Electronic Excitations in Epicocconone Analogues: TDDFT

Article pubs.acs.org/JPCA

Electronic Excitations in Epicocconone Analogues: TDDFT Methodological Assessment Guided by Experiment Olga A. Syzgantseva,† Vincent Tognetti,† Laurent Joubert,*,† Agathe Boulangé,‡ Philippe A. Peixoto,‡ Stéphane Leleu,‡ and Xavier Franck*,‡ †

Theoretical Chemistry Group and ‡ Bioorganic Chemistry Group, UMR CNRS 6014 and FR 3038, Université de Rouen et INSA de Rouen, F-76821 Mont St. Aignan Cedex, France S Supporting Information *

ABSTRACT: In this work we present a combined theoretical and experimental study of UV/vis absorption spectra of novel organic chromophores derived from epicocconone. A computational protocol, consistent with experimental findings, is proposed in the framework of time-dependent density functional theory. More precisely, the influence of density functional, basis set, and solvation effects is assessed through theory−experiment matching. On the one hand, it is shown that global hybrid functionals fail to describe excitation spectra for the whole training set. On the other hand, range-separated hybrids allow a description of the complete set of epicocconone derivatives on equal footing, while the double-ζ basis set is shown to be sufficiently accurate for the screening of the spectroscopic properties in epicocconone analogues. The inclusion of solvent effects within a polarizable continuum model appears to be compulsory to decrease the residual dispersion. State specific solvation, on the contrary, does not provide a significant consistency/accuracy improvement. Besides, conformational transformations in investigated compounds and their influence on electronic absorption spectra are pointed out. A systematic choice of the same conformation for each compound from the training set enhances consistency and accuracy of our theoretical model. Lastly, a TDDFT-based calibration is proposed for prediction of absorption wavelengths in epicocconone analogues.

1. INTRODUCTION Current demand in protein detection and identification calls forth the development of new efficient analytical tools. For this reason, staining of bioorganic molecules and cellular organelles with fluorescent markers becomes a boosting research area. Although a significant number of protein fluorophores have been proposed, they are not deprived of shortcomings: some of them are not cell-permeable, have inherent fluorescence, or are cytotoxic. Moreover, they could suffer from narrow Stokes’ shift and excitation wavelength incompatible with common laser sources.1 Thus, the query for an improved protein stain remains a challenging task. Epicocconone, a small organic molecule extracted from fungus Epicoccum nigrum, is a novel protein marker2 (Figure 1). Poorly fluorescent in its native form, it becomes highly fluorescent when covalently bound to primary amines, namely, in proteins.3 Among its advantages as a fluorescent protein marker are a large Stokes’ shift (∼90 nm), low detection limit, cell permeability, and nontoxicity.1,2,4,5 Besides, it can be excited with different laser sources as it has two excitation wavelengths: 520 and 395 nm.5 However, it is bleached rapidly upon irradiation4 and has a low quantum yield.1,6 Therefore, a modification of its structure in order to overcome these drawbacks could be envisaged. However, the design of new compounds, analogues of epicocconone, requires an understanding of the underlying processes at the molecular level. Nowadays, an oriented search © 2012 American Chemical Society

for molecules with predetermined properties seems unimaginable without theory−experiment interplay. Computational chemistry provides efficient tools to get an atomic-scale insight on geometry transformations and electronic structure changes. However, adequate results usually require a calibration of theoretical observables with experimental data. The first step on the way of theoretical modeling of epicocconone and its derivatives is an assessment of the methodology allowing a correct description of electronic structure transformations for a given class of substances. For this purpose, it is quite common to fit theoretical wavelengths7−9 of excitation or fluorescence spectra with experimental ones. On the one hand, this permits validation of the accuracy of the theoretical description and, on the other hand, the obtained model can serve for the prediction of spectroscopic properties of new compounds with a similar chemical structure. Theoretical approaches allowing simulation of UV/vis spectra vary from parameter-based semiempirical to highly accurate post Hartree−Fock methods. Semiempirical methods are known to give system dependent results and suffer from the lack of transferability between classes of compounds.9,10 The large molecular size and the extended conformational space of Received: May 30, 2012 Revised: July 22, 2012 Published: August 10, 2012 8634

dx.doi.org/10.1021/jp305269y | J. Phys. Chem. A 2012, 116, 8634−8643

The Journal of Physical Chemistry A

Article

Figure 1. Classification of aminated epicocconone analogues.

Detected λmax corresponds to the highest intensity Imax signal of the first absorption band.

epicocconone and its derivatives exclude systematic application of highly accurate multiconfigurational and multireference ab initio post Hartree−Fock wave function methods. This is, by the way, not always necessary, as time-dependent density functional theory (TDDFT) provides a comparable accuracy and a higher efficiency ratio,8 so this level of theory will be adopted in our work. In this paper we present the characteristics of absorption spectra of aminated epicocconone derivatives and make a fit between experimental and theoretical absorption wavelengths λmax for the first vertical electronic transition in these compounds. This transition occurs in the butylamine adduct of epicocconone at approximately 520 nm and leads to a fluorescent de-excitation at 610 nm. A series of newly synthesized epicocconone analogues11−13 containing 16 molecules and the natural fluorophore itself, in their aminated form, has been selected as a training set. These compounds can be separated in two groups: first and second generations (Figures 1 and S1). The difference between them resides, respectively, in a simple keto- or a 1,3-diketo-group (eventually enolized) of the side chain part connecting the molecular scaffold with the R substituent. Although some DFT studies of epicocconone have been previously reported,14,15 none of them addresses methodological aspects of its electronic structure description. So, the objective of this work is the elaboration of computational procedure (density functional, basis set, solvation effects), consistent with the experimental findings, in order to apply it in further investigations of new compounds from the epicocconone family.

3. COMPUTATIONAL DETAILS Structural optimizations of ground states were carried out within density functional theory (DFT). An extensive screening of structural conformations was accomplished with the PBE016 functional in gas phase and Pople’s 6-31++G(d,p)17−20 basis set. Although, for ground states optimization of organic molecules, triple-ζ basis set 6-311G(d,p)21,22 is recommended,9 a simple double-ζ basis set gives close geometrical parameters,8 allowing economy of computational time and effort. Diffuse functions were applied both to hydrogen and heavy atoms to provide an improved description of weak intramolecular hydrogen bonds. The minimum nature of the obtained stationary points was confirmed by frequency calculations. Absorption spectra were simulated using TDDFT.23−25 Only singlet−singlet excitations are taken into account. Although convergence of the wavelengths corresponding to the low-lying excited states was rapidly achieved, the first 20 excited states were included in the excitation scheme to ensure a correct treatment of the upper-lying states in future optimization procedures. The performance of several hybrid functionals, well-known for a correct description of optical properties of organic dyes, was assessed. Two conventional hybrids, PBE016 and B3LYP,26,27 as well as two range separated hybrids LC-PBE (with variable μparameter according to Hirao long-range correction scheme)28 and CAM-B3LYP29 were taken into account. The geometries obtained at PBE0/6-31++G(d,p) level in gas phase were systematically reoptimized for each considered functional including solvent effects. If it does not allow to estimate the performance of purely TD-DFT part, separated from geometry quality issues, it gives an overall assessment of each functional, indispensible in further research on electronic structure in epicocconone derivatives. The assessment of basis set 6-31++G(d,p)17−20 sufficiency was shown with respect to 6-311++G(d,p), 6-31+G(2d,p), 6-311+ +G(2d,p), 6-31++G(2df,2p), 6-311++G(2df,2p)17,18,21,22 basis sets. Convergence of excitation energies and their ratio to methodological error were taken as a criterion of basis set adequacy. The polarizable continuum model (IEFPCM formulation,30 overlapping spheres with UFF-radii), in its nonequilibrium approximation,31,32 was systematically applied to calculate vertical excitation energies to simulate aprotic acetonitrile solvent. According to numerous studies, this model is a valid approximation in the absence of specific solvent−solute interactions. Once performance of density functionals is assessed, the influence of state specific (nonequilibrium)

2. EXPERIMENTAL SECTION Epicocconone derivatives of the first and second generations were synthesized and purified according to the previously reported procedure.11,12 For absorption measurements, butylamine adducts were produced from epicocconone analogues in acetonitrile solution as follows. To prepare stock solutions, 1−2 mg of each analyte was diluted in 1 mL of DMSO (Sigma, quality Bio Ultra, for molecular biology). A total of 10 μL of 0.15 M butylamine (Fluka, purity superior to 99%) solution in acetonitrile (VWR quality HPLC) is added to 30 μL of stock solution, this mixture was stirred up and centrifuged. Completed up to 1 mL by acetonitrile, transparent solution was transferred into 10 mm quartz UV-cuvette (Varian), where it was diluted once again with 2 mL of acetonitrile. Absorption spectra were registered with a Varian−Cary 50 Scan spectrometer at temperature 25 °C in the interval 250−600 nm with a resolution of 1.5 nm. Blank solution spectrum was first recorded and then deduced from spectra of analyte solutions. 8635



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Figure 2. Groups subject to rotation and tautomer forms in aminated epicocconone derivatives.

Figure 3. Nomenclature of conformations: 1 and 2 indicate position of carbonyl group or oxygen atom with respect to an imaginary plane, perpendicular to the projection plane and passing through the straight line, which connects two carbon atoms of two different keto-groups (red dashed line); 1 corresponds to the left-hand side; 2 corresponds to the right-hand side.

solvation33−37 on consistency and accuracy of model was also checked for the best one of them. Finally, to evaluate the effect of PCM-solvent inclusion, gas phase simulations were made for the most performant functional. All calculations were carried out with the Gaussian 09 ab initio package,38 while molecular pictures were obtained with the GaussView39 program. Fitting between theoretical and experimental absorption wavelengths is made using simple linear regression. The following parameters were taken as criteria of model adequacy: coefficient of determination R2, regression standard deviation sr, and mean absolute error (MAE). Formulas used to calculate these parameters as well as a detailed procedure of statistical treatment are given in Supporting Information (section III).

theoretical and experimental excitation wavelengths at different levels of theory. 4.1. Conformational Analysis. Experimentally determined structural model was taken as a basic geometry for simulations.2,12 Stereochemistry of asymmetric carbon atoms was defined according to the configuration of synthetic analogues reported previously.12 It can be easily seen (Figures 2 and S1) that several groups in epicocconone and its derivatives are subject to rotations around the simple bonds forming various structural configurations. Indeed, if the molecular scaffold of butylamine adduct constituted of two carbon rings, is quite rigid, a large number of conformations is provided by rotations of three side groups: the butylamine one, the alcohol chain (propan-2-ol, (2-methyl)propan-2-ol, or propan-1,2-diol), and the keto- or β-diketogroup side chain with R substituent (Figure 2). The most energetically favorable conformations of the “butylamine” and “propanol” side chains are quite obvious from empirical steric effects consideration. They can be obtained within standard optimization procedures, and moreover, their eventual rotations do not influence the absorption spectra. Therefore, they will not be discussed hereafter. On the contrary,

4. RESULTS AND DISCUSSION It is straightforward that characteristics of theoretical absorption spectra depend on the molecular configuration (structure, conformation) for which simulation is made. For this reason, an unavoidable step of spectra modeling is to determine the most stable structures for a given compound. So, in the first part of this section we discuss the geometrical characteristics of studied fluorophores. In the second part, we address the fitting between 8636



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As conformations for most of the compounds in the first generation is qualitatively similar, rotational profiles around different dihedral angles for Ia structure were thoroughly studied and then generalized for all compounds of the first generation. The rotation around the first dihedral angle (a) reveals the existence of two stable conformations 12_up and 12_down: the CO bond tends either upward or downward with respect to the 2-furanone ring (Figures 4 and S2). Energetically, these two configurations are indistinguishable. The same conformation types are stable for other compounds of the first generation. The rotation around the second dihedral angle (Figure 4b) transforms conformation 12 into 11 (Figure 5). The last one has a similar double-well rotational profile as 12, with up and down minimum structures. So Ia compound features four conformational minima and four transition states between them. Conformations based on 11 (up and down) structure are less stable than 12 at gas phase (PBE0) and almost degenerate in energy in solvent (PCM/PBE0 or CAM-B3LYP; Figures 5, S2, and S3). Transition states connecting the minima are situated 3− 4 kcal/mol above them (PBE0/6-31++G(d,p)). So, in the following, a preference toward 12 conformation in first generation analogues is retained. It is supported by recent findings of X-ray spectroscopy on crystallized Id compound.12 Ic is more stable in 122 conformation, the side carbonyl group for this configuration being always oriented upward (down configuration is not observed). The conformation 121 is only 1.3 kcal/mol less stable than 122; the side keto-group being oriented downward with respect to the 2-furanone cycle of the molecular scaffold. If is more stable in 121 configuration. Ig derivative is peculiar: in the most stable conformation, H atom of OH phenyl group forms a hydrogen bond with the side keto-group (122 configuration). Distances O−H and H···O are of ∼1.0 and ∼1.6 Å, respectively. All stable configurations of these molecules are splitted into two conformations up and down (see Figure 5 for Ia). They are very close in energy and, moreover, their formal relative stability depend on density functional and inclusion of solvent effects. So there is no way to discriminate systematically up and down configuration using electronic energy or Gibbs free energy as a criterion (differences are lower than 1 kcal/mol). Second Generation. Second generation compounds, including epicocconone, have some common features. All of them, but Il and Im, are enolizable. Tautomerization of one or another keto-group in β-diketo−enol is energetically indistinguishable. Indeed, for most second generation compounds, the energy difference between two tautomer forms is close to 0.5 kcal/mol (PBE0/6-31++G(d,p)), with a preference to enolization of the first keto-group (Figure 2). In epicocconone it is a little bit higher (0.9 kcal/mol) and, in contrast with other compounds of second generation, enolization of second keto-group is preferred (Figures 2, 6, S1b). Tautomerization allows placing the 1,3-diketo- side chain and R radical practically in the same plane as molecular scaffold (planar conformation, 122) that extends π-conjugation. The twisted nonplanar conformation (121) is much less stable: its relative energy is ∼16 kcal/mol in gas phase and ∼13 kcal/mol in solvent (PBE0) with respect to the planar one (122). The high relative energy of 121 conformation suggests that the rotation barrier for epicocconone and second generation derivatives is even higher. 111 and 112 conformations of epicocconone are less stable by more than 8 kcal/mol in comparison with 122. Strans conformation of epicocconone is preferred to s-cis by 1.2 kcal/mol (Figure 6). This is in line with higher intensity of the

keto- or β-diketo- side chains can be subjected to hindered rotations. Then, conformations can be regarded as individual compounds giving different excitation wavelengths in the spectrum. Apart from side chain rotation, possible tautomer forms should be taken into account. In butylamine adducts one can imagine β-enaminone ↔ β-iminenol and β-diketon isomers (Figure 2). In the following, we will first focus attention on the common features for analogues of both or each generation and then describe the peculiarities of certain compounds. Finally, we will discuss the influence of the structure on excitation wavelength for energetically close lying conformations. One common feature of all aminated structures of considered fluorophores is the instability of β-iminenol with respect to βenaminone. This is in line with previously published results for epicocconone butylamine adduct.15 Instability of β-iminenol with respect to β-enaminone turns out to be characteristic for that class of compounds as shown recently by Gilli et al.40 To study the side keto-chain conformations, a simplified nomenclature has been adopted (Figure 3). Position 1 corresponds to the left-hand side; position 2 corresponds to the right-hand side. For instance, in conformation 11, both oxygen atoms of carbonyl groups are on the same side (left) from the imaginary plane, while in conformation 122, the first (from the top) carbonyl group is situated to the left of this plane (1), while the two others are to the right of it (2). First Generation. All first generation compounds (Figures 1, S1a) have only one carbonyl group in the side chain. The simplest is the Ia compound, having phenyl radical as Rsubstituent. Ib, Ie, and Ih are derived from Ia by addition of a functional group into the para-position of the aromatic ring. Ic has a 2-furanyl R-group and Id has a naphthyl group in place of the phenyl. If and Ig have methoxy- and hydroxy- groups in the ortho-position of the phenyl ring. Evidently, the energy profile for rotation of R-side group in Ia, Ib, Ie, and Ih compounds should be very close, as parasubstitution in the aromatic phenyl ring does not create supplementary steric hindrance. Compounds Ic, Id, If, and Ig also should have qualitatively the same potential wells but different rotation barriers either due to the different nature of the aryl radical or to ortho-substitution in the phenyl ring. Two principal sources of conformational changes are rotations around the single bond between R and the carbonyl side group (Figure 4a) and rotation around the bond connecting the

Figure 4. Dihedral angles between carbonyl group and benzene ring (a) and carbonyl group and double bond of 2-furanone cycle (b).

carbonyl side group to the molecular scaffold (Figure 4b). It can be easily seen that any first generation compound may adopt these two types of conformations: 12 and 11. Besides some of them (Ic, If, Ig), having an O-substituent in the ortho-position of the aromatic side group, split into other configurations, like 122 and 121 or 111 and 112 (the last figure in this notation indicates the position of the third oxygen atom). 8637



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Figure 5. Stability and excitation wavelengths of the most stable Ia conformations: PBE0/6-31++G(d,p) gas phase and solvent.

Figure 6. Stability and excitation wavelengths of the most stable epicocconone conformations: PBE0/6-31++G(d,p) gas phase and solvent.

Figure 7. Stability and excitation wavelengths of the most stable Im conformations: PBE0/6-31++G(d,p) gas phase and solvent.

electronic excitation in s-trans conjugated 1,3-dienes with respect to s-cis. The In compound behaves particularly: N atom of the pyridine group can form a H-bond with hydrogen of β-diketo− enol OH group. This leads to a planarization and a stabilization of

121 In-conformation by about 8−9 kcal/mol in comparison to other compounds of second generation, although 122 is still energetically favored. The Im and Il derivatives, having a 2-methyl-1,3-diketo-group, instead of a simple 1,3-diketo one, are not enolizable (Figure 7). 8638



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Figure 8. HOMO−LUMO excitation in butylamine adducts of epicocconone and Ik.

from one functional to another. Interestingly, the difference between λmax(12_up) and λmax(12_down) is systematic for all functionals and all first generation compounds. It equals 5 nm for most of them, the wavelength being higher for the 12_down conformation. This suggests a systematic choice of the same conformation rather than that based on a formal stability. This would certainly decrease the contribution of unaccounted systematic error into a statistical one; besides, this would not introduce supplementary unphysical dispersion associated with data scattering. Finally, assuming that both conformations contribute to the spectrum by a superposed signal, a1λ1 + a2λ2, with comparable coefficients ai, regression with respect to linear dependent λ1, λ2 or a1λ1 + a2λ2 is invariant (R2 is not affected). This is not the case if λmax are taken from a different series. 4.2. Methodological Aspects. The selection of computational protocol for the TDDFT simulation of absorption spectra implies the choice of the density functional approximation (DFA), basis set, and solvation models. Numerous studies8,9,41 have shown that the DFA choice has the strongest influence on the theoretical model consistency and accuracy, the environment effects, and the basis set extent being of lesser importance. For this reason, in this section we first address the density functional adjustment procedure and then turn toward basis set consistency and solvent effects discussion. Density Functional. The type of electronic transition is a factor that mostly conditions the choice of density functional. According to our simulations, the first electronic vertical transition in the butylamine adduct of epicocconone and its derivatives is monoelectronic and mainly corresponds to an excitation of one electron from HOMO to LUMO (Figure 8), in agreement with previously published results.14,15 So, the selected density functional should give a proper description of the HOMO−LUMO gap. Pure LDA or GGA functionals, well-known to underestimate the HOMO−LUMO gap and, as a result, excitation energies between frontier orbitals,8 were directly excluded from consideration. Hybrid functionals, containing a part of exact

Indeed, enolized Im derivative is 0.6 kcal/mol (PBE0) less stable in gas phase than its simple β-diketo form. In solvent, its stability is further decreased (Erel (PBE0) = 2.7 kcal/mol). Calculations with PCM/CAM-B3LYP even ensures this observation: for Im enol is destabilized by 4.7 kcal/mol and for Il enol is destabilized by 5.2 kcal/mol. Summarizing the above observations, most of the second generation compounds present a planar 122 conformation with first enolized keto-group, with the exception of epicocconone in which enolization of the second keto-group is favorable (Figures 2 and S1b). Influence of Conformation on Excitation Wavelength. Examples of epicocconone and Im analogue (Figures 6 and 7) show that different conformations can give different excitation wavelengths, though not all of them can be observed in the spectrum. Indeed, the intensity of absorption is proportional to the concentration of species. According to Boltzmann’s distribution, conformations with relative energy higher than RT at ambient temperature (∼0.6 kcal/mol) can be put off consideration, as their contribution to the integral intensity will be proportional to the Boltzmann factor exp[−ΔErel/RT]. As for configurations of closer energy, the differences in excitation wavelengths are on the order of 2−3 nm for the first and second generation compounds, staying within experimental uncertainty. On the contrary, some compounds of first generation have conformations that are quite close in energy but have larger differences in excitation wavelengths (5−7 nm). As it can be seen for the simplest representative of the first generation Ia, slight differences in stability correspond to significant changes in the excitation wavelengths (see 11 vs 12 conformation). Even if in the gas phase conformation 11 is ∼3 kcal/mol above 12, inclusion of solvent effects makes them almost degenerate (Erel(Ia_11_down) ∼ 0.3 kcal/mol). Moreover, for the whole ensemble of exchange-correlation functionals discussed below, 12_up and 12_down conformations are almost energetically indistinguishable (ΔErel < 1 kcal/ mol). Their relative stability according to electronic energy (with or without zero-point correction) and Gibbs free energy alter 8639



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Table 1. Experimental and Theoretical Wavelength of the First Excitation in Aminated Epicocconone Derivativesa LC-PBE epi Ia Ib Ic Id Ie If Ig Ih Ii Ij Ik Il Im In Io Ip

CAM-B3LYP

exp

PBE0

B3LYP

0.20

0.30

0.40

0.47

gas

noneq

st. sp.

520 462 452 465 464 453 469 463 460 498 505 512 488 489 525 518 525

495 436 433 442 440 433 436 444 435 468 470 471 440 440 480 476 487

518 451 449 458 456 449 452 461 451 486 488 488 454 454 499 494 507

477 445 441 453 447 442 444 455 444 465 468 469 455 456 475 471 477

438 411 406 418 413 407 408 416 408 429 431 434 427 427 439 435 441

409 382 377 387 383 377 380 383 378 401 403 405 402 401 411 406 413

394 367 362 370 367 362 365 366 363 386 388 390 386 387 396 391 398

406 371 368 380 372 368 368 373 370 391 393 394 384 385 401 396 405

444 410 405 415 412 405 410 411 407 433 435 437 423 424 444 439 446

436 406 402 411 408 403 407 408 404 426 428 430 417 418 437 432 439

a For compounds of first generation, wavelengths for 12_up conformation are presented. For the second generation, the wavelength of the most stable conformations are given. “gas”, “noneq”, and “st. sp.” stand for gas phase, nonequilibrium, and nonequilibrium state specific solvation, respectively.

Hartree−Fock (HF) exchange, are known to remedy this drawback. Our attention has been focused on two families of hybrid functionals: PBE-based and BLYP-based. We have taken two global hybrids (GH), PBE0 and B3LYP, comprising, respectively, 25 and 20% of HF-exchange and wellknown for their good performance in simulation of electronic properties of organic molecules.7−9 Besides, we have considered two range-separated hybrids (RSH), allowing graduate, distancedependent inclusion of exact exchange via an adjustable parameter: LC-μPBE and CAM-B3LYP. The smaller is μ, the higher is the distance from which HF-correction becomes effective. Variation of this parameter for the first one, LC-μPBE, from its default value (0.47) to 0.20 helps to depict the role of the exact exchange part for the proper description of electronic structure in epicocconone derivatives and provide a better consistency between theory and experiment. The second RSH, CAM-B3LYP, has a greater HF contribution at short-range and is known for its performance in description of delocalized excited states.7−9 This strategy would allow the improvement of the HOMO−LUMO gap description and, as a consequence, the correlation between theory and experiment. Experimental and computed excitation wavelengths are given in Table 1. It can be seen that no one of used functional enables a direct comparison of theoretical and experimental values without linear regression correction. Indeed, all functionals give a systematic underestimation of calculated wavelength. For this reason we only refer in the following to statistically corrected parameters reflecting the quality of the given model. Table 2 summarizes characteristics of the obtained regression models. As one can see, global functionals give the worse description over the complete set of molecules. For instance, PBE0 is characterized by 10 nm standard deviation and 0.87 determination coefficient. Meanwhile, particularly high deviations from the model are observed only for three compounds: natural compound epicocconone and nonenolizable 1,3-diketo derivatives Il and Im. If these compounds are excluded from the training set, determination coefficient R2 rises from 0.86 to 0.97 and standard deviation of regression diminishes by a half (10 vs 5

Table 2. Regression Parameters for Global (PBE0, B3LYP) and Range-Separated Hybrid Functionals (LC-PBE (ω = 0.47, 0.40, 0.30, 0.20), CAM-B3LYP); PCM, 6-31++G(d,p)a functional

conf.

R2

sr, nm

MAE, nm

PBE0 B3LYP LC-PBE (0.47) LC-PBE (0.47) LC-PBE (0.40) LC-PBE (0.40) LC-PBE (0.30) LC-PBE (0.30) LC-PBE (0.20) LC-PBE (0.20) CAM-B3LYPb CAM-B3LYP CAM-B3LYP CAM-B3LYP (st.sp.) CAM-B3LYP (gas)

up up up down up down up down up down mixed up down up up

0.87 0.85 0.95 0.95 0.94 0.95 0.95 0.94 0.93 0.89 0.95 0.98 0.97 0.98 0.95

10 11 6 6 7 7 6 7 7 9 6 4 5 4 6

8 8 5 5 5 5 4 4 5 7 5 3 4 3 4

a Conf., conformation of the first generation compounds; st.sp., state specific solvation; gas, gas phase. bMost stable compounds (with respect to Gibbs-free energy).

nm). In this case, experimental wavelengths for Im, Il, and epicocconone are situated completely out of the 99% confidence interval (∼3σ) for theoretical prediction. The same observation is valid for the B3LYP functional. Fail of global functionals to describe electronic excitations in these molecules may be related to unaccounted long-range interactions. Range separated hybrids, as it can be deduced from Table 2, perform better than global ones. It is an expected result, as HOMO and LUMO orbitals are quite delocalized in considered molecules, so long-range correction of exchange seems to be indispensable for appropriate simulation of valence excitations. One of the primary sources of improvement is a better description of Il and Im compounds and epicocconone. The LC-PBE functional shows the best results for μ = 0.30. 8640



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compounds of second generation, in their most stable configuration, have a side carbonyl group CO slightly oriented upward. It cannot be excluded that the excitation wavelength is merely dependent on the sign and absolute value of the dihedral angle between the carbonyl group and the 2-furanone cycle (“conjugation” angle). Its sign, positive or negative, would explain the systematic shift between up and down configurations. Although, this question needs deeper consideration, both from theoretical and experimental points, it is beyond the scope of the present article. Basis Set Sufficiency. In the present section, sufficiency of the 6-31++G(d,p) basis set, used to assess the density functional and the solvation solvation, is shown. To elucidate the effects of the 631++G(d,p) basis set on the geometry of aminated epicocconone derivatives with respect to 6-311++G(d,p), three representative compounds (epicocconone; Ia, first generation; Ik, second generation) were optimized with these basis sets using PBE0, in the gas phase, and changes in internal coordinates have been analyzed. The highest changes in bond lengths, angles, and dihedrals are associated with side keto- (or diketo-) and enaminone groups (Table S1). Besides, excitation wavelengths obtained at PBE0/6-311++G(d,p) and PBE0/6-31++G(d,p) levels differ only by 2−4 nm. To evaluate the impact of basis set increase on the convergence of excitation wavelengths, vertical excitations on PBE0/6-31+ +G(d,p) geometry have been accomplished on TD-PBE0 level in gas phase for 6-31++G and 6-311++G basis sets including (d,p), (2d,p), or (2df,2p) polarization functions. It turns out that basis set 6-31++G(d,p) gives already converged wavelengths within 1−2 nm (Table S2). The differences are comprised within an uncertainty of ±3 nm related to apparatus resolution (lowest estimation of methodological experimental error). Moreover, a slight wavelength shift induced by basis set change is systematic (is almost constant and has the same sign), so should not affect correlation. Solvent Effects. Although PCM-solvation with acetonitrile as a solvent was used in all calculations of DFA assessment, no state specific solvation of the first excited state was applied for the moment. To test the necessity of this quite time-consuming procedure for the calculation of the absorption spectrum, we have applied it for the most performant functional: CAMB3LYP. As it is indicated in the Table 2, no improvement is brought by inclusion of this refinement. Excitations in molecules from the training basis set are as well described as for simple CAM-B3LYP. It is observed that inclusion of specific solvation for the first excited state shifts down the excitation wavelengths systematically by 3−4 nm for the first generation compounds and 7−8 for the second generation and epicocconone (Table 1). Thus, the sign of the wavelength shift is the same and, moreover, its absolute value is constant, even if it is not the same, for the first and the second generations. Then, it is straightforward that the quality of the model would not be affected by the introduction of this feature. As a conclusion, state specific solvation is not imperative for the simulation of the first vertical excitation in aminated epicocconone derivatives. However, its necessity for emission spectra simulation certainly cannot be excluded. To test the possibility to reduce computational effort, we have also considered the regression model for gas phase excitations for CAM-B3LYP. Consistency and accuracy diminish in this case: R2 drops from 0.98 to 0.95 and sr increases from 4 to 6 nm. So, solvent effects seem unavoidable if accurate and consistent results are targeted.

Minimal discrepancies between model and experimental wavelengths for Im, Il, and epicocconone are observed for this value of μ. Besides, for lower values of μ (especially at 0.20), absolute error for Ic, If, and Ig goes up. This can be due not only to the ability of each functional to describe excitations in respective molecules, but also to the changes in geometry. Indeed, it is known that some long-range corrected functionals give poor geometries9,41,42 and, as a consequence, less-consistent excitation energies. As indicated by the correlation coefficient and the standard deviation, the most performing functional is CAM-B3LYP (R2 = 0.98). Prediction of excitation wavelengths for new compounds with 95% confidence is possible within ∼2sr, that is, ±8 nm (Figure 9) according to eq 1: λexp = 1.77λtheor − 262

(1)

Figure 9. Fitting of experimental absorption wavelengths with theoretical ones obtained at the PCM/CAM-B3LYP/6-31++G(d,p) level. Red broken lines delimit the 95% confidence interval (approximately 8−9 nm from the regression curve on each side). Formulas used for calculation of confidence intervals are given in Supporting Information.

Residual dispersion seems to be related, in the first place, to the difficulty of localization of the maximum in the experimental spectrum. Another source of uncertainty is the use of only one conformation as a theoretical reference, without simulation of spectra broadening due to the presence of several minima degenerate in energy. Thus, further methodological improvements would act within experimental data dispersion. Nevertheless, it should be remarked that sr = 4 nm, in context of actual computational studies on the UV/vis molecular spectrum,7−10,41,43−49 represents a high precision for the prediction of excitation wavelength. Another important remark concerns the influence of chosen conformations on correlation and dispersion of regression model. When the PCM/CAM-B3LYP/6-31++G(d,p) approach is used, the parameters of regression model, based on theoretical values for the (formally) most stable conformations (according to Gibbs free energy) of first generation compounds, are determined. A decrease of R2 (0.98 → 0.95) and an enlargement of sr (4 → 6 nm) is observed with respect to systematic choice of one of them (12_up). Moreover, choice of conformation 12_up for all compounds of first generation systematically (see LC-PBE and CAM-B3LYP fits) gives higher correlated and more accurate calibration curves than 12_down. It can be related to the fact that Ic and all 8641



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5. CONCLUSIONS This work represents a first step toward the oriented molecular design of pro-fluorescent epicocconone analogues. Absorption spectra of novel generations of epicocconone derivatives are communicated for the first time. A computational methodology consistent with these experimental data is established. Timedependent density functional theory permits a correct description of the lowest excited state in the butylamine adduct of epicocconone and its derivatives. The highest impact on the quality of results is related to the choice of density functional approximation. Evaluation of its performance reveals a higher consistency theory−experiment for the range separated hybrids with respect to the global hybrids, although failure of the last ones is mostly associated with their insufficiency for particular compounds. Convergence of 6-31++G(d,p) basis, with respect to the methodological precision threshold, is confirmed. It opens horizons for extensive studies of spectroscopic properties in epicocconone derivatives at an affordable computational cost. The range-separated hybrid functional CAM-B3LYP is shown to be the most performant for simulation of the first excited state in this family of compounds. An equation based on this calibration model (PCM/CAM-B3LYP/6-31++G(d,p)) is proposed for the quantitative prediction of absorption wavelength in similar compounds within the 95% probability margins ±8 nm. Inclusion of solvent effects turns out to be indispensible, as the gas phase simulations give lower correlation and accuracy. Although specific solvation of the first excited state is not crucial to attain the desired characteristics. A detailed conformational analysis has shown influence of a given molecular geometry on the simulated absorption spectrum. Thorough tracing of the geometrical configuration for which λmax is calculated is a prerequisite of accuracy of the theoretical model. The dependence of excitation wavelengths and oscillator strengths on conformation is in line with recent observations on fluorescence enhancement for organic chromophore molecules encapsulated in molecular matrices50,51 or micelles.14 Indeed, one reason for better fluorescence characteristics, among others, may reside in a possibility of conformational fixation during excitation−de-excitation processes, as it is described previously for other fluorescent compounds.50 Further investigations of photoprocesses in epicocconone derivatives are in progress and will be reported shortly.

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Région Haute Normandie for Ph.D. thesis funding. L.J and V.T. thank the CNRS for a “Chaire d’excellence”.

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ASSOCIATED CONTENT

S Supporting Information *

Chemical structures of studied aminated epicocconone analogues, relaxed scan for conformations changes, details about the statistical treatment, and basis set assessment. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the ANR-BLAN-732-01 grant for financial support. Computational center IDRIS is acknowledged for providing HPC resources. A.B. and P.A.P. are grateful to the 8642



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Electronic Excitations in Epicocconone Analogues: TDDFT

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