Onset of the Electronic Absorption Spectra of Isolated and Ï-Stacked

Article pubs.acs.org/JPCB

Onset of the Electronic Absorption Spectra of Isolated and π‑Stacked Oligomers of 5,6-Dihydroxyindole: An Ab Initio Study of the Building Blocks of Eumelanin Deniz Tuna,*,†,⊥ Anikó Udvarhelyi,‡,⊗ Andrzej L. Sobolewski,§ Wolfgang Domcke,† and Tatiana Domratcheva‡ †

Department of Chemistry, Technische Universität München, 85747 Garching, Germany Department of Biomolecular Mechanisms, Max-Planck-Institut für Medizinische Forschung, 69120 Heidelberg, Germany § Institute of Physics, Polish Academy of Sciences, 02668 Warsaw, Poland ‡

S Supporting Information *

ABSTRACT: Eumelanin is a naturally occurring skin pigment which is responsible for developing a suntan. The complex structure of eumelanin consists of π-stacked oligomers of various indole derivatives, such as the monomeric building block 5,6-dihydroxyindole (DHI). In this work, we present an ab initio wave-function study of the absorption behavior of DHI oligomers and of doubly and triply π-stacked species of these oligomers. We have simulated the onset of the electronic absorption spectra by employing the MP2 and the linear-response CC2 methods. Our results demonstrate the effect of an increasing degree of oligomerization of DHI and of an increasing degree of π-stacking of DHI oligomers on the onset of the absorption spectra and on the degree of red-shift toward the visible region of the spectrum. We find that π-stacking of DHI and its oligomers substantially red-shifts the onset of the absorption spectra. Our results also suggest that the optical properties of biological eumelanin cannot be simulated by considering the DHI building blocks alone, but instead the building blocks indole-semiquinone and indole-quinone have to be considered as well. This study contributes to advancing the understanding of the complex photophysics of the eumelanin biopolymer.

1. INTRODUCTION Eumelanin is a naturally occurring brown pigment, which is found in human skin, in the iris, and in hair. The photoinduced changes taking place in eumelanin are responsible for developing a suntan. The building blocks of eumelanin belong to the many naturally occurring sunscreen molecules found in biology1−6 (and synthetic derivatives thereof),5,7−9 which protect the genetic information encoded in the nucleic acids from photodamage and subsequent mutation. Three derivatives of indole, namely, 5,6-dihydroxyindole (DHI), indole-2carboxylic acid (ICA), and 5,6-dihydroxyindole-2-carboxylic acid (DHICA), are the main building blocks of eumelanin (apart from the oxidized forms of 5,6-dihydroxyindoles, that is, indole-semiquinones and indole-quinones). These monomers are metabolites of the amino acid tyrosine and form oligomeric and polymeric units through oxidative polymerization. The resulting oligomeric subunits constitute the complex composition and amorphous structure of eumelanin. Considerable progress in elucidating the structure of eumelanin has been made in recent years.10−19 Although the complex structure of eumelanin is still not fully elucidated due to its amorphous and insoluble character, a structural model for eumelanin extracted from sepia off icinalis © 2016 American Chemical Society

(the common cuttlefish) has been proposed (cf. Figure 1 of ref 15) that describes it as consisting of three levels of aggregation of oligomers of DHI, ICA, and DHICA.15 The first level of aggregation is constructed by π-stacking of the oligomers, which leads to the formation of protomolecular discs that act as the building blocks for the second level of aggregation. In the second level, these protomolecular discs aggregate via edge-toedge interaction to form filaments and larger substructures. In the third level, these substructures aggregate to form large particles of dimensions of up to 200 nm.15 For the present work, we consider only the first level of aggregation of this structural model, that is, the formation of π-stacked layers of DHI oligomers. A number of experimental studies are available on eumelanin. D’Ischia and co-workers have studied the reaction sequence from DHI to the eumelanin polymer,20 presented a structural model for eumelanin,15 shown the potential of DHI for various application purposes,21 demonstrated the superior ability of DHICA over DHI to scavenge free radicals,22 and analyzed the surprising dimerization of semiquinone free radicals generated Received: February 22, 2016 Published: March 22, 2016 3493

DOI: 10.1021/acs.jpcb.6b01793 J. Phys. Chem. B 2016, 120, 3493−3502

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The Journal of Physical Chemistry B by radiolysis of DHI.23 They have also provided several reviews on the topic of eumelanin.15,19,21 Recent experimental evidence by Brash and co-workers suggests that melanin may also have a deleterious effect by promoting the development of melanoma, even hours after exposure to sunlight has ceased.24 To date, a number of spectroscopic studies have been carried out on eumelanin. Simon and co-workers have performed extensive experiments on eumelanin from natural sources.11,25−32 The research group of Sundström has systematically18 experimented on the monomeric building blocks of eumelanin (on DHI,33 on ICA,34 and on DHICA35−38) in solution, leading to the determination of the time scales of photophysical processes and to the proposal of mechanisms for excited-state deactivation. Some studies are also available on dimers and oligomers, in which fluorescence lifetimes and mechanisms for radiationless energy dissipation have been determined: it was shown that the DHICA dimer can deactivate via excited-state intramolecular proton transfer or via solventassisted intermolecular excited-state proton transfer and that it exhibits a significantly shorter excited-state lifetime than DHI. 37,38 The research groups of Meredith 39−42 and Warren43,44 have used various spectroscopic techniques (for example, pump−probe, EPR, and IR spectroscopy) to study other aspects of naturally derived eumelanin and its building blocks. Computational studies on the monomeric building blocks are available in abundance. Several excited-state properties, such as the electronic structure of the lowest-lying excited states, have been elucidated.34,41,45−50 A photochemical mechanism for radiationless excited-state deactivation involving intramolecular excited-state proton transfer has been identified for monomeric DHI.50 Studies on the dimeric and oligomeric forms are also available.40,49,51 Stark et al. have simulated the absorption spectra of monomers, oligomers, and π-stacked oligomers with semiempirical methods.52−54 D’Ischia and co-workers have investigated the UV-absorption profiles of oligomers up to trimers employing the TDDFT method and a polarizable continuum model.55 Okuda and co-workers have analyzed the reactivity toward oligomer formation through oxidative polymerization56 and computed the vibrational spectra of DHI and its oxidation products.57 Meng and Kaxiras have simulated the nonadiabatic Ehrenfest dynamics of oligomers up to tetramers at the TDDFT level and identified two mechanisms for excited-state deactivation.58 Buehler and coworkers have simulated the formation of four-layered π-stacked tetramer sandwiches59 and computed the absorption spectra of isolated and π-stacked species using an excitonic-coupling model.60 Only last year, Prampolini, Cacelli, and Ferretti have presented a study on the non-covalent interactions and geometrical preferences of the π-stacked species as well as their absorption spectra,61 while Ghosh and co-workers have presented a study of the ionization potentials of DHI and its oligomers.62 Most recently, Marchetti and Karsili have performed reaction-path explorations and surface-hoppingdynamics simulations on dimers and trimers of reduced and oxidized DHI moieties and have demonstrated that these units can undergo ultrafast radiationless excited-state deactivation via intramolecular excited-state proton transfer from OH or NH groups to adjacent keto groups.63 The absorption spectrum of eumelanin is broad, featureless, and monotonically increasing toward higher energy.13,15,16,18,28 D’Ischia and co-workers have shown that the spectrum of DHI eumelanin exhibits the same features as the spectrum of

naturally occurring eumelanin.22 These properties of the experimental spectrum allow one to combine the computed absorption spectra of a rather small number of building blocks for obtaining a match with the experimental spectrum. Meredith and co-workers have shown, for example, that the experimental absorption spectrum can be reproduced by linear combination of 11 Gaussian functions of varying width, whose peak positions are evenly distributed throughout the UV/vis region.13 Since the structural elucidation of eumelanin has led to the identification of many types of building blocks, a number of possibilities for combining these building blocks to match the experimental spectrum can be found. For example, Kaxiras and co-workers have shown that a small number of isomers of the cyclic porphyrin-like DHI tetramer can be used to fit the experimental spectrum.49,64 In essence, it is not clear to date which components dominate in the structure of eumelanin. It is thus also unclear which components contribute most to the experimentally obtained absorption. In this study, we aim to elucidate the effects of scaling the DHI monomer along two “chemical directions”the degree of oligomerization and the degree of π-stacking of the oligomersin as systematic a way as possible (given the limitations of the chosen computational approach). To date, several studies have presented computed absorption spectra of larger oligomers and π-stacked oligomers of the building blocks of eumelanin. All of these spectra were computed either with semiempirical methods45,52−54,60 or with the linear-response TDDFT method.23,46,49,51,55,58,61,64 Naturally, these are the methods of choice when dealing with the computation of the excitation energies of large molecular systems.65,66 Nevertheless, in this paper, we present a study of the UV-absorption behavior of isolated oligomers and π-stacked structures of 5,6-dihydroxyindole (DHI) employing a computational ab initio wave-function approach: we use the MP2 method for the optimization of ground-state equilibrium geometries and the linear-response CC2 method for the computation of vertical excitation energies. The CC2 method has been well-tested in the past 15 years and found to predict reasonably accurate excitation energies for most organic molecular systems.65−68 To our knowledge, the present work presents the first study on large components of eumelanin that is conducted with an ab initio wave-function treatment. Wavefunction approaches are free from empirical parameters derived from experiments and thus unbiased with respect to the experimental absorption spectra that we aim to explore. Hence, the use of a wave-function approach may offer new insight into the photophysics of the building blocks of eumelanin. As already mentioned above, the structure of eumelanin has been proposed to consist of oligomers of DHI, ICA, and DHICA as well as π-stacked structures of oligomers.15 In this work, we focus solely on the oligomers of DHI. We have considered all possible conformers of the monomer, all possible constitutional isomers of the dimers (of which there are ten), a selection of the possible isomers of the trimers (of which there are already a little over 100 isomers), and a number of isomers of the tetramers and pentamers. We have also considered twolayered π-stacked monomers, dimers, and trimers as well as three-layered π-stacked monomers and dimers. We have simulated the onset of the electronic absorption spectra of these species by using the linear-response CC2 method for the computation of the excitation energies of the two lowest excited singlet states. Our results demonstrate the effect of an increasing degree of oligomerization of isolated DHI and of 3494


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Figure 1. Selection of optimized structures of DHI oligomers and π-stacked DHI species studied in this work. For details, consult the Computational Methods section.

an increasing level of π-stacking of oligomers of DHI on the red-shift of the absorption spectra toward the visible region of the spectrum.

between the excitation energies of the various isomers at each level of oligomerization is smaller than the fwhm value used for the convolution of the stick spectra (20 nm). The two lowest excited singlet states are either locally excited ππ* states, where the involved π orbitals are located on the same region of a DHI moiety or layer, or charge-transfer ππ* states, where charge is dislocated from one region to another region of the same layer or dislocated from one layer to another layer. The two lowest excited states show no signs of Rydberg character. For these reasons, we have settled on using a nonaugmented triple-ζ basis set, namely the cc-pVTZ set. The orientations of the two OH groups of each DHI subunit were chosen arbitrarily. The vertical excitation energies of the two lowest excited singlet states of the three conformers of monomeric DHI (that is, the syn−anti form, the anti−syn form, and the anti−anti form) show that the effect of the orientation on the vertical excitation energies ranges from 0.00 to 0.05 eV (cf. Table S2 in the Supporting Information). It should be safe to assume that in oligomeric structures a random distribution of the possible orientations occurs and that an arbitrary selection of these orientations is therefore a reasonable approach. In recent years, it has been shown that the dispersion interaction of π-stacked species is well described by many dispersion-corrected density functionals and that MP2 is outperformed by such empirically corrected DFT methods.70−74 To assess a possible discrepancy introduced by our use of the MP2/cc-pVDZ method for the geometry optimizations of the π-stacked oligomers, we optimized the π-stacked monomers and the triply π-stacked monomers at the TPSS-D3/cc-pVDZ level75,76 and compared the vertical excitation energies computed at the CC2/cc-pVTZ level to the ones obtained for the ground-state equilibrium geometry optimized at the MP2/cc-pVDZ level. This comparison is tabulated in Table S1 of the Supporting Information. Upon S0 geometry optimization at the TPSS-D3/cc-pVDZ level of theory, the CC2 vertical excitation energies of both the doubly stacked and the triply stacked DHI monomers increase by ∼0.1 eV. Another increase of ∼0.1 or ∼0.2 eV, respectively, can be observed by computing the CC2 vertical excitation energies of the doubly and triply stacked DHI monomers, respectively, of the ground-state equilibrium geometries optimized at the TPSS-D3/aug-cc-pVTZ level. This might suggest that our use

2. COMPUTATIONAL METHODS All ground-state equilibrium geometries were optimized with the MP2 method using the cc-pVDZ basis set. A selection of structures of the optimized ground-state equilibrium geometries considered in this work is shown in Figure 1. The vertical excitation energies of the lowest excited singlet states of the ground-state minima were computed with the linear-response CC2 method69 and the cc-pVTZ basis set. Because of the considerable computational cost of these calculations for the larger species considered in this work and due to our interest in simulating the onset of the absorption spectra for the different species, we have computed only the two lowest excited singlet states for the majority of structures. This approach was sufficient to obtain the lowest-lying ππ* excited state of sizable oscillator strength. However, for a few structures the two lowest-lying excited singlet states both exhibit a weak oscillator strength. In such cases, we also computed the excitation energy of the S3 state. The electronic absorption spectra were simulated by averaging the vertical excitation energies and oscillator strengths of all the considered conformers or isomers of a given DHI species (that is, by computing the arithmetic mean irrespective of the Boltzmann factors of the individual isomers) and convoluting the obtained averaged stick spectrum with Gaussian functions of 20 nm fwhm. A Boltzmann averaging was not used due to the small number of isomers considered for each species. Inspection of Tables S2−S6 in the Supporting Information shows that the variation in the excitation energies between different conformers and isomers of a given DHI species is fairly narrow, which suggests that averaging over different conformers or isomers is a reasonable approach. More specifically, the standard deviations of the S1 excitation energies of the different isomers of the dimers, trimers, tetramers, and pentamers range from 13 to 17 nm, whereas the standard deviations of the S2 excitation energies range from 4 to 11 nm. (The standard deviations for the corresponding excitation energies of the three conformers of the DHI monomer are negligible, giving values of 0 and 1 nm.) Thus, the spread 3495


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the averaged spectrum of the trimers, which sets on at ∼350 nm. From hereon, the degree of red-shift becomes less pronounced: the averaged spectrum of the selected tetramers sets on at ∼370 nm, and the spectrum of the selected pentamers sets on at ∼380 nm. These findings suggest that an increasing degree of oligomerization of DHI leads to a less and less pronounced degree of red-shift in the absorption spectrum. Interpolation of these results suggests that the onset of the absorption can be expected to reach a more or less constant value for the higher oligomers; that is, the shift of the absorption spectrum from the UV toward the visible region seems to reach a plateau with increasing degree of oligomerization. Stark et al. have simulated the absorption spectrum of the DHI monomer at a semiempirical level of theory (the pairexcitation configuration interaction method based on an AM1 Hamiltonian),52 whose onset was found at ∼450 nm,52 which deviates significantly from our result of ∼290 nm. For a hexamer of DHI (only one isomer was considered) they found the onset at ∼600 nm.54 The CC2 vertical excitation energy of the S1 state of the three conformers of the monomer (cf. Table S2 in the Supporting Information) computed by us compare very well with the values obtained at the TDDFT/PBE0/6311++G** level by Il’ichev and Simon.46 The value obtained by these authors at the TDDFT/B3LYP/6-311++G** level is ∼0.2 eV lower. The excitation energy of the S2 state obtained by us is lower than the values obtained with both density functionals by ∼0.4 and ∼0.6 eV, respectively.46 Prampolini, Cacelli, and Ferretti have also computed the absorption spectrum of the DHI monomer at the TDDFT/B3LYP/augcc-pVDZ level. They found the onset at ∼340 nm,61 in contrast to the value of ∼290 nm found by us. The spectra computed by d’Ischia and co-workers for selected dimers and trimers employed a polarizable-continuum model; thus, we refrain from making any direct comparisons.55 The above comparisons show that our CC2 results compare fairly well with previously reported TDDFT results. Experimental absorption spectra of the DHI monomer18,33 and of selected DHI dimers and trimers55 in aqueous solution are also available. These experimental spectra have shown that in going from the monomer to the dimers to the trimers, the onset of the absorption spectrum is shifted from ∼375 nm33 to ∼500 nm55 to >500 nm.55 All the other computational and experimental studies that have been mentioned in the Introduction but are not addressed for comparison here have considered partially or fully oxidized forms of DHI. A comparison to our results is therefore impossible. 3.2. π-Stacked Oligomers. The π-stacking of DHI structures is the second factor to consider for the description of the absorption properties of eumelanin. The geometry optimizations of the π-stacked structures yield a sheet-to-sheet distance of ∼3.2−4.0 Å. This value agrees reasonably well with the structural model derived from experimental observations.12,15,16,18,59 Figure 3 shows the onset of the electronic absorption spectra of the two-layered π-stacked monomers, dimers, and trimers as well as the three-layered triply π-stacked monomers and dimers. The numerical values for the vertical excitation energies and oscillator strengths of these species are shown in Table S7 of the Supporting Information. Because of the very low oscillator strengths of the two lowest excited singlet states of the triply stacked monomers, we calculated the three lowest excited states to obtain an excited state with a large

of the MP2 method for the optimization of the π-stacked structures introduces an error of 0.1−0.3 eV into the absorption spectra of these species. However, when looking at the absolute CC2 S0 energies, this implication becomes less compelling. For the stacked monomers, the (MP2/cc-pVDZ)-optimized ground-state equilibrium geometry yields a lower CC2 S0 energy than the (TPSS-D3/cc-pVDZ)-optimized geometry. Only the use of the much larger aug-cc-pVTZ basis set yields a (TPSS-D3)-optimized geometry that gives a lower CC2 S0 energy. In the case of the triply stacked monomers, the CC2 S0 energy obtained for the (MP2/cc-pVDZ)-optimized geometry is the absolute lowest among the three tested levels of theory. Even the TPSS-D3/aug-cc-pVTZ optimization of the groundstate equilibrium geometry gives a structure whose CC2 S0 energy is 2 mEh higher in energy than that of the (MP2/ccpVDZ)-optimized geometry. These CC2 energies thus show that the MP2-optimized ground-state equilibrium geometries of the π-stacked DHI species are fairly reasonable. All calculations were performed with Turbomole 6.3.177,78 employing the resolution-of-the-identity (RI) approximation.

Figure 2. Onset of the electronic absorption spectra of oligomers of 5,6-dihydroxyindole. The spectral envelopes were obtained by convolution of the stick spectra using Gaussian functions of 20 nm fwhm. The stick spectra are averaged over all computed isomers for each degree of oligomerization. For details, consult the Computational Methods section.

3. RESULTS 3.1. Isolated Oligomers. Figure 2 shows the onset of the averaged electronic absorption spectra of the isolated monomers, dimers, trimers, tetramers, and pentamers of DHI. We considered all three possible conformers of the DHI monomer, all ten possible constitutional isomers of the dimer, 15 isomers of the trimers, nine isomers of the tetramers, and three isomers of the pentamers. The vertical excitation energies and oscillator strengths of the individual conformers or isomers as well as the resulting mean values, which were used for the generation of Figure 2, are shown in Tables S2−S6 of the Supporting Information. In Figure 2, the onset of the averaged absorption spectrum of the DHI monomers is found at ∼290 nm. The onset of the averaged spectrum of all possible DHI dimers is red-shifted toward ∼325 nm. Another considerable red-shift is found for 3496


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monomers to triply stacked monomers. The stacked trimers exhibit a spectrum which sets on in the cyan/green region of the visible spectrum at ∼490 nm, and thus, compared to the averaged absorption onset of the 15 isomers of isolated DHI trimers at ∼350 nm, the level of red-shift now amounts to 140 nm. It is noteworthy that the oscillator strengths for all the stacked species are significantly lower than what was found for the isolated oligomers (cf. Figure 2). Prampolini, Cacelli, and Ferretti have computed the absorption spectrum of π-stacked DHI dimers at the TDDFT/B3LYP/aug-cc-pVDZ level. They, like us, found the onset at ∼390 nm.61 Meng and Kaxiras have found that the absorbance of stacked tetramers sets on at ∼800 nm and that the spectrum shows only one peak, apart from which it is featureless.64 The stacked tetramers, however, are too costly to compute at the level of theory chosen by us. Table 1 shows a summary of the onsets of the absorption spectra of isolated and π-stacked (fully reduced) DHI species reported herein and in previous computational or experimental studies.

Figure 3. Onset of the electronic absorption spectra of π-stacked monomers and oligomers of 5,6-dihydroxyindole. The spectral envelopes were obtained by convolution of the stick spectra using Gaussian functions of 20 nm fwhm. For details, consult the Computational Methods section.

Table 1. Onset of Simulated Absorption Spectra (in nm) of Isolated and π-Stacked Oligomers of DHI Computed at Various Levels of Theory; Some Experimentally Obtained Values Are Given for Comparison

oscillator strength (i.e., larger than 0.05). Unfortunately, the same problem occurs for the triply stacked dimers, but in this case the large computational cost prohibits the computation of three excited states. However, at the fairly affordable CCS/ccpVDZ level (coupled cluster with singles excitations, which is equivalent to CIS), the S3 state is a strongly absorbing ππ* state, which is 0.3 eV higher in energy than the weakly absorbing S2 state. This suggests that the low-intensity onset of the absorption profile derived from the S1 and S2 excitation energies is followed by a high-intensity absorption profile. Because of the large computational cost, we computed only one structure for each of the stacked species. An exception was made for the stacked dimers, for which we present the averaged absorption spectrum of the stacked 2,2-, the stacked 2,4-, and the stacked 4,4-dimers. The S1 and S2 excitation energies vary more strongly between these three isomers, giving standard deviations of 34 and 13 nm. This indicates that different isomers for a given class of the stacked oligomers can show a significantly larger spread in the excitation energies than what was found for different isomers of the isolated oligomers. Also, the oscillator strengths of the excitation energies found for the stacked 2,2-dimers are one order of magnitude smaller than the corresponding oscillator strengths for the 2,4- and 4,4-dimers (cf. Table S7). Figure 3 shows that the onset of the absorption of the stacked monomers is red-shifted by ∼20 nm compared to the averaged spectrum of the isolated monomers and is found at ∼310 nm. The addition of another level of π-stacking in the triply stacked monomers shifts the onset of the absorption spectrum by a mere 15 nm to ∼325 nm. The onset of the averaged absorption of the stacked dimers is found at ∼390 nm and, thus, almost in the visible spectral region. Compared to the onset of the averaged absorption of all possible isomers of dimeric DHI, whose absorption sets on at ∼325 nm (cf. Figure 2), the absorption of the stacked dimers is red-shifted by 65 nm. The addition of another level of stacking when going to the triply stacked dimers shifts the onset to ∼460 nm and thus exhibits a significantly more pronounced red-shift effect than what is shown for the transition from doubly stacked

CC2 (this work) isolated oligomers monomers dimers trimers tetramers pentamers hexamers π-stacked oligomers stacked monomers stacked dimers stacked trimers stacked tetramers triply stacked monomers triply stacked dimers

290 325 350 370 380

TDDFT55,61,64 34061 40055,a 43055,a

PECI/ AM152,54 45052

expt33,55 37533 50055 >50055

60054,b 310 390 490

39061 80064

325 460

a These calculations employed a polarizable-continuum model. bOnly one isomer was considered.

The optimized ground-state equilibrium geometry and the molecular orbitals involved in the electronic transitions for the S1 and S2 states of the largest structure considered in this work, the triply π-stacked dimers consisting of 102 atoms, are shown in Figure 4. The structure demonstrates that dispersion interaction between the layers is by no means the only type of interaction but that instead there are numerous intrasheet and intersheet hydrogen bonds stabilizing the structure. If one considers only the indole scaffolds, the sheet-to-sheet distance varies between 3.0 and 4.0 Å depending on the points of measurement. This rather wide variability in the sheet-to-sheet distance is due to the imperfect parallelity of the sheets. If intersheet oxygen-to-oxygen distances are also considered, these can be found to be as low as 2.73 Å due to strong intersheet hydrogen bonds. The molecular orbitals involved in the S1 and S2 excitations demonstrate the pronounced delocalization between separate DHI moieties of the same oligomer but also between different layers of the π-stacked 3497


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transition from isolated monomers to stacked monomers, from isolated dimers to stacked dimers, and from isolated trimers to stacked trimers indicates that the larger the base unit, the more pronounced the red-shift on the onset of the absorption spectra upon a single level of π-stacking. Similarly, the observed redshift for the transition from doubly stacked monomers to triply stacked monomers and from doubly stacked dimers to triply stacked dimers indicates that the larger the base unit, the more pronounced the red-shift on the onset of the absorption spectra upon adding the third π-stacked layer to a doubly π-stacked structure. In conclusion, our results suggest that π-stacking leads to a more profound red-shift on the onset of the absorption spectra than an increasing degree of oligomerization. The comparison between an increasing degree of oligomerization for the isolated oligomers (cf. Figure 2) and an increasing degree of π-stacking for monomers and small oligomers (cf. Figure 3) shows that π-stacking has a larger impact on the red-shift of the electronic absorption spectrum than the size of oligomers. This suggests that in the framework of the structural model for eumelanin, which was proposed by d’Ischia and co-workers and which was summarized in the Introduction,15 the intense brown color of eumelanin may be due to the π-stacking found in the first level of aggregation. The two-layered π-stacked complexes of oligomers of medium length (trimers to heptamers) may be the main absorbing subunits in the structural mixture of eumelanin. Figure 4. Molecular structure of the ground-state equilibrium geometry of the triply π-stacked dimers shown from two perspectives in part (a). The sheet-to-sheet distance at selected points and the length of selected hydrogen bonds is given in Å. SCF molecular orbitals involved in the excitation of the S1 and S2 states are shown in part (b).

structure. The S1 state involves mainly a HOMO → LUMO transition; the S2 state involves mainly a HOMO−1 → LUMO transition.

4. DISCUSSION AND CONCLUSIONS In the present work, we have explored the effect of increasing oligomerization of DHI and of π-stacking of monomers and oligomers of DHI on the onset of the electronic absorption spectra. While the absorption spectra of oligomers and of πstacked species of oligomeric building blocks of eumelanin have been studied in the past using semiempirical methods52−54,60 or the TDDFT method,23,46,49,51,55,58,61,64 our contribution is the first to employ an ab initio wave-function electronic-structure approach. Specifically, we have used the MP2 method for the optimization of the ground-state equilibrium geometries and the linear-response CC2 method69 for the calculation of the vertical excitation energies. Our results on the onset of the absorption spectra of the oligomers shown in Figure 2 suggest that an absorption in the visible region is hard to achieve by isolated oligomers alone. It seems that a red-shift of the absorption toward the visible region can only go so far before the onset of the absorption spectra plateaus. Interpolation of our results on monomers to pentamers indicates that the red-shift becomes saturated for the higher oligomers. Our results on the π-stacked species shown in Figure 3 suggest that two effects connected with π-stacking exist, which depend on the size of the base unit, that is, the isolated to-be-stacked oligomer. The observed red-shift for the

Figure 5. Onset of the electronic absorption spectra (in nm) of isolated and π-stacked oligomers of DHI.

The above-mentioned trends are summarized in Figure 5. Although our data set is rather limited due to the large computational cost, it may still be insightful to compare the effects found for the different types of arrangements. The curve for the isolated oligomers suggests that upon higher degrees of oligomerization a plateau will be reached, which might lie just below the threshold to the visible spectral range. The progression of the curves for the doubly and triply stacked species remains open, however. Because of our limited data set, these trends should be treated with caution, since we considered only one isomer for each of the stacked species (with the exception of the doubly stacked dimers, for which we averaged over three isomers). Hence, it is possible that this 3498


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from DHI to indole-quinone to indole-semiquinone.47 In summary, our results point to the fact that the reduced form of dihydroxyindole alone is not sufficient to simulate the absorption characteristics of eumelanin but that it is seemingly necessary to include all three types of chromophores, namely, dihydroxyindoles, indole-semiquinones, and indole-quinones, in any simulation of the absorption spectrum of eumelanin. This conclusion has previously been suggested by d’Ischia and co-workers based on the results of TDDFT calculations of excitation energies of DHI oligomers.55 As already mentioned above, one of the limitations of our study is the relatively small sample size of the large oligomeric structures starting with the tetramers and, of course, of all the π-stacked species. Unfortunately, this could not be avoided since the geometry optimizations and especially the computation of vertical excitation energies of the larger species are too costly to be performed for a larger number of isomers. In future, novel and more efficient ab initio methods could be used to confirm the trends presented in this study for a larger sample size of isolated trimers to decamers and of multiply π-stacked oligomers. Newer, more efficient variants of the CC2 method and similar linear-response methods, such as ADC(2),86 will allow the computation of such larger species of more than 100 atoms more routinely in the future. Such variants are, for example, the spin-scaled CC2 methods,68 the pair-naturalorbitals variant of CC2 or ADC(2),87,88 and the tensorhypercontracted EOM-CC2 method.89 A different approach could be taken by using a semiempirical linear-response method, such as the TD-ZINDO method proposed by Neuhauser and co-workers.90,91 The computational efficiency as well as the black-box character of such methods could allow for the rapid screening of the excitation energies of several thousands of building blocks of eumelanin. Our use of an ab initio wave-function approach is justified by our intention of predicting the effect on the absorption spectra of oligomeric and π-stacked DHI structures, rather than a reproduction of experimentally measured observations. Although the chosen computational level of theory becomes prohibitively expensive for the larger supramolecular structural elements of eumelanin, the analysis presented above and the comparison to the previously reported semiempirical and TDDFT studies has shown that the use of a computational level that is free from empirical influence may provide new insight. In this way, we were able to predict that the consideration of DHI species alone is most likely not sufficient to simulate the experimental absorption spectrum of eumelanin and that the other chromophores, the oxidized forms of DHI, are necessary as well. It should be kept in mind, however, that the structures considered in this work are optimized in the vacuum phase, whereas eumelanin is a condensed material found in a highly complex amorphous state. In conclusion, we have contributed new insight into the absorption properties of eumelanin by analyzing the effect of oligomerization and π-stacking of one of its building blocks on the onset of the electronic absorption spectra.

picture changes when the spectra of a larger sample of conformers and isomers of the larger stacked species were considered. The π-stacking of eumelanin species also introduces excitonic-coupling effects,79−85 which are likely to play a crucial role in the absorption spectrum of this biopolymer. Recently, Buehler and co-workers have shown that this excitonic coupling can rationalize one of the key optical properties of eumelanin, namely the monotonical increase in the absorption intensity toward higher energy.60 Future studies on the excitonic couplings in π-stacked building blocks of eumelanin, such as the characterization of Frenkel, charge-transfer, and resonance states, could further advance the state of knowledge on this biomaterial. One of the most obvious features of the experimental absorption spectrum of eumelanin, that is, the monotonically increasing absorbance toward higher energy, is not reproduced by the isolated oligomers of increasing chain length (cf. Figure 2). We find the reversed behavior, that is, the absorbance, grows stronger toward longer wavelengths. It is, however, possible that this behavior merely seems like a violation, since we only compute the first two excited states. Higher-lying excited states, which show a stronger absorbance, could lead to the correct behavior of the total spectrum. Previous studies have shown that the higher-lying excitations starting with S3 can be significantly stronger-absorbing than S1 and S2.33,46,61 Compared to the experimental spectrum of naturally occurring eumelanin, the onset of the absorbance of the stacked trimers, which is found in the most long-wave region (cf. Figure 3), is too far off from the 800 nm region in which the UV/vis absorbance of eumelanin sets on. This could indicate that the stacked structures of larger oligomers may be crucial in the long-wavelength absorption of eumelanin. In contrast to what has been pointed out for the isolated oligomers above, the experimental observation of the absorbance growing stronger with increasing energy is found for the stacked species. (However, we stress again that we only computed two excitation energies to determine the onset of the spectra.) It is also noteworthy that the oscillator strength for the S1 excitations are lower for the stacked species than for the isolated oligomers. For the monomers and dimers this trend is consistent for the progression f S1(isolated) > f S1(doubly stacked) > f S1(triply stacked) (with f denoting the oscillator strength). By using an ab initio wave-function approach, we have predicted the significance and the limitations of the reduced DHI species for the simulation of the broad absorption spectrum of naturally occurring eumelanin. Our results hint at the fact that the DHI species may not be sufficient to simulate the absorption characteristics of this highly complex amorphous biomaterial. The building blocks derived from the oxidized forms of DHI, namely indole-semiquinones and indolequinones, seem to be necessary to obtain a realistic simulation of the absorption characteristics of eumelanin. Several of the previous computational studies have considered monomers or oligomers of these oxidation products of DHI.45−49,52−54,58−61,63,64 It is therefore well-established that the absorption of these oxidized species is significantly redshifted from the reduced DHI species, the latter of which we have considered exclusively in this study. The significant redshift found for indole-semiquinones and indole-quinones can be understood by the decreasing HOMO−LUMO gap in going

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b01793. Comparison of CC2 S0 energies and S1 and S2 vertical excitation energies for MP2- and TPSS-D3-optimized 3499


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ground-state minima of the doubly stacked and triply stacked monomers; tables listing all computed vertical excitation energies and oscillator strengths of all species considered in this work; Cartesian coordinates of all optimized ground-state equilibrium geometries (PDF).

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; phone +49 208 306 2155 (D.T.). Present Addresses ⊥

D.T.: Max-Planck-Institut fü r Kohlenforschung, 45470 Mülheim an der Ruhr, Germany. ⊗ A.U.: Novartis Pharma AG, 4002 Basel, Switzerland. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.T. is grateful for a Ph.D. fellowship granted by the International Max Planck Research School of Advanced Photon Science (IMPRS-APS) and for support by the TUM Graduate School. A.U. acknowledges financial support from the Boehringer Ingelheim Fonds and the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences (HGS MathComp). A.L.S. acknowledges a grant by the National Science Center of Poland (Grant 2012/04/A/ ST2/00100). W.D. acknowledges partial support for this work by a research grant of the Deutsche Forschungsgemeinschaft (DFG) and by the DFG Cluster of Excellence “Munich-Centre for Advanced Photonics” (MAP). T.D. acknowledges the support from the Minerva Program of the Max Planck Society.

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