Molecular Reorganization Energy as a Key Determinant of J-Band

Article pubs.acs.org/JPCA

Molecular Reorganization Energy as a Key Determinant of J‑Band Formation in J‑Aggregates of Polymethine Dyes Alexander Petrenko*,† and Matthias Stein Molecular Simulations and Design Group, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, 39106 Magdeburg, Germany ABSTRACT: This work demonstrates the feasibility of the theory of extended multiphonon electron transitions for the description of optical spectra of polymethine dyes and J-aggregates using quantum chemistry. The formation of a strong absorption band in dye monomers and a J-band in their aggregates is uniformly explained from the electron−nuclear resonance condition. The redistribution of optical band intensities among cyanine dyes with the solvent is also explained. The dependence of the possibility of J-band formation in aggregates on the dye structure is successfully predicted. The results presented provide an insight for rational molecular design and application of polymethine dyes.

1. INTRODUCTION Polymethine molecules are made of an odd number of methine (CH) groups with alternating single and double bonds. Cyanine dyes are members of the polymethine group and may be used as fluorescent probes in nucleic acids and tumor imaging.1,2 The polymethine chain is the major structural feature determining the spectral-luminiscent properties of polymethine dyes. A change in length of only one vinylene group in symmetrical polymethine dyes gives rise to a change in absorption and fluorescent band of ∼100 nm. One interesting property of cyanine dyes (Figure 1A) is the ability to form aggregates in semipolar media and, among them, J-aggregates.3 The formation of supramolecular aggregates in solution of the “sandwich”-type can be detected by a disappearance of the monomer absorption and luminescent bands and appearance of a new narrow and intense absorption band (J-band), which is red-shifted with respect to the monomer band. J-aggregates currently attract an increasing interest due to their potential applications in nanoscience.4−6 In the J-aggregates (Figure 1B), four dye molecules assemble to chromophores of the brickwork structure as thick as three bricks, and these chromophores organize the J-aggregates that look like long thin rods.7,8 Such a structure minimizes the exciton effects between J-aggregate chromophores in the optical line shape. In refs 9−11, an attempt of unified description of optical properties of polymethine dyes and their J-aggregates had been made based on the theory of multiphonon electron transitions.12 According to the new approach, the theory of extended multiphonon electron transitions (EMET), the effect of the J-band appearance is the property of individual Jchromophores consisting of few dye monomers. The model to describe the electronic structure and transition dynamics of the J-chromophore is an extension of that for a polymethine dye © 2015 American Chemical Society

monomer but which takes into account an increase of the Jchromophore length in comparison to the dye chromophore by a π-π stacking interaction of the heterocyclic rings. The EMET theory ascribes the most intense absorption band in a series of a cyanine dye and the J-band to an electron nuclear resonance that occurs at the specific length of the polymethine chain. This approach and model were applied to describe spectroscopic data obtained in the classical experiments of Brooker et al.13 and Herz14 but limited to just these examples, whereas at present, there are hundreds of different polymethine dyes, which potentially can exhibit a J-band after aggregation.15−17 Several parameters in the model have to be justified. The most important is the strength of electron−nuclear coupling, measured by the nuclear reorganization energy (RE). To this end, we here focus on quantum chemical computation of REs in vinylogous series of several representative polymethine dyes. We also perform numerical calculations to provide interpretation for a wide set of experimental optical spectra of dye monomers and J-aggregates. In the original work on EMET theory (2001−2002),9−11 the choice of parameters of the model, in particular, the increase of RE in J-aggregate chromophores in comparison to the monomer, was not well-justified. Some kind of justification came a decade later from high level quantum chemical calculations of reorganization energy in π-π stacked molecular dimer cations.18 In general, theoretical interpretations based on high level ab initio calculations are instrumental in understanding the nature of π-π interactions,19,20 as well as their energetic and geometrical significance in stabilizing the selfReceived: February 6, 2015 Revised: April 9, 2015 Published: June 19, 2015 6773

DOI: 10.1021/acs.jpca.5b01269 J. Phys. Chem. A 2015, 119, 6773−6780

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The Journal of Physical Chemistry A

resonance. The formation of a strong absorption band is shown to depend on the resonance parameter. Manipulating RE is suggested as a means to achieve the resonance and build up a strong absorption band. After discussions of monomers, we move to J-aggregates formed by monomers. We emphasize that the role and importance of the resonance parameter are the same as in the monomer cases.

2. METHODS Reorganization Energy. The reorganization energy (RE), termed λ from here on, can be divided into two terms: internal RE λi and solvent RE λs (λ = λi + λs). The solvent RE depends mainly on solvent polarity.22−26 The solvent RE describes the solvent molecule reorientation upon excitation of the polymethine dye from the ground into the excited state. It is considered as an adjustable tunable parameter whose value is 0.2−0.6 eV.27,28 We compute the internal RE “spectroscopically” as half the of energy difference between the vertical excitation and fluorescence energies29 following: (a) two separate optimizations of the structure of the isolated molecular cation in the ground state (S0) and in the first singlet excited state (S1); (b) the single-point calculations of the S0 → S1 excitation energy of the cation at the ground state geometry ΔE(S0), and at the S1 excited state geometry ΔE(S1). To this end, λi can be represented as the following: λ i = [ΔE(S0) − ΔE(S1)]/2

Figure 1. (A) Chemical structure of a thiacyanine dye cation with the varying length of a polymethine chain. A monovalent counterion is not shown. (B) A polymethine dye molecule and its brickwork-structured J-aggregate. The dye chromophore lengthening (6d → 8d) is a result of supramolecular J-aggregation through π-π electron interaction of heterocyclic rings, where d being the C−C bond length of a single methine group. Figure adapted with changes from reference.11

(1)

Full geometry optimizations for polymethine thiacyanines (n = 0−7) in the S0 and S1 states were performed completed using the GAUSSIAN 09 program30 at the HF/6-31G(d,p) and CIS/ 6-31G(d,p) levels, respectively. Excitation energies ΔE(S0) and ΔE(S1) are then calculated at the CIS/6-31G(d,p) level. The calculated REs were compared with REs obtained from the resonance condition between extended electronic motion and nuclear reorganization motion during the electronic transition. According to the EMET approach to the nature of optical transitions in polymethine dyes, the resonance occurs when the characteristic time of extended electronic motion becomes equal to the characteristic time of vibration-like motion of the nuclear reorganization. The timescale τn of nuclear reorganization is defined as τn = ℏ/λ, where λ is the RE. That of electronic motion τe is defined as τe = R(J1/2m)−1/2, where R, J1, and m are the effective length of the dye polymethine bridges, the energy of an electron in the initial state, and the mass of an electron, respectively. The effective length R is assigned11 to be 2.8(n + 2) Å, where n is the number of methine groups in the polymethine chain (see Figure 1A). J1 ≡ J1(n) is the experimental resonance value for thiacyanine, which depends on n. We introduce the resonance parameter θ = τe/τn. The resonance occurs when θ = 1/2, according to the EMET theory. This condition will be extensively exploited in the discussion. Theoretical Absorption Spectra. We also computed and plotted the theoretical absorption spectra of a few polymethine dyes and their aggregates. Theoretical absorption spectra depend on λ, R, J1 and two other parameters of EMET theory: the dumping parameter (γ) and the energy of an electron in its final state (J2). Readers may refer to section 3 of ref 10 for the formulas employed. As already mentioned above, the EMET theory of polymethine dyes and J-aggregates is based on the theory of multiphonon electron transitions. Compared to the Hamiltonian of the standard theory of multiphonon electron transitions,12 in the EMET theory the Hamiltonian complicated

assembling supramolecular structures. Thus, it is natural to apply this type of calculations to justify the foundations of EMET theory. Our main motivation is to demonstrate the feasibility of the EMET approach to the description of optical transitions in polymethine dyes and J-aggregates using quantum chemistry. Quantum chemical calculations and the analysis of parameters entering into the EMET theory are essential to study the possibility of forming the electron−nuclear resonance state, which gives rise to the strong absorption band. Our results provide a benchmark for predicting the electron−nuclear resonance states. We compute RE for a vinylogous series of thiacyanines (n = 0−7), whose structural formula is represented in Figure 1A. The optical spectra of these dyes were studied in a classical experiment of Brooker et al.13 and collected in ref 21. The EMET theory of optical transition was applied to the detailed analysis for transformation of these spectra with an increasing length of the polymethine chain.10 Thiacyanine dyes are characterized by two benzothiazole heterocyclic components connected by a polymethine bridge having the odd number of carbons. The structure of these dyes reflects the generic cyanine dye structure. Any cyanine dye can be generated by the substitution of benzothiazole with quinoline, benzoxazole, indole, and other heterocylic fragments. In the following, we first describe how RE is computed and define the resonance parameter. Then, polymethine dye monomers and their spectra are discussed. Computed RE are compared to those required for the electron−nuclear 6774


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The Journal of Physical Chemistry A by the additional electronic potential well V2(r − R) separated from the initial well V1(r) by the distance R ≡ |R| H=−

+

ℏ Δr + V1(r) + V2(r − R) + 2m 1 2

⎛

∑ ℏωk⎜⎜qk2 − k

⎝

1/2 ⎛ λ⎞ ⎜ ⎟ ξ = ⎜1 − ⎟ J1 ⎠ ⎝

∑ Wk(r)qk

are formulated from elementary functions.

k

⎞ ∂ ⎟ ∂qk2 ⎟⎠

3. RESULTS AND DISCUSSIONS Reorganization Energy for Different Dye Monomers and Solvents. We begin with presenting results for various thiacyanine dye monomers. Table 1 has included internal

(2)

where r is the radius vector of electron, qk are the real normal phonon coordinates, ωk are the eigenfrequencies of the normal vibrations, and k is a phonon index; term

∑ Wk(r)qk

Table 1. Computed Internal Reorganization Energies λi (in eV) in a Vinylogous Series of Thiacarbocyanine Dyes n n n n n n n n

is due to the electron−phonon coupling. The reorganization energy of nuclear vibration defined in the theory in the following form: λ = ℏ ∑ ωkqk̃ 2

(4)

k

where q̃k are the normal phonon coordinates corresponding to the equilibrium positions of the nuclei when the electron is in the initial or final state. With the use of the methods of classical radiation theory and the Einstein model for nuclear vibrations ωk = const ≡ ω, the following expression for the light absorption factor (optical extinction coefficient is proportional to this factor) has been obtained:10 K = K 0 exp W W=

(5)

sinh βT 1 − ωτ Θ 4ωτ Θ2 cosh t

(6)

where βT =

ℏω ℏ ,τ= 2kBT λ

(7)

and t=

ωτe ⎡ AC + BD θ2 2Θ(Θ − 1) ⎢ 2 + + 20 2 2 2 θ ⎣ A +B (Θ − 1) + (Θ/θ0) θ0 +

⎤ ⎥ 1⎦

0.42 0.14 0.09 0.06 0.06 0.09 0.23 0.35

(11) 1/2

where A = 1.375[J1(n)/J1(3)] eV. Varying the nature of solvents can also bring dyes with n = 2 or n = 4 to fulfill the resonance condition due to the parallel shift of theoretical curve RE(n) in Figure 2A up (if the solvent RE increases) or down (if the solvent RE decreases), as shown in Figure 2B. If the solvent RE is increasing or the solvent polarity is high, the most intense absorption band occurs for the n = 2 dye. If it is decreasing or the solvent polarity is low, the most intense band occurs for the n = 4 dye. As the resonance parameter deviates from 1/2, the most intense absorption band weakens. As a support to these statements, we refer to experimental results from literature. First, we compare the experimental data of Kachkovski et al.32 to Brooker’s data for thiacyanine dyes (Table 2). The former used an unipolar solvent dichloromethane with ε = 8.93, whereas the latter used a polar solvent

R 2J1 /m

where Δ defines the thermal effect energy related to the heat absorption in elementary extended multiphonon transition. The energy ℏΩ of the absorbed photon and thermal effect Δ are related by the law of conservation of energy: ℏΩ = J1 − J2 + Δ

0 1 2 3 4 5 6 7

λres(n) = A/(n + 2) eV

(8)

Rλ λ λ θ= , Θ = , θ0 = , τe = Δ γ ℏ 2J1 /m

= = = = = = = =

reorganization energies calculated using the “spectroscopic” formula 1. In general, the behavior of the internal RE on the length of a polymethine bridge at small n can be explained from torsional contributions. At small n, the internal RE decreases as the chain length increases. The reason is the decrease of torsional reorganization energies due to the increase in heterocycle distances. This was also observed in ref 31. Beyond n > 4, the RE begins to rise with increasing n again resulting from increased degrees of freedom without a further steric gain. We compare the calculated RE to that required for the resonance (Figure 2A). We assume the solvent RE to be 0.22 eV for every polymethine dye with chain length n. The solvent reorganization energy is expected to be the property of the solvent molecules only, their polarity, and their translational and rotational ease to adopt to a slightly modified structure of the polymethine dye. For each series of polymethine dye, this is expected to remain constant as the chain length n increases. The value of 0.22 eV is a reasonable guess because it enables the n = 3 dye to be at resonance. The theoretical resonance condition θ = 1/2 determines functional form of resonance curve λres (n) (red ● in Figure 2A) as following:

1 ⎛ ωτ sinh βT ⎞ 2 ⎛ cosh t ⎞ ⎜⎜coth βT − ⎟⎟ ln⎜ ⎟− 2 ⎝ 4π cosh t ⎠ ωτ ⎝ sinh βT ⎠ + (βT − t )

λi

parameter/structure

(3)

k

(10)

(9)

Expressions A = A(θ , Θ, θ0 , ξ), B = B(θ , Θ, θ0 , ξ), C = C(θ , Θ, θ0 , ξ), D = D(θ , Θ, θ0 , ξ)

and factor K0 = K0(θ, Θ, θ0, ξ, βT, t, E, J1, m), where 6775


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that a change of solvent can affect the most intense absorption bands. In more polar solvents, a shorter polymethine dye absorbs more intensely. The thiapyrylocyanine case is more sensitive to changes in solvent polarity than a thiacyanine dye.33 We calculated internal RE of thiapyrylocyanine dyes for n = 2−4, which show a similar trend to that of thiacyanine dyes shown in Figure 2. Lastly, a similar behavior can be observed for 1,1′-diethyl-2,2′-cyanine dyes. The n = 0 case of this dye is the popular pseudoisocyanine that has been the subject of numerous investigations and nanotechnology applications. These data also agree with our prediction that the most intense absorption band occurs for a lower n as solvent RE or the solvent polarity are increasing. Therefore, the experimental data justify the EMET approach for the description of optical transitions in polymethine dyes. Polymethine Dyes at Overresonant Conditions. The resonance parameter can be larger than 1/2 so that the system behaves in the over-resonance regime. Such cases are observed experimentally.34 The theoretical absorption band of this monomer dye consists of two sub-bands: a low-energy Lband and a high-energy D-band.10 The D-band is relatively weak at the condition of the resonance. The deviation of the system from the resonance, however, enhances the D-band and reduces the L-band. Lepkowicz et al., reported that, for the given cyanine with an 11-carbon conjugated chain, 3,3′-diethyl9,11,15,17-di(β,β-dimethyltrimethylene) thiapentacarbocyanine (PD 1659), it is possible to significantly increase the relative intensity of short wavelength sub-band of visible spectra of PD 1659 by increasing the solvent polarity.35 The EMET theory allows to attribute this effect to an increase in solvent RE as discussed above. The theory predicts the blue shift of the maximum of the D-band with increasing solvent RE. This blue shift can also be clearly seen from the experimental spectra. Theoretical formulas allow us to successfully reproduce the effect of transformation in experimental spectra of PD 1659 by increasing RE (Figure 3). Aggregate Formation. We now discuss results about aggregate formation by the above thiacyanine dye monomers. The EMET from Egorov’s approach for J-aggregates tells us that the same resonance condition applies for both a monomer and an aggregate. Changes from a monomer to an aggregate (1) increase in RE and (2) increase in effective length R of the J-chromophore in the aggregate. The RE usually increases by 0.1 eV, and the effective length by 2d, where d is the C−C bond length of a single methine group. We can justify these increases in R and RE from our quantum chemical calculations. First, in the J-aggregate chromophore model (see Figure 1B),11 the dye monomers

Figure 2. (A) Comparison of reorganization energies in vinylogous series of thiacyanine. Lines are calculated reorganization energy (black) and reorganization energy required for the resonance λres(n) (red), respectively. Computed values correspond to a solvent reorganization energy of 0.22 eV. (B) Demonstration that varying solvent RE can bring n = 2 or n = 4 thiacyanine dyes into resonance condition due to the parallel shifts of theoretical curve RE(n) of Figure 2A up (more polar solvent, λs = 0.27 eV, ■) or down (less polar solvent, λs = 0.17 eV, blue ▲). The reorganization energy required for the resonance λres(n) is shown by red ●.

(methanol) with ε = 32.63. Due to changes in solvent polarity, the relative intensities of the absorption bands for the n = 2 and n = 4 dyes have changed. Second, Kachkovski et al. provide absorption spectra for thiapyrylocyanine dyes in DMSO (ε = 46.7) and dichloromethane (see above). It can clearly be seen

Table 2. Relative Variation of Absorption Spectra in Vinylogous Series of Cyanine Dyes in Different Solvents: Water (1), DMSO (2), Methanol (3), and Dicloromethane (4)a dye/n

n=0

n=1

n=2

n=3

n=4

n=5

n=6

11,13

0.32 − 0.54 0.38 0.81 0.35 0.44

0.65 0.40 0.91 0.72 0.93 0.92 1.00

0.94 0.60 1.00 0.92 1.00 1.00 0.99

1.00 1.00 0.65 0.97 − − −

0.63 0.80 0.48 1.00 0.24 − −

0.12 0.49 0.09 0.46 − − −

− 0.27 − − − − −

thiacyanine-(3) thiacyanine-(4)32 thiapyrylocyanine-(2)32 thiapyrylocyanine-(4)32 thiapyridocyanine (2)34 1,1′-diethyl-2,2-quinocyanine-(3)52 1,1′-diethyl-2,2′-quinocyanine-(1)52 a

In calculations spectral data from literature was used. Absorption coefficients at the maximum of the long wave band of each dye in series (in relative units) are given. 6776


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dyes, the expected increase in RE and effective length R of Jaggregate chromophores will move the resulting aggregate structure out of range of resonance for n = 3 and even further out of resonance for n > 3 (see Figure 2). In other words, only thiacyanine dyes with n < 3 have the possibility to match the resonance condition (via increase of RE and R) and thus to form J-chromophores of the J-aggregate. No experiment so far has reported the J-band of a thiacyanine dye with n ≥ 3, to the best of our knowledge (see Table 3). Moreover, the theory Table 3. Thiacyanine Dyes Exhibiting J-Band Effect after Supramolecular Aggregation n 2 1 0 0

Figure 3. Transformation of theoretical spectra of thiacyanine dye PD 1659 upon increasing the reorganization energy (in eV): RE = 0.18 (black), 0.22 (red), 0.35 (blue), 0.38 (pink), and 0.47 (green). Corresponding values of J2 (in eV) are taken to be 2.71, 2.73, 2.85, 2.88, and 2.97. J1 = 3.4 eV, γ = 0.11 eV, and R = 1.96 nm.

chemical name

ref

3,3′-trimethylammoniumpropyl-2,2′thiadicarbocyanine (DiSC3+(5)) 3,3′-disulfopropyl-5,5′-dichlorothiacarbocyanine 3,3′-dioctadecylthiacyanine 3,3′-disulfopropyl-5,5′-dichlorothiacyanine (THIAMS)

6, 45 53 54 3, 46

rationalizes the optical spectra for the 1,1′-diethyl-2,2′-cyanine family of dyes. A J-band is not observed except for 1,1′-diethyl2,2′-cyanine with n = 0 in water. This is consistent with the fact that the most intense absorption band occurs for the n = 1 dye in aqueous solution (Table 2). This means (in terms of Figure 2) that for a vinylogous series of that cyanine in aqueous solution, the intersection of calculated RE(n) curve with resonance curve to take place at n = 1. Only the cyanine dye with n = 0 has the possibility to reach the resonance condition (via increase of RE and R) by forming J-chromophores of Jaggregates. No J-band is reported for either the second member of this dye family with n = 1, pinacyanol (1,1′-diethyl-2,2′carbocyanine),37−40 nor the third member 1,1′-diethyl-2,2′dicarbocyanine with n = 2.41 This is an a posteriori justification of the EMET theory for optical transitions in polymethine dyes and J-aggregates. Effect of Charges Side Chains on J-Aggregates. This theory can explain how charged side groups of a thiacyanine dye influence the J-band of its aggregate. The charged side groups polarize the solvent environment completely to saturation and thus lower the solvent RE upon excitation of the dye core. As we can see from the data of Table 3, there is no J-band effect experimentally detected for 3,3′-diethylthiacarbocyanine and 3,3′-diethylthiacyanine with neutral side chains. Upon substitution of ethyl groups by charged side chain groups, the RE is lowered to match resonance values and gives rise to a typical J-band. The “J-band” of 3,3′-diethylthiacarbocyanine,42 for example, has a D-band more intense than an L-band, typical for the system deviating from the resonance. Most likely, the 3,3′-diethylthiadicarbocyanine J-aggregates slightly deviate from resonance.43,44 That is why aggregates of this dye have been named “J-like” aggregates.44 The J-aggregate of a tricationic substitute of this dye with long charged side chains replacing the neutral ethyl groups displays a typical J-band (Table 3).6,45 Thus, the decrease in RE yields a pronounced J-band in theoretical spectra, as expected. J-Engineering. A simplified mechanistic picture based on Figure 2 provides explanations for additional experimental observations. There are several factors contributing to the changes in RE and effective length R: the prolonged time of aggregation,46,47 increasing the solvent polarity48,49 and the strong interaction of J-aggregates with polymer molecules (in composite structures),50 semiconducting, and metal surfaces.47

are π-stacked, and the 2pσ-2pσ overlap integral (0.114) of adjacent C atoms of interacting monomers at the van der Waals distance (3.4 Å) is comparable in magnitude to the 2pπ-2pπ orbital overlap integral (0.34) of adjacent C atoms at the C−C bond distance (1.4 Å).36 This leads to an increase in effective distance R as the dye molecules aggregate and form J-chromophores. Second, a higher level quantum chemical calculation of RE in the model π-stacked ethylene dimer cation confirmed the increase in RE as molecules are stacked.18 When the distance between π-stacked ethylene molecules decreases from 7.0 to 5.0 Å, the RE computed at the multireference MR-CISD+P level (with Pople’s correction to account for higher-order excitations) changes from 0.281 to 0.314 eV. We should expect a further increase in RE if the intermolecular distance is even shorter, as is the case in a van der Waals complex. Our ab initio calculations for S0 and S1 states of an ethylene dimer (with the distance between πstacked ethylene molecules of 3.4 Å), using the GAUSSIAN 09 program30 (MP2 for ground state geometry optimization and CIS(D) for excited state geometry optimization options) with the aug-cc-PVDZ basis set gave the calculated S0 → S1 internal RE of a stacked dimer is 0.61 eV, compared to 0.28 eV for a monomer. Since electrons are more delocalized in polymethine dyes, the increase in RE will be less than the 0.33 eV for the ethylene case. These simple considerations confirmed the increase in RE and effective length R of dye chromophore in J-aggregates compared to monomers, in agreement with fitting to the Herz experimental data14 presented in ref 11. The deviation from resonance condition alters the theoretical spectra of a J-aggregate, as also shown for the monomer. A theoretical J-band of a J-aggregate also consists of two subbands: a low-energy L-band and a high-energy D-band. The Dband is relatively weak in the condition of the resonance. A deviation of the system from the resonance, however, enhances the D-band and reduces the L-band. The EMET theory predicts that no thiacyanine dye with n ≥ 3 were to exhibit a Jband effect after supramolecular dye aggregation. For n ≥ 3 6777


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The conventional exciton approach, that considers the J-band to be a result of complete exciton delocalization over molecular building blocks of the aggregate,55 does not take into consideration the concrete chemical three-dimensional structure of individual molecules. Therefore, the EMET theory does not replace the exciton approach but rather complements it. Taking into account the Frenkel exciton effects is the next step in the EMET theory development.56,57 But clearly, however, the molecular reorganization energy will be a major determinant in J-band formation in polymethine dyes Jaggregates.

These factors contribute to a deviation of the resulting structure from electron−nuclear resonance leading to a disappearance of the J-band (broadening and hypsochromic shift).51 These factors can systematically be exploited to tune J-band properties to match desired application needs, for example in nanoscience. Here, we demonstrate that the deviation of J-chromophore of Jaggregate from resonance explains Harrison experimental data on transformation of the J-band of THIAMS dye (see Table 3) after significant increase of dye concentration.46 We can recover the resonance parameters by fitting theoretical formulas to experimental data. Theoretical formulas based on the EMET approach successfully reproduce the Harrison absorption curves (Figure 4). Most likely, the significant increase of dye

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +49-3916110-284. Fax: +49-391-6110-403. Notes

The authors declare no competing financial interest. † This research was performed while A. Petrenko was at Chemistry Department, Pohang University of Science and Technology, Namgu, Pohang 790-784, Korea

■

ACKNOWLEDGMENTS This work was supported in part by the Max-Planck-Society for Advancement of Science and the “Research Centre Dynamic Systems: Biosystems Engineering (CDS)” funded by the Federal State of Saxony-Anhalt.

■

Figure 4. Transformation of theoretical spectra of J-aggregate with deviation from resonance condition. The black line describes a J-band with the following parameters: λ = 0.2 eV, γ = 0.11, R = 1.68 nm, J1 = 5.5 eV, and J2 = 3.72 eV; the red line describes a “J-band” with the following parameters: λ = 0.4 eV, γ = 0.15, R = 2.8 nm, J1 = 5.5 eV, and J2 = 4.0 eV. Presented theoretical spectra reproduce transformation of sharp J-band of THIAMS dye (Table 3) in aqueous solution at 0.80% w/w dye into broad “J-band” at 3.53% w/w dye.46

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concentration leads to inclusion of additional dye monomer units into the J-aggregate chromophore (see Figure 1B) and thus this resulted in the increasing of reorganization energy of modified J-chromophore from the resonant value 0.2 eV to the nonresonant value of 0.4 eV (see the Figure 4 caption). The new “J-band” has a D-band more intense than an L-band, typical for the system deviating from the resonance and characterized by broadening and hypsochromic shift in comparison with resonance J-band (Figure 4).

4. CONCLUSION The presented results of our study give a definite justification of the theory of extended multiphonon electron transitions for description of optical spectra of polymethine dyes and Jaggregates. The formation of a strong optical absorption band in a polymethine dye monomer and an aggregate is successfully explained in a unifying concept. The resonance parameter and the reorganization energy are proposed to be key quantities to achieve such a strong absorption band (the J-band in the case of aggregates). Our results also provide an example for predicting the electron−nuclear resonance states and a basis for rational molecular design of functionalized cyanines. 6778


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Molecular Reorganization Energy as a Key Determinant of J-Band

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