.843 2.525

∆E +0.002 +0.001 +0.001 +0.001 +0.001 +0.001

LR geometry ωfluo Gas LR 6.147 5.861 4.756 4.287 3.860 3.305 3.256 2.660 2.837 2.226 2.519 1.906

cLR 6.112 4.742 3.858 3.258 2.839 2.519

cLR geometry ωfluo Gas LR cLR 6.098 5.815 6.063 4.746 4.297 4.732 3.862 3.308 3.860 3.264 2.670 3.267 2.845 2.236 2.847 2.526 1.915 2.525

If one now turns towards the geometrical effects, we note that the LR–cLR structural variations are very small and this is noticeable not only from the total energy differences (∆E), but also by the cLR ωfluo computed on different structures. For the latter, the variations are of the order of 0.05 eV for CN3 and tend to decrease with the length of the conjugated path to attain ca. 0.01 eV for the longest chain considered. The differences between the solvated and gas-phase geometries are also very small, but the ωfluo computed on 9 ACS Paragon Plus Environment


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the cLR excited-state structure is not systematically bracketed by its LR and gas counterparts, contrary to what was found in several small chromophores. 35 In Figure 1 we present the geometrical parameters obtained for the longest chain, and, although no general cLR–LR trend can be found (e.g., no systematic increase or decrease) it is clear that the variations of bond lengths and valence angles when varying the environmental model are mostly trifling. 36 1.3 30 3 1. 30 1.3

04 1.4 99 3 . 1 01 1.4

1.3 1.3 83 1.3 89 88

01 1.4 99 3 . 1 01 1.4

1.3 1.3 93 1.3 97 95

123.8 124.1 123.7

1.3 1.3 98 1.3 99 99

121.5 121.4 121.3

123.4 123.6 123.3 123.5 123.4 123.6

124.2 124.1 124.3

125.1 124.9 124.9

Figure 1: Excited-state geometrical parameters obtained for CN13. Left: bond lengths in ˚ A, right: valence angles (italics) in degrees. The black, blue and red values correspond to gas, LR and cLR results.

In short, the large LR–cLR differences noted for cyanines can be attributed to a pure electronic effect, LR yielding accurate geometries, similar to the one obtained through gas phase of cLR optimizations.

Fluoroborates Let us now turn towards the more realistic fluoroborate compounds. The TD-DFT optimizations in gas phase reveal that BF1, BF2 and BF4 belong to the Cs point group, the plane of symmetry including the central BF2 unit, whereas, BF3 is a C1 molecule. In Figure 2, we provide views of the ES geometries of BF1. Clearly, both gas and cLR optimal structures are slightly bent with fluorine atoms located asymmetrically with respect to the π-conjugated skeleton, whereas the LR structure is a pseudo-C2v molecule with fluorine atoms located almost perfectly symmetrically. In other words, the LR model yields larger structural variations with respect to gas phase than its cLR counterpart. The effect is similar for BF2 (see graphical abstract), but in that case LR still yields a slightly bent structure. For BF3, the three geometries are qualitatively similar. The same holds for BF4 for which all approaches 10 ACS Paragon Plus Environment

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foresee a nearly coplanar π-conjugated skeleton with a strongly asymmetric BF2 group. The energetic data are collected in Table 4, and the difference of total cLR energies are almost unaffected by the selected geometry (variations of ca. 0.01 eV), but for the gas-phase structure of BF4 that yields a +0.023 eV difference. For the two first dyes, the emission energies computed on cLR and gas phase geometries are rather close, while using LR structures yields larger fluorescence energies. This last outcome also holds for BF3 for which the computed ωfluo on the cLR structure is bracketed by its gas and LR counterparts. On the contrary, for BF4 gas and LR structures are similar and cLR provides larger emission energies. If one compares the cLR ωfluo computed on LR and cLR geometries, the cLR structural effects are -0.063 eV, -0.031 eV, -0.128 eV and +0.061 for BF1, BF2, BF3 and BF4, respectively. These values are, as expected, smaller than the “energetic” cLR corrections that amounts to +0.379 eV, +0.310 eV, +0.234 eV and +0.216 eV, 49 respectively, but are not completely negligible, especially for the asymmetric BF3. It is also noteworthy that the “geometric” cLR effect differs significantly for the four BFx dyes, though they all belong to the same class of molecules, hinting that the relative values of the transition energies are affected by a cLR optimization, not only the absolute values.

Figure 2: Top and bottom views of the optimal excited-state structures of BF1 obtained in gas phase (left), with LR (center) and cLR (right) schemes.



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Table 4: Relative cLR energies (∆E, in eV) and cLR fluorescence transition energies (ωfluo , in eV) obtained for the BFx dyes. See caption of Table 3 for more details.

Compound BF1 BF2 BF3 BF4

∆E +0.006 +0.007 +0.013 +0.023

Gas geometry ωfluo Gas LR 2.637 2.277 2.894 2.593 3.776 3.536 3.519 3.236

cLR 2.618 2.907 3.747 3.423

∆E +0.013 +0.013 +0.008 +0.002

LR geometry ωfluo Gas LR 2.702 2.313 2.962 2.632 3.985 3.721 3.504 3.199

cLR 2.682 2.942 3.955 3.415

cLR geometry ωfluo Gas LR cLR 2.639 2.278 2.619 2.899 2.597 2.911 3.858 3.610 3.827 3.523 3.224 3.476

BF2 and BF4 have been synthesized and their emission spectra measured in dichloromethane. The emission energies are 512 nm 50 and 396 nm, 51 respectively. We notice that our cLR//cLR vertical emission energies attain 425 nm and 357 nm, respectively, and these values remain strongly underrated compared to experiment. The computed values are quite far from the measurements and we attribute this effect to the cyanine nature of the systems, though difficulties to describe the ES geometries of BFx could also play a role. In fact, we cannot simply judge of the quality of the solvent model based single solvent measurements, as the intrinsic error of the (TD-)DFT part plays a crucial role. Further studies of solvatochromic shifts are therefore needed.

Conclusions and Outlook Using a new computational approach allowing to perform optimization of the excited-state geometries with a corrected Linear-Response environmental model, we have investigated the structures and fluorescence energies of a series of cyanine derivatives. For increasingly long model cyanine chains, we found that the gas, LR and cLR excited-state structures are extremely similar though the solvatochromic effects given by LR and cLR approaches are vastly different for fluorescence (and absorption) energies. For fluoroborates, LR has a tendency to yield excited-state structures that are significantly more planar than their gas phase counterpart whereas cLR geometries are rather twisted consistently with the gas


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phase prediction. This consequently affects the computed emission energies that are larger when one used LR structures (average difference of ca. +0.07 eV difference with respect to the cLR geometries). This cLR geometrical corrections generally present the correct sign to bring the theoretical values closer to their experimental counterpart for the particularly challenging cyanines, but remain too small to account, by themselves, for the difficulty to model cyanines/fluoroborates with TD-DFT. We are currently performing an investigation on a series of dyes allowing comparisons of emission energies measured in several solvents, so to allow a focus on solvatochromic effects rather than absolute transition energies.

Acknowledgement S.C thanks the European Research Council (ERC, Marches - 278845) for her PhD grant. D.J. acknowledges the European Research Council (ERC) and the Région des Pays de la Loire for financial support in the framework of a Starting Grant (Marches - 278845) and a recrutement sur poste stratégique, respectively. B.M. thanks the ERC for financial support in the framework of the Starting Grant (EnLight - 277755). This research used resources of 1) the GENCI-CINES/IDRIS (Grants c2013085117), 2) CCIPL (Centre de Calcul Intensif des Pays de Loire) and 3) a local Troy cluster.

References (1) Dierksen, M.; Grimme, S. The Vibronic Structure of Electronic Absorption Spectra of Large Molecules: A Time-Dependent Density Functional Study on the Influence of Exact HartreeFock Exchange. J. Phys. Chem. A 2004, 108, 10225–10237. (2) Santoro, F.; Improta, R.; Lami, A.; Bloino, J.; Barone, V. Effective Method to Compute Franck-Condon Integrals for Optical Spectra of Large Molecules in Solution. J. Chem. Phys. 2007, 126, 084509.



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(3) Charaf-Eddin, A.; Planchat, A.; Mennucci, B.; Adamo, C.; Jacquemin, D. Choosing a Functional for Computing Absorption and Fluorescence Band Shapes with TD-DFT. J. Chem. Theory Comput. 2013, 9, 2749–2760. (4) Goerigk, L.; Grimme, S. Assessment of TD-DFT Methods and of Various Spin Scaled CISn D and CC2 Versions for the Treatment of Low-Lying Valence Excitations of Large Organic Dyes. J. Chem. Phys. 2010, 132, 184103. (5) Send, R.; K¨ uhn, M.; Furche, F. Assessing Excited State Methods by Adiabatic Excitation Energies. J. Chem. Theory Comput. 2011, 7, 2376–2386. (6) Jacquemin, D.; Planchat, A.; Adamo, C.; Mennucci, B. A TD-DFT Assessment of Functionals for Optical 0-0 Transitions in Solvated Dyes. J. Chem. Theory Comput. 2012, 8, 2359–2372. (7) Winter, N. O. C.; Graf, N. K.; Leutwyler, S.; Hattig, C. Benchmarks for 0–0 Transitions of Aromatic Organic Molecules: DFT/B3LYP, ADC(2), CC2, SOS-CC2 and SCS-CC2 Compared to High-Resolution Gas-Phase Data. Phys. Chem. Chem. Phys. 2013, 15, 6623–6630. (8) Runge, E.; Gross, E. K. U. Density-Functional Theory for Time-Dependent Systems. Phys. Rev. Lett. 1984, 52, 997–1000. (9) Casida, M. E. In Time-Dependent Density-Functional Response Theory for Molecules; Chong, D. P., Ed.; Recent Advances in Density Functional Methods; World Scientific: Singapore, 1995; Vol. 1; pp 155–192. (10) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999–3094. (11) Laurent, A. D.; Adamo, C.; Jacquemin, D. Dye Chemistry with Time-Dependent Density Functional Theory. Phys. Chem. Chem. Phys. 2014, doi: 10.1039/C3CP55336A. (12) Tozer, D. J. Relationship Between Long-Range Charge-Transfer Excitation Energy Error and Integer Discontinuity in Kohn-Sham Theory. J. Chem. Phys. 2003, 119, 12697–12699.


Page 14 of 19

Page 15 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(13) Dreuw, A.; Head-Gordon, M. Failure of Time-Dependent Density Functional Theory for Long-Range Charge-Transfer Excited States: the Zincbacteriochlorin-Bacteriochlorin and Bacteriochlorophyll-Spheroidene Complexes. J. Am. Chem. Soc. 2004, 126, 4007–4016. (14) Peach, M. J. G.; Benfield, P.; Helgaker, T.; Tozer, D. J. Excitation Energies in Density Functional Theory: an Evaluation and a Diagnostic Test. J. Chem. Phys. 2008, 128, 044118. (15) Laurent, A. D.; Jacquemin, D. TD-DFT Benchmarks: A Review. Int. J. Quantum Chem. 2013, 113, 2019–2039. (16) Schreiber, M.; Bub, V.; F¨ ulscher, M. P. The Electronic Spectra of Symmetric Cyanine Dyes: A CASPT2 Study. Phys. Chem. Chem. Phys. 2001, 3, 3906–3912. (17) Fabian, J. TDDFT-Calculations of Vis/NIR Absorbing Compounds. Dyes Pigm. 2010, 84, 36–53. (18) Send, R.; Valsson, O.; Filippi, C. Electronic Excitations of Simple Cyanine Dyes: Reconciling Density Functional and Wave Function Methods. J. Chem. Theory Comput. 2011, 7, 444–455. (19) Boulanger, P.; Jacquemin, D.; Duchemin, I.; Blase, X. Fast and Accurate Electronic Excitations in Cyanines with the Many-Body Bethe–Salpeter Approach. J. Chem. Theory Comput. 2014, 10, 1212–1218. (20) Grimme, S.; Neese, F. Double-Hybrid Density Functional Theory for Excited Electronic States of Molecules. J. Chem. Phys. 2007, 127, 154116. (21) Jacquemin, D.; Zhao, Y.; Valero, R.; Adamo, C.; Ciofini, I.; Truhlar, D. G. Verdict: TimeDependent Density Functional Theory “Not Guilty” of Large Errors for Cyanines. J. Chem. Theory Comput. 2012, 8, 1255–1259. (22) Moore II, B.; Autschbach, J. Longest-Wavelength Electronic Excitations of Linear Cyanines: The Role of Electron Delocalization and of Approximations in Time-Dependent Density Functional Theory. J. Chem. Theory Comput. 2013, 9, 4991–5003.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(23) Loudet, A.; Burgess, K. BODIPY Dyes and Their Derivatives: Syntheses and Spectroscopic Properties. Chem. Rev. 2007, 107, 4891–4932. (24) Ulrich, G.; Ziessel, R.; Harriman, A. The Chemistry of Fluorescent Bodipy Dyes: Versatility Unsurpassed. Angew. Chem. Int. Ed. 2008, 47, 1184–1201. (25) Chibani, S.; Le Guennic, B.; Charaf-Eddin, A.; Maury, O.; Andraud, C.; Jacquemin, D. On the Computation of Adaiabtic Energies in Aza-Boron-Dipyrromethene Dyes. J. Chem. Theory Comput. 2012, 8, 3303–3313. (26) Chibani, S.; Le Guennic, B.; Charaf-Eddin, A.; Laurent, A. D.; Jacquemin, D. Revisiting the Optical Signatures of BODIPY with Ab Initio Tools. Chem. Sci. 2013, 4, 1950–1963. (27) Chibani, S.; Charaf-Eddin, A.; Le Guennic, B.; Jacquemin, D. Boranil and Related NBO Dyes: Insights From Theory. J. Chem. Theory Comput. 2013, 9, 3127–3135. (28) Chibani, S.; Charaf-Eddin, A.; Mennucci, B.; Le Guennic, B.; Jacquemin, D. Optical Signatures of OBO Fluorophores: A Theoretical Analysis. J. Chem. Theory Comput. 2014, 10, 805–815. (29) Cammi, R.; Mennucci, B. The linear Response theory for the Polarizable Continuum Model. J. Chem. Phys. 1999, 110, 9877–9886. (30) Cossi, M.; Barone, V. Time-Dependent Density Functional Theory for Molecules in Liquid Solutions. J. Chem. Phys. 2001, 115, 4708–4717. (31) Caricato, M.; Mennucci, B.; Tomasi, J.; Ingrosso, F.; Cammi, R.; Corni, S.; Scalmani, G. Formation and Relaxation of Excited States in Solution: A New Time Dependent Polarizable Continuum Model Based on Time Dependent Density Functional Theory. J. Chem. Phys. 2006, 124, 124520. (32) Improta, R.; Scalmani, G.; Frisch, M. J.; Barone, V. Toward Effective and Reliable Fluorescence Energies in Solution by a New State Specific Polarizable Continuum Model Time Dependent Density Functional Theory Approach. J. Chem. Phys. 2007, 127, 074504.


Page 16 of 19

Page 17 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(33) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G.; Guido, C. G.; Mennucci, B.; Scalmani, G.; Frisch, M. J. Practical Computation of Electronic Excitation in Solution: Vertical Excitation Model. Chem. Sci. 2011, 2, 2143–2161. (34) Charaf-Eddin, A.; Le Guennic, B.; Jacquemin, D. Optical Signatures of Borico Dyes: a TDDFT Analysis. Theor. Chem. Acc. 2014, 133, 1–9. (35) Chibani, S.; Laurent, A. D.; Blondel, A.; Mennucci, B.; Jacquemin, D. Excited-State Geometries of Solvated Molecules: Going Beyond the Linear-Response Polarizable Continuum Model. J. Chem. Theory Comput. 2014, 10, 1848–1851. (36) 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. et al. Gaussian 09 Revision D.01. 2009; Gaussian Inc. Wallingford CT. (37) For the large and quite floppy BF4, standard optimization thresholds have been applied. (38) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215–241. (39) Li, R.; Zheng, J.; Truhlar, D. G. Density Functional Approximations for Charge Transfer Excitations with Intermediate Spatial Overlap. Phys. Chem. Chem. Phys. 2010, 12, 12697– 12701. (40) Isegawa, M.; Peverati, R.; Truhlar, D. G. Performance of Recent and High-Performance Approximate Density Functionals for Time-Dependent Density Functional Theory Calculations of Valence and Rydberg Electronic Transition Energies. J. Chem. Phys. 2012, 137, 244104. (41) Leang, S. S.; Zahariev, F.; Gordon, M. S. Benchmarking the Performance of Time-Dependent Density Functional Methods. J. Chem. Phys. 2012, 136, 104101. (42) Jacquemin, D. New Cyanine Dyes or Not? Theoretical Insights for Model Chains. J. Phys. Chem. A 2011, 115, 2442–2445.



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(43) Valsson, O.; Filippi, C. Photoisomerization of Model Retinal Chromophores: Insight from Quantum Monte Carlo and Multiconfigurational Perturbation Theory. J. Chem. Theory Comput. 2010, 6, 1275–1292. (44) Guido, C. A.; Jacquemin, D.; Adamo, C.; Mennucci, B. On the TD-DFT Accuracy in Determining Single and Double Bonds in Excited-State Structures of Organic Molecules. J. Phys. Chem. A 2010, 114, 13402–13410. (45) Guido, C. A.; Knecht, S.; Kongsted, J.; Mennucci, B. Benchmarking Time-Dependent Density Functional Theory for Excited State Geometries of Organic Molecules in Gas-Phase and in Solution. J. Chem. Theory Comput. 2013, 9, 2209–2220. (46) Bousquet, D.; Fukuda, R.; Maitarad, P.; Jacquemin, D.; Ciofini, I.; Adamo, C.; Ehara, M. Excited-State Geometries of Heteroaromatic Compounds: A Comparative TD-DFT and SACCI Study. J. Chem. Theory Comput. 2013, 9, 2368–2379. (47) Bousquet, D.; Fukuda, R.; Jacquemin, D.; Ciofini, I.; Adamo, C.; Ehara, M. Benchmark Study on the Triplet Excited-State Geometries and Phosphorescence Energies of Heterocyclic Compounds: Comparison Between TD-PBE0 and SAC-CI. J. Chem. Theory Comput. 2014, (48) These values have been determined with the cLR approach on cLR optimized geometries. (49) These values are the cLR-LR fluorescence energy differences determined on optimal LR geometries. (50) Schmitt, A.; Hinkeldey, B.; Wild, M.; Jung, G. Synthesis of the Core Compound of the Bodipy Dye Class: 4,4’-Bora-(3a,4a)-Diaza-s-Indacene. J. Fluores. 2009, 19, 755–758. (51) Xu, S.; Evans, R. E.; Liu, T.; Zhang, G.; Demas, J. N.; Trindle, C. O.; Fraser, C. L. Aromatic Difluoroboron β-Diketonate Complexes: Effects of π-Conjugation and Media on Optical Properties. Inorg. Chem. 2013, 52, 3597–3610.


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Graphical Abstract

Excited-state LR-PCM

N F

N

B

cLR-PCM

F

BODIPY


A PCM Investigation - American Chemical Society

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