Bridging Electronic and Optical Absorption Properties - ACS Publications

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Essential States Model for Merocyanine Dye Stacks: Bridging Electronic and Optical Absorption Properties David Bialas,† Chuwei Zhong,† F. Würthner,‡,§ and Frank C. Spano*,† †

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Department of Chemistry, Temple University, 130 Beury Hall, 1901 N. 13th Street, Philadelphia, Pennsylvania 19122, United States ‡ Institut für Organische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany § Center for Nanosystems Chemistry, Universität Würzburg, Theodor-Boveri-Weg, 97074 Würzburg, Germany S Supporting Information *

ABSTRACT: An extension of the essential states model is developed to investigate the absorption and electronic properties of a highly dipolar merocyanine dye and double and quadruple π-stacks formed upon the folding and selfassembly of appropriate spacer-tethered bis(merocyanine) dyes. Our analysis reveals that a simple two-state model is not sufficient to adequately describe the absorption features of a single chromophore. However, by including an additional bridge state, the absorption features are well described and reasonable values for the permanent and transition dipole moments are obtained. We show that the low-energy absorption band of the folded double stack results from vibronic coupling, whereas the additional absorption shoulder observed in the spectrum of the self-assembled quadruple stack is due to a transition to a lower excited state. Furthermore, the chromophores within both π-stacks exhibit an increase in the charge-transfer character in the ground state with respect to the single chromophore arising from polarizability effects, which are not accounted for in the conventional Frenkel exciton theory. These insights are of significant importance for the proper design of functional materials based on merocyanines and dipolar chromophores in general.

1. INTRODUCTION

Although the optical features of many dye aggregates can be explained by the conventional exciton theory,15,30,31 the model may be overly simplistic for dye aggregates composed of highly polarizable chromophores hosting optical transitions which are accompanied by significant intramolecular charge transfer. Non-Kasha behavior may arise in aggregates of donor−acceptor (and donor−acceptor−donor) chromophores, due to polarizability effects not normally considered in the conventional exciton model.32,33 For example, a squaraine-based red-shifted H-aggregate (alias “nonfluorescent J-aggregate”) has recently been reported,32,33 in defiance of the Kasha scheme. It has been shown that strong quadrupole−quadrupole interactions which stabilize the excited state relative to the ground state are responsible for the spectral shift in red-shifted H-aggregates.34 Merocyanines35 are a class of polar dyes with exceptional optical properties and unique self-assembly behavior arising from their large dipolar character.36 The push−pull chromophores consist of a donor (D) and an acceptor group (A) that are covalently linked by a (poly)methine chain containing an

Dye assemblies play an important role in the field of organic photovoltaics,1−3 electronics,4,5 and photonics6,7 as well as artificial photosynthesis8,9 and biological imaging.10,11 Their effectiveness for such varied applications strongly depends on their optical and electronic properties, which are considerably influenced by interchromophoric interactions.12−15 Therefore, it is of prime importance to establish structure−property relationships to design materials with desired features and functionalities, which is still a challenging task.16−20 A first attempt to relate the geometric arrangement of chromophores and the optical properties of the dye assemblies was achieved by Davydov21 and Kasha22−24 in the 1960s based on the exciton model. Accordingly, dye aggregates can in general be classified into H- and J-aggregates depending on the orientation of the chromophores. A head-to-tail orientation leads to a bathochromic shift of the absorption with respect to the monomeric chromophore,25,26 and these types of aggregates are called J- or Scheibe aggregates, named after their discoverers Jelley27 and Scheibe.28 In contrast, Haggregates (H for hypsochromic) are characterized by a faceto-face arrangement, resulting in a blue shift of the main absorption peak.15,29 © XXXX American Chemical Society

Received: May 9, 2019 Revised: June 27, 2019

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DOI: 10.1021/acs.jpcc.9b04430 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. (a) Neutral (|N⟩), bridge (|B⟩), and zwitterionic (|Z⟩) resonance structures of merocyanine 1 as well as the schematic representation of the monomeric dye. The black bold arrow represents the vector of the ground-state dipole moment. (b) Chemical structure of bis(merocyanine) 2 and illustration of its folding process into a double π-stack as well as (c) molecular structure of bis(merocyanine) 3 and the schematic representation of the dimerization resulting in a quadruple π-stack with an antiparallel orientation of the ground-state dipole moments.

odd number of carbon atoms.37 In general, the electronic character of these dyes is rationalized by two resonance structures, that is, the neutral (D−A) and the respective zwitterionic states (D+−A−).38−40 Chromophores in the socalled “cyanine limit” exhibit sharp absorption bands because of the equal contributions of neutral and zwitterionic admixtures in both the ground and excited states.41−46 However, a simple two-state model cannot explain the alternating π-charge densities along the polymethine chain, as is evident from the chemical shifts in the 13C nuclear magnetic resonance (NMR) spectrum.47,48 Therefore, intermediate charge-transfer states have been suggested to rationalize the electronic and optical absorption properties of merocyanine dyes.49,50 Despite their large ground-state dipole moments, merocyanine dyes have been successfully used as p-type semiconductors in organic field-effect transistors51 and organic photovoltaics in combination with fullerenes as n-type semiconductors.52 This seems striking at first glance as a large ground-state dipole moment should result in low chargecarrier mobilities according to the dipolar disorder model developed by Bässler.53,54 However, the chromophores tend to self-assemble because of electrostatic interactions, forming πstacks with antiparallel ground-state dipole moments, which cancel each other to produce a total dipole moment of zero.36 Thus, gaining insight into the changes of the dipolar character and optical properties of merocyanine dyes upon aggregation should aid in the construction of dye assemblies with desired properties. A theoretical description linking the polar character of chromophores with the optical properties of the dye assemblies is given by the essential states model (ESM) as pioneered by Painelli et al.,55−57 which is an improvement upon the conventional Frenkel exciton model based on two-state (S0, S1) chromophores.24,58 The latter model does not account for the significant changes induced in the ground- and excitedstate properties of DA and DAD chromophores because of the intermolecular interactions or interactions between a chromophore (or aggregate) and the solvent environment. For example, in the Frenkel exciton model, the molecular ground-state (S0) and excited-state (S1) properties of the

individual chromophores (like the permanent dipole and quadrupole moments) are fixed and independent of interactions between molecules. This may be a good approximation for less polarizable chromophores like oligoacenes and perylene diimides, but in strongly polarizable DA and DAD chromophores, this is generally not the case. Painelli and co-workers55−57 addressed the problem by introducing diabatic “essential” electronic states for each chromophore, which can then mix together to form the molecular (adiabatic) states in response to intermolecular interactions or interactions between such chromophores and the solvent environment. Hence, in the ESM (but not the Frenkel exciton model), the permanent dipole moment in the molecular ground state can change in response to interactions with other molecules or with the solvent. In this work, we investigate the absorption properties of the highly dipolar merocyanine chromophore 1 (originally introduced with the name ATOP = amino-thienyl-dioxocyano-pyridine for photorefractive applications)59 as well as the double and quadruple π-stacks obtained upon the aggregation of bis(merocyanine) dyes 2 and 3, respectively, by applying the ESM (Figure 1). The diphenylacetylene spacer that connects the two chromophores in bis(merocyanine) 2 enables a folding in nonpolar solvents, resulting in a stack of two chromophores with antiparallel aligned ground-state dipole moments (Figure 1b). In contrast, the rigid naphthalene spacer moiety in bis(merocyanine) 3 provides an interchromophoric distance of ∼7 Å, enabling the intercalation of an additional chromophore to form the quadruple π-stacks (Figure 1c). The structures of the double60 and quadruple chromophore stacks61 have been confirmed by in-depth NMR studies and additionally by singlecrystal X-ray analysis in the case of bis(merocyanine) 3. The dye stacks exhibit significantly different absorption properties in comparison to the single chromophore of merocyanine 1, indicating a pronounced coupling between the chromophores within the stacks as described by the exciton theory in previous work.60,61 By applying the ESM, we now provide a more sophisticated model, considering also vibronic coupling and polarizability effects. Our investigations reveal that a two-state model considering just a neutral |N⟩ and zwitterionic state |Z⟩ is indeed not sufficient to adequately describe the absorption B


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transition to vibrational modes with a frequency of ∼1200 cm−1.63,64 In the following, we denote the intense absorption peak as the 0−0 band and the additional absorption shoulders as 0−1 and 0−2 bands, respectively, as indicated in Figure 2a, where, for example, 0−1 denotes the transition from the electronic ground state with vibrational quantum v = 0 to the first electronic excited state with v = 1. Like in the case of merocyanine 1, a very sharp (ν̃1/2 = 700 cm−1) and intense absorption band with an extinction coefficient of 287 500 cm−1 can be observed for bis(merocyanine) 2, which nearly equals twice the extinction coefficient of merocyanine 1 (Figure 2b, Table 1). The hypsochromic shift (Δν̃ = 1200 cm−1) of the absorption maximum in comparison to merocyanine 1 indicates the presence of a π-stack containing two chromophores with a pronounced H-type coupling61 arising from folding (Figure 1b), as no concentration dependence can be observed (Figure S3). Notably, the absorption maximum of 2 resides at the position of the 0−1 band of the monomer (Figure 2a,b). Furthermore, two additional shoulders at lower (ν̃max = 18 500 cm−1) and higher energies (ν̃max = 21 000 cm−1) can be observed, which are nearly located at the same position as the 0−0 and 0−2 bands of the monomeric dye 1, respectively. In contrast to dyes 1 and 2, the absorption spectrum of bis(merocyanine) 3 shows significant changes upon varying the concentration (Figure S4), giving evidence for an intermolecular self-assembly process. Upon increasing the concentration, the monomer band at 18 700 cm−1 decreases, whereas a new absorption band evolves, which exhibits a distinctly larger hypsochromic shift (Δν̃ = 2000 cm−1) compared to the absorption maximum of the double stack of bis(merocyanine) 2. This indicates a self-assembly into πstacks of four chromophores as analyzed by in-depth 2D NMR spectroscopy and single-crystal X-ray diffraction in our previous work.61 The data obtained from the concentrationdependent spectra were fitted employing a dimer model (for further details, see the Supporting Information), and the respective ideal dimer spectrum (Figure 2c) shows an intense absorption band at 20 700 cm−1 together with a weak absorption band at shorter wavelengths (17 500 cm−1, Table 1). Notably, the absorption band is considerably broadened (ν̃1/2 = 1800 cm−1) compared to merocyanine 1 and bis(merocyanine) 2. As a consequence, the molar extinction coefficient of 155 700 cm−1 is nearly reduced by a factor of 2 compared to bis(merocyanine) 2 bearing also two chromophores per molecule (note that the molar extinction coefficient refers to 1 mole of molecules of the respective bis(merocyanine) dye). In summary, merocyanine 1 and bis(merocyanine) 2 and 3 represent the ideal model systems for the investigation of the

and electronic properties of the single chromophore of 1. However, by introducing a bridge state |B⟩ as an intermediate state, in which the positive charge is located at the methine bridge and the negative charge at the acceptor group (Figure 1a), the experimental absorption spectrum of merocyanine 1 as well as of the dye stacks of bis(merocyanine) dyes 2 and 3 can be well reproduced, providing also reasonable values for the permanent and transition dipole moments.

2. UV/VIS ABSORPTION SPECTROSCOPY Figure 2a shows the UV/vis absorption spectrum of merocyanine 1 in 1,4-dioxane, a solvent of low polarity

Figure 2. UV/vis absorption spectrum of (a) merocyanine 1 and (b) bis(merocyanine) 2 in 1,4-dioxane (c = 4 × 10−6 M, 293 K). (c) Ideal spectrum of a quadruple stack obtained by the self-assembly of two bis(merocyanine) 3, as calculated from the nonlinear regression analysis of the data obtained from concentration-dependent UV/vis absorption studies in 1,4-dioxane at 293 K.

(relative permittivity εr ≈ 2.2).62 We can exclude the presence of aggregates arising from the intermolecular self-assembly of the dipolar dye by concentration-dependent UV/vis studies revealing no spectral changes upon increasing the concentration up to 4 × 10−5 M (Figure S1). The sharp absorption band at 18 600 cm−1 (ν̃1/2 = 700 cm−1, Table 1) is characteristic for merocyanine dyes in the so-called “cyanine limit”.43 These dyes have a similar geometry in the ground and excited states (i.e., each state has roughly equal admixtures of the diabatic neutral and zwitterionic states in the ground state; see Figure 1), resulting in a small change of the permanent dipole moment upon electronic excitation.38,45 Two additional absorption shoulders are present at higher energies, which can be attributed to the vibronic progression of the main absorption peak arising from the coupling of the electronic

Table 1. UV/Vis Absorption Data of Merocyanine 1 and Bis(merocyanine) Dyes 2 and 3a in 1,4-Dioxane at 293 K (c = 4 × 10−6 M) ν̃max/cm−1 (εmax/M−1 cm−1) ν̃1/2/cm−1b

merocyanine 1

bis(merocyanine) 2

bis(merocyanine) 3

18 600 (131 500) 19 800 (39 000) 21 000 (9300) 700

18 500 (21 300) 19 800 (287 500) 21 000 (42 500) 700

17 500 (11 300) 20 700 (155 700) 1800

The data given for bis(merocyanine) 3 refer to the ideal dimer spectrum obtained from the global fitting analysis of the data obtained from concentration-dependent UV/vis absorption spectroscopy in 1,4-dioxane at 293 K. bFull width at half-maximum relating to the most intense absorption band. a

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chromophore of dye 1. The overall dipole moment does not completely vanish as the chromophores exhibit a rotational displacement, as evident from the geometry-optimized structure (Figure S7). In contrast, the total dipole moment of the quadruple πstack of bis(merocyanine) 3 is equal to zero, which can be rationalized by the point symmetry of the aggregate structure (Figure 3c). As in the case of bis(merocyanine) 2, an interchromophoric distance of ∼3.5 Å can be found within the stack. Thus, the naphthalene spacer moiety provides an ideal distance of ∼7 Å between the two merocyanine chromophores of a molecule allowing the intercalation of an additional chromophore. TDDFT calculations on the geometry-optimized structure of the two-chromophore (“double”) π-stack of bis(merocyanine) 2 reveals two nondegenerate excited states with considerably different oscillator strengths (Table S1). Although the transition to the higher excited state is strongly allowed (f = 1.6099), the lower excited state bears no significant oscillator strength ( f = 0.0032). This is in accordance with the conventional exciton theory predicting H-type coupling between the face-to-face arranged chromophores that results in a hypsochromic shift of the absorption.15,24 According to the results obtained from TDDFT calculations, we should expect only one absorption band in the spectrum of folded bis(merocyanine) 2, indicating that the additionally observed side bands are due to vibronic coupling, which is not taken into account by TDDFT. As for the double π-stack, the transition to the highest excited state of the quadruple stack of bis(merocyanine) 3 is strongly allowed (f = 0.9642, Table S1). Additionally, the transition to one of the lower excited states is weakly allowed (f = 0.0470), so that we can attribute the low energy absorption band in the spectrum of 3 to the transition to a lower electronic excited state. Therefore, our results obtained from the TDDFT calculations suggest that the low-energy absorption band of the double π-stack corresponds to the vibronic progression of the main, intense absorption band, whereas in the case of the quadruple stack, the transition to a lower excited state causes the additional absorption shoulder.

optical absorption properties of a highly dipolar chromophore and the respective π-stacks with different but defined sizes.

3. COMPUTATIONAL STUDIES To gain deeper insight into the electronic structure of the monomeric chromophore 1 as well as the structural arrangement of the chromophores within the dye stacks of bis(merocyanine) dyes 2 and 3, geometry optimizations were performed at the level of density functional theory (DFT). The def2-SVP basis set65 in combination with the long-range corrected ωB97XD functional66 was used, which also includes dispersion correction being necessary to adequately describe the geometries of π-stacked molecules.67,68 Computational calculations were done for the gas phase. In addition, we performed time-dependent DFT (TDDFT) calculations on the geometry-optimized structures, employing the same basis set and the long-range corrected ωB97 functional,69 to obtain information about the excited-state properties of the single chromophore and the stacks. Only one electronic excited state was considered for each chromophore as the higher excited states lay outside the visible region of the absorption spectrum, which is not the focus of this work. The geometry-optimized structure of merocyanine 1 (Figure 3a) exhibits a large ground-state dipole moment of 13.5 D, in

Figure 3. Geometry-optimized structure of (a) merocyanine 1 and (b) folded bis(merocyanine) 2 as well as (c) dimer of bis(merocyanine) 3. Benzyl and butyl groups were replaced by methyl groups for the optimization. The hydrogen atoms of bis(merocyanine) dyes 2 and 3 are omitted in the figure for clarity reasons. The colored circles in panel (a) indicate the centers of the donor (D), bridge (B), and acceptor (A) moieties.

4. SIMULATIONS BASED ON ESM The optical properties of dye aggregates comprising polar chromophores can be significantly affected by polarizability effects arising from intramolecular charge transfer, which are not taken into account within the exciton model.15,34 Therefore, we employ the ESM, as pioneered by Painelli et al.,55−57 to study the absorption features of monomeric merocyanine 1 and the dye stacks of bis(merocyanine) dyes 2 and 3. We further extend the model to account for the coupling of the electronic transition to vibrational modes, as evident from the observed vibronic progression in the spectrum of merocyanine 1 (Figure 2a). 4.1. Monomer. The electronic structure of merocyanine dyes is often described by a superposition of the neutral and zwitterionic states.38−40 However, Dähne et al. showed the importance of an additional polymethine state, needed to explain the charge alternation along the polymethine chain,41 and Mustroph et al. proposed intermediate states, in which the positive charge is located at the (poly)methine bridge and the negative charge at the acceptor moiety, respectively.49 By considering these states, it is possible to explain the alternating π-electron densities along the polymethine chain, as evident

good agreement with the results obtained from electro-optical absorption measurements (13.6 D).70 Thus, the ground state is characterized by a significant amount of charge-transfer character, which is also evident from the electrostatic potential surface obtained from the DFT calculations (Figure S6a). The magnitude of the transition dipole moment calculated by TDDFT (9.7 D) is in accordance with the value estimated by the integration of the experimental absorption spectrum (9.7 D). However, the excited-state energy is overestimated by TDDFT, which is commonly observed for merocyanine dyes.71,72 The double π-stack of folded bis(merocyanine) 2 shows a distance of ∼3.5 Å between the antiparallel aligned chromophores, corresponding to the ideal van der Waals distance of π-stacked molecules (Figure 3b).73−75 The antiparallel orientation of the chromophores within the stack leads to a significant lowering of the magnitude of the total ground-state dipole moment to 2.0 D with respect to the single D


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spectrum, whereas the second excited state |e2⟩ is too high in energy and thus causes only absorption in the UV region (Figure 4). To account for the coupling of the electronic transition to the C−C vinyl stretching mode of the π-conjugated system of the merocyanine chromophore, we include, in addition to the electronic Hamiltonian, the vibronic term78

from the chemical shifts in the 13C NMR spectra.47 These states have been further suggested for cyanine64,76 and merocyanine dyes49 to rationalize the vibronic progression observed in the UV/vis absorption spectra. In addition, Painelli et al. showed that a simple two-state model is not sufficient to describe the absorption properties of the D−A dyes Fc-PTM and Me9Fc-PTM and that a third state (the so-called “bridge state”) is necessary to describe the spectral features.77 Therefore, we consider three diabatic electronic states (i.e., the essential states) to construct the Hamiltonian for the monomer of dye 1 (Figure 4). The neutral state |N⟩ is directly

Ĥ mon,vib = ℏωvibb†b + ℏωvibλB(b† + b + λB)|B⟩⟨B| + ℏωvibλZ (b† + b + λ Z)|Z⟩⟨Z|

The Hamiltonian in eq 2 represents the coupling of a single vibrational mode of frequency ωvib to the three essential states. The coupling to state i is described by the Huang-Rhys factor λi2, where i = N, B, Z with λN2 = 0. The operator b† (b) creates (annihilates) one vibrational quantum in the unshifted nuclear potential well-defining the neutral state. Computational studies suggest a collection of singly excited-state vibrations causing the high-energy band in a merocyanine dye,72 whereas theoretical investigations by Mustroph and Towns reveal the domination of one vibration giving rise to the vibronic progression observed for polymethine dyes.79 Thus, we employ one vibrational mode that is coupled to all three essential states, which can also be regarded as an effective mode. In addition, we assume that λB > λZ as the positive charge at the bridge of the merocyanine chromophore should lead to a larger structural distortion than in the case of the zwitterionic state, where the charge is localized on the rigid thiophene moiety. Furthermore, we chose to use no solvent model as the absorption spectra for merocyanine 1 as well as for the dye stacks of bis(merocyanine) dyes 2 and 3 were recorded in the same solvent. In this way, solvent effects are already taken into account by the choice of parameters used for the simulation of dye 1, which are subsequently used for the calculated spectra of the dye stacks (vide infra). Besides, dye 1 shows only small spectral changes upon solvent variation (Figure S2), revealing only weak solvatochromism. The overall Hamiltonian for the monomer is then defined by

Figure 4. Schematic illustration of the three-state model employed for merocyanine 1 without vibronic coupling. The diabatic states (left) are coupled by the coupling parameter t giving rise to the adiabatic states (right).

coupled to the bridge state |B⟩, where the positive charge is located at the methine bridge and the negative charge at the centroid of the acceptor unit, thus representing an intermediate state of the intramolecular charge transfer from the donor to the acceptor moiety. The bridge state is also directly coupled to a zwitterionic state |Z⟩ with the positive charge at the donor moiety, as displayed in Figure 4. We assume the same coupling strength t between consecutive states, indicating the same probability for the electron transfer from the bridge to the acceptor unit and from the donor to the bridge moiety, respectively, thereby decreasing the number of adjustable parameters. Accordingly, the electronic Hamiltonian for the monomer is then defined as

Ĥ mon = Ĥ mon,el + Ĥ mon,vib

(3)

With the Hamiltonian described in eq 3, we obtain the spectrum displayed in Figure 5a using the parameters listed in Table 2. The electronic coupling t as well as the energy of the bridge (ηB) and zwitterionic state (ηZ) mainly influence the position of the absorption maximum. Hence, the values were adjusted to find a good agreement with the experimental absorption maximum resulting in a coupling strength of t = 14 000 cm−1 and zwitterionic and bridge-state energies of ηZ = 2100 cm−1 and ηB = 3100 cm−1, respectively. Employing these values, the transition to the electronic excited state |e2⟩ is too high in energy to appear in the visible region, and therefore only the lower excited state |e1⟩ is responsible for the spectral signature of the merocyanine chromophore displayed in Figure 5a. The signatures of the higher energy vibronic bands are dictated by the Huang-Rhys factors λZ2 and λB2 as well as by the vibrational frequency ωvib. The best result was achieved for λZ2 = 1.00 and λB2 = 2.70 in combination with a frequency of ωvib = 1150 cm−1, in accordance with the C−C stretching mode in polymethine dyes.63,64 With these values, the side bands can be adequately reproduced (Figure 5a). We have also simulated the absorption spectrum with a smaller line width to

Ĥ mon,el = ηB|B⟩⟨B| + ηZ|Z⟩⟨Z| + t(|N⟩⟨B| + h. c. ) + t(|B⟩⟨Z| + h. c. )

(2)

(1)

where ηB and ηZ are the diabatic energies of the bridge and zwitterionic states, respectively, and h.c. represents the Hermitian conjugate. The energy level of the neutral state is set to zero, and we place both charge-separated states above the neutral state as the charge separation should be less favored. In addition, we assume the bridge state to be higher in energy than the zwitterionic state because of the less stabilized positive charge at the bridge moiety (Figure 4), in full agreement with the three-state model introduced by Painelli et al.77 Diagonalization of the Hamiltonian in eq 1 provides the electronic ground state |g⟩ and two excited states |e1⟩ and |e2⟩ representing the adiabatic states (Figure 4) that are responsible for the absorption. With the parameters used for our simulations (vide infra), only the transition to the lower excited state contributes to the visible region of the absorption E


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significantly smaller than the diabatic HR factors (1 and 2.7) used in the calculated spectrum. To further justify the chosen set of parameters, we compare the ground state (μg) and transition dipole moments (μeg) calculated within the ESMwhich depend on the parameters used for the simulationswith the values determined by UV/ vis and electro-optical absorption measurements (Table 3; for Table 3. Ground-State (μg) and Transition Dipole Moment (μeg) as well as the Difference between the Permanent Dipole Moments in the Excited and Ground States (Δμ) of Merocyanine 1a μg/D μeg/D Δμ/D

Figure 5. Simulated absorption spectra (red line) of (a) merocyanine 1 and bis(merocyanine) dyes (b) 2 and (c) 3 using the parameters listed in Table 2. Also shown are the (a,b) corresponding experimental spectra (black lines) in 1,4-dioxane (c = 4 × 10−6 M, 293 K) as well as (c) the ideal dimer spectrum of bis(merocyanine) 3 calculated from the global fitting analysis of the data obtained from concentration-dependent UV/vis absorption studies in 1,4-dioxane at 293 K (black line) for comparison.

merocyanine 1

bis(merocyanine) 2

bis(merocyanine) 3

2100 3100 14 000 1.00 2.70 1150 550

2100 3100 14 000 1.00 2.70 1150 550 3.1 7

2100 3100 14 000 1.00 2.70 1150 900 3.1 4

7

electro-optical absorption measurements70

13.5 10.7 1.4

13.6 9.7 1.4

a

The values were determined within the ESM and by electro-optical absorption measurements.

further details, see the Supporting Information). To this end, we located the charges in the bridge and zwitterionic states on the respective atoms of the chromophore, as displayed in Figure 4a, using the geometry-optimized structure obtained from DFT calculations. By doing so, a ground-state dipole moment of μg = 13.5 D is obtained, which is in very good agreement with the experimental value of μg = 13.6 D obtained from electro-optical absorption measurements,70 confirming the strong dipolar character of the merocyanine chromophore. In accordance with the cyanine limit, our simulations reveal an almost equal contribution of the zwitterionic (25%) and neutral states (27%) in the ground state (Table S3), which are coupled through the bridge state (48%). In addition, the transition dipole moment calculated by the integration of the absorption spectrum (μeg = 9.7 D70) agrees well with the value obtained from the ESM (μeg = 10.7 D). A characteristic feature of merocyanine dyes close to the cyanine limit is the negligible change of the dipole moment upon optical excitation, that is, a difference of permanent dipole moments in the excited and ground state Δμ ≈ 0.38,45 Indeed, the analysis of EOAM reveals only a slightly larger dipole moment in the excited state (Δμ = 1.4 D),70 in full agreement with the model’s prediction of an increase by Δμ = 1.4 D (Table 3). Thus, the employed parameters provide appropriate values for the permanent dipole moments as well as for the transition dipole moment and are therefore consistent with the experimental results. In addition, we have simulated the absorption spectrum of merocyanine 1, applying a two-state model, that is, considering only the neutral and zwitterionic states. As evident from the calculated spectrum (Figure S11, red line), the vibronic progression cannot be reproduced with a parameter set that gives reasonable values for the dipole moments (Table S2). A decent fit is obtained assuming a higher energy of the zwitterionic state (ηZ) (Figure S11, blue line and Table S2), which however contradicts the results of EOAM revealing a small difference of the permanent dipole moments in the excited and ground states (Table S2).70 Hence, a two-state model is not sufficient to describe the absorption properties of merocyanine dye 1, which is in line with the considerations by Mustroph et al., suggesting the importance of bridge states to account for the vibronic fine structure observed in the absorption spectra of cyanine64 and merocyanine dyes49 as

Table 2. Parameters Used for the Simulation of the UV/Vis Absorption Spectra of Merocyanine 1 and the Double and Quadruple π-Stacks of Bis(merocyanine) Dyes 2 and 3, Respectively, Displayed in Figure 5a ηZ/cm−1 ηB/cm−1 t/cm−1 λZ2 λB2 ωvib/cm−1 σ/cm−1 ε vmax

ESM

σ represents the full width at 1/e of the absorbance and vmax the cap on the total number of vibrational quanta per electronic state.

a

visualize the fine structure of the spectrum (Figure S9). Accordingly, the spectrum exhibits three absorption bands with a spectral separation of ∼1150 cm−1, which equals the vibrational energy employed in our model. Indeed, when vibronic coupling is neglected, the absorption spectrum exhibits just one absorption band lacking the high-energy side bands (Figure S10). Therefore, we can clearly attribute the absorption shoulder to the vibronic progression of the main absorption band. At this point, we want to emphasize that in contrast to the vibronic exciton theory, where the Huang-Rhys factor can be determined from the intensity ratio of the 0−1 and 0−0 bands, the Huang-Rhys factors within the ESM refer to the diabatic states before mixing. Thus, the effective or adiabatic HuangRhys factor determined from the absorption spectrum differs significantly from those corresponding to the diabatic states, as also emphasized by Zheng et al. for squaraine dyes.34 For example, the effective HR factor from Figure 5 based on the ratio of the first two vibronic peaks is approximately 0.3, F


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neglected (Figure S13). Although the one at lower energies is forbidden (f ≈ 0), a large oscillator strength of f = 0.34 is obtained for the one at higher energies, in agreement with the TDDFT calculations (Table S1) and the exciton theory for Haggregates. To gain deeper insight into the spectral differences between the monomer of merocyanine 1 and the double π-stack of bis(merocyanine) 2, we have simulated the absorption spectrum of the latter with varying π−π distances (Figure 6).

well as with the simulations done by Painelli et al. for the D−A dyes Fc-PTM and Me9Fc-PTM.77 4.2. Double and Quadruple π-Stacks. After having fixed the parameters for the monomer, we now move to the double and quadruple π-stacks of bis(merocyanine) dyes 2 and 3, respectively. To this end, we extend the monomer Hamiltonian to the aggregates. Thus, the electronic part of the Hamiltonian for a double π-stack with N = 2 chromophores and a quadruple π-stack (N = 4) takes the form Ĥ aggregate =

∑

(n) ̂ Ĥ mon + VCoul

(4)

n = 1, N

which represents the sum of the monomer Hamiltonians and an additional term V̂ Coul accounting for the Coulomb coupling between the chromophores. This Coulomb term represented in the diabatic basis is defined by ̂ = VCoul

1 ∑ 4πεε0 Y = D,B,A

∑∑ m

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