Interplay between solvent models and predicted optical spectra: A TD-DFT study of 7-OH-coumarin

Chemical Physics Letters 556 (2013) 122–126

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Interplay between solvent models and predicted optical spectra: A TD-DFT study of 7-OH-coumarin José P. Cerón-Carrasco a,⇑, Mathieu Fanuel a, Azzam Charaf-Eddin a, Denis Jacquemin a,b,⇑ 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 October 2012 In final form 23 November 2012 Available online 1 December 2012

a b s t r a c t Using time-dependent density functional theory, we investigate the solvatochromic effects on the optical spectra of a typical hydroxy coumarin, considering its enol, keto, anionic and cationic forms. The absorption and fluorescence transitions energies have been computed within both the linear-response (LR) and the more refined state specific (SS) approaches, with explicit solvent molecules. These energies have also been used to compute 0–0 transitions and vibrationally resolved spectra. We show that the SS approach is mandatory to describe the solvent response due to the large increase of dipole moment upon the excitation while hydrogen bonds tune both absorption and emission energies. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction As density functional theory (DFT) [1] for ground-state (GS) properties, time-dependent formulation (TD-DFT) [2–4] has become the most popular theoretical approach for exploring electronically excited states (ES) [5–7]. Indeed, though TD-DFT transition energies depend significantly on the selected functional, TD-DFT generally outperforms simpler semiempirical approximations [8] and provides accurate results for medium-sized and large molecules that are often out of reach for highly correlated methods, e.g., CASPT2 and EOM-CC [9,10]. As other models, TD-DFT can be combined to the well-known polarizable continuum model (PCM) [11] to simulate bulk solvent effects. In the PCM-TD-DFT framework, the ‘‘classical’’ linear-response (LR) [12,13] has been extensively applied to study dyes in solution [14–18]. In the LR model, the cavity surrounding the solute is based on the GS electron density, and this model, can only be viewed as a first (though often valuable) approximation of solvent effects. To obtain more physically sound values, one needs to achieve a more refined description of the cavity surrounding the ES. In the framework of the calculation of absorption and emission spectra, several models have been recently proposed, including the corrected linear-response scheme (cLR) [19], the vertical excitation model (VEM) [20] and the state-specific (SS) approximation [21,22]. In these three alternative (PCM-) TD-DFT approaches the energy of the ES is computed with a more adequate polarization of the cavity,

⇑ Corresponding authors at: CEISAM, UMR CNRS 6230, BP 92208, Université de Nantes, 2 Rue de la Houssinière, 44322 Nantes Cedex 3, France. E-mail addresses: [email protected] (J.P. Cerón-Carrasco), [email protected] (D. Jacquemin). 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2012.11.075

Denis.

which provides a more realistic picture of optical spectra in solution [23]. In this Letter, we use the LR and SS methods to compute the transition energies for several coumarins. Coumarins absorb light in the near-UV region and emit blue-green light. Accordingly, they have been widely used as fluorescent probes, laser dyes, chromophores for dye-sensitized solar cells or chemosensors for detecting metals [24–27]. Since ES dipole moments (l) tend to be much larger than their GS counterpart [28], the absorption and emission maxima of coumarins are very sensitive to the solvent polarity [29]. The significant differences between GS and ES electronic distributions make coumarins excellent working examples for PCM-TD-DFT calculations. It is therefore unsurprising that the LR, cLR and SS approaches have already been used to compute the vertical absorption and emission phenomena of coumarins, and more specifically of the prototype C153 fluorophore [30,31,21,32]. Here, we compute the vertical transitions for the unsubstituted coumarin and its 7-hydroxy derivative, considering several forms for the latter (see Figure 1), which we have previously investigated with CIS and TD-DFT (LR) calculations [33]. Additionally, we calculate for the first time the adiabatic and 0–0 energies in a fully consistent way (see below) The results for a larger panel of coumarins (e.g. 4-OH, 4-Me,7-OH and 4-Me,7-OMe derivates) can be found in the Supporting information (SI), but we have limited ourselves to one relevant example here, for the sake of compactness. In addition, we go beyond the pure PCM solvent model by using explicit/implicit solvent models. 2. Methodology All calculations have been performed with the GAUSSIAN09 program [34] using different solvent (EtOH, MeOH and water). The

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corrected for nonequilibrium effects to offer a data that is directly comparable to the crossing point of absorption and fluorescence curves (AFCP) [38],

O

O 1

EAFCP ðSS; neqÞ ¼ E0—0 ðSS; eqÞ þ

HO

O

O

O

O

2

where the corrections,

OH

3

rightmost

i 1 h vert-a DE þ DEvert-f 2

term

introduces

the

ð4Þ nonequilibrium

DEvert-a ¼ Evert-a ðSS; neqÞ  Evert-a ðSS; eqÞ vert-f

DE

HO

O

OH

O

O

O

5

4

Figure 1. Chemical structures of investigated molecules: (1) unsubstitued coumarin and (2) enol, (3) keto, (4) cation, and (5) anion forms of 7-OH-coumarin.

GS (S0 ) geometries have been optimized with PBE0/6-31+G (d) [35] whereas ES (S1 ) have been determined at the same level. Results obtained at CAM-B3LYP/6-31+G (d) [36] level are available in SI. The subsequent vibrational calculation are used to confirm that the stationary points are true minima in the potential energy surface (no imaginary frequencies), to obtain zero-point vibrational energies (ZPVE) and to compute vibrationally resolved spectra (see below). Within the vertical approximation the absorption energies, Evert-a , corresponds to the difference of the GS and ES energies computed for the GS optimal geometries,

Evert-a ¼ EES ðRGS Þ  EGS ðRGS Þ

ð1Þ vert-f

and emission energies (fluorescence), E optimized ES structures,

, are calculated on the

Evert-f ¼ EES ðRES Þ  EGS ðRES Þ

ð2Þ adia

As discussed elsewhere [37], the adiabatic energies, E , that is the difference of the total energies computed for the ES and GS at their respective optimal geometries can be obtained as a by-product of absorption and emission calculations. The 0–0 energies are computed by subtracting the difference of ZPVE between the two states, DEZPVE , from the adiabatic energies,

E

0—0

adia

¼E

ZPVE

 DE

ð3Þ

To quantify solvent effects, transitions energies have been computed with LR and SS schemes in both equilibrium (eq) and nonequilibrium (neq) limits. In the former, the solvent is fully relaxed with respect to the ES density, whereas, in the latter, only the electrons of the solvent have adapted to the new electronic configuration of the solute. We underline that as both Eadia and E0—0 involve optimized GS and ES structures and, they should be a priori solely computed in the equilibrium limit. However, E0—0 has been

vert-f

¼E

ðSS; neqÞ  E

vert-f

ðSS; eqÞ

ð5Þ ð6Þ

We redirect the interested reader to Ref. [37] for a longer discussion of this procedure. Although PCM model is very effective to reproduce bulk effects in aprotic media, the inclusion of the explicit molecules of the first hydration shell is sometimes needed to account for specific solute– solvent interactions, e.g., hydrogen bonds [39,40]. Consequently, calculations for coumarins in water (2, 4 and 5) have been also performed with an hybrid discrete/continuum solution model by including three explicit solvent molecules in the vicinity of oxygen atoms (see Figure 2). More specifically, water molecules have been placed at ca. 2.0 with the oxygen/hydrogen atom oriented towards hydrogen bond donors/acceptors of the coumarin. The water molecules positions determined in the GS are used as starting point for ES geometry optimizations. For the ES, we have fully optimized the water position within the equilibrium PCM model. Vibrationally resolved spectra within the harmonic approximation were computed for coumarins in water by using the FCCLASSES program [41–43]. The reported spectra have been simulated at 298 K using a convoluting GAUSSIAN functions presenting a half width at half maximum (HWHM) that has been adjusted to allow meaningful comparisons with experiments (typical value: 0.04 eV). 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 106. 3. Results All the PCM-optimized structures present a planar geometries for both in the GS and in ES and consequently belong to the C s point group. This finding is consistent with previous calculations that demonstrated that the inclusion of both solvent and electron correlations effects are mandatory to correctly reproduce the planar symmetry of coumarins in their ES [33]. In contrast, optimizations performed with discrete/continuum models yield, as expected, a C 1 symmetry (Figure 2)). Nevertheless, inspection of these structures reveals that coumarins remain almost completely planar, the largest deviation originating in the oxygen atom inside the cycle, but the effect is as small as a 30 out of plane deviation.

Figure 2. Enol (2), cation (4) and anion (5) structures of 7-OH-coumarin interacting with three explicit water molecules optimized in the GS.

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J.P. Cerón-Carrasco et al. / Chemical Physics Letters 556 (2013) 122–126 Table 1 PBE0/6-31+G(d) absorption and fluorescence energies for coumarins in gas phase and a experimental curves crossing point (EAFCP exp ).

Normalized Intensity

2 4 5

250

Coumarin

Evert-a

Evert-f

DEZPVE

Eadia

E0—0 ¼ EAFCP

EAFCP exp

1 2 3b 4 5

4.264 4.241 3.062 3.712 3.424

3.536 3.825 2.342 3.008 2.954

0.141 0.145 0.074 0.115 0.092

3.900 4.033 2.702 3.360 3.189

3.759 3.888 2.628 3.245 3.097

3.543 3.483 3.163 3.028

a

Average point between the experimental A and F maxima. 3 has no experimental absorption signature, no determination of AFCP could be performed. b

300

350

400

450

500

Wavelength (nm) Figure 3. Solvent effects on the vibronic shapes for coumarins 2, 4 and 5 in water (PCM). Absorption is plotted with full lines and fluorescence with dashed lines.

Figure 4. Computed PCM-PBE0/6-31+G(d) total density difference between the ground and the excited state of coumarin 3 and 5 (isocontour value 0.0004). Blue (purple) regions indicate density increase (decrease) upon electronic transition. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Accordingly, the degradation of the symmetry can be mainly attributed to the explicit water molecules rather than a structural change in the coumarins geometries. In Table 1, we present the PBE0/6-31+G (d) transition energies obtained in gas phase, as well as the experimental AFCP energies [44–48]. Even within this rough approximation, TD-DFT correctly reproduces the ordering for both absorption (1 > 2 > 4 > 5) and fluorescence energies

(2 > 1 > 4 > 5 > 3); see experimental values listed in Ref. [49,33]. It also is noticeable that for coumarin 4 the computed Evert-a in gas phase differs by only 0.036 eV from the experimental maximum of absorption. However, in spite of this qualitative agreement, the energies listed in Table 1 cannot obviously provide a picture of solvatochromic effects. In addition, for both 1 and 2, large deviations between experimental and theoretical EAFCP – the most meaningful theory/experiment comparison – are found in Table 1. Let us now turn to the PCM-TD-DFT results that are listed in Table 2. The reader can find vibrationally resolved absorption and emission bands for the three dyes soluble in water in Figure 3. These spectra have been simulated within the LR approximation, the only available model for computing ES vibrational modes. As can be seen in the movies provided in SI, the two characteristic peaks present in the absorption spectrum of 2 can be interpreted, on the one hand, as a breathing mode of both the aromatic rings and, on the other hand, as the stretching of the carbonyl group. Table 2 also allows to pinpoint significant differences between LR and SS vertical energies. Indeed, the absolute average LR/SS deviations for the vertical energies are 0.107 eV (Evert-a ), 0.092 eV (Evert-a eq neq ) and vert-f 0.187 eV (Eeq ), with maximal deviations obtained for dyes 3 and 5. Consistently, the same magnitude of SS-LR difference is also observed for both adiabatic and 0–0 energies, e.g., the corresponding E0—0 LR-SS deviations are 0.126, 0.097, 0.097, 0.097, 0.288, 0.047 and 0.274 eV going down the column in Table 2. In the same vein, coumarins 3 and 5 also possess the largest gas-SS absolute deviations for E0—0 : 0.428 and 0.258 eV, respectively. This outcome is consistent with the fact that the LR model cannot reproduce solvatochromic effects when electronic transitions induce a large change in the dipole moment (Dl) [19,21,22]. Although a fair comparison of dipole moments requires the use of counterions [50], the GS/ES difference of total densities displayed in Figure 4 for coumarins 3 and 5 reveals a charge-transfer between the two cycles of the coumarins upon the electronic transition, consistent with large Dl. Table 2 also allows to quantify the neq effects on the AFCP energies as measured by the second term of Eq. 4, a correction that has often been overlooked previously. As can be seen from the difference between the E0—0 (SS,eq) and the EAFCP (SS,neq) values, the neq corrections are relatively small but non-negligible: they range from for 0.024 eV (3) to 0.092 eV (1). They can be compared to the corrections brought by the vibrational terms that are larger (between 0.097 eV for 5 and 0.143 eV for 1). Since coumarin 2 is soluble in EtOH, MeOH and water, these data can be used to follow the impact of the solvent on the spectra. It is worth mentioning that the calculated transitions energies for 2 are consistent with the expected impact of solvent polarity, the only exception being the non-equilibrium absorption. However, experimentally the maximum of absorption of 2 is observed at the same wavelength for the three selected solvents [33], which fits TD-DFT predictions. In addition, the maximum difference vert-a between the Evert-a LR;neq and ESS;neq is trifling (<0.05 eV). The same conclusion holds for the vertical fluorescence, that also undergoes a

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J.P. Cerón-Carrasco et al. / Chemical Physics Letters 556 (2013) 122–126 Table 2 Predicted solvent effects for coumarins in water using a series of continuum solvent models and the PBE0/6-31+G(d) approach. Evert-a

Coumarin

Solvent

(LR,eq)

(SS,eq)

(LR,neq)

(SS,neq)

(LR,eq)

(SS,eq)

(SS,neq)

1 2

3 4 5

EtOH EtOH MeOH water EtOH water water

4.148 3.968 3.962 3.953 3.053 3.597 3.236

4.008 3.976 3.968 3.954 3.362 3.601 3.514

4.148 4.122 4.127 4.125 3.228 3.744 3.453

4.252 4.112 4.114 4.109 3.452 3.821 3.652

3.559 3.582 3.576 3.566 2.633 3.264 3.029

3.446 3.767 3.764 3.758 2.899 3.166 3.298

3.386 3.751 3.747 3.740 2.857 3.079 3.252

Coumarin

Solvent

DEZPVE

Eadia

(LR,eq)

(LR,eq)

(SS,eq)

(LR,eq)

(SS,eq)

(SS,neq)

1 2

EtOH EtOH MeOH water EtOH water water

0.143 0.111 0.111 0.110 0.099 0.107 0.097

3.854 3.775 3.769 3.759 2.843 3.430 3.132

3.727 3.871 3.866 3.856 3.131 3.384 3.406

3.710 3.663 3.658 3.649 2.744 3.323 3.035

3.584 3.760 3.755 3.746 3.032 3.276 3.309

3.676 3.820 3.820 3.815 3.056 3.343 3.355

3 4 5

Evert-f

E0—0

EAFPC

Table 3 Predicted absorption-fluorescence Stokes shifts both in gas phase and using a series of continuum solvent models within the PBE0/6-31+G (d) approach. Coumarin

1 2

3 4 5

Solvent

EtOH EtOH MeOH water EtOH water water

Gas

Continuum

0.728 0.416

0.720 0.704 0.470

Discrete/continuum

(LR,eq)

(SS,eq)

(SS,neq)

0.589 0.386 0.386 0.397 0.420 0.333 0.207

0.562 0.209 0.204 0.196 0.464 0.435 0.216

0.866 0.361 0.367 0.369 0.595 0.742 0.400

(LR,eq)

exp

(SS,eq)

(SS,neq) 0.821 0.591

0.366

0.240

0.448

0.345 0.247

0.442 0.243

0.713 0.424

0.636 0.651

Table 4 Predicted solvent effects for coumarins in water using a series of hybrid explicit/continuum solvent models and the PBE0/6-31+G (d) approach. Coumarin

Evert-a

Evert-f

(LR,eq)

(SS,eq)

(LR,neq)

(SS,neq)

(LR,eq)

(SS,eq)

(SS,neq)

2 4 5

3.822 3.531 3.276

3.828 3.644 3.551

3.994 3.681 3.476

4.006 3.841 3.689

3.456 3.186 3.027

3.588 3.202 3.316

3.558 3.128 3.273

Coumarin

DEZPVE

2 4 5

E0—0

Eadia

EAFPC

(LR,eq)

(LR,eq)

(SS,eq)

(LR,eq)

(SS,eq)

(SS,neq)

0.114 0.111 0.088

3.639 3.358 3.152

3.708 3.423 3.433

3.525 3.247 3.064

3.594 3.312 3.346

3.668 3.373 3.394

minor solvatochromic change (<0.02 eV) regardless the theoretical approach (LR/SS). The computed Stokes shift are listed Table 3. The gas phase Stokes shifts nicely agree with the values extracted from experimental spectra (a match exceeding the typical TD-DFT accuracy), but more importantly, the LR values tend to be significantly less accurate than the SS ones. As PCM neglects the presence of H-bonds in water, we have also added explicit water molecules to the model. The geometries of coumarin 2, 4 and 5 were optimized by including three explicit water molecules in the first hydration shell (Table 4). Interestingly, the impact of H-bonds on the magnitude of EAFCP SS;neq energies is only 0.030 and 0.039 eV for charged coumarins, 4 (cation) and 5 (anion), respectively, but attains 0.147 eV for coumarin 2 (neutral). Part of this difference can be ascribed to the changes in the hydration pattern upon transition. Indeed, in 2, the water molecules in the

vicinity of the ether oxygen departs from the plane of coumarin when the ES structure is optimized, whereas less drastic variations are noted for 4 and 5. As result, explicit water molecules better stabilizes the ES than GS of coumarin 2, which in turns explain the above trends. Finally, the comparison of data collected in Tables 1, 2 and 4 provides an overall picture of both implicit and explicit solvent effects. The calculated transition energies for coumarin 2 indicate a red shift when moving from the gas to the solvated phase. Specifically, the EAFPC SS;neq decreases from 3.888 (gas-phase) to 3.815 eV in PCM (water) but is as small as 3.668 eV for the discrete/continuum solvent model, that is H-bonds have a larger impact on the optical property than the dielectric effects. The latter energy is the closest to the experimental AFCP of 3.483 eV [47], the error now lying in the ±0.25 eV range, that is often viewed as the typical TD-DFT

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deviation. For coumarin 4 and 5, the computed AFCP energies are significantly larger in solution than in gas phase, and the addition of explicit solvent molecules plays only a minor role. This is in obvious contrasts with 2 and illustrates the difficulty to obtain balanced environmental effects, even within a family of structures. For 4 and 5, large deviations between experiment and theory pertain and part of this effect could be due to the presence of counterions that have been shown recently to tune the AFPC point of charged species [50]. According to AFPC energies listed in Tables 1 and 4, coumarin 2 increases from 3.245 to 3.733 eV and coumarin 5 from 3.097 to 3.394 eV when moving from gas phase to discrete/ continuum model, which in turns results in an overestimation of 0.210 and 0.366 eV respect to the experimental values.[46] Similar trends are found with the CAM-B3LYP range-separated functional (see ASI). We conclude that when solvent effects are mandatory for the study of optical spectra, as in the case of coumarin derivates, the selected approach (LR, SS. . .) and solvent conditions (eq/neq, explicit/implicit) affects significantly to the theoretical predictions, so that one should be cautious to have a physically pertinent model.

4. Conclusions In this Letter, we have presented calculations of the absorption and fluorescence of coumarin and its 7-OH derivate with a focus on environmental effects. Our calculations have been carried out by combining the time-dependent density functional theory (TDDFT) with both the implicit (linear-response and state-specific schemes) and explicit solvent models, in order to accurately reproduce all kinds of interactions. We conclude that coumarins 3 and 5, that undergoes a significant dipole moment increase upon transition, are largely affected by the implicit solvent effects and the polarization of the cavity, with a minor contribution of explicit water molecules. On the contrary, the increase of the dipole moment is much smaller in coumarin 2 and consequently the SS/LR discrepancy is smaller but H-bonds significantly tune the transition energies. This illustrates that to obtain a balanced description of the optical spectra, a complete description of environmental effects could be necessary, even within a same family of dyes.

Acknowledgments J.P.C.C. acknowledges the fellowship provided by the Fundación Séneca, Agencia de Ciencia y Tecnología de la Región de Murcia, within its Postdoctoral Research Staff Training Program. D.J. acknowledges the European Research Council (ERC) and the Région des Pays de la Loire for financial support in the framework of Starting Grant (Marches - 278845) and a recrutement sur poste stratégique, respectively. This research used resources of the GENCI-CINES/ IDRIS (Grant c2012085117), of the CCIPL (Centre de Calcul Intensif des Pays de Loire) and of a local Troy cluster.

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2012. 11.075.

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