Accurate and Inexpensive Prediction of the Color Optical Properties of

Article pubs.acs.org/JPCA

Accurate and Inexpensive Prediction of the Color Optical Properties of Anthocyanins in Solution Xiaochuan Ge,† Iurii Timrov,† Simon Binnie,† Alessandro Biancardi,† Arrigo Calzolari,*,†,‡ and Stefano Baroni†,§ †

SISSA − Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 265, I-34136 Trieste, Italy CNR-NANO, Istituto Nanoscienze, Centro S3 via Campi 213A, I-41125 Modena, Italy § THEOS − Theory and Simulation of Materials, Ecole Polytechnique Fédérale de Lausanne, Station 12, 1015 Lausanne, Switzerland ‡

ABSTRACT: The simulation of the color optical properties of molecular dyes in liquid solution requires the calculation of time evolution of the solute absorption spectra fluctuating in the solvent at finite temperature. Time-averaged spectra can be directly evaluated by combining ab initio Car−Parrinello molecular dynamics and time-dependent density functional theory calculations. The inclusion of hybrid exchangecorrelation functionals, necessary for the prediction of the correct transition frequencies, prevents one from using these techniques for the simulation of the optical properties of large realistic systems. Here we present an alternative approach for the prediction of the color of natural dyes in solution with a low computational cost. We applied this approach to representative anthocyanin dyes: the excellent agreement between the simulated and the experimental colors makes this method a straightforward and inexpensive tool for the high-throughput prediction of colors of molecules in liquid solvents.

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INTRODUCTION Color is pervasive in human life: every visual perception of the world around us is influenced by color. Colors characterize and distinguish natural and artificial objects, living and inanimate beings. This justifies the enormous interest in the physiology and physical chemistry of color perception and their applications in the visual arts, biomedical sciences, agriculture, and such economic activities as textile, painting, makeup, or food industries.1 The color of objects is affected by the presence of specific molecular or polymeric aggregates, which can be either natural or synthetic, known as pigments and dyes. Pigments are chromatic, achromatic, or fluorescent particles, both organic and inorganic, that are insoluble and almost unperturbed by the substrate they are incorporated in. Dyes, instead, are organic molecular structures that are completely soluble in a solvent or in a polymeric blend. When a dye is applied it penetrates into the substrate as a solute; that is, it directly interacts with the embedding medium. This is what happens, for instance, in biological systems (such as leaves, flowers, or fruits), where the dyes are dissolved in aqueous solutions contained in chloroplasts and vacuoles. The color they express critically depends on the chemico-physical equilibria of the solution and may change as a function of the physiological cycle of the system: the color variation of fruits upon ripening is a clear example of this process. Thus, the study of molecular dyes cannot leave the solvent and its interaction with the solute out of the picture. Many traditional colorants are toxic (e.g., they may contain heavy metals), and hence their use in such applications as the © 2015 American Chemical Society

food, pharmaceutical, or cosmetic industries would be dangerous to the health or the environment. In this regard, natural dyes (such as, chlorophylls, anthocyanins, carotenoids, betaalanine, and tannins) may be a valid alternative;2 however, their application on a large scale will rest on our ability to engineer their optical properties to specific color functions, which, in turn, will require a deep understanding of the relations among color function, molecular structure, and the interaction with the environment. These relations are addressed for the specific but wide and important family of anthocyanin dyes. Anthocyanins3 are natural dyes responsible for the bright and diverse coloration of many flowers (e.g., pansies, pelargonium, or delphiniums) and fruits (e.g., berries, eggplants, and grapes). Unlike other plant colorants, such as chlorophyll and carotenoids, anthocyanins are water-soluble, and they are usually found in an aqueous environment in nature, for example, in the vacuole of plant cells.3 These molecules have long been used in the food industry as colorants,2,4 additives,5 or antioxidant agents.6−8 Their metabolic activity in human beings9,10 is also being investigated for potentially beneficial effects against aging, in the treatment of diabetes, or even in cancer prevention.11−13 Anthocyanins are polyphenolic derivatives, belonging to the flavonoid family.14 They are glycosides of polyhydroxy and polymethoxy derivatives of 2-phenylbenzopyrylium backbone, whose structure is shown in Figure 1. The corresponding Received: February 6, 2015 Revised: March 31, 2015 Published: April 1, 2015 3816

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gas-phase spectrum of flavylium anthocyanins is characterized by one-to-three absorption peaks in the visible range, depending on the number of oxygens in the B ring; (ii) the computed optical gap opens up by a few hundreds of millielectronvolts when moving from a PBE GGA exchangecorrelation (XC) functional38 to a B3LYP hybrid functional,39,40 while the overall shape of the spectrum is roughly independent of the functional in use; (iii) the corresponding simulated color in the gas-phase model of the dye shifts from greenish (GGA) to salmon-pinkish (hybrid); (iv) the effect of the dielectric screening of the water solvent on the computed spectrum, as accounted for via a polarizable continuum model (PCM),41 is mainly a small red shift in the lowest-lying absorption lines, which hardly affects the simulated color; and (v) thermal fluctuations of the molecular structure, as modeled by ab initio (AI) MD for an explicit-solvent model of a watersolvated cyanin molecule, dramatically affect the optical properties at the PBE level (no hybrid-functional simulations were attempted), resulting in the filling of the gaps between the absorption lines in the visible range and turning the simulated greenish coloration into deep purple. While being essential to achieve an acceptable accuracy in the prediction of molecular absorption spectra, hybrid functionals are computationally more costly than semilocal GGA functionals, particularly when using a plane-wave (PW) representation of molecular orbitals. This prevents one from using these techniques for the simulation of the optical properties of systems with hundreds of atoms, as in the case of molecules in an explicit solvent environment. We present an alternative technique to simulate the optical properties of natural dyes in explicit water solvent, which conjugates the high accuracy typical of hybrid functional approaches and the low computational cost of standard GGA calculations. In particular, we devised a morphing procedure that allows us to recover the color expressed by the hybrid spectrum for an explicitly solvated molecule from the GGA spectrum for the solvated molecule and the hybrid spectrum for the isolated molecule. The direct comparison with the experimental colors confirms the accuracy of the present method, which can be thus profitably used for the prediction and the design of the color optical properties of molecules in liquid solvents.

Figure 1. Anthocyanidin 2-phenylbenzopyrylium backbone in the positively charged f lavylium configuration.

aglycone form is known as anthocyanidin. The core of the anthocyanidin is a 15-carbon structure forming two aromatic rings (A and B in Figure 1) joined by a third C3O ring (C). The presence of two CC bonds in the C ring distinguishes anthocyanins from other flavonoids and imparts a positive charge to the molecule, which results to be a cation (known as f lavylium) in its stable form at low pH. The phenylbenzopyrylium core of anthocyanins is typically modified by the addition of a wide range of chemical groups through hydroxylation, acylation, and methylation. Glycosylation considerably enhances the stability of anthocyanidins, and that is why these molecules are usually found in their anthocyanin form in biological systems.15 The most common anthocyanins occurring in nature are derived from the monoglycosylation at position R3 (Figure 1) of the six principal anthocyanidins, namely, pelargonidin, cyanidin, peonidin, delphinidin, petunidin, and malvidin.3 Despite the minor chemical differences, these molecules express a wide range of colors, providing most of the pink, orange, red, violet, and blue colors of fruits and flowers. Because anthocyanins express their chromatic function in solution, their color also shows a strong dependence on the environment, such as the concentration,15 the acidity,16−18 the polarity,19,20 and the temperature21−23 of the solvent, or the presence of otherwise optically inert substances in solution, which alter its color (copigmentation).16,24,25 This paper is meant to be a step toward the identification of accurate and cost-effective methods for elucidating the interplay among chemical structure, environment (specifically water solvation and temperature), and color function of these dyes in the f lavylium state, which is the most typical charge state assumed by anthocyanins in the biological systems.3 Quantum-mechanical numerical modeling techniques, based on density functional theory (DFT)26 and time-dependent DFT (TDDFT),27 are considered to be state-of-the-art to investigate the electronic, structural, and optical properties of complex molecular systems in complex embedding environments. These techniques were recently employed to address the optical properties of anthocyanins in gas phase28,29 or using implicit solvent models.30−33 The latter only describe the solvent as a continuum dielectric medium, affecting the polarization properties of the solute. Rather, they completely neglect specific solute−solvent effects, such as hydrogen or halogen bonding or thermal fluctuations. On the contrary, explicit solvent models are usually adopted only to investigate the hydration or dynamical properties of solutes via molecular dynamics (MD) or QM/MM approaches.34,35 The simultaneous treatment of dielectric and thermal effects due to the solvent on the optical properties of molecules is quite rare.36,37 The main results of previous theoretical works on anthocyanins29,32,37 can be summarized as follows: (i) the

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METHOD AND COMPUTATIONAL DETAILS Simulations were performed within (TD)DFT using pseudopotentials and PW basis sets with periodic boundary conditions in a (20 × 20 × 12) Å3 supercell. The QUANTUM ESPRESSO suite of open-source computer codes42,43 was used throughout, along with pseudopotentials from its public repository.44 We considered both the PBE38 GGA and hybrid B3LYP39 parametrizations for the XC functional. PBE simulations were carried out using ultrasoft pseudopotentials44,45 and a 25/200 PW basis set.46 Hybrid-functional calculations were performed with norm-conserving pseudopotentials44 and a 60/240 Ry basis set.46 We studied anthocyanins in the f lavylium charged state, which is the most stable under acidic conditions (pH ≲ 3).3 Molecules in the gas phase were simulated in charged supercells neutralized by a compensating uniform background. Solvation effects were simulated by AIMD on an explicitly solvated model of the dye in which the solute molecule is surrounded by 96 water molecules, which account for the first solvation shell, plus a Cl− counterion to neutralize the system. AIMD was performed using the Car−Parrinello47 Lagrangian formulation 3817

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The Journal of Physical Chemistry A as implemented in the cp.x component of the QUANTUM ESPRESSO distribution.42,43 Water molecules were first thermalized by a long classical MD run while keeping the anthocyanin molecule frozen. The whole system was then thermalized for 5 ps with AIMD in the NVT ensemble48,49 at room temperature (T = 300 K). This equilibration phase was then followed by a 10 ps production microcanonical run, during which absorption spectra were collected on the fly every 0.5 ps, using a newly developed version50 of the turboTDDFT component51 of the QUANTUM ESPRESSO distribution.42,43 Color is simulated following the tristimulus colorimetry theory,52 as codified by the international CIE commission.53 Once the absorption coefficient of a material is known, the color of a sample can be expressed by three color indexes, X, Y, and Z, defined as37 XYZ = N

__ _

∫ I0(λ)e−κ(λ)Sxy z(λ) dλ

(1)

where I0(λ) is the incident radiation or illuminant. In the present case we used the standard D65 illuminant,54 which mimics the solar spectrum in the visible range. κ(λ) is the absorption coefficient calculated with TDDFT approach previously described. N is a normalization constant and S is the effective thickness traversed by the light beam in the sample. The functions x y z(λ) are the tristimulus colormatching functions, as defined by the CIE standard (CIE 1931, 2° standard observers55). They describe the physiological response of human retina to red, green, and blue colors, respectively. When the XYZ values are known, other color representations (e.g., RGB or CIELAB) may be trivially obtained through linear transformations.52 A java applet to simulate the color expressed by an a given absorption spectrum is being distributed with the TDDFT component of QUANTUM ESPRESSO.

Figure 2. Time-averaged absorption spectra (PBE) and color of (a) pelargonin-, (b) cyanin-, and (c) delphinin-solvated molecules (straight line). Gas-phase results (dashed line) and experimental colors for dye in water solution at room temperature and under acidic condition are also included for comparison.

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RESULTS AND DISCUSSION Flavylium Anthocyanins in Water Solution: Explicit Solvent Model. Simulating the color optical properties of anthocyanins in the gas phase results in a poor agreement with experiments performed in solution.29,37 There are two important effects on the absorption spectra of anthocyanins induced by the presence of the solvent. The first is the introduction of a polarizable medium, which affects the dielectric response of the molecule; the other is due to the thermal fluctuations of the molecular structure in the solvent. Explicit solvent models account for both of these effects in a natural way.37 We adopt the same procedure previously used in the case of cyanin37 to address the effects of the different “decoration” of the B-ring chromophore29 on the optical properties of cyanin, pelargonin, and delphinin. For each molecule, we first performed AIMD with explicit water molecules; then, we sampled the trajectory every 0.5 ps and we calculated the TDDFT spectra on the fly; finally, we time-averaged the resulting spectra. Notably, the size of the resulting simulation cell (∼400 atoms and ∼1000 electrons) prevents the use of hybrid functionals that may be too demanding, particularly when using PW basis sets. Because the main effect of using a hybrid functional is an almost rigid blue shift of the lowest energy peaks of the GGA spectrum, we first considered the dielectric and thermal effects of solvent on the optical properties of anthocyanins at the PBE level, which is nonetheless able to catch the main properties of

Figure 3. Absorption spectra of dehydrated anthocyanins and their simulated colors of (a) pelargonin, (b) cyanin, and (c) delphinin for PBE (straight line) and B3LYP hybrid (dashed line) XC functionals. Experimental colors for dye in water solution at room temperature and acidic condition are included for comparison.

the absorption spectra (but the frequencies). We then propose a simple but effective way to correct the optical spectrum thus obtained to estimate the chromatic properties of the molecules in solution with an accuracy comparable to that achievable from full hybrid-functional simulations. (See the next section.) Figure 2 shows the average spectra calculated with explicit water at room temperature (straight lines) for pelargonin (panel a), cyanin (panel b), and delphinin (panel c) dyes, respectively. Solvation results in an overall broadening and red shift of the absorption peaks. The former effect is mainly due to the thermal vibrations that change the atomic and electronic properties of the molecule, resulting in a set of spectra that differ in the shape (e.g., number of peaks) and in the frequency 3818

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analysis of the response charge density described by Malcıoğlu et al.37 The broadening and the bathochromic shift of the solvated spectra determine a general darkening of the molecular colors and a reduction of the perceived red component. The resulting hues are thus turned to magenta, purple, and blue. Again, the comparison between PBE results and experimental colors is not fully satisfactory. (See Figure 3.) Because we cannot afford calculating spectra with hybrid functional for the entire solvated system, we calculated, as the best compromise, the averaged spectra for the dehydrated phase with B3LYP hybrid functionals; the results are shown in Figure 3 (dashed lines). As expected, hybrid functionals lead to a blue shift in the spectra with respect to the PBE, and the intensity of peaks at short wavelength are slightly reduced, in agreement with what was observed in the gas phase. The choice of the functional does not modify the broadening of the spectra that is, instead, a genuine dynamical effect induced by thermal bath. The resulting simulated colors are now very close to the experimental ones. Color Morphing Procedure. The results previously reported indicate that to obtain a realistic description of the color optical properties of anthocyanins in solution, it is essential to account for the thermal fluctuations of the molecular geometry, which result from the solvation process, and to utilize hybrid XC functionals, which are, in general, too expensive to be used routinely for explicit-solvent models. To address these conflicting requirements, we propose a three-step morphing procedure that allows us to capture the main features of the spectra that would result from a hybrid-functional TDDFT calculation, using much less expensive GGA spectra as the sole ingredient. We start from the observation that the hybrid and GGA spectra are very similar and the differences, while depending very little on the molecular geometry, can be summarized as (i) an almost rigid shift of the lowest energy peaks and (ii) a partial rescaling of their relative intensities (see, e.g., Figure 3).29,37 The morphing therefore consists of a linear transformation of the frequency argument of the GGA spectra, so as to make their low-frequency peaks coincide with those obtained using a hybrid functional, and in a rescaling of the corresponding oscillator strengths, so as to match the relative intensities. Following is a description of each one of the three steps of the procedure. Step 1. To compute the frequency and intensity scaling factors, we start from the calculation of the absorption spectra of the molecule in gas phase, performed with both GGA and

Figure 4. Simulated and experimental spectra of (a) dehydrated and (b) solvated cyanin dye, obtained from direct TDDFT calculations and morphing procedure. “DE-HYD” indicates that averages are taken along a dehydrated AIMD trajectory, while “SOLV” indicates averages taken along an AIMD trajectory for the solvated molecule, explicitly including the effects of the surrounding water molecules. “PBE” and “B3LYP” indicate the XC functional used to simulate the spectrum, while “morph” indicates a spectrum obtained upon PBE→B3LYP morphing; “EXP” indicates experimental data at low pH.32,56,57

features:37 the single sharp peaks that characterize the gas-phase spectra are here replaced by unstructured bands over the entire visible range. The latter effect is partially due to the broadening of the spectra and to a minor extent due to the dielectric effect of the medium. To prove this issue, we computed the spectra of the dehydrated anthocyanins by removing the water molecules and the counterion from the same snapshots used for the spectra in solution. The results are shown in Figure 3 (straight lines) for pelargonin (panel a), cyanin (panel b), and delphinin (panel c) dyes, respectively. For all systems we observe a hyperchromic (i.e., enhancement of the absorption intensity) and a bathochromic shift (i.e., red shift) due to the presence of the solvent, especially for the lowest energy contributions. Comparing solvated and dehydrated spectra, we note that the spectra of delphinin and pelargonin are only slightly affected by the dehydration, maintaining almost the same spectral shape. On the contrary, the change in cyanin spectra is significant, especially the position of the peak at ∼460 nm, which is strongly blue-shifted by the dehydration. In this case, the chromophore (ring-B) seems particularly sensitive to presence of the solvent. The formation of H bonds between −OH group of cyanin and the nearest neighbor water molecules enhances the dipolar character of the B ring, in agreement with the

Figure 5. Color palette for selected anthocyanins, simulated with different techniques. Labels refer to caption of Figure 4 3819

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entire class of molecular dyes in solutions and paves the way for an explicit account of further elements such as copigments, molecular stacking, and metal ions, which are known to be crucial in the characterization and design of anthocyanin colors.

hybrid functionals. We then define a linear transformation of the frequency as Ω(ω) = αω + β

(2)

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where the α and β fitting parameter are chosen in such a way that the positions of the absorption peaks in the GGA morphed spectrum κGGA (Ω(ω)) coincide with those of the hybrid spectrum, κHYB(ω). For each one of these peaks, we then define a renormalization factor, s(i), as the ratio between the hybrid and GGA oscillator strengths f: s(i) = f HYB(i)/f GGA(i) (here “i” is a label that identifies the peak). Step 2. Once the frequency and intensity scaling factors have been computed, we proceed to morph the GGA absorption spectra computed for each snapshot generated in an AIMD run, as t κMORPH (ω) = κGGA ̃ t (Ω(ω))

Corresponding Author

*Phone: +39-059-2055627. E-mail: [email protected]. it. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Dr. Rebecca Robbins, Dr. Tom Collins, and Dr. Tersilla Virgili for very fruitful discussions and to the technical staff of the CINECA supercomputing center for invaluable help in the porting and optimization of our computer codes. Computational resources were supplied by PRACE under grant TIER-0 CHROMATOLOGY. This work was partially supported by Mars Chocolate North America LLC.

(3)

where t identifies the snapshot and κGGA is the spectrum obtained from the GGA one by scaling each one of the lowfrequency peaks by the s scaling factors determined at Step 1. Step 3. Once the GGA spectra have been individually morphed for each snapshot, the final morphed spectrum is obtained by averaging over the entire snapshot of a given AIMD trajectory 1 κMORPH (ω) = ̅ T

∑ t

t κMORPH (ω)

AUTHOR INFORMATION

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REFERENCES

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(4)

where T is the number of snapshots. This morphing procedure simply requires the evaluation of the calculations of the solvated spectra at the standard GGADFT level (PBE in the present case) as in Figure 2, and two single calculations for the molecule in gas phase are assumed as the reference: one with the GGA and one with the hybrid functional. This dramatically reduces the computational cost for the evaluation of the color. To test the performance of this method, in Figure 4a, we display the modification of the PBE dehydrated spectrum of cyanin with respect to the B3LYP that we explicitly simulated using TDDFT. The good agreement between the B3LYP and morphed spectra shows the quality of the proposed procedure. By applying the same morphing transformations to the PBE spectrum computed in explicit water solution, we can estimate rather inexpensively the screening effect of the solvent, as shown in Figure 4b. The effect of morphing on color modeling is summarized in Figure 5, where the simulated colors of various anthocyanins are displayed as obtained from different methods. On account of the negligible additional cost of morphing, the improvement over plain PBE predictions is impressive.

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CONCLUSIONS We have demonstrated the importance of a proper account of the thermal fluctuations and of the choice of XC functional in the description of the color optical properties of anthocyanins in solution. The use of accurate hybrid functionals is hardly compatible with the computational requirements set by an explicit solvation model of the system. The morphing technique proposed in this paper allows one to approximate the spectra calculated by hybrid functionals with others obtained from much cheaper GGA calculations. The color resulting from this technique is in excellent agreement with experimental results. This strongly enhances our ability to predict the color of an 3820

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DOI: 10.1021/acs.jpca.5b01272 J. Phys. Chem. A 2015, 119, 3816−3822

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The Journal of Physical Chemistry A Strawberry (cv Camarosa) by LC using DAD and ESI-MS Detection. Eur. Food Res. Technol. 2002, 214, 248−253.

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DOI: 10.1021/acs.jpca.5b01272 J. Phys. Chem. A 2015, 119, 3816−3822