EFP models

Computational and Theoretical Chemistry xxx (2014) xxx–xxx

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Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc

Modelling solvent effects on the absorption and emission spectra of constrained cyanines with both implicit and explicit QM/EFP models Siwar Chibani a, Denis Jacquemin a,b,⇑, Adèle D. Laurent a a b

CEISAM, UMR CNRS 6230, BP 92208, Université de Nantes, 2, Rue de la Houssinière, 44322 Nantes Cedex 3, France Institut Universitaire de France, 103 bd St Michel, 75005 Paris Cedex 5, France

a r t i c l e

i n f o

Article history: Received 31 December 2013 Received in revised form 28 March 2014 Accepted 28 March 2014 Available online xxxx Keywords: BODIPY dyes Solvatochromism Optical spectra TD-DFT EFP

a b s t r a c t In this contribution, we have combined Time-Dependent Density Functional Theory with both implicit solvation using variations of the well-known Polarisable Continuum Model (Linear-Response, corrected Linear-Response and State-Specific schemes) and explicit solvation approaches, to investigate the solvatochromic shifts undergone by three recently synthesised dyes. These dyes, an aza-BODIPY, a BODIPY and a so-called NBO fluorophore all present excited-states developing a significant cyanine-like character, that is known to be challenging for density-based theories. Our investigation reveals dramatic influence of the selected environmental model on both the predicted sign and amplitude of the solvent shifts. The impact of solvation on the 0–0 energies and vibronic band shapes is also discussed and comparisons with experimental data are performed. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Time-Dependent Density Functional Theory (TD-DFT), and more precisely Casida’s adiabatic approximation to TD-DFT [1], has certainly become the most applied ab initio scheme for probing the energy and the nature of electronically excited-states [2]. This success is first to be explained by the exceptional computational cost/accuracy ratio offered by TD-DFT. Indeed, for most excitedstates, one can expect a typical error of ca. 0.2–0.3 eV on the transition energies (see our recent review [3] devoted to benchmarks for complete bibliography) but nevertheless systems with several hundreds of atoms can be treated, a feat hardly attainable with correlated wavefunction-based theories. However, TD-DFT suffers from flaws, that can be attributed, firstly, to the application of the adiabatic approximation, and, secondly, to the selection of a specific exchange–correlation functional to perform calculations. Obviously, one cannot dissociate both aspects [4], though they are rarely treated simultaneously. Letting aside both high-spin and Rydberg excited-states, the two most problematic families of low-lying excited states for TD-DFT are, on the one hand, ChargeTransfer (CT) states [5,6], and, on the other hand, cyanine-like states [7,8]. TD-DFT behaves differently for those two families. Indeed, the CT energies predicted by adiabatic TD-DFT are highly ⇑ Corresponding author at: CEISAM, UMR CNRS 6230, BP 92208, Université de Nantes, 2, Rue de la Houssinière, 44322 Nantes Cedex 3, France. E-mail address: [email protected] (D. Jacquemin).

dependent on the selected exchange–correlation functional and tend to be underestimated with global hybrid functionals (e.g., B3LYP) [6]. On the contrary, the transition energies estimated by TD-DFT for cyanines are both less dependent on the nature of the exchange–correlation functional, and, systematically too large [9]. For CT states, a pragmatic answer to the problem is the use of range-separated hybrid functionals that allow a more physically-sound description of situations in which the electron and the hole are strongly separated [10–12]. For cyanines there is no CT effects, both electronic states being delocalised over the full carbon skeleton, and the main difficulty is to capture the differential correlation between the two states, that is exceptionally large [13,14]. Though the most modern exchange–correlation functionals are able to alleviate the cyanine problem to some extend [13– 15], it remains true that almost all TD-DFT evaluations provide too large transition energies compared to the most accurate reference values determined with quantum Monte-Carlo or high-order coupled-cluster methods [16]. Apart from the nature of the considered state, another challenge may arise when comparing experimental and theoretical optical spectra: the impact of the surroundings. Most measurements are performed in condensed phases, and this should be accounted for to reach accurate transition energies, as medium effects often significantly differ for the ground and excited states (the latter being typically more polar) [17]. Fortunately, several environmental models have been coupled to TD-DFT. As for DFT, one can split these models into two categories: continuum (or implicit) and

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S. Chibani et al. / Computational and Theoretical Chemistry xxx (2014) xxx–xxx

explicit approaches, the latter being often performed in the framework of hybrid quantum mechanics/molecular mechanics (QM/ MM) calculations, the chromophore being treated with QM and the solvent molecules with MM. Irrespective of the selected strategy, a specific excited-state question arises: how should one model the reaction of the medium to the change of electronic density of the considered chromophore? There is not trivial answer, and several methods have been designed [17]. In the widely used implicit model, namely the Polarisable Continuum Model (PCM) [18], several approximations have been designed to quantify the polarisation of the cavity (and hence of the solvent) following absorption or emission of a photon by the solute [19–23]. In the simplest Linear-Response approach (LR), the change in the PCM charges located on the surface of the cavity is calculated on the basis of transition densities [19,20]. In the more refined corrected Linear-Response (cLR) [21] and State-Specific (SS) models [22], the polarisation of the cavity is optimised as a function of the one-particle density matrix between the ground and the excited state using perturbative and self-consistent approaches, respectively. In explicit QM/ MM solvation models, a similar question appears, as the simple representation of the solvent molecules by MM is not enough to properly model the interactions of these molecules with the excited state of the solute. Again, several approximations are available to tackle the problem [24–29]. Here, we select three molecules derived from the hallmark BODIPY fluorophore (see Fig. 1; 1 is an aza-BODIPY, 2, a BODIPY and 3, a NBO dye) [30,31] to evaluate how different environmental models are able to capture the solvatochromic effects. This training set stands as a rather tough test for all models, as these BODIPY structures can all be viewed as constrained (in the cis conformation) cyanines. The selection of these three molecules was performed on the basis of previous works in our group [32–34], that indicated that LR- and SS-PCM models do not yield the same accuracies for the different subgroups shown in Fig. 1. Indeed, while the SS-PCM model was very efficient in reproducing the evolution of the 0–0 energies in the BODIPY family (the determination coefficient, R2 , is close to unity for a large panel of BODIPY) [33], it provided inconsistent data for NBO dyes, a series for which LR-PCM was more accurate in terms of both absolute and relative values [34]. To the best of our knowledge, only 2 was considered in a previous theoretical work [33], 1 and 3 being free of previous ab initio calculations, but for simple vertical TD-DFT or HOMO–LUMO calculations performed in gas-phase in connection with the experimental analysis [35,36]. Though performed for another molecule, we also note that a previous QM/MM calculation performed on a fluoroborate has recently appeared [37]. For all three molecules very recent experimental data are available for both absorption and fluorescence in several solvents [35,36,38], allowing straightforward comparisons.

have been given in previous works [32,40], so that we only provide a brief summary here. We have selected Truhlar’s M06-2X metaGGA global hybrid functional [41], as it stands as one of the most accurate functional for evaluating excited-state properties of organic dyes [40,42,43], and it has also been shown to be efficient for both BODIPY and NBO derivatives [33,34]. Except when noted, the 6-31G(d) atomic basis set was used for our calculations as it delivers a good balance between computational cost and accuracy for these derivatives [32]. Indeed, it has been shown that cyanine transition energies are not significantly sensitive to the size of the applied basis set [14–16]. In the same vein, for the specific case of aza-BODIPY, we have demonstrated that, while the inclusion of diffuse orbitals in the basis set decreases the estimated transition energies, both the cLR-LR and SS-LR differences are almost independent of the applied atomic basis set [32]. As we mainly focus on relative solvatochromic shifts, and not on absolute comparisons with experimental wavelengths, there are probably no reasons to use more extended basis sets in this work. Nevertheless, large atomic basis set test calculations, performed for molecule 3, confirmed that solvatochromic shifts are indeed nearly unchanged (±0.01 eV) with respect to 6-31G(d). We also underline that comparisons of absolute energies with experimental data include corrections obtained with 6-311+G(2d,p), following the method described in Ref. [40]. The ground-state and excited-state geometries have been optimised using DFT and TD-DFT respectively, thanks to the implementation of analytical gradients in Gaussian09. Next, the vibrational frequencies have been systematically computed for both states through analytical (DFT) and numerical (TD-DFT) differentiations. This allowed to confirm that all structures are true minima of the considered potential energy surface as well as to determine zero-point corrections (ZPVE) for all cases. As stated in the Introduction, implicit solvation has been modelled through the PCM model [18], considering LR, cLR and SS approaches for the treatment of the TD part of the problem. Let us underline that the geometries have been systematically optimised in the considered solvent (with LR-PCM TD-DFT for the excited state). In addition, one can use either the equilibrium (eq) or non-equilibrium (neq) limits of the PCM model, that is considering a complete relaxation of the solvent (slow phenomena) or frozen nuclei (fast phenomena), respectively. Both PCM limits have been used here, depending on the considered electronic process. In the neq limit, one goes from an equilibrium ground-state to a non-equilibrium excited-state for the absorption and from an equilibrium excitedstate to a non-equilibrium ground-state for the emission, whereas in the eq approach all states are considered in equilibrium. During the relaxation (optimisation) of the excited-state geometry, the environment has time to adapt, and therefore excited-state geometries are determined in the eq limit, and this holds for vibrational frequencies computed in the excited-state. In short, our absorption and emission energies are listed in their non-equilibrium limits, whereas all other data, e.g., geometries, zero point corrections and 0–0 energies, correspond to the equilibrium case. Notable exceptions are the LR-PCM fluorescence energies that are rather ill-defined in non-equilibrium (they have therefore been determined in equilibrium).

2. Methods QM calculations were carried out with the Gaussian09 program [39], tightening both self-consistent field (10 9 a.u.) and geometry optimisation (10 5 a.u.) convergence thresholds. The details of the protocol used to compute transition energies with PCM-TD-DFT

N

NH2

N B F F

Cl

N

N F

1

B

N

N

F

2

N F

B

O F

3

Fig. 1. Representation of the systems investigated here.

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S. Chibani et al. / Computational and Theoretical Chemistry xxx (2014) xxx–xxx

In order to provide a complementary light, the solute–solvent specific interactions have also been modelled thanks to an atomistic model. Molecular dynamics (MD) in gas phase have been performed for the three dyes using the amber force field [44], BODIPY parameters being taken from the work of Song et al. for a dye very similar to 2 [45], that was consequently not considered here for the MD simulations, as it has been tackled previously [37,45]. The missing parameters of 1 and 3 have been obtained within the GAFF forcefield [46] and atomic charges computed at the HF/6-31G(d) level of theory using the Restrained ElectroStatic Potential (RESP) charge fitting procedure [47]. It is worth noting that fluoroborate groups are tricky to treat using classical force field as they might form halogen bonds between the fluorine atoms and solvent molecules that are often poorly described (overestimation of repulsion effects), and that parameters are still under development today [48]. After a minimisation and a 100 ps equilibration the production run lasted 2 ns within the canonical ensemble (0.2 fs time step). Fifty snapshots have been extracted from the production simulation and vertical TD-DFT computations at the M06-2X/6-31G(d) level of theory were carried out for the three molecules. This scheme is denoted QM (gas)//MD hereafter. For 1 MD simulations have been also performed in dichloromethane whereas, for 3, both dichloromethane and water have been considered. A standard MD simulation protocol was used for each solvated chromophore. After a preliminary minimisation step of the dye in gas phase it has been solvated within a periodic box (15 Å between the dye and wall). Each solvated system was first minimised with the dye restrained and the solvent unrestrained. The solvent was further equilibrated with the restrained dye with the constant number-pressure–temperature (NPT) ensemble at 300 K and 1 atm for 100 ps (a 1 fs time step). Production MD simulations of 2 ns in the NPT ensemble (T = 300 K and P = 1 atm) were performed for all solvated compounds. Long-range electrostatic interactions were calculated using the particle mesh Ewald method [49,50]. The SHAKE [51] algorithm was used to restrain covalent hydrogen bonds. All trajectories were generated with NAMD [52]. Similarly to QM (gas)//MD calculations, coordinates of solvent molecules and of the dye were extracted each 40 ps to perform TD-DFT computations using two schemes available in the QChem 4.1 package [53]. In the QM/PCM//MD scheme each LR-TD-DFT computation was carried out on the extracted bare chromophore from the MD simulation embedded into an implicit solvent. Within the QM/EFP//MD, solvent molecules within 4 Å around the dye are described with the Effective Fragment Potential (EFP) method [25,54–57]. EFP is a non-empirical polarisable force field recognised for its accurate description of non-covalent interactions [54,58–64] and for its efficiency in determining the excited energies of solvated systems [29,65,66]. To summarise calculations of the spectra when considering the dynamics have been exploited with implicit QM/PCM methods (so called QM/PCM//MD) and hybrid QM/EFP scheme (so called QM/EFP//MD). Molecular dynamics allow us (i) to observe if the dynamics of the system influence the dye spectra and (ii) to treat solvent molecules with EFP (and not ‘‘simply’’ with an implicit model). Hereafter the QM/EFP//MD scheme is named as an explicit model to underline the difference with PCM. Vibrationally resolved spectra within the harmonic approximation were computed using the FCclasses program (FC) [67–69]. The reported spectra were simulated using a convoluting Gaussian function presenting a half width at half maximum (HWHM) that was adjusted to allow direct comparisons with experiments (0.04 eV for 1 and 0.08 eV for 3). A maximal 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 1012 . The final FC factors was at least 0.8.

3

3. Results and discussion In Fig. 2, we present density difference plots for the three investigated fluoroborates. It is obvious that the excitations are delocalized but do not present a significant CT character, even for the asymmetric 3. Indeed, one notices alternating domains of increase and decrease of density, which is typical of cyanine-like transitions in small molecules [14]. Interestingly, the computed ground (excited) state gas phase dipole moments are 0.9 (0.1), 6.8 (5.7) and 5.2 (6.9) D for 1, 2 and 3, respectively. Therefore, 1 is rather non-polar, whereas the absorption of a photon slightly decreases (increases) the polarity of 2 (3). The excited-state geometries of the dyes presenting side phenyl rings are more planar compared to the ground state structures, especially for 3. Indeed, the dihedral angles measuring the twist between the side rings and the core of the chromophores go from 37 to 32 (19 to 2) degrees for 1 (3) when going from the ground to the excited state, independently of the media. The vertical TD-DFT gas phase absorptions computed for 1, 2 and 3 attain 3.35, 3.59 and 3.92 eV, respectively, whereas the corresponding emission values are 3.10, 3.13 and 3.53 eV. In Table 1 we present the PCM solvatochromic shifts (non-equilibrium limit, gas phase data as reference) obtained for these three dyes, considering solvents that have been actually used during spectral measurements. For 1, the LR model predicts a systematic decrease of the transition energies in condensed phase, with a rather limited impact of the selected solvent for absorption but a strong positive solvatochromic trend for fluorescence. This is in sharp contrast with both cLR and SS models predicting an increase of the transition energies in solution compared to the gas-phase reference. The cLR model indicates a nearly null impact of the medium, which is consistent with the very small dipole moments of 1, whereas the SS approach yields small but significant differences between apolar and polar environments (larger variations being obtained for absorption than for emission). Experimentally [35], there is unsurprisingly no gas phase data available, but going from hexane to acetonitrile induces an hypsochromic displacement of +0.03 eV for absorption, and the three models, despite the differences underlined above, do correctly restore this effect (LR: +0.02 eV, cLR: +0.01 eV; SS: +0.04 eV). For emission, comparisons of the measured wavelengths for the same pair of solvents yield a ca. +0.02 eV shift [35], and only cLR (+0.01 eV) and SS (+0.02 eV) restore this shift, LR miserably failing ( 0.10 eV) [70]. For the meso-substituted BODIPY, 2, the amplitude of the solvent shifts (compared to gas) are predicted to be largely positive with SS, slightly smaller with cLR and negligible (absorption) or negative (emission) with LR, hinting that 1 cannot be viewed as an exceptional case in terms of LR/cLR–SS discrepancies. Only data in two solvents have been published for 2 [38], and the methanol/ethyl acetate shifts are +0.05 eV and +0.04 eV for absorption and fluorescence values, respectively; this observed negative solvatochromism being consistent with the decrease of the dipole moments when going from the ground to the excited states (see above). For absorption, the three models are again satisfying for quantifying methanol/ethyl acetate shifts despite the significant differences in the gas-to-condensed phases shifts. Indeed, the obtained data, +0.04 eV (LR), +0.03 eV (cLR) and +0.07 eV (SS), are consistent with the measurements. For the emission, only the two latter PCM models provide satisfying data: 0.03 eV (LR), +0.02 eV (cLR) and +0.04 eV (SS). Finally, in 3, a more standard behaviour is predicted (see Table 1), as the increase of polarity of the medium yields bathochromic displacements. The amplitudes of the gas-solvent shifts clearly rank LR > SS > cLR and the emission shifts are roughly twice their absorption counterparts. Experimentally [36], the THF-hexane positive solvatochromism is rather modest: 0.01/ 0.03 eV for absorption/emission, and this can be compared to the predicted

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Fig. 2. Gas M06-2X density difference plots for molecules 1 (left), 2 (centre) and 3 (right). The used contour threshold is 0.0004 a.u, red (blue) zones indicating increase (decrease) of the electron density upon excitation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 1 Computed solvatochromic shifts (in eV) for vertical absorption and emission. The gas phase values are used as references. Three PCM models in their non-equilibrium limit have been applied (but for the LR emission computed in eq, see Methods). Dye

Solvent

Absorption LR

cLR

Table 2 Computed difference of zero-point energies between the excited and ground states, DEZPVE , and 0–0 energies, E0 0 , in eV for the three compounds under consideration.

SS

LR

cLR

SS

1

Hexane Dichloromethane Acetonitrile Methanol

0.06 0.05 0.04 0.04

0.01 0.02 0.02 0.02

0.01 0.04 0.05 0.05

0.07 0.15 0.17 0.17

0.00 0.01 0.01 0.01

0.01 0.03 0.03 0.03

2

Ethyl acetate Methanol

0.01 0.03

0.08 0.11

0.16 0.23

0.08 0.11

0.14 0.16

0.18 0.22

3

Hexane Dichloromethane Tetrahydrofuran Acetonitrile Water

0.11 0.12 0.11 0.13 0.13

0.02 0.03 0.03 0.03 0.03

0.05 0.07 0.07 0.07 0.07

0.16 0.20 0.33 0.39 0.40

0.05 0.06 0.08 0.10 0.10

0.07 0.10 0.13 0.15 0.15

values of 0.02/ 0.17, 0.01/ 0.03 and 0.02/ 0.06 eV with LR, cLR and SS, respectively. Note that for 3, adding water to THF eventually induces a huge redshift of the emission band (ca. 0.5 eV). This effect can be attributed to the formation of nanoparticles in solution [36], a fact, that is of course not accounted for by using a standard continuum approach. Several conclusions arise from this PCM study: (1) gas-solvent shifts can be vastly different with LR and cLR/SS models; (2) when considering the variations of the absorption and emission wavelengths between two solvents, the three models are rather consistent for absorption, but going beyond LR is clearly required for emission; (3) cLR solvent shifts are generally smaller than their SS counterparts; and (4) the results obtained with both cLR and SS are in reasonable agreement with experiment. In Table 2, we present the difference of ZPVE between the two states as well as the 0–0 energies for the three dyes. The ZPVE corrections are almost independent of the environment, though they have a slight (non-systematic) tendency to decrease when the polarity of the medium increases. These differences of ZPVE are in the 0.08 to 0.10 eV range, which is quite typical for organic molecules [71,72]. The 0–0 energies follow the same trends as the vertical transition energies noted above, that is, LR systematically foresees smaller values than the gas phase reference, whereas with cLR and SS, this behaviour does not hold, at least for the two first compounds. This analysis of the solvatochromic effect using implicit solvent model is valuable; however, the dynamic of the dye, as well as specific interactions with the solvent molecules might also be important. A complementary work was therefore performed with MD for two of the three compounds in order to sample the conformational landscape of each dye in both gas and condensed phases. Analysing the conformational changes of the chromophores 1 and 3 we observe that the fluoroborate core possesses, in both cases, a similar geometry as in QM computations. However the phenyl side

DEZPVE

E0

LR

LR

cLR

SS

3.094 3.042 2.973 2.955 2.956

3.112 3.133 3.139 3.162

3.120 3.153 3.163 3.139

0.085 0.084 0.086

3.256 3.110 3.073

3.331 3.353

3.374 3.411

0.113 0.118 0.083 0.103 0.099 0.098

3.553 3.466 3.275 3.311 3.255 3.246

3.573 3.536 3.562 3.556 3.555

3.555 3.498 3.520 3.507 3.504

Dye

Solvent

1

Gas Hexane Dichloromethane Acetonitrile Methanol

0.102 0.094 0.083 0.081 0.081

Gas Ethyl acetate Methanol Gas Hexane Dichloromethane Tetrahydrofuran Acetonitrile Water

Emission

2

3

0

rings do twist with a relatively small amplitude but in both directions for 3: 46% of the simulation time between 10 and 0 degrees and 46% of the simulation time between 0 and 10 degrees, independently of the solvent. Similarly to what is found in the QM computations, the phenyl side groups of 1 possess a larger amplitude of fluctuation (up to ±45 degrees) compared to 3. The same amount of time is spent with a positive and negative dihedral angle between the phenyl and the fluoroborate core (30% between 15 and 0 or between 0 and +15 degrees) as for 3 but the last 40% are spread between + (or )15 and + ( )45 degrees. The average value obtained after 50 QM (gas)//MD calculations is 2.95 and 3.53 eV for 1 and 3, respectively, and this follows the trends of the static gas phase computations, though both values are significantly smaller with the MD sampling (see above) [73]. A large panel of snapshots was necessary to reach a relevant statistics in the present case, as the considered dyes are flexible (rotation of the phenyl group). Consequently, the standard deviation for the excited state energies is rather large, in the 0.07–0.10 eV range. Table 3 reports the solvatochromic shifts obtained with several approaches for the two fluorophores when going from gas phase to DCM or water. Starting our analysis with 3 in water, we first underline that the shift obtained with the QM (PCM)//MD scheme ( 0.04 eV) has the same sign as its static counterpart (see above) and presents an amplitude closer to the cLR and SS results than to the LR-PCM value listed in Table 1. As stated in the methodological section, QM/EFP calculations were also performed on the snapshots extracted from the simulation (QM/EFP//MD). Two distinct production runs have been carried out: (i) MDf in which the structure of dye is frozen while the solvent molecules are free and (ii) a classical MD in which both solvent and dye are relaxed. The water molecules being explicitly treated with EFP, we have tested the impact of the number of solvent ‘‘EFP molecules’’ on the obtained

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S. Chibani et al. / Computational and Theoretical Chemistry xxx (2014) xxx–xxx Table 3 Average solvatochromic shifts (in eV) of the vertical absorption obtained with the TDDFT//MD method using both implicit and explicit schemes to describe the solvent. Listed values correspond to the gas-solvent shifts computed from average transition energies obtained over 50 snapshots, using the gas phase data as reference. Solvent

Method

1

Dichloromethane

QM/PCM//MD QM/EFP//MD

0.37 0.32

3

Dichloromethane

QM/PCM//MD QM/EFP//MD QM/PCM//MD QM/EFP//MD QM/EFP//MDf

0.06 0.09 0.04 0.08 0.37

Water

Absorption

0.8

Relative Intensity

Dye

0.6 0.4 0.2 0 18000

20000

22000

24000

26000

28000

30000

-1

E / (cm ) Dichloromethane Gas Dichloromethane (Exp)

1 0.8

Relative Intensity

spectrum. Test calculations show that considering water molecules within 4 Å around the chromophore is satisfactory for reaching convergence, i.e., the variation of the excitation energies is less than 0.004/0.01 eV when including 112/214 water molecules (6/ 8 Å cutoff) instead of 51 (4 Å cutoff). The solvatochromic shift obtained with QM/EFP//MDf, +0.37 eV, is much larger and in the opposite direction compared to the QM(gas)//MD value. In the QM/EFP//MDf scheme the chromophore is kept in the geometry optimised at the PCM-DFT level, and the associated standard deviation is trifling (0.02 eV), indicating that the sizeable fluctuation obtained in the non-constricted approach (0.07–0.1 eV, see above) is related to geometrical deformations of the chromophore and not to specific solute–solvent interactions. The latter statement could be related to a poor description (too repulsive) of the halogen bonds between the fluoroborate and solvent bonds. In addition, we point out that the absolute excitation energy computed with QM/EFP//MDf equals 3.92 eV, that is, exceeds its PCM counterpart (3.80 eV) by 0.12 eV. The solvatochromic shifts obtained from the fully relaxed calculations are significantly smaller than the QM/ EFP//MDf data (0.08–0.37 = 0.29 eV, see Table 3), showing that the sampling of the chromophore is crucial for those dyes, despite their quite constrained aromatic nature. The QM/EFP//MD results are much closer to the pure QM computations than the QM/EFP// MDf, but the sign of the solvent shift obtained with explicit and implicit protocols remains different even for the relaxed MD. This inconsistency could not be completely resolved here, but is probably related to polarisation embedding that is neglected in the TD-DFT computation within the QM/EFP method. Actually in a previous work [74] we were able to reproduce the experimental shift (due to a complexation) only when considering both the electrostatic and the polarisation embedding while neglecting the polarisation embedding led to a positive shift as it is the case in this study. In DCM, the 0.06 eV and +0.09 eV solvatochromic shifts obtained with the QM/PCM//MD and QM/EFP//MD methods, respectively, provide the same trend (both sign and amplitude) as in water. Beyond solvatochromic shifts, the two data allowing the most straightforward comparisons between experimental and theoretical results are, on the one hand, vibrationally resolved band shapes, and, on the other hand, absorption–fluorescence crossing points [75] and we applied approaches described elsewhere [40,43] to compute both properties. The data, determined with a purely implicit model, are compared to experiment in Fig. 3 for 1 and 3 (2 has not clear cut band shape experimentally), and one notices that: (1) there is a really neat agreement between experimental and TD-DFT band shapes; (2) the positions of the absorption–emission crossing point is overshot on the energy scale, as expected (see Section 1); (3) the solvent effects have a rather modest impact on the band topology for 1 but a stronger influence for 3; and (4) for 3, the PCM calculations yield a better agreement with measurements than their gas phase counterparts for both absorption and emission band shapes.

Dichloromethane Gas Dichloromethane (Exp)

1

0.6 0.4 0.2 0 16000

20000

24000

28000

32000

36000

40000

-1

E / (cm ) Fig. 3. Comparison between experimental and theoretical absorption (full) and emission (dotted) band shapes for 1 (top) and 3 (bottom). The red curves are computed in gas phase, the black curves are the calculations in dichloromethane whereas the green curves are the experimental measurements in the same solvent. For 1, the experimental curve is adapted from Wang et al. Dyes Pigm., 99 (2013) 240–249, Copyright (2013) with permission from Elsevier. For 3, the experimental curve is adapted with permission from Kubota et al. Org. Lett. 78 (2013) 7058–7067, Copyright (2013) American Chemical Society. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

4. Conclusions and outlook We have used three fluoroborate compounds to assess several computational protocols allowing to quantify solvatochromism on both absorption and emission. It turns out that the three popular PCM model adapted for TD-DFT calculations, namely LR, cLR and SS, may yield vastly different conclusions when comparisons are made with gas-phase data and this is true not only for the amplitude of the medium effects, but also for the direction (sign) of the shifts as well as for the relative importances of solvatochromism for absorption and emission. When comparing different solvents, the three PCM models have been found satisfying for absorption whereas, for emission, only cLR and SS can be viewed as accurate, the latter often providing larger solvatochromic shifts than the former. The inclusion of dynamical effects within an explicit solvation approach has demonstrated that the spectra is highly influenced by the geometry of the chromophore itself (and not so much by specific solute–solvent interactions), so that having an accurate structure is of primary importance. This was the case here with the selected functional, as nicely shown by the very good agreement between the experimental and theoretical band shapes computed with a vibronic approach. The solvatochromic effects as obtained through MD are rather complex to understand due to the complex interplay between many factors. In particular here, the flexibility of the dye makes the MD calculations rather challenging.

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