Solvent Polarity Effect on Nonradiative Decay Rate ... - ACS Publications

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Solvent Polarity Effect on Nonradiative Decay Rate of Thioflavin T Vitali I. Stsiapura,*,† Siarhei A. Kurhuzenkau,†,∥ Valery A. Kuzmitsky,‡ Oleg V. Bouganov,§ and Sergey A. Tikhomirov§ †

Yanka Kupala State University, Grodno, Belarus Institute for Command Engineers of the Ministry for Emergencies of the Republic of Belarus, Minsk, Belarus § Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus ‡

S Supporting Information *

ABSTRACT: It has been established earlier that fluorescence quantum yield of thioflavin T (ThT)a probe widely used for amyloid fibrils detectionis viscosity-dependent, and photophysical properties of ThT can be well-described by the fluorescent molecular rotor model, which associates twisted internal charge transfer (TICT) reaction with the main nonradiative decay process in the excited state of the dye. Solutions of ThT in a range of polar solvents were studied using steady-state fluorescence and sub-picosecond transient absorption spectroscopy methods, and we showed that solvent effect on nonradiative transition rate knr cannot be reduced to the dependence on viscosity only and that ∼3 times change of knr can be observed for ThT in aprotic solvents and water, which correlates with solvent polarity. Different behavior was observed in alcohol solutions, particularly in longer n-alcohols, where TICT rate was mainly determined by rotational diffusion of ThT fragments. Quantum-chemical calculations of S0 → S1 transition energy were performed to get insight of polar solvent contribution to the excited-state energy stabilization. Effect of polar solvent on electronic energy levels of ThT was simulated by applying homogeneous electric field according to the Onsager cavity model. Static solvent effect on the excited-state potential energy surface, where charge transfer reaction takes place, was not essential to account for experimentally observed TICT rate differences in water and aprotic solvents. From the other side, nonradiative decay rate of ThT in water, ethylene glycol, and aprotic solvents was found to follow dynamics of polar solvation knr ∼ τS−1, which can explain dependence of the TICT rate on both polarity and viscosity of the solvents.

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INTRODUCTION Photophysical properties of thioflavin T (ThT) have received much attention recently due to extensive use of this fluorescent probe for detection of amyloid fibrils1−5insoluble protein aggregatesrelated to several neurodegenerative disorders.6−9 It has been established that fluorescence quantum yield Φ of ThT is highly dependent on viscosity/temperature ratio η/T10−15 Φ ≈ (η /T )α α ≤ 1

nonradiative deactivation channel. In nonviscous media TICT process rate is considerably higher than of the radiative transition, and majority of photoexcited ThT molecules deactivates via nonradiative TICT process. However, hindrance of twisting by surrounding solvent or matrix molecules translates into decrease of nonradiative transition rate and therefore results in viscosity-dependent fluorescence of ThT. Main point of the fluorescent molecular rotor model,10,12,22 that is, possibility of photoinduced charge transfer process coupled to a twisting coordinate φ, relies on quantum chemical calculations of ThT in the ground and excited states. ThT molecule has nonplanar geometry in the ground S0 state with torsion angle φ ≈ 37−40° between BTZ and DMA fragments (Figure 1B). Calculations of the excited-state properties using semiempirical10−12,22 and time-dependent density functional theory (TDDFT)23−26 methods have shown that change of the twisting coordinate from φ ≈ 37−40° to φ = 90° in the excited S1 state leads to (i) decrease of E(S1) energy with minimum

(1)

and the dye exhibits photophysical properties that are typical for fluorescent molecular rotors.16−20 According to the molecular rotor model, an efficient nonradiative decay process (e.g., intramolecular charge transfer) in the excited state is coupled to a large-amplitude internal motion (twisting, bending, isomerization, etc.) of the molecule accompanied by significant solvent shell rearrangement, which results in viscosity-dependent fluorescence. In the case of ThT, a twisted internal charge transfer21 (TICT) process coupled to a twisting movement along C−C bond between benzthiazole (BTZ) and dimethylaniline (DMA) fragments (Figure 1A) takes place in the excited state and represents the main © 2016 American Chemical Society

Received: March 11, 2016 Revised: June 27, 2016 Published: June 28, 2016 5481

DOI: 10.1021/acs.jpca.6b02577 J. Phys. Chem. A 2016, 120, 5481−5496

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It was stressed26 that the molecular rotor model for ThT photophysical processes is similar to the model developed by Glasbeek and co-workers for Auramin O.38 According to Glasbeek model the first excited electronic singlet state is represented by a mixture of two diabatic states, an emissive (F) state, and a dark (D) state. State F is initially populated, and an intramolecular twist coordinate z determines transition between adiabatically coupled states F and D. Diffusion of the initial population distribution from F state along the twisting coordinate toward the dark state D is accompanied by a decrease of the effective radiative rate, since adiabatic coupling between the states makes S1 → S0 transition dipole moment dependent on twist coordinate z. Glasbeek model was successfully applied26 to describe nonradiative decay rate of electronically excited ThT in 1-propanol at room temperature, and the obtained value of the rotational diffusion coefficient Dr corresponded to Brownian rotation of an object with a size of phenyl ring. Thus, it was concluded that the solvent viscosity12,14 (or related to it dielectric relaxation rate15,37,39) is the main factor influencing nonradiative deactivation rate and fluorescence quantum yield of the probe. For instance, viscosity change from 1 mPa·s (aqueous solution of ThT at room temperature) to ∼1000 mPa·s (ThT in glycerol at ambient conditions) results in ∼300 times increase of fluorescence quantum yield11 from Φ ≈ 3 × 10−4 to 0.099 and corresponding growth of fluorescence decay lifetime from τF ≈ 1 ps to ∼0.5 ns. However, it was noticed that even for the cases of almost complete immobilization of the probe12,39,40 (when bound to amyloid fibrils or in rigid matrices at low temperatures) its Φ does not approach unity. This discrepancy can be explained by (i) existence of at least one more nonradiative process depopulating LE state in ThT or (ii) nonrigid fixation of the rotor molecule in the matrix;12 that is, ThT is located inside of “rigid cavities” formed by surrounding matrix molecules, and some “cavities” do have enough free space to allow twisting. Phosphorescence spectrum with maximum at 585 nm was observed by Huppert et al.39 for ThT solution in 1-propanol at low temperatures. Ghosh and Palit demonstrated recently36 that intersystem crossing takes place for solutions of ThT in acetonitrile at room temperature (with low efficiency of triplet formation but readily detectable) and that triplet states population can be responsible for the fluorescence quantum yield Φ decrease. Phosphorescence and photosensitizing properties of ThT in complexes with polynucleotides were reported earlier.41,42 Although intersystem crossing processes seem to be not very efficient for ThT in nonviscous solvents, it can be quite possible that photochemical reactions involving triplet states of ThT are responsible for ThT photodegradation and photoproducts formation observed by Hsu et al.43 Solvent viscosity is the principal but not the only factor governing photophysics and fluorescence intensity of ThT, and it has been observed that other solvent properties have effect on LE → TICT transition rate as well.15,27 Huppert and coworkers13,39 drew attention to the fact that TICT process for ThT dissolved in water takes place faster than the expected thermally driven diffusive motion along the twisting coordinate (2). It was proposed13,39 that dependence of E(S1) potential on twisting angle φ for ThT (Figure 1B) may be considered as application of the external torque −∂E(S1)/∂φ, which affects diffusional motion and results in an increased TICT rate. Interactions of ThT with polar solvent molecules can modify E(S1) dependence on φ changing the external torque

Figure 1. Schemes of thioflavin T cation structure (A) and solvent polarity effect on S1-state energy dependence of thioflavin T vs twisting angle φ (B). (A) S, C, and N atoms are shown in yellow, cyan, and blue colors, respectively. Fragments of benzothiazole (BTZ) and dimethylaniline (DMA) are shown in boxes. (B) Schematics of dependencies of the ground-state energy E(S0) (black line) and excited-state energies E(S1) for two solvents with different polarities (blue and red lines) vs φ angle are shown. ΔE denotes energy change during transition from LE to TICT state. Polarity effect on the groundstate potential energy surface is not shown for clarity.

located at φ = 90°, (ii) essential charge redistribution between BTZ and DMA fragments, and (iii) decrease of the S1 → S0 transition oscillator strength to f ≈ 0 for conformation with φ = 90°. Validity of the molecular rotor model for ThT photophysics description was extensively studied in solvents of different viscosities,12,14,15,27 in confined media (e.g., reverse micelles28 and porous silicon29), for ThT bound to amyloid fibrils,11,30−32 and polynucleotides.33−35 Formation of intermediate nonfluorescent TICT state was demonstrated27,36,37 using subpicosecond time-resolved absorption spectroscopy. Nonradiative transition from fluorescent locally excited (LE) state (i.e., S1 state at φ ≈ 30−40°) to nonfluorescent TICT state (i.e., S1 state at φ ≈ 90°) proceeds essentially as a barrierless process (activation energy of ∼370 ± 100 cm−1 was reported for ThT in glycerol12) and its rate is limited by rotational diffusion of BTZ and DMA fragments along the twisting coordinate. The results of Huppert group15 demonstrated close to linear dependence of nonradiative transition rate knr of ThT versus η/T over wide temperature range in several glass-forming n-alkanols, and it was concluded that for longer alcohols (1-butanol and 1-pentanol) knr became independent of the molecular character of the solvent and was determined solely by viscosity values. Therefore, nonradiative LE-TICT transition can be welldescribed, at least for ThT dissolved in longer alcohols, by rotational Brownian diffusion of ThT fragments relative each other with the following rate kRBD =

kBT 3ηVThT

(2)

where VThT is the effective hydrodynamic volume of ThT twisting fragments, and kB is the Boltzmann constant. 5482

DOI: 10.1021/acs.jpca.6b02577 J. Phys. Chem. A 2016, 120, 5481−5496

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The Journal of Physical Chemistry A magnitude and, hence, explain the polarity effect on LE → TICT transition rate for ThT. Solvent effects on dye photophysics are usually considered as manifestation of general (related to solvent polarity) and specific (e.g., hydrogen bond formation, etc.) solute−solvent interactions. Short-range repulsive intermolecular interactions associated with solvent−solute “collisions” govern dynamics of charge transfer reactions, which involve large-amplitude intramolecular motions,44 and the effect of these collisions can be associated with a friction coefficient ξ related to the solvent viscosity. The friction coefficient quantifies effect of dynamic solvent interactions on the reaction coordinate motion, and its origin can be found either in the dielectric relaxation hydrodynamics of the solvent or in specific solvent− solute interactions. While purely hydrodynamic description (e.g., by Stokes−Einstein−Debye model) predicts ξ to be proportional to the solvent viscosity η, accounting for nonspecific (i.e., dielectric friction45,46) and specific (e.g., Hbonds formation) solvent effects usually results in breakdown of linear dependence ξ ∼ η/T. Note that specific interactions of ThT molecule with polar solvent are possible due to presence of amino group as well as N and S heteroatoms in the dye structure. Usually, pH dependence of absorption and emission spectra can give insight of groups in the dye molecule that are involved in specific interactions with protic solvents. Ionic transition from cation to neutral form of ThT does not proceed via deprotonation step, but reversible hydroxylation of ThT occurs at alkaline pH (pKa ≈ 9);47 that is, ThT cation does not exhibit properties of an acid. Data reported by Hackl et al.48 about pH dependence of ThT absorption spectra revealed that protonation of dimethylamino group takes place in acidic media (pKa ≈ 1.5) producing dication with absorbance peak at 308 nm, and one can expect dimethylamino group of ThT to have H-bond acceptor properties at neutral pH. Therefore, ThT in the ground state is capable to form a hydrogen bond with protic solvents. Weakening or breakage of the H bond can be expected upon ThT photoexcitation, and it may have effect on TICT process dynamics in the excited state of the dye. It is well-known that solvent polarity has significant influence on energetics and dynamics of intramolecular charge transfer21,44,49−52 by changing potential energy surface on which the reaction occurs (static effect) and by introduction of additional dielectric friction caused by polar solute/solvent interactions (dynamic effect). The latter effect is related to dielectric coupling that exists between the charge separation process in the solute and the solvent dipoles, thus allowing the solvent molecules to retard progress of the charge transfer reaction.44 Dynamics of solvent relaxation has been extensively studied by the time-dependent Stokes shift method using polar fluorescent probe molecules (such as coumarin153) in polar solvents, as well as molecular simulation methods.50,52−55 Time evolution of the dielectric solvation is well-understood and is usually classified into three regimes spanning different time scales.50,52,55,56 Initial Gaussian response results from the inertial rotational motions of solvent molecules in the first solvation shell of the solute and may account for 60−80% of the total solvent relaxation in such solvents as water or acetonitrile. After the inertial response is complete, a subsequent librational relaxation takes place characterized by damped oscillatory rotational motions of solvent molecules

followed by a diffusive rotational relaxation on a slower time scale. Theoretical models for dynamic solvent effects on electron transfer51,57,58 (ET) usually employ implicit dielectric continuum models of solvation, where polar solvent is considered as a polarizable continuum dielectric medium with Debye relaxation dynamics. The solvent degrees of freedom are reduced to a single collective coordinate that is used to describe solvent effect on chemical or photophysical processes in the solute. Several regimes of intramolecular ET reaction were distinguished based on strength of electronic coupling matrix element VDA between donor and acceptor states of the solute and dynamics across the reaction coordinate.58 In adiabatic regime (i.e., strong electronic coupling VDA) if activation barrier ΔG# for ET reaction is small (ΔG# < kBT) the rate of ET process is limited by polar solvent relaxation dynamics kET ≈ 1/τL, where τL is the longitudinal relaxation time associated with dielectric relaxation following a rapidly induced change of charge distribution in the solute molecule. This behavior, that is, kET limited by solvent dynamics, was experimentally observed for ET in the excited state of 9,9′bianthryl,59,60 several TICT reactions in alcohols,61,62 and ET in bimolecular complexes.63 More general approaches taking into account dissipative effects in polar medium using generalized Langevin equation60 and multimode Brownian oscillator model64 were applied earlier to describe dynamics of the system over the collective solvent coordinate and its impact on charge transfer processes in the solute. Recently, it was reported65 that accounting for multiple relaxation time scales, including a short-time inertial response, can be important for correct prediction of rate constants for ET reactions in such solvents as water, acetonitrile, and methanol. In the present paper we study the effect of polar solvent on photophysical properties of ThT using steady-state fluorescence and sub-picosecond transient absorption spectroscopy methods. Quantum-chemical calculations of the excited states of ThT molecule in homogeneous electric field were conducted to model solvent reaction field with the goal to get insight of polar solvent contribution to the excited-state energy stabilization. Here, we used simple Onsager cavity model to estimate static effect of polar solvent on potential energy surface of the excited S1 state and test the hypothesis13,39 that the external torque −∂E(S1)/∂φ can be responsible for the increased TICT rate. Dynamic solvent effects on charge transfer process in ThT as well as possible influence of specific interactions are discussed.

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EXPERIMENTAL MATERIALS AND METHODS Thioflavin T (ThT) of UltraPure grade quality (>95% purity, desalted) was purchased from Anaspec (USA) and used without further purification. Spectrally grade ethanol, 2propanol, N,N-dimethylformamide (DMF), and butanol were purchased from Sigma (USA), while methanol and pyridine were purchased from Fluka (USA). Acetonitrile was from Riedel-de Haen (Germany) and acetone of analytical grade qualityfrom Ekos-1 (Russia). Aqueous solutions were prepared using bidistilled water. Freshly prepared solutions were used to minimize issues caused by ThT photodegradation. Data of solvents viscosities η and dielectric permittivity ε dependencies on temperature were taken from ref 66 and 67. It is important to emphasize that purity of ThT sample is critical for reliable measurements of fluorescence parameters 5483

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where T̃ = Eprob/Eref and T̃ 0 = E0prob/E0ref are energy ratios of the probe and reference pulses passed through the investigated sample at excitation and without it, respectively. Typically, 30 measurements were averaged to give a wavelength-dependent signal at every time step. The transient spectra are recorded in the range of 400−800 nm with a resolution of ∼1.5 nm. We estimate the absolute error for ΔD as 0.001. The transient spectra were corrected for the group velocity dispersion of the probe pulse. The experiments were performed at room temperature. The instrument response function (IRF) of the spectrometer was estimated to have Gaussian shape with full width at halfmaximum of ∼230 fs. Transient absorption curves ΔD(t) were fitted using a set of exponentials convolved with the IRF function according to the following expression

and determination of the emission quantum yields. It was reported43 that quite fast degradation of ThT (even in solid state) takes place producing oxidized (dThT-1) and demethylated (dThT-2, dThT-3) products of the dye. Highly fluorescent dThT-1 product with absorption at 325 nm could not be excited at our experimental conditions (λex = 415 nm). However, absorbance peaks of demethylated products dThT-2 and dThT-3 are located at 370 and 397 nm, respectively, and potentially could affect results of ThT fluorescence quantum yield measurements. In ref 43 it was reported that ratio of absorbances D412/D330 for ThT in aqueous solution can serve as useful indicator of the dye degradation level. ThT degradation during storage was accompanied by D412/D330 ratio change from 13.4 to 4.5 for pure dye and stored sample of ThT correspondingly. Absorbance ratio D412/D330 for ThT sample used in this study was ∼12.1 (Figure SI14) showing quite low level of ThT degradation products, and we did not perform any additional purification of the dye sample before the measurements. The Measurements of Steady-State Absorbance and Fluorescence. Absorption spectra were recorded using Specord 200 PC (Analytik Jena, Germany) spectrophotometer. Fluorescence emission and excitation spectra were measured using the CM2203 spectrofluorometer (Solar, Belarus). Fluorescence quantum yields were measured by the method of Williams et al.68 using emission of ThT in butanol (Φ = 0.004311) and Coumarin1 in ethanol (Φ = 0.73 for argonpurged and Φ = 0.68 for air-saturated solutions69) as standards. Spectral bandwidths of excitation and emission monochromators were set at 5 nm. Transient Absorption Studies. Transient absorption measurements in sub-picosecond and picosecond time domains were performed in a 0.5 cm quartz cell using a homemade original femtosecond spectrometer, described elsewhere.27,70 Briefly, spectrometer is based on Ti:Al2O3 pulse pumped oscillator and a regenerative amplifier, both operating at 10 Hz repetition rate. The Ti:Al2O3 master oscillator was synchronously pumped with doubled output of feedback controlled hybrid mode-locked picosecond-pulsed Nd:YAG laser. The duration and energy of the pulses after the amplifier were ∼150 fs and 0.5 mJ, respectively, tunable over the spectral range of 760−820 nm. The fundamental output of the Ti:Al2O3 system (800 nm output wavelength was set for present study) was split into two beams in the ratio of 1:4. A more intense beam passed through a controlled delay line and then was used for the generation of the second (λexc = 400 nm) harmonic, which was utilized as exciting pulse. The second beam of fundamental frequency was used for generation of a femtosecond supercontinuum (by focusing into a 1 cm path length cell with water), which served as the probe radiation. The supercontinuum radiation was split by a beam splitter into two beams (probe and reference) of identical intensity, which were focused by mirror optics to overlap on the sample together with pump beam. The diameters of the spots of probe and pump beams within the sample were ∼0.5 and 2 mm, respectively. The spectra of the signal beam pulse as well as the reference one were recorded for every laser flash by a polychromator equipped with silicon CCD matrix and transmitted to the computer. The differential absorbance signal ΔD (λ, Δt) is obtained as

ΔD(t ) =

∑ αi i

⎛ (t − t )2 ⎞ ⎛ t⎞ 1 0 ⎟ exp⎜ − ⎟⊗ exp⎜ − 2 2 τ π σ 2σ ⎝ i⎠ ⎠ ⎝ (3)

where αi and τi were the amplitude and lifetime of ith exponential component, respectively, ⊗ is the convolution sign, t0 is the time of the probe pulse arrival, and σ is the width parameter of IRF. Deconvolution analysis was performed using Marquardt nonlinear least-squares method.71,72 To improve accuracy of τi parameters estimation the global analysis approach73,74 was utilized, that is, set of kinetics curves registered at different wavelengths was simultaneously fitted using exponential components with shared lifetimes. Time resolution of the femtosecond spectrometer was limited mainly by pump and probe pulse durations and was estimated as 0.1 ps. Quantum-Chemical Calculations. Geometries of ThT conformers in the ground S0 state with constrained dihedral angle φ between BTZ and DMA fragments were optimized using density functional theory (DFT) method with B3LYP functional75,76 and 6-31G(d) basis set.77 Angle φ values were constrained in the range from 0° to 90° with 10° step. After geometry optimization the molecule was reoriented in such a way that two carbon atoms connecting BTZ and DMA fragments were located along x-axis as shown in Figure 1, and coordinates origin was located at center-of-mass of the molecule. Homogeneous electric field was applied along the x-axis (Figure 1) to simulate effect of polar solvent on the energy of electronic transition S0 → S1 in ThT conformers. Energies of electronic transitions and excited-state properties were calculated by TDDFT and semiempirical INDO/S78−80 methods. All calculations (with the exception of INDO/S) were performed using Firefly QC package,81 which is partially based on the GAMESS (US)82 source code. INDO/S calculations were performed using set of programs developed by one of the authors (V.A.K).

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RESULTS AND DISCUSSION 1. Dependence of Fluorescence Quantum Yield on Viscosity/Temperature. Steady-state fluorescence spectra of ThT in pyridine, DMF, acetone, acetonitrile, aqueous, and alcohol solutions were recorded at temperatures within 293− 323 K range and fluorescence quantum yields Φ of the dye in polar solvents were measured (Table 1). Because of extremely

ΔD(λ , Δt ) = log(T0̃ /T̃ ) 5484

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Table 1. Fluorescence Quantum Yield Φ of ThT in Polar Solvents at 298 K and Parameters of Its Linear (5) and Power-Law (1) Dependencies on Viscosity/Temperature in the Range of 293−323 K

a

solvent

index of refraction nD

dielectric constant ε

Φ, 1 × 10−4 at 298 K

water methanol ethanol 2-propanol 1-butanol pyridine DMF acetonitrile acetone

1.333 1.328 1.361 1.377 1.399 1.507 1.427 1.342 1.356

78.3 32.7 24.5 19.9 17.5 12.3 36.7 35.9 20.7

4.1 5.0 16.0 27.5 43 17.6 5.5 3.9 4.3

rel error ε(Φ), %

a, 1 × 10−4 a,b

b, 1 × 10−4 a,b K/(μPa·s)

αa,c

1.8(1) 2.6(7) 2.7(3) −1.0(6) 7.5(6) 5.0(8) 0.7(8) 0.3(12) 0.8(7)

0.77(6) 1.2(5) 3.68(9) 4.36(14) 4.11(8) 4.2(3) 1.7(3) 3.2(11) 3.3(7)

0.50(4) 0.42(7) 0.80(2) 1.04(4) 0.77(1) 0.68(2) 0.84(8) 0.92(9) 0.78(8)

16 11 6 4 8.7 11 11 8

Standard deviation is shown in parentheses. bParameter of linear relation Φ = a + b(η/T). cParameter of power-law relation Φ = C(η/T)α.

Table 2. Spectral Propertiesa of ThT Absorption and Fluorescence in Polar Solvents

low fluorescence intensity series of 5−7 solutions with increasing ThT concentration (absorbance did not exceed 0.1) for each solvent (Supporting Info, Figures SI1−SI5) were used to determine quantum yields Φ at 298 K. These values were used as references to calculate fluorescence quantum yields at other temperatures. It is important to note that due to presence of impurities and Raman scattering the background emission had significant contribution in total fluorescence signal, and one must take this into account to get reliable data of fluorescence quantum yield. We used the following procedure to subtract the background emission. Raman peaks in fluorescence spectra of pure solvent were fitted by Gaussian functions. This set of Gaussians with constrained shapes was used for subsequent analysis. Spectra of ThT fluorescence (and fluorescent impurities, if present) were described by an additional log-normal function

solvent

Δfb

ν̅abs, cm−1

Δνa̅ bs, cm−1

methanol ethanol 2-propanol 1-butanol H2O AN acetone DMF pyridine

0.309 0.289 0.276 0.264 0.320 0.306 0.284 0.275 0.214

23 800 23 700 23 600 23 500 24 000 23 800 23 800 23 600 23 200

3200 3200 3200 3200 3600 3200 3300 3400 3100

b

f (λ|a0 , λ 01 , w , ρ) = a0 ·

(

(λ − λ 01)(ρ2 − 1) wρ

ln(ρ)2

2

)

+1

⎤ ⎥ ⎥ ⎥ ⎥⎦

Stokes shift, cm−1

4400 4300 4500 4500 3800 3400 3500 3400 3600

3400 3400 3200 3200 4100 3800 3600 3600 3200

ε−1 2ε + 1

−

n2 − 1

2n 2 + 1

.

time scale of ThT fluorescence (several picoseconds) comparable with vibrational and solvent relaxation times (i.e., fluorescence emission occurs before relaxation processes are over), conclusions based on spectral shifts analysis may be not very reliable. In our opinion smaller Stokes shifts and broadening of the emission spectra for ThT dissolved in alcohols reflect slower solvent relaxation dynamics in comparison to TICT rate. This may indicate involvement of specific interactions between the solute and protic solvents. As it was discussed earlier the dimethylamino group of the dye has proton-acceptor properties, and ThT in the ground state is capable to form a hydrogen bond with protic solvents. Possible formation of this bond in the ground state and breakage upon ThT photoexcitation may alter solvent relaxation and TICT process dynamics in the excited state. However, in contrast, spectral properties of ThT emission in aqueous solutions are closer to properties of ThT dissolved in aprotic solvents and do not exhibit significant contribution of specific interactions. Therefore, analysis of spectral properties of ThT fluorescence in polar solvents does not allow to get unambiguous conclusions about involvement of specific interactions of the dye with protic solvents. Figure 2 shows dependencies of ThT fluorescence quantum yield in different solvents as functions of η/T ratio. Power-law (1) and linear (5) models were utilized to fit the data and the best-fit parameters are shown in Table 1. Data analysis using power-law equation revealed that values of power α span range from ∼0.5 to 1.0; that is, ThT indeed demonstrates properties typical for molecular rotors. Because of quite limited temperature range that was used in this study both models (power-law

(4)

where a0 is amplitude, λ01 is center wavelength, w is width, and ρ is asymmetry parameter. Emission spectrum of ThT sample at the lowest temperature (and with the highest intensity) for the particular solvent was fitted using log-normal functions and the set of Gaussians with constrained peak shapes to find optimal parameters values for the log-normal curves. Then the set of Gaussian and log-normal functions with constrained shape parameters (only amplitudes of the peaks were allowed to vary) was used to decompose fluorescence spectra and separate ThT emission from the background one. Areas under log-normal curves were used for fluorescence quantum yield calculations at temperatures other than 298 K. Spectral properties of ThT fluorescence described using lognormal function (4) are presented in Table 2. On the basis of band shape properties of ThT fluorescence one can divide the solvents used into two groups: (1) alcohols and (2) water and aprotic solvents. Lower values of Stokes shift (3200−3400 cm−1) and more broad emission spectra (Δνf̅ l = 4300−4500 cm−1) were observed for ThT in alcohols. There is a trend of Stokes shift increase with higher values of ε−1

Δν̅fl, cm−1

a Peak positions ν̅abs and ν̅fl of absorption and emission spectra as well as their bandwidths (FWHM) Δν̅ a bs and Δν̅ f l are shown.

Δf =

⎡ ⎢ ln(2)ln exp⎢ − ⎢ ⎢⎣

ν̅fl, cm−1 20 400 20 400 20 400 20 300 19 900 20 000 20 200 20 000 20 000

n2 − 1

orientational polarizibility Δf = 2ε + 1 − 2n2 + 1 for ThT in water and aprotic solvents that might indicate more polar nature of the excited state of the dye. Taking into account short 5485

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Figure 2. Dependence of fluorescence quantum yield Φ on η/T for ThT in solvents of different polarity. Different scales are shown (A, B). Change of η/T was achieved by varying temperature of the solution. Linear fits are shown with solid lines.

Figure 3. Rate constants ratio knr/kr dependence on η/T (A) and on dielectric constant ε at η/T = 2 and 3 μPa·s/K (B) for ThT in different solvents. Ratio knr/kr was calculated using eq 7 and shown as a function of η/T within (solid lines) and beyond the measurements range (dots).

So, in this case fluorescence quantum yield will be equal to

and linear) can satisfactorily describe dependence of the emission quantum yield of ThT on η/T. The subsequent analysis is based on the results of fitting with linear function. One can see that data points within each subset, corresponding to a particular solvent, can be described using a linear relation

Φ = a + b(η /T )

Φ=

kr k r + k nr

(6)

Combining eqs 5 and (6) one can get the following expression for the ratio of nonradiative and radiative rate constants

(5)

However, differences in properties among the solvents led to significant variation of slope and intercept values (Table 1), preventing the whole set of data points from being described with a unif ied linear dependence. Therefore, one can see that the ratio of viscosity/temperature is the main but not the only parameter that determines fluorescent properties of ThT. Let us consider deactivation of the locally excited LE state (corresponding to the S1 state at φ ≈ 37°) of ThT and assume that it can be described solely by radiative transition with rate constant kr and nonradiative TICT process knr = kLE‑TICT. These assumptions are valid for ThT dissolved in the solvents of low viscosity studied here, where knr ≫ kr. So, we employ the usual neglecting of nonradiative S1→ S0 internal conversion from LE state. As to singlet-to-triplet conversion, it was shown36,41 that this process takes place for photoexcited ThT, but its efficiency is rather low and has negligible contribution in our experimental conditions.

k nr 1 1 = −1= −1 kr Φ a + b · (η / T )

(7)

that can be used to account for dependence of knr/kr ratio on η/T variable and compare effects of polarity on LE-TICT transition rate for solvents with the same η/T ratio (Figure 3). It is noteworthy that the minimal knr among the studied solvents (radiative rate kr depends on refractive index of the solvents;83,84 however, variation of its magnitude is estimated to be ∼1.3 times only) at specific η/T value is observed for 1butanol, that is, for the solvent where LE-TICT transition can be fairly well-described as a rotational diffusion process and which rate (2) is considered to be determined15 strictly by solvent viscosity. Thus, LE-TICT rate knr for ThT dissolved in other polar solvents (both protic and aprotic) exceeds the Brownian diffusion rate (2). 5486

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Figure 4. Time-resolved absorption spectra of ThT in acetone. (A) Evolution of transient absorption spectra at different time delays after excitation (λex = 400 nm). Sharp peak at 450 nm in transient spectrum at 0 ps time delay corresponds to induced Raman signal of the solvent. (B) Transient absorption curves of ThT in acetone recorded at 425, 470, and 490 nm. Solid lines correspond to least-squares fitting curves using (eq 3).

Table 3. Parametersa of Transient Absorption Kinetics for Thioflavin T in Polar Solvents at Room Temperature η, mPa·s

ε

τS,b ps

acetone acetonitrile

0.306 0.369

τ(LE), ps

τ(TICT), ps

20.7 35.9

0.58 0.26

12.1 ± 0.4 8.9 ± 1.0 4

0.544

32.7

5.0

DMF

0.794

36.7

0.91

pyridine H2O

0.879 0.890

12.3 78.3

3.4c 0.34

ethanol

1.074

24.5

16.0

1-propanol

1.945

20.1

26.0

2-propanol 1-butanol

2.038 2.544

19.9 17.5

63

14.7 41.6

103 15.0

1.0 ± 0.1 0.7 ± 0.1 0.8 0.61 2.0 ± 0.1 2.2 1.9 ± 0.1 1.6 3.4 ± 0.3 1.3 ± 0.1 0.9 4.6 ± 0.2 4.4 6.9 8.1 6.4 ± 0.2 11.8 ± 0.6 10.6 12.1 16.1 17.6

methanol

solvent

1-pentanol ethylene glycol

3.51 17.64

6.0 ± 0.2 9.1 ± 0.6 6.5 24 ± 8 3.8 ± 0.1 28 ± 2

70 ± 9 360 ± 60

ref this this 36 14 this 37 this 36 this 27 37 27 37 15 37 27 27 15 37 15 14

work work

work work work

Solvent viscosity η, dielectric constant ε, and solvent relaxation times τS at 298 K are also shown. bData from refs 53 and 88. cLongitudinal relaxation τL is shown from ref 89.

a

Using dielectric permittivity ε as a measure of solvent polarity one can see correlation of knr increase with growth of ε value (Figure 3B) showing that alteration of solvent polarity can be accompanied by ∼3−4 times change of the nonradiative rate constant. Similar plot of knr/kr dependence on ε − 1

stimulated emission 450−600 nm) and induced absorption bands at 470 and 720 nm. In accordance with earlier reported data27 we assign the induced absorption band at 720 nm to an absorption from emissive LE state and the one at 470 nm to an absorption from the dark TICT state. Intense peak of stimulated emission at 490−500 nm is attributed to radiative transition from LE to the ground S0 state. Similar spectral features were observed by Ghosh and Palit for ThT in acetonitrile;36 however, they reported the stimulated emission band to be shifted by ∼50 nm to the red and located at 550 nm (compare with transient spectra of ThT in acetonitrile in Figure SI6). Before the analysis of transient absorption data we would like to note that earlier studies of time-resolved fluorescence of ThT have shown significantly nonexponential character of its decay kinetics (at least three exponentials are needed for the fitting), and average decay lifetime has been found to be strongly dependent on emission wavelength (especially in short-

2ε + 1

function is shown in Figure SI13 (Supporting Information). 2. Transient Absorption Spectroscopy Studies. Subpicosecond time-resolved absorption spectra for ThT in several polar solvents (methanol, acetone, acetonitrile, DMF, pyridine) were measured. Figure 4 shows dynamics of transient absorption spectra of ThT in acetone after excitation with pump pulse at 400 nm. Transient absorption spectra of ThT in all studied solvents have similar behavior: besides the bleaching band (negative signal in 420−440 nm range) related to depopulation of the ground state of the dye one can see rise and decay of gain band (negative signal in the spectral range of 5487

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Figure 5. Polarity effect on transient absorbance of ThT near the peak of stimulated emission band for solvents with similar viscosities. (A) ThT in acetone and acetonitrile. (B) ThT in DMF, water, and pyridine. Solid lines correspond to least-squares fitting.

wavelength range of the fluorescence spectrum). Lifetime distribution12 and stretched exponential37,39 models were applied to describe ThT fluorescence decay. Taking into account quite sufficient noise level in experimental data of transient absorption, the main goal of data analysis was to recover average lifetime of stimulated emission signal from LE state that can be associated with fluorescence decay. Time-dependent Stokes shift of the stimulated emission band, caused by processes of structural and solvent relaxations in the excited state, complicates transient absorption kinetics at the “blue” wing (450−480 nm) of the emission band; therefore, we limited analysis of kinetics data to 480−580 nm range. Unfortunately, absorption band from TICT state occurs in the same spectral range, and that is why we used biexponential model to determine average values of LE- and TICT-state lifetimes. To increase statistical accuracy of the fitting we used global analysis approach, where kinetics curves at different wavelengths are fitted simultaneously using biexponential model with common lifetimes. In this case, however, we neglected dependence of LE- and TICT-state lifetimes on wavelength within 480−580 nm spectral range. Transient absorption curves were fitted using a set of exponentials convolved with the pump−probe correlation function IRF according to eq 3. We found that kinetics curves in the range of 480−580 nm for each solvent can be fairly welldescribed using biexponential model with common lifetimes (Table 3 and Figures SI8−SI12). The short-lived component with negative pre-exponential factor was assigned to emission from LE state, and the long-lived component was attributed to absorption from TICT state. Results of femtosecond timeresolved fluorescence as well as transient absorption measurements reported by other groups are shown in Table 3. One can see that LE-state lifetime τ(LE) for acetonitrile, methanol, ethanol, and butanol obtained from the transient absorption measurements correspond fairly well to the results measured by fluorescence up-conversion technique.14,37 Table 3 shows that solvent polarity has essential effect on LEstate deactivation rate and that higher values of dielectric permittivity correlate with enhancement of the internal chargetransfer process. Acetone has lower viscosity than acetonitrile, and one can expect LE-TICT transition rate for ThT in acetone to be faster. However, knr = 1/τ(LE) is ∼1.4 times higher for ThT in acetonitrile than in acetone (Figure 5A and Table 3), and we believe this behavior in aprotic solvents to be related to polarity.

Another group of solvents with similar viscosities but different polar propertiesDMF, water, and pyridinealso demonstrates correlation of the internal charge-transfer rate with polarity (Figure 5B), and transition from pyridine to water results in ∼2.6-fold increase of LE-TICT rate. These data correspond fairly well to the results shown in Figure 3B where knr/kr ratio is changing by ∼3−4 times for isoviscous solutions of ThT in water and pyridine. Water and pyridine have different protic properties and possible effect of specific interactions on LE-TICT kinetics in these solvents should be discussed. Considering alternative mechanisms of LE-state deactivation related to specific solute− solvent interactions one should take into account relatively short time scale of LE-TICT transition (picosecond range). It is well-known that photoinduced proton transfer to solvent or proton-coupled electron transfer reactions can proceed in fs and ps ranges85,86 and efficiently compete87 with intramolecular charge transfer process for LE-state deactivation. Dimethylamino group of the dye has proton acceptor properties and formation of intermolecular hydrogen bond with protic solvents (water or alcohols) is possible. ThT does not have labile protons, and in aprotic solvents like pyridine one can expect specific intermolecular solute−solvent interactions to be absent or significantly less pronounced. In this regard we would like to note that knr/kr dependencies on η/T for aprotic pyridine and protic 1-butanol with similar dielectric constants are very close (Figure 3A). In our opinion, this demonstrates relatively small contribution of specific interactions between dimethylamino group of ThT and protic solvents on TICT dynamics. Therefore, the results both of fluorescence quantum yield studies and transient absorption measurements clearly demonstrate that solvent effect on LE-TICT transition rate for ThT cannot be reduced to the dependence on viscosity only, and ∼3−4 times enhancement of TICT rate over the diffusional limit (2) for ThT can be observed. One can conclude that, besides viscosity, solvent polarity has a major contribution in solvent effect on TICT dynamics in the excited state of ThT in aprotic solvents. 3. Quantum-Chemical Calculations of Thioflavin T in Homogeneous Electric Field. Our motivation of quantumchemical calculations was to examine static solvent effect on the excited-state potential energy surface (PES) where TICT process occurs and test the hypothesis that dependence of the excited S1-state energy E(S1) on angle φ for ThT may be 5488

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dependent on choice of the coordinates origin (normally center-of-mass position of the molecule is used for multipole moments calculation) and orientation.93−95 However, the twisting motion for ThT does not lead to a significant change of the center-of-mass position, and we believe that we can compare calculated values of dipole moments for different ThT conformers. Moreover, change of dipole moments for the same geometry of the molecule can be calculated without ambiguity (see discussion of electron transition properties estimation for charged molecules in Supporting Information). Quantum-chemical TDDFT//B3LYP/6-31G(d) calculations of ThT conformers in vacuum give results (Figure 6) similar to

considered as application of a photoinduced external torque −∂E(S1)/∂φ to the dye molecule that accelerates the twisting rate to exceed the Brownian diffusion limit (2). TDDFT and INDO/S calculations of ThT conformers with the constrained twisting coordinate φ were performed. We limited our analysis of solvent effects to the Onsager cavity modela relatively simple continuum solvation model,90 which provides qualitatively correct results91 and can be used to describe spectral properties of solvatochromic dyes as well as dynamics of polar interactions52 (including, for instance, dielectric friction88). Let us consider effect of polar medium on energy states of the solute molecule. According to the Onsager model the solute molecule is represented by a point dipole μ0 located in the center of an empty spherical cavity of radius a, which is surrounded by a structureless polarizable dielectric medium with permittivity ε. Electric field of the solute dipole moment induces polarization of dielectric medium, which in its turn creates a reactive field R in the cavity center R=

2(ε − 1)μ0 (2ε + 1)a3

(8)

and solvation energy ΔEsolv can be estimated as (when work for the solvent polarization is taken into account) 1 ΔEsolv = − μ0 R 2

(9)

Therefore, if we neglect specific solvent−solute interactions (i.e., hydrogen bond formation, etc.) the polar solvent effect can be simulated by applying a homogeneous electric field parallel to solute dipole moment. For instance, for a spherical cavity of ThT size with a ≈ 7 Å the reactive field acting on μ0 = 1 D (Debye) will be (in atomic units, a.u.) |R| =

2(ε − 1) × 1.4 × 10−4 a.u. (2ε + 1)

that is, 1.24 × 10−4 a.u. and 1.37 × 10−4 a.u. for pyridine and water, respectively. It is important to note that ThT has nonzero charge and that interactions of ThT cation with polar solvent will significantly affect its solvation energy. The total charge of the dye does not change during TICT process, and contribution of ion−solvent interactions to the solvation energy will be the same for both LE and TICT states. However, center-of-charge location within ThT molecule is different before (LE state) and after (TICT state) the charge transfer, which may have essential effect on relative energy change during LE-TICT transition in polar dielectric environment. On the basis of TDDFT calculation data (see below) we found that center-of-charge position for ThT in the excited state changes by ∼1.4 Å during LE-TICT transition (i.e., when twisting angle changes from φ = 40° to 90°). Contribution of the ion−solvent interactions in TICT energy stabilization due to charge relocation from the center of the cavity with radius a = 7 Å was estimated using Kirkwood ε−1 expansion92 to be ∼660 2ε + 1 cm−1 or ∼330 cm−1 for the polar solvents studied. This magnitude is relatively small in comparison to the energy of dipole−solvent interactions (∼16%) and is not taken into account in the following discussion. Additional difficulty due to nonzero charge of ThT is that one should be cautious while estimating dipole moment of a charged molecule, since its magnitude and direction are

Figure 6. TDDFT calculations of ThT in vacuum. (A) Dependence of the excited-state energy E(S1*) on twisting coordinate. (B) Changes in dipole moments along x axis and in charges q of BTZ fragment upon vertical S0 → S1* transition for different ThT conformers calculated by TDDFT. (C) Dipole moments of the ground and first excited singlet states of ThT, calculated at center-of-mass of the molecule. ThT geometries with constrained φ angle were optimized in the ground state using B3LYP/6-31G(d) method. 5489

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Figure 7. Effect of external electric field on energy of S0 → S1* transition for ThT. Calculations using TDDFT//B3LYP/6-31G(d) (A, C) and INDO/S//RHF/6-31G(d) (B). Effect of the reactive field on energy of S0 → S1* transition of ThT was recalculated using eqs 8 and (9) in terms of dielectric constants of the medium (C). Conformers geometries were optimized in the ground S0 state. Electric field was directed along x axis.

the earlier reported data.22−26 Geometries of ThT conformers in the ground S0 state with constrained dihedral angle φ between BTZ and DMA fragments were optimized using B3LYP/6-31G(d) method, and properties of the excited states were calculated by TDDFT. Note that geometries of ThT in the ground and excited states are quite different; for instance, significant bending of the molecule in the excited state was reported25 earlier. Therefore, use of ThT geometries optimized for the ground S0 state in TDDFT calculations must be justified. Main goal of the molecular modeling was to support the experimental data about fluorescence from LE state and help with their interpretation. Short time scale of ThT fluorescence (up to several picoseconds) indicates that the emission occurs from a state that is not vibrationally equilibrated, and we suppose that nuclei positions do not have time to change considerably. Therefore, we believe that use of geometries optimized for the S0 state can provide at least qualitative description of the excited-state PES properties (particular in the vicinity of LE state).

Assuming that the initially populated LE state can be associated with conformations at φ ≈ 40° and nonfluorescent TICT state with conformations at φ ≈ 90° one can see that LE and TICT states energy difference E(S1*, φ ≈ 40°) − E(S1*, φ ≈ 90°) is ΔE ≈ 5300 cm−1 when solvent effect is not taken into account. INDO/S method gives lower value of the energy difference ΔE ≈ 2200 cm−1 for conformers optimized using RHF/6-31G(d). In accordance with the earlier reported data22 Figure 6 shows that vertical S0 → S1* transition is accompanied by significant change of dipole moment Δμ = μ(S1) − μ(S0) directed mainly along the longest axis of the molecule from BTZ toward DMA fragment. Conformers of ThT with geometries optimized in the ground S0 state were oriented to align the longest axis of the molecule with x axis of the coordinates system (Figure 1A). Comparison of changes in dipole moments and charges of BTZ fragment upon vertical S0 → S1* transition for different ThT conformers (Figure 6) allows evaluation of the effective distance between BTZ (acceptor) and DMA (electron donor) components rDA = 5.9 Å. Dipole moments of LE and 5490

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The Journal of Physical Chemistry A TICT states were calculated to be μ(LE) = 16.4 D and μ(TICT) = 23.2 D, respectively, and difference in their values was mainly related to 0.24e charge transfer over rDA distance (BTZ charge in S1* state q(BTZ, S1*) = 0.036e and −0.204e at twist angles φ = 40 and 90°). We assume that all the solvent relaxation processes are completed for ThT molecule in the ground state and that it resides in a state characterized by twisting angle φ ≈ 40°, a surrounding solvent shell configuration corresponding to energy minimum, and some value of the reactive field R(S0). Change of dipole moment Δμ upon ThT photoexcitation and transition to LE state will induce polar solvent repolarization creating a time-dependent reactive field increment, growing from 0 to ΔR, and directed along the x axis. Since Δμx value (Figure 6B) increases with twisting coordinate (∼13 D at φ = 40° and ∼23 D at φ = 90°) one can expect more pronounced effect of energy stabilization due to polar solvation for ThT conformations with φ ≈ 90°. It is important to note that the intramolecular charge-transfer process between DMA and BTZ moieties also proceeds along the x-axis and, therefore, could be affected by the reactive field ΔR of polar solvent repolarization. This indeed can be demonstrated by applying external electric field along x-axis, which is simulating effect of the reaction field ΔR on energy of S1*−S0 transition (Figure 7). For example, in the case of aqueous solution a reactive field of 1.8 × 10−3 a.u. is expected for ThT in LE state. Change of the external field from 0 to 0.003 a.u. leads to decrease of the transition energy by ∼1240 and 4470 cm−1 (TDDFT) or ∼830 and 4140 cm−1 (INDO/S) for conformers with φ = 40° and φ = 90°, respectively. Using eqs 8 and (9) the reactive field effect on energy of S1*−S0 transition can be represented in terms of dielectric constants of the medium (Figure 7C), and one can see that growth of dielectric constant from ε = 1 to 80 results in transition energy decrease by ∼460 and 2380 cm−1 for ThT conformers with φ = 40° and φ = 90°, respectively. It is noteworthy that for the polar solvents in this study, where dielectric constant varies in the range from 10 to 80, the static effect of polar solvation on S1*−S0 transition energy is not very essential: differences of only ∼60 and 300 cm−1 were found for ThT conformers with φ = 40° and φ = 90°, respectively. 4. Static and Dynamic Solvent Effects on Twisted Internal Charge Transfer Rate. Considering only the static effect of polar solvent, that is, changes of the excited-state PES caused by solvation, one can estimate its influence on chargetransfer dynamics using Marcus model,57 which gives the following expression for the ET rate constant ⎡ ΔG # ⎤ kET = A exp⎢ − ⎥ ⎣ kBT ⎦

ΔG # =

state (entropy change was neglected and E(S1*) energies were estimated by TDDFT) will be ΔG = ΔGvac ∼ E(S1*, φ = 90°) − E(S1*, φ = 40°) = −5300 cm−1

(11)

For the case when solvent relaxation rate is faster than the charge transfer rate one can estimate the free energy change ΔG = ΔGvac −

(μTICT 2 − μLE 2 ) ⎛ ε − 1 ⎞ ⎜ ⎟ ⎝ 2ε + 1 ⎠ a3

⎛ ε−1⎞ −1 ⎟ cm = −5300 − 4100⎜ ⎝ 2ε + 1 ⎠

(12)

that is, ca. −7270 and −7110 cm−1 for DMF and pyridine, respectively. One can see that ThT transfer from pyridine to DMF has insignificant effect on ΔG value (∼2% change), which shows that static solvent effect, that is, change of the excitedstate PES due to solvation, cannot be responsible for ∼1.8 times difference in LE-TICT rate (Table 3). The obtained LE-TICT energy change is almost twice larger than ∼3000 cm−1 reported by Erez et al.26 when the conductorlike screening model (COSMO) was used in TDDFT calculations to account for solvation in 1-propanol. Discrepancy between the results is related to the approach used for excitedstate energy determination. We should emphasize that dependence of E(S1*) values on twisting coordinate in both cases were calculated for Franck−Condon excited states of the molecule, that is, for geometries corresponding to the ground state. Treatment of solvation effects (e.g., COSMO or PCM methods) during geometry optimization of ThT conformers in the ground state will give structures in equilibrium with the solvent, and vertical transition energy S0−S1* will report underestimated values ΔG in comparison to the ones calculated in vacuum (ΔGvac ≈ 5300 cm−1) due to destabilization of the solute energy in the excited state by the nonmatching solvent configuration. In our approach we obtained energy stabilization by solvent reorientation after the transition to the Franck− Condon state. However, it is important to note that only the lower bound of the energy change can be estimated, since structural relaxation of ThT in the excited state is not taken into account and which, in our opinion, will additionally increase absolute value of ΔG. Solvent reorganization energy for charge transfer process in ThT can be estimated with the following equation λs =

(μTICT − μLE )2 ⎛ ε − 1 n2 − 1 ⎞ − ⎜ ⎟ ⎝ 2ε + 1 a3 2n2 + 1 ⎠

(13)

giving values ∼200 cm−1. We should note that this estimate of λs accounts only for solvent reorganization during charge hopping at a fixed geometry of the dye molecule and does not include intramolecular reorganization energy as well as energy of solvent shell rearrangement around ThT needed for the twisting motion λtwist. In the case of weak coupling between donor and acceptor states in the dye molecule our estimates of ΔG and λs predict quite significant activation energy ΔG# of the charge-transfer process for ThT; however, experimentally observed kinetics of LE-TICT transition indicates absence of any noticeable activation barrier12,15 (except activation barrier of the solvent viscous flow). Mukamel and co-workers25 estimated twisting time for the unconstrained photoexcited ThT molecule to be

(10)

(λ + ΔG)2 − VDA 4λ

where A is a preexponential factor, ΔG# is activation energy, λ is reorganization energy, ΔG is free energy change during the charge transfer, kB is Boltzmann constant, and VDA is matrix element of electronic coupling between donor and acceptor states. Depending on ratio of solvent relaxation and charge-transfer rates two limiting cases can be considered. When solvent repolarization process is much slower than TICT rate the change in free energy ΔG during transition from LE to TICT 5491

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The Journal of Physical Chemistry A ∼0.4 ps. Experimental twisting times τLE in acetonitrile, acetone, and water are close to this limit (Table 3) showing that damping friction from the surrounding solvent molecules slows the TICT process rate by ∼2−3 fold only. We do not have reliable information about the value of VDA matrix element and its dependence on polarity to quantitatively test validity of the photoinduced external torque model. The data of TICT dynamics for ThT dissolved in water and aprotic solvents are in qualitative agreement with the model that facilitation of the motion along the twisting coordinate φ can be related to the external torque −∂E(S1)/∂φ. However, difference in ΔG values for DMF (−7270 cm−1) and pyridine (−7110 cm−1) seems not to be sufficient to account for ∼1.8 times change in TICT dynamics. Moreover, different situation occurs for ThT solutions in alcohols, particularly in longer n-alcohols (butanol, pentanol), where solvent polarity does not have essential effect on chargetransfer dynamics. Twisting rate of the molecular rotor in alcohols of different polarity (ethanol, propanol, butanol, pentanol) can be fairly well-described in the framework of the diffusion-limited process (2) and obeys the following empirical dependence τnr = 4.6η (where τnr and η are measured in ps and mPa·s, respectively). We would like to emphasize that the external torque model considers only the static solvent effect, that is, influence of polarity on the excited-state PES where TICT reaction takes place, but influence of solvent dynamics is not taken into account. Essentially barrierless character of TICT reaction in the excited state of ThT suggests strong electronic coupling, which may indicate adiabatic regime of the reaction. Dielectric continuum theory predicts58 that rate of the barrierless adiabatic electron transfer is limited by solvent relaxation dynamics and depends on longitudinal relaxation time τL AD kET

1/2 1⎛ λ ⎞ ≈ ⎜ ⎟ τL ⎝ 16πkBT ⎠

Figure 8. Dependence of the product of LE-TICT transition rate knr and solvation response time τs on dielectric constant for ThT in different polar solvents at room temperature. Solvent relaxation times τS and knr = 1/τ(LE) were taken from Table 3.

has relation96 to Debye relaxation time τD of the solvent, which can be measured by dielectric dispersion methods and depends on viscosity η and hydrodynamic volume of the solvent molecule VS. ε τL = τD ∞ (15) ε

τD =

3ηVS kBT

(16)

where ε∞ = n and ε = optical and static dielectric constants. Combining eqs 14−16 one can get the following relation of the rate of barrierless adiabatic electron transfer reaction to viscosity and dielectric constant of the solvent 2

(14)

AD kET

Maroncelli et al. demonstrated52,53,88 using the timedependent fluorescence Stokes shift technique that effective times τs of solvation response function S(t) are in good correspondence with longitudinal relaxation times (at least for solvents with dielectric constants ε < 50) and can provide satisfactory estimates for the case when solvents cannot be described by the model with a single Debye response. Validity of eq 14 for the case of ThT can be easily tested if AD we notice that kAD ET τL (or kET τS) should be a constant if temperature is not changing and we can neglect variations in λ values for different solvents. Solvent relaxation times τS from refs 53 and 88 are shown in Table 3. One can see that knrτS product is approximately constant (knrτS ≤ 1) for aprotic solvents, water, and ethylene glycol (Figure 8). Hence, dynamics of the twisted internal charge transfer in ThT follows the dynamics of polar solvation knr ∼ τS−1 for this group of solvents. In n-alcohols knr values exceed solvation response rates τS−1, and deviation from eq 14 can be seen. Figure 8 shows that TICT process rate is considerably faster than reorientation dynamics of solvent molecules in associative liquids like n-alcohols, which can be a reason for fluorescence spectra broadening for ThT in alcohols (Table 2). Solvent-controlled dynamics of electron transfer in water, ethylene glycol, and aprotic solvents according to eq 14 gives natural explanation why LE-TICT process rate in these solvents depends both on viscosity and polarity. Longitudinal time τL

1/2 kBT ε ⎛ λ ⎞ ≈ ⎜ ⎟ 3ηVS n2 ⎝ 16πkBT ⎠

(17)

which can explain correlation of nonradiative decay rate knr of ThT with dielectric constant value of polar solvents observed in Figure 3B.

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CONCLUSIONS 1. Steady-state fluorescence data of ThT in polar solvents with different protic properties demonstrate that, although fluorescence quantum yield dependence in any particular solvent within temperature range of 293− 323 K can be well-described by a linear function Φ = a + b(η/T), differences in molecular properties among the solvents lead to significant variation of parameter a and b values. Thus, the total data set of Φ for all studied solvents does not obey a simple unified linear dependence, which suggests effect of other solvent properties besides viscosity. We observed a correlation between the ratio knr/kr of nonradiative and radiative deactivation rates in ThT and polar properties of the solvents, and increase of dielectric constant ε from 12 to 80 in isoviscous media could account for ∼3−5 times growth in knr/kr value. Sub-picosecond transient absorbance measurements also demonstrate correlation of solvent polarity with deactivation rate knr of the fluorescent LE state, showing enhancement of the TICT process with DOI: 10.1021/acs.jpca.6b02577 J. Phys. Chem. A 2016, 120, 5481−5496

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The Journal of Physical Chemistry A higher ε for almost isoviscous solvents (i.e., water, DMF, pyridine). The obtained results are in agreement with the model that charge-transfer process, accompanied by twisting of BTZ and DMA molecular fragments, represents the main nonradiative channel of LE-state deactivation. Effect of specific interactions with solvent on fluorescence properties of ThT has complicated and controversial character. Differences in fluorescence spectral properties and TICT dynamics were found for ThT dissolved in alcohols and aprotic solvents. It was found that LE-TICT process rate for ThT in alcohols with exception of methanol at room temperature can be fairly well-described in the framework of the diffusionlimited process and obeys the following empirical dependence τnr = 4.6η (where η and τnr are in mPa·s and ps, respectively). From the other side, fluorescence of ThT in aqueous solution shows spectral features similar to the properties of the dye in aprotic solvents, which may indicate relatively small contribution of specific interactions between the solute and protic solvent molecules. The same conclusions can be drawn from close behavior of knr/kr dependencies on η/T for aprotic pyridine and protic 1-butanol, which have similar dielectric constants (Figure 3A). In our opinion, broadening of fluorescence spectra and slowing of LE-TICT rate in alcohols indicate about relative change in time scales of charge-transfer process and solvent relaxation in these associative solvents. Thus, one can conclude that in addition to viscosity, which is the principal factor governing the nonradiative LE-TICT rate, the solvent polarity and protic properties have significant effect on ThT photophysics. 2. TDDFT and INDO/S calculations of ThT were performed, where polar solvent effect was taken into account by applying a homogeneous electric field according to the Onsager cavity model. In agreement with the earlier studies it was found that transition from fluorescent LE state (φ ≈ 40°) to nonfluorescent TICT state (φ ≈ 90°) is accompanied by the excited S1 state energy change by −5300 cm−1 (TDDFT) and charge transfer ΔQ = 0.24 between DMA and BTZ fragments over a distance of rDA = 5.9 Å along the longest axis of the molecule. Change of the external electric field from 0 to 0.003 a.u., which was directed along the longest axis of ThT and simulated the reactive field of the polar medium, led to decrease of the S0 → S1* transition energy by ∼1200 and 4500 cm−1 for ThT with φ = 40° and 90°, respectively (a reaction field of 1.8 × 10−3 a.u. is expected for ThT with φ = 40° in case of the aqueous solution). It is noteworthy that for the polar solvents in this study, where dielectric constant varies in the range from 12 to 80, the static effect of polar solvation on S1*− S0 transition energy is not very essential: differences of only ∼60 and 300 cm−1 were found for ThT conformers with φ = 40° and φ = 90°, respectively. 3. We examined static solvent effect on the excited-state PES of ThT and tested the hypothesis that dependence of the excited S1-state energy E(S1) on angle φ may be considered as application of the external torque −∂E(S1)/∂φ, which can account for acceleration of the twisting rate. On the basis of TDDFT calculations we estimated change in Gibbs free energy during transition

from LE to TICT state (neglecting the entropy change) to be ΔG ≈ −7300 and −7100 cm−1 for aprotic solvents DMF (ε = 36.7) and pyridine (ε = 12.3), respectively. This small difference in ΔG is probably not sufficient to account for ∼1.8 times alteration of LE-TICT rate observed for ThT solutions in DMF and pyridine. The external torque model, which takes into account only static solvent effect, provides qualitative agreement with the experimental data of TICT dynamics in water and aprotic solvents. However, this model cannot explain TICT dynamics for ThT in alcohols (particularly in longer ones, like butanol and pentanol), where solvent polarity does not have appreciable influence. We propose that dynamic solvent effect may also play a considerable role in charge-transfer dynamics in the excited state of ThT. Taking into account that experimentally observed kinetics of LE-TICT transition indicates absence of any noticeable activation barrier12,15 (except activation barrier of the solvent viscous flow) we suggest adiabatic regime of electron transfer reaction in ThT to occur with the rate limited by solvent relaxation dynamics knr ∼ τS−1. It was found that rate of LE-TICT transition for ThT solutions in water, ethylene glycol, and aprotic solvents follows the dynamics of polar solvation fairly well. This behavior allows to explain the dependence of the reaction rate on both viscous and polar properties of the solvents. In alcohols TICT process is considerably faster than reorientation dynamics of solvent molecules, which can be a reason for smaller Stokes shifts and fluorescence spectra broadening (Table 2) observed for ThT in these associative solvents.

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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.jpca.6b02577. Steady-state absorption and fluorescence spectra of ThT in 1-butanol, DMF, pyridine, acetonitrile, and acetone. Transient absorption spectra of ThT in acetonitrile and methanol as well as exponential-associated spectra of transient absorption for ThT in acetone, methanol, acetonitrile, DMF, and pyridine. Plot of rate constants ratio knr/kr dependence on (ε − 1)/(2ε + 1) at η/T = 2 and 3 μPa·s/K for ThT in different solvents. Additional discussion of invariance of electron transition properties for charged molecules relative to a coordinate origin displacement. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: +375-152-743414. Cell: +375-29-7650657. Fax: +375152-731910. E-mail: [email protected]. Present Address ∥

Siarhei A. Kurhuzenkau, Department of Chemistry, University of Parma, Parco Area delle Scienze 17/A, Parma, 43124, Italy. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Belarusian Republican Foundation for Fundamental Research (Grant Nos. F16MC-021 and F16R5493

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209) and Ministry of Education of Belarus (Project No. 3.04 of Convergence-2020). We gratefully acknowledge Dr. V. Tarkovsky for providing the sample of Coumarin 1.

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