Modeling the Nonradiative Decay Rate of Electronically Excited

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Modeling the Nonradiative Decay Rate of Electronically Excited Thioflavin T Yuval Erez,† Yu-Hui Liu,‡ Nadav Amdursky,§ and Dan Huppert*,† †

Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel Department of Physics, School of Mathematics and Physics, Bohai University, Jinzhou 121013, China § Department of Materials and Interfaces, Faculty of Chemistry, Weizmann Institute of Science, Rehovot 76100, Israel ‡

ABSTRACT: A computational model of nonradiative decay is developed and applied to explain the time-dependent emission spectrum of thioflavin T (ThT). The computational model is based on a previous model developed by Glasbeek and co-workers (van der Meer, M. J.; Zhang, H.; Glasbeek, M. J. Chem. Phys. 2000, 112, 2878) for auramine O, a molecule that, like ThT, exhibits a high nonradiative rate. The nonradiative rates of both auramine O and ThT are inversely proportional to the solvent viscosity. The Glasbeek model assumes that the excited state consists of an adiabatic potential surface constructed by adiabatic coupling of emissive and dark states. For ThT, the twist angle between the benzothiazole and the aniline is responsible for the extensive mixing of the two excited states. At a twist angle of 90
, the S1 state assumes a charge-transfer-state character with very small oscillator strength, which causes the emission intensity to be very small as well. In the ground state, the twist angle of ThT is rather small. The photoexcitation leads first to a strongly emissive state (small twist angle). As time progresses, the twist angle increases and the oscillator strength decreases. The fit of the experimental results by the model calculations is good for times longer than 3 ps. When a two-coordinate model is invoked or a solvation spectral-shift component is added, the fit to the experimental results is good at all times.

’ INTRODUCTION The fluorescence of thioflavin T (ThT) is known to increase by 3 orders of magnitude upon binding to amyloid fibrils.2,3 As a consequence, ThT plays a leading role as a fluorescent sensor in the research field of Alzheimer’s, Parkinson’s, type II diabetes, and other amyloid-related diseases.4
6 ThT became the standard of measurement for the detection of amyloid fibrils, in vitro quantification,7,8 kinetics,9,10 and inhibition11,12 measurements. Although ThT has been used in research for more than 50 years, only recently has the photophysics of ThT begun to be revealed.13
16 By measuring the effect of the solution viscosity on the emission lifetime of ThT, in addition to performing quantum molecular calculations, both Stsiapura et al.15
17 and Nath et al.13,14 have shown the involvement of a photoinduced twisted intramolecular charge-transfer (TICT) excited electronic state in ThT photophysics. In this case, the crossing to the TICT state involves the dihedral-angle rotation, which has been theoretically investigated by Zhao and co-workers using the timedependent density functional theory (TDDFT) method.18,19 The fluorescence behavior is also related to many important nonadiabatic processes.20
23 This bond connects the benzothiazole moiety with the dimethylanilino ring of the ThT (Scheme 1). At an angle of 90
, the excitation state assumes a TICT character. By calculating the energies of the potential curve of ThT, in both the ground and excited electronic states, Stsiapura et al. showed that, at a dihedral angle of θ = 90
, the oscillator strength is close to zero, r 2011 American Chemical Society

Scheme 1

meaning that the TICT state is very weakly fluorescent.15,17 To prove their hypothesis, they changed the solution viscosity, thus altering the ThT quantum yield and emission lifetime.15 They also followed the change in the TICT excited state in several solutions with the use of femtosecond transient-absorptionspectral dynamics.16 Nath et al. also stressed the importance of viscosity in ThT photophysics.13,14 They used both time-correlated single-photon counting (TCSPC) and up-conversion techniques to follow the ThT emission lifetime in acetonitrile
ethylene glycol solvent mixtures.14 They showed that the ThT emission lifetime varies from 0.61 ps (in pure acetonitrile) to 17.64 ps (in pure ethylene glycol). They also used insulin amyloid fibrils to show that TICT plays a role in ThT binding to amyloid fibrils.13 In our previous studies we showed that by varying the temperature24 and pressure25 of a viscous alcohol solution, the Received: May 15, 2011 Revised: June 27, 2011 Published: June 28, 2011 8479

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value of the nonradiative rate constant, knr , is directly proportional to the viscosity of the solution. We found that knr decreased by about 3 orders of magnitude when the temperature of 1-propanol was lowered to 88 K. We also found significantly good correspondence between the temperature dependence of knr of ThT and the dielectric relaxation times of the 1-propanol solvent.24 In a more recent study,25 we used a diamond-anvil cell to increase the hydrostatic pressure acting on ThT in 1-propanol, 1-butanol, and 1-pentanol. In this way, we were able to increase the alcohol viscosity by raising the hydrostatic pressure. At elevated hydrostatic pressures of ∼2 GPa, knr decreased by more than 3 orders of magnitude. In this way, we found remarkably linear correlation between the decrease of knr and the increase in the solvent viscosity. We used a simple model calculation connecting the nonradiative rate and the angular-rotation velocity, Ω, of the phenyl ring of aniline with respect to the benzothiazole of the ThT. We previously24 discussed the nonradiative processes of ThT in accordance with known models of nonradiative processes: the Bagchi
Fleming
Oxtoby (BFO)26 model, the inhomogeneous nonradiative model of Agmon and co-workers,27 and an extension to the inhomogeneous model with the use of the Agmon and Hopfield28 theory, based on solving the Debye
Smoluchowski diffusion equation. Glasbeek and co-workers developed a model describing the nonradiative rate of auramine O. Auramine O, shown in Scheme 2, exhibits a nonradiative mechanism1,29 similar to that of ThT. To explain the experimental results, adiabatic coupling between a locally excited emissive state (F) and a nonemissive excited state (D) is considered. Torsional diffusion motions of the phenyl groups in the auramine O molecule are held responsible for the population relaxation along the adiabatic potential of the mixed state, S1 (comprising the F and D states). In this paper, we use the basic concepts of the latter model, which was considered to be the most suited to semiquantitatively describe the nonradiative processes of ThT. The time-resolved experimental fluorescence data of ThT in 1-propanol were used to demonstrate the applicability of the modified Glasbeek model to nonradiative processes where two electronic states are mixed by the twist of the angle between two ring sub-systems. Quantummechanical (QM) calculations were employed to construct the ground and excited states as well as the transition dipole moment as a function of the angle between the aniline and the benzothiazole. It was found that the Glasbeek model qualitatively describes the time-resolved spectroscopy of ThT in viscous solvents.

’ EXPERIMENTAL SECTION A fluorescence up-conversion technique was employed in this study to measure the time-resolved emission of ThT. The laser used for fluorescence up-conversion was a cavity-dumped Ti:sapphire femtosecond laser (Mira, Coherent), which provides short, 150 fs, pulses at around 800 nm. The cavity dumper operated with a relatively low repetition rate of 800 kHz. The second harmonic of the laser, operating over the spectral range of 370
420 nm, was used to excite the ThT in the liquid samples.

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The fluorescence up-conversion system (FOG-100, CDP, Russia) operated at 800 kHz. The samples were excited by pulses of ∼8 mW on average at the second harmonic generation (SHG) frequency. The time response of the up-conversion system is evaluated by measuring the relatively strong Raman
Stokes line of water shifted by 3600 cm
1. It was found that the full width at half-maximum (fwhm) of the signal is 280 fs. Samples were placed in a rotating optical cell to avoid degradation. ThT was purchased from Sigma-Aldrich. All of the measurements were carried out with the use of fresh solutions of ThT at the desired concentration and solvent. 1-Propanol of analytical grade was purchased from Merck (Germany). All chemicals were used without further purification.

’ SUMMARY OF EXISTING MODELS OF NONRADIATIVE PROCESSES Several models have been suggested in the past to describe nonradiative processes in which a certain intramolecular coordinate affects the nonradiative rate. Such models are, in principle, adequate for molecules consisting of two aromatic subsystems bridged by a single carbon
carbon bond or a longer carbon chain. In such molecular systems, twisting of the angle between the rings gives rise to an efficient nonradiative process, in which the rate is limited by the rotation time. The rotation time may depend on the solvent viscosity, which is the case for ThT and auramine O. Such molecules are also referred to as molecular rotors. Cyanine dyes and many other compounds, such as stilbene and its derivatives, are good examples of such molecular systems in which the nonradiative rate is large and strongly dependent on the solution viscosity. In 1983, Bagchi, Fleming, and Oxtoby26 suggested a model for nonradiative decay that is based on nonadiabatic curve crossing. The internal-conversion (IC) process occurs only at the intersection of the ground and excited potential curves. Following the excitation, at time t the population distribution, p(z,t), diffuses toward the curve-crossing point and decays back to the ground state. This suggests that, in viscous media, fluorescence decay begins with a time delay during which the nonradiative process is not effective until the population reaches the curve-crossing point. Up to now, such a delay has not been observed in the experimental results for ThT and many other molecules. An additional model for the nonradiative process was proposed by Agmon et al. to fit the time-resolved emission of (p-hydroxybenzylidene)dimethylimidazolinone (p-HBDI) in lowtemperature water
glycerol samples.27 p-HBDI is a model compound for the green fluorescent protein (GFP) chromophore. It consists of two aromatic-ring subunits connected by a bridge of one carbon atom. They used a nonlocal sink term, k(z), that permits a nonradiative process not only at the curve-crossing point but for all molecular configurations. The model does not include diffusion and is aimed at molecular systems in a frozen matrix. The z-coordinate is the angle between the two rings of the GFP chromophore. When the two rings are at 90
, the nonradiative rate is maximal. The nonradiative process is inhomogeneous since it occurs at all angles but at different rates, and therefore, instead of having a single rate constant, knr, it depends on the configuration of the z-coordinate. An important feature of the inhomogeneous model is that the time-resolved emission is nonexponential since knr depends on the “distance” from the point of intersection and thus does not have a fixed single value. An extension to the inhomogeneous frozen model can include population diffusion along the excited-state potential curve 8480

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toward the curve-crossing point. Such a process is well-described by the Agmon
Hopfield equation,28 which is usually applied to electron transfer in floppy-environment-like proteins:
 ∂pðz, tÞ ∂2 p D ∂ ∂V ¼D 2 þ p
kðzÞp ð1Þ ∂t ∂z kB T ∂z ∂z In this expression, p(z,t) represents the probability density of finding a value of p at time t at a given value of z. The decay of p(z,t) is affected both by diffusion propagated under the driving force determined by the excited-state potential curve and by the nonradiative process that consumes the excited population, where the rate is a function of z. As described above, the model that we thought to be the most promising in explaining the nonradiative decay rate as well as the time-resolved and time-integrated fluorescence of ThT is a model suggested by Glasbeek et al.1,29 They applied their model to explain the nonradiative process of auramine O (see Scheme 2).30 Auramine O is weakly fluorescent in low-viscosity solvents and fluorescent in viscous solvents. This type of fluorescence behavior is also found in ThT. Immediately after a short-pulse excitation, the initial population distribution resides in an excited emissive state (F, according to Glasbeek et al.). It then diffuses by torsional motion toward a dark state denoted by D. The emissive state is coupled to D as a function of the normalized twist angle coordinate z. The adiabatic coupling of the two excited states is given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 ð2Þ ½FðzÞ
DðzÞ2 þ 4C2 S1 ðzÞ ¼ ½FðzÞ þ DðzÞ
2 2 where F(z) and D(z) are the potential curves along the normalized twist angle coordinate of the emissive and dark diabatic states, respectively, and C is the coupling-strength parameter. This approach was developed a decade earlier by Fonseca and Barbara and their co-workers31,32 to phenomenologically model adiabatic excited-state electron transfer in which solvation dynamics is involved and where the solvent generalized reorganization coordinate z determines the adiabatic coupling strength. Since the S1 state is a z-dependent mixture of fluorescent and nonfluorescent zerothorder states, the transition dipole moment, M(z), of the optical transition S1 f S0 is also z-dependent. The normalized S1 f S0 transition dipole moment decreases as a function of z: 
 2C 2 1 arctan MðzÞ ¼ cos ð3Þ 2 FðzÞ
DðzÞ The transition dipole moment is small for the dark state and large for the emissive state, and therefore, M(z) strongly depends on z. The Glasbeek model was also used by Meech and co-workers33 to quantify the torsional dynamics of auramine O in nanoconfined water in aerosol OT reverse micelles. The QM calculations of both Nath et al.13,14 and Stsiapura et al.15
17 indicate that, indeed, the transition dipole moment, M(z), of the ThT S1 f S0 transition decreases by a factor of about 100 as a function of the C2
C20 rotation angle from the initial position around 33
to 90
. At 90
, the excited state is in its TICT nonemissive state with an oscillator strength f ≈ 0.01. The potential curve of S1 shows a distinctive minimum at 90
, whereas the ground state shows a low maximum. The Glasbeek model incorporates a dark state, which for ThT is the TICT state. The adiabatic coupling approach provides a continuous mixing of the emissive LE state with the dark TICT state. As the twist angle around C2
C20 increases to 90
, the oscillator strength is largely reduced with time. The evolution of the population-distribution

Figure 1. Emission spectra of ThT in 1-propanol at room temperature: (a) steady-state emission, (b) time-resolved emission up-conversion signals, measured at several wavelengths, (c) computer stretched-exponential fits of the experimental up-conversion signals shown in (b).

function, p(z,t), is calculated by the Debye
Smoluchowski diffusion equation, where z is a normalized twist-angle coordinate.

’ EXPERIMENTAL RESULTS OF THE STEADY-STATE AND TIME-RESOLVED EMISSION OF THT Figure 1a shows the steady-state emission of ThT in 1-propanol at 298 K. As seen in the figure, the emission band is structureless and asymmetric, skewed to higher wavelengths. 8481

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Table 1. Fitting Parameters of ThT Fluorescence in 1-Propanola
e λ (nm)

a1

τ1

R1

τ2

R2

440

0.96

2000

0.6

450 460

0.96 0.96

2300 3500

0.66 0.72

0.04

28

0.85

0.04 0.04

77 47

0.7 0.7

470

0.97

4700

0.75

480

0.97

5900

0.78

0.03

40

0.7

0.03

40

490

0.96

7200

0.7

0.85

0.04

34

500

0.98

7700

0.85

0.92

0.02

28

0.85

a2

λ (nm)

a1

τ1

a2

τ2

τf

510

0.9

8400

0.1

300

8400

520 540

0.8 0.6

9400 11400

0.2 0.4

500 600

9400 11400

560

0.4

13400

0.6

800

13400

The signals were fit by the following equation: y = ∑ai exp[
(t/τi)Ri]. b τ1 values are in femtoseconds. c τ2 values are in picoseconds. d The signals were fit by the following equation: y = a1 exp[
(t/τ1)] + a2(1
exp[
(t/τ2)]) exp[
(t/τf)]. e τ1, τ2, and τf values are in femtoseconds. a

Figure 1b shows the time-resolved emission of ThT in propanol measured at several wavelengths. The fluorescence upconversion technique with ∼200 fs time resolution was used to monitor the fluorescence signals. The sample was excited at 374 nm with the use of a cavity-dumped mode-locked Ti:sapphire laser. The laser provided pulses of about 150 fs at 700 kHz. The average lifetime of the fluorescence depends strongly on the emission wavelength: the longer the monitoring wavelength, the longer the lifetime. At long wavelengths, (λ g 510 nm), the signal shows a rise followed by a relatively long decay. A two-stretched-exponent function was used to fit the experimental data. This function was convoluted with the instrument-response function of the fluorescence up-conversion optical setup. The deconvoluted fits are shown in Figure 1c. The important point to notice in Figure 1b,c as well as in Table 1 is the large difference in the fluorescence-decay times of the various measured signals; the longer the wavelength, the longer the decay time. The decay times of the major component for the signals measured at 450, 470, 490, 510, and 560 nm are 2.3, 4.7, 7.2, 8.4, and 13.4 ps, respectively (see Table 1). The large difference in the fluorescence lifetimes is attributed to the unique nonradiative process in ThT and probably is also valid for other molecules in which the rotation of a ring subunit (for ThT, the aniline ring) is responsible for population and spectral shifts as well as mixing between fluorescent and dark states, leading to nonradiative relaxation. In the fitting of the experimental data, a stretched exponential function, exp[
(t/τ)R], was used rather than the pure exponents. The value of the major decay-component stretching factor, R, strongly depends on the monitored emission wavelength; the shorter the wavelength, the smaller the value of R (see Table 1). Thus, the deviation from pure exponential decay increases the shorter the emission wavelength. Figure 2a shows the constructed time-resolved spectra of ThT in 1-propanol at several times. The spectra were constructed with the use of a procedure similar to that described by Maroncelli et al.34 Figure 2b shows the normalized time-resolved spectra shown un-normalized in Figure 2a. As seen in Figure 2b, there is a time-dependent red spectral shift of about 1000 cm
1, and the

Figure 2. Constructed time-resolved emission spectra at several times: (a) the intensity at short time is normalized, (b) normalized intensity of all spectra.

bandwidth increases by about 700 cm
1. It is important to note the strong reduction in the fluorescence intensity with time. The nonradiative model used in this study explains the large reduction in the fluorescence intensity as well as the dynamic red shift of the fluorescence band. Similar data analysis for water by Nath et al. reveals approximately the same features of the constructed timeresolved spectra.

’ MODELING OF THE THT NONRADIATIVE PROCESS FOLLOWING THE GLASBEEK MODEL The ground and two excited electronic states were calculated by quantum chemical calculations, all carried out with the TURBOMOLE program suite.35
41 The geometrical optimizations for the ground state were performed with the use of densityfunctional theory (DFT) with Becke’s three-parameter hybridexchange function with the Lee
Yang
Parr gradient-corrected correlation functional (B3LYP functional).27 The triple-ζ valence quality with one set of polarization functions (TZVP) was chosen as the basis set throughout.28 Fine quadrature grids 4 were also employed.29 The TDDFT method was used at the same level to calculate the energy in the excited state of the dye at different dihedral angles. In addition, considering the solvent effects, the conductor-like screening model (COSMO) was also used in all the calculations.41,42 The potential-energy curve of the 8482

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Figure 3. Potential energy curves of the ThT ground and first excited states as a function of the twist angle.

Figure 4. Oscillator strength as a function of the normalized twist angle.

ThT molecule was calculated along the dihedral twist angle, θ. All the energies in the curve respond to the minimum of the groundstate structures with the fixed dihedral angle. In the calculation, we used an average environment dielectric constant of ε = 20.1, the value for 1-propanol at room temperature. The absolute value of the S1(θ) potential curve in energy units strongly depends on the solvent dielectric constant. The difference between the energies of the S1 potential at z = 0 and z = 1 is smaller by about a factor of 2 when the calculations include the effective dielectric constant of ε = 20.1. The ground- and excitedstate potential curves as a function of the torsion angle z are similar to those calculated by Nath et al.13,14 and Stsiapura et al.15,16 At a twist angle of 90
, the ground- and excited-state potential curves have a maximum and minimum, respectively. These changes lead to an angle dependence of the energy gap S1(θ)
S0(θ). Thus, we expect a red fluorescence band shift with the twist angle. The time-dependent experimental fluorescence band energy shift is about 1100 cm
1. The calculated maximum band shift for 1-propanol from z = 0 to z = 1 is about 4000 cm
1. The twisting of the aniline with respect to the benzothiazole ring not only reduces the fluorescence energy but also mixes the locally excited (LE) state with the charge-transfer (CT) state. The mixing reduces the transition dipole moment (M(z)) and the oscillator strength f. The pure radiative lifetime increases with the decrease in f, and therefore, the fluorescence rate (photons/s) decreases. At a twist angle of 90
, the fluorescence intensity decreases by about 2 orders of magnitude, and thus, the photon count rate of the fluorescence up-conversion signal is reduced by 2 orders of magnitude compared to the initial value at t = 0 within the duration of the laser excitation pulse. Stsiapura and co-workers16 used a femtosecond pump
probe technique in their time-resolved ThT study in several liquids. They found that the TICT excited state decays nonradiatively to the ground state by conical intersection. The nonradiative decay times found in their study and in our previous work25 are shorter by a factor of 2 than the dielectric-relaxation times, τD, of the alcohols. τD = 60, 120, 300, and 600 ps for methanol, ethanol, 1-propanol, and 1-butanol, respectively. Figure 3 shows the calculated QM ground- and excited-state potential electronic curves as a function of rotation. Figure 4 shows the calculated transition dipole moment in units of oscillator strength as a function of the normalized

twisting coordinate z. The oscillator strength decreases from a value of ∼1 to about 0.01 at a twist angle of 90
. Glasbeek et al. used an analytical expression (eq 3 in this paper) for the dependence of the transition dipole moment as a function of the normalized twist angle coordinate z. In our calculations, we set z = 0 and z = 1 at 0
and 90
twist angles, respectively. It is also possible to deduce the oscillator strength as a function of z, the normalized twist angle, from ab initio calculations. As seen in Figure 4, the CT-state oscillator strength (z = 1 in the figure) is low, ∼0.01, whereas for the LE state (z = 0 in the figure) it is rather large, ∼1.1. The plot of f versus z is quasi-symmetric with a minimum at a twist angle of 90
for which it exhibits only CT-state character. Short-laser-pulse excitation leads to an excited-state population with initial twist angles that mimic the ground-state populationdistribution function at equilibrium positioned around the minimum of the ground-state potential curve at 33
. For the population distribution function at t = 0, Glasbeek et al. used p(z,0), a lognormal line-shape function defined by three parameters: the position, the width. and the asymmetry of the distribution peak. We used the initial distribution on the excited-state potential at t = 0, p(z,0), as calculated from the ground-state potential curve. Prior to the laser-pulse excitation, the ground-state distribution is at equilibrium at the minimum of the S0 potential curve at 33
. An important procedure in their model1 is the time evolution of the excited-state population as a function of the normalized twist-angle coordinate z. The rotation of the aniline ring in a viscous liquid medium is diffusive in nature. Therefore, they used the Debye
Smoluchowski equation to calculate p(z,t) along the excited-potential curve. We used the same strategy to evaluate p(z,t). For this purpose, we employed the user-friendly SSDP program of Agmon and Krissinel.42 This program enables a numerical solution to the Debye
Smoluchowski equation under certain initial and boundary conditions. The input parameters in our case are (1) the ground- and excited-state potential-energy curves, which we calculated by ab initio methods, and (2) the rotational-diffusion constant Dr, which is an adjustable parameter inversely proportional to the solvent viscosity. The ground-statepotential curve, S0(z), provides the initial population distribution function p(z,0) on the excited state, S1(z), at t = 0 immediately after the short-pulse excitation. Figure 5 shows the excited-state population-distribution function, p(z,t), as a function of z at 8483

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Figure 6. Time-resolved emission spectra of ThT (dotted lines) at several times. Computed fits (solid lines) with Dr = 0.1 ps
1 (see the text).

This relation is the central result of the Glasbeek model. g(ν0(z),ν
ν0(z)) is a line-shape function characteristic of the Franck
Condon factor. ν0(z) is the twist-angle-dependent energy gap between the excited state and the ground state (see Figure 7). For the Franck
Condon line-shape function, g, we used a log-normal function: ( exp½
lnð2Þflnð1 þ RÞ=γg2  R >
1 ð5Þ gðνÞ ¼ h 0 R e
1 R  2γðν
ν0 ðzÞÞ=Δ Figure 5. Calculated population distribution of ThT at several times as a function of the normalized twist angle: (A) Dr = 0.1 ps
1, (B) Dr = 0.33 ps
1.

several times. The initial population at t = 0 is redistributed as time progresses and is shifted toward the minimum of the potential curve at z = 1, where the twist angle between the two ring systems is 90
. At this angle, the oscillator strength is only about 0.01, whereas at angles between 0 and 40
, it is close to 1. The time dependence of the population distribution strongly depends on the rotational-diffusion constant as well as the slope of the potential curve, which is the driving force for population migration. Since the width of the distribution is relatively small, the time-dependent population seen in Figure 5 shows an approximate resemblance to a simple chemical scheme, A f B, where A denotes the initial distribution at z = 0.36 (θ = 33
) and B the final position of the distribution function at z = 1 (θ = 90
). In accordance with such a simple description, we expect that the initial fluorescent population will decrease and the population of the dark state, i.e., the CT state, will increase with time. Since the CT state is a “dark” state, the population transfer leads to fluorescence decay at a rate that depends on both the rotational-diffusion constant, Dr, and the slope of the potential curve, determined by the depth of the S1 minimum potential curve at 90
. The time-dependent fluorescence at time t and frequency ν, Ifl(ν,t), is proportional to Z Ifl ðν, tÞ  dz gðν0 ðzÞ;ν
ν0 ðzÞÞjMðzÞj2 pðz, tÞν3 ð4Þ

ν0(z) is the peak position. Its value depends on the twist angle. γ is the asymmetry parameter. (For a symmetric Gaussian shape, γ = 0.) Δ represents the bandwidth. For simplicity, we assume that the line shape function, g, shifts with time to the red but the asymmetry and the bandwidth are independent of z. Figure 6 shows the experimental and calculated time-resolved emission spectra of ThT in 1-propanol at several times, 5, 7.5, 10, 15, 20, and 25 ps. As can be seen, the fit is good at all times. The adjustable fitting parameters are as follows: 1. The log-normal parameters used for the Franck
Condon line shape of the spectra were asymmetry, γ,
0.4, width 3300 cm
1, and the initial position at t = 0, 20800 cm
1. 2. The red shift of the spectra as a function of z. This parameter is calculated from the energy of the gap between the S1(z) and S0(z) states. Figure 7 shows the calculated gap, S1(z)
S0(z), as a function of z. 3. The rotational-diffusion constant, Dr, of the ring system. This constant is related to the macroscopic shear-diffusion constant of the solvent. 4. The decay time of the CT state of ThT in 1-propanol. We used τ = 80 ps. This time is in accordance with that of Stsiapura et al.16 and our previously reported pump
probe results.25 As mentioned above, we were unable to obtain a quantitative fit at short times. This might be due to our inability to find the correct fitting parameters (there are three such adjustable parameters in the model). It may also be that the model is limited in providing a full description of all the time-resolved processes that govern the time-resolved emission at a particular wavelength. For example, the solvation dynamics also contribute to the red shift of 8484

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Figure 7. Calculated difference of the potential energy as a function of the normalized twist angle (see the text).

Figure 8. Peak location of the ThT time-resolved emission spectrum as a function of time.

the emission band and not only through the rotation of the aniline ring. Solvation of the newly formed excited state of coumarine dyes shifts the emission band to the red by almost 3000 cm
1. The short-time experimental results, up to about 5 ps, show faster dynamics than those at longer times (t g 5 ps). We were able to obtain a reasonable fit for the short-time experimental results by using values of the rotational-diffusion constant that differ by a factor of 3. Figure 8 shows the peak position of the experimental timeresolved emission spectrum as a function of time. The peak position 50 fs after excitation is at about 20 800 cm
1. With time, the peak position shifts to the red. The plot shown in Figure 8 clearly shows that the rate of the red shift of the peak position at short times is rather large whereas at longer times (t g 3 ps) it decreases by a factor of 3. Figure 9 shows both the experimental and modeled time-resolved fluorescence intensity at the band peak as a function of time. The peak intensity drops with time. This observation is the major result of the Glasbeek model. The initial excited population immediately after laser-pulse excitation possesses LE-state character. The emission intensity is large since the oscillator strength f ≈ 1. With time, the aniline ring rotates, the twist angle reaches 90
, and the S1 state assumes TICT character for which the oscillator strength is reduced by about 2

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Figure 9. Peak intensity of the ThT time-resolved spectrum as a function of time, normalized by the intensity of the shortest time measurement (50 fs): experimental (circles) and modeled (squares).

orders of magnitude. This drop in the oscillator strength is responsible for the large decrease in the fluorescence intensity as a function of time seen in Figures 6 and 9. Figure 9 also shows the model calculation of the emissionband peak intensity, Ip(t), as a function of time for a rotationaldiffusion constant of Dr = 0.1 ps
1. The calculated decay profile of Ip(t) shows a slightly convex shape, whereas the experimental values clearly show a concave shape. We were able to fit both the intensity of the time-resolved emission spectra and peak position of the first 3 ps by increasing the rotational-diffusion constant by a factor of 3.3 to Dr = 0.33 ps
1 and also by increasing the total amplitude of the band shift from 3000 to about 4000 cm
1. The data analysis as described above led us to suggest that the experimental results indicate that two processes rather than a single process are taking part in the excited-state dynamics of ThT in viscous solvents. We already mentioned that solvation dynamics contribute to the time-dependent red band shift, which could explain the rapid component of about 3 ps we observe in the time-resolved spectra. An additional plausible mechanism that might take place in the excited-state dynamics of ThT is the inclusion of a rotation of the dimethylamino group at the para position (see Scheme 1). The TICT-state photophysics was extensively studied by Grabowski et al. for the prototype molecule (dimethylamino)benzonitrile (DMABN).43,44 They stressed the importance of the 90
rotation of the dimethylamino group with respect to the phenyl to obtain a TICT state. Nath et al.13 calculated the potential-energy curves of the ground and excited states as a function of the twist of the dihedral angle between the dimethylamino plane and that of the phenyl ring. Figure 6 in their paper shows the variations in the potentialenergy curves as a function of the twist angle. The ground-state curve shows a minimum at 0
and a maximum at 90
, while the excited state shows a shallow minimum of about 0.2 eV at 90
. The authors found a barrier of about 0.2 eV to the twist angle, positioned at 65
, thus preventing a full twist motion. Therefore, these calculations do not support the idea that an additional rotation axis, that of the dimethylamino group, may reach a full twist of 90
on the potential surface of the excited state. The rotation time of this group should be faster than that of the phenyl ring since the volume of this functional group is smaller and the driving force is comparable to that for the phenyl ring. Calculations made by Nath et al. support that a certain drop in 8485

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the S1
S0 energy is associated with a 90
twist of the dimethylamino group. The major part of the S1
S0 timedependent energy gap is attributed to the twist of the angle of the phenyl ring with respect to that of the benzothiazole. Furthermore, advanced calculations of S1 as a function of the angle of the dimethylamino group with respect to the phenyl group may reveal that the barrier is much smaller and a full twist can occur. Such calculations would require the solvent structure to be taken into account in solvent
solute interaction. If this is the case, then the short time component in the time-resolved spectra may be assigned to it. Meech and co-workers33,45,46 found that the time-resolved fluorescence spectra of auramine O like we find in ThT also consists of two time components. The band shift rate of the first moment of the fluorescence as well as the rate of loss of fluorescence intensity is faster at short times. Accurate fitting of the time-resolved emission spectra of auramine O was achieved using a time-dependent diffusion coefficient, D(t), rather than a time-independent D. They suggested the diffusion time dependence to arise from the medium’s time-dependent friction reflecting dynamics on a broad range of time scales spanning the reaction dynamics. The friction recovered from their calculations suggests strongly hindered motion in the confined droplet and can be qualitatively related to the solvation dynamics measured in sodium bis(2-ethylhexyl) sulfosuccinate (AOT). For the purpose of auramine O data fitting in a confined water droplet and in decanol, they used a biexponential time-dependent diffusion coefficient: DðtÞ ¼

∑ai exp½
ðt=τi Þ

ð6Þ

The formal definition of D(t) for a certain potential energy surface was given earlier in the works of Hynes and coworkers47,48 and of Oxtoby and co-workers.49,50 For the estimation of D(t), the solvation correlation function, C(t), must first be determined from fitting of the time-dependent fluorescence Stokes shift.51 C(t) is a nonexponential decay function. At short times, it is believed to assume a Gaussian shape due to inertial orientational motions. At longer times, where friction plays a larger role in associative liquids such as alcohols, C(t) exhibits a rather long tail. In both ThT and auramine O, the time-resolved fluorescence band intensity decay rate in alcohols is much faster than the long time components of C(t) on one hand and shorter by approximately a factor of 2 than ÆC(t)æ on the other hand. Thus, the long time components of C(t) are not effective parameters for the determination of the nonradiative rate of auramine O and ThT.

’ SUMMARY In the current study, we developed a computational model to simulate the steady-state and time-resolved emission of the ThT molecule (Scheme 1) in viscous solvents. The development was based on the conceptual guidelines of a model suggested by Glasbeek et al., who used their model to explain the time-resolved spectra of auramine O (Scheme 2).1 Both molecules show similar interesting emission behavior which is related to nonradiative processes that take place as a result of the rotation of molecular rotors. For both molecules, the emission intensity strongly depends on the solution viscosity, with steady-state emission spectra growing more intense as the viscosity increases. For ThT, the timeresolved emission shows that the average fluorescence decay times are proportional to the solution viscosity.14
16,25 The constructed time-resolved emission spectra of ThT shown in Figure 6 exhibit

a large decrease of the fluorescence intensity with time. Our previous study and those of others14,16,24 revealed that, for a viscosity of about 1 cP, the fluorescence decay times are about 1 ps. The Glasbeek model1,29 is based on the construction of an excited-state adiabatic potential curve as a function of the twist angle between the two submolecular aromatic units (see Schemes 1 and 2). The adiabatic curve consists of two electronic states, an emissive state and a nonemissive dark state. Upon photoexcitation, the molecule is first in the LE emissive state. With time, the twist angle grows and the excited state assumes a TICT character with a low oscillator strength, leading to a short effective fluorescence lifetime for both ThT and auramine O. The rotation of the aniline subsystem is diffusive and thus depends on friction with the solvent. The model developed here is based on the principles mentioned above. Quantum-mechanical calculations were used to construct both the ground- and excited-state potential curves (Figure 3) as well as the oscillator strength (Figure 4) as a function of the normalized twist angle z. The calculated excited state indeed shows that the emissive-state character leads to a decrease in the oscillator strength by a factor of 100 at a twist angle of 90
. The Debye
Smoluchowski equation was used to calculate the time-dependent population-distribution function at several times as a function of the twist angle (Figure 5). The bestfit parameters to the experimental time-resolved emission spectra were found. The most important adjustable fitting parameter is the rotational-diffusion constant, Dr, which was found to be 0.1 ps
1. The model accounts for the dynamic red band shift and the time dependence of the decrease in the time-resolved intensity of the emission spectra at intermediate and long times (t g 5 ps). It was found that the experimental time-resolved spectra at short times strongly deviate from the behavior at intermediate and long times, and thus, the results at short times could not be fitted. It was possible to fit the short-time results (t < 5 ps) with the use of a value of Dr 3.3 times that used for the intermediate and long times. The rotational-diffusion coefficient, Dr = 0.1 ps
1, obtained for the best fit for the long times, is consistent with the value predicted by calculation of a rotating object of the size of a phenyl ring in a viscous medium with η = 2.4 cP, the viscosity of 1-propanol—the solvent used here for the experiments. The faster decaying components observed for the short times (t e 5 ps) are explained by solvation dynamics taking place prior to and during aniline rotation. As a consequence, a time-dependent Stokes shift takes place.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Phone: 972-3-6407012. Fax: 972-3-6407491.

’ ACKNOWLEDGMENT This work was supported by grants from the James-Franck German-Israeli Program in Laser-Matter Interaction. N.A. thanks the Clore scholars program for financial assistance. Many thanks are due to Professor M. Glasbeek and Professor H. Zhang for helpful discussions. The results of quantum chemical calculations described in this paper were obtained on the homemade Linux cluster of group 1101, Dalian Institute of Chemical Physics. 8486

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