Fast Photoinduced Reactions in the Condensed Phase Are

Feature Article pubs.acs.org/JPCA

Fast Photoinduced Reactions in the Condensed Phase Are Nonexponential Ron Simkovitch, Rinat Gepshtein, and Dan Huppert* Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel ABSTRACT: Time-resolved measurements of photoinduced reactions reveal that many ultrafast reactions in the femto- to picosecond time scale are nonexponential. In this article we provide several examples of reactions that exhibit a nonexponential rate. We explain the wide range of the nonexponential reaction by the lack of time separation between τs, the characteristic fast equilibration time of the population in the reactant potential well, and the longer time τe, the characteristic time to cross the energy barrier between the reactant and the product.

■

INTRODUCTION An important concept in chemical kinetics is the rate coefficient. For a unimolecular reaction of some species A, the rate coefficient k appears in the first-order-kinetics law, dA/ dt = −kA. However, it should be remembered that even for unimolecular processes, the existence of a rate coefficient as a time independent constant requires additional assumptions.1 Usually, different reaction rates are expected for individual vibrational states of the reactant. Thus, a single timeindependent macroscopic rate coefficient will not be anticipated in a multilevel system. The observed macroscopic rate coefficient is an average of many microscopic rates. In the latter case, k = ΣiPiki, where each ki is a rate coefficient associated with an individual state i, and Pi is the corresponding probability of being in this state. The rate coefficient, k, is therefore time-independent only when the probabilities Pi remain constant during the chemical reaction. The situation in which the relative population distribution of the molecular states remains constant, even if the overall population decays as the reaction proceeds, is sometimes referred to as a quasi-steady state. This occurs when the relaxation process that maintains a thermal equilibrium between vibrational states is faster than the chemical process studied. In such a case, {Pi} remain thermal (Boltzmann) probabilities during the time of the chemical reaction.

Scheme 1. Water-Reservoir Scheme of Four Communicating Vessels (Description in Text)

vessels through a water-permeable membrane. Water can flow from each vessel through pipes I−IV. The water flow rate of each pipe is Pi ∝ piki, where pi is the water height that determines the hydrostatic pressure, and ki is related to the diameter of the pipe. If the exchange of water between vessels is much faster than the flow through the pipes, then the water height is the same in all the vessels at all times during the flow of water. On the contrary, if the water exchange rate between vessels is slow in comparison to the flow through the pipes, then the water levels in the system will be different. In this case, the total water flow cannot be attributed to a single rate and the flow rate out of the reservoir will be described by the summation of the individual vessels rates. In this article we provide several examples of photoinduced reactions that occur in the excited state. These reactions show

■

COMMUNICATING VESSELS AS AN ANALOG OF A REACTING CHEMICAL SYSTEM Scheme 1 shows a drawing that qualitatively describes a reactive system that includes reactive sublevels (such as vibrational levels). In this system the total rate coefficient depends on the sublevels’ individual rates. The subsystem in Scheme 1 displays a large water reservoir consisting of four communicating vessels (regions I−IV). Each vessel is filled with water, and water can penetrate the adjacent © XXXX American Chemical Society

Received: September 2, 2014 Revised: November 10, 2014

A

DOI: 10.1021/jp508856k J. Phys. Chem. A XXXX, XXX, XXX−XXX

Feature Article

The Journal of Physical Chemistry A

for example, the relaxation time in either of the reactant and product wells, the correlation time τc of the coupling to the bath, the time τe for a trajectory to cross the barrier region, the time τR required to lose or gain the excess energy ES, etc. All of these various time scales will, of course, be of importance in the detailed description of the rate of escape, k,

that the reactant population decreases nonexponentially, whereas, according to conventional unimolecular theories, it is expected to decrease exponentially. Below, we summarize the concept of the derivation of a chemical reaction rate coefficient and the assumptions for its validity. We follow the seminal review of Hänggi, Talkner, and Borkovec2 on the formulation and derivation of the rate coefficients of chemical reactions. In an activated process, the reactant is in a potential well and the coordinate x describes the dynamics of the chemical process reaction. In the condensed phase, x is coupled to the solvent or to the solid environment (Scheme 2). For the reactant to escape from the well, x(t) must acquire enough energy to reach the barrier E+b .

k ∼ τe−1

The crucial requirement for a separation of time scales is that τe should be much longer than all other relevant time scales of the system dynamics. In this sense, τs stands for the collection of all fast time scales relevant to the process of activation. The motivation of this article is to show that in many of the photoinduced reactions this fulfilment is not achieved, because these reactions are too fast for the required time separation. Most authors presenting experimental results of excited-state nonexponential decay signals, refer one of the exponents of the multiexponential fit to a definite process, whereas the other time components are explained by intramolecular vibrational energy redistribution, solute−solvent interactions prior to or after the reaction takes place, and cooling processes of the molecular system as either a reactant or a product. In the current article we emphasize the origin of the nonexponential decay of the signal obtained in photoinduced processes and refer the major part of the excited-state signal decay to the reactive process. The message we wish to convey in this article is that reactive-process dynamics do not necessarily follow exponential kinetics. In the examples we show and discuss in this article, the reaction kinetics are nonexponential. Modeling the Nonexponential Concept. To demonstrate the transition from nonexponential decay to exponential decay of a photoreactive population, we used a reactive model based on a simple one-dimensional generalized reactive coordinate, r. The reactant population is distributed in a harmonic potential given by

Scheme 2. Double-Well Scheme

To form the product, it must later lose the excess energy to become trapped inside the product well. To observe a timeindependent rate coefficient, the time τs for fast equilibration of the population in the reactant well should be well separated from the longer time scale of escape, τe. τe ∼ τs exp(E b±/εs)

τe ≫ τs

(2)

(1)

V (r ) = A ·(r − R )2

Eb±

where is the barrier height between the reactant and the product. εs is the energy gained by rapid fluctuations of the reactant molecule interacting with the environment. In the above discussion of time-scale separation between the activation process and the relaxation of the local system, it is assumed that all of the rapid fluctuations of the various time scales could be characterized by single local-system relaxation time τs. However, in reality many different fast time scales exist,

(3)

−2

where A = 0.11 Å ·J and R = 25 Å; R is the position of the potential well minima. The large value of R is of no significance and is used for computation purposes. The population distribution has a Gaussian shape along the reaction coordinate and is given by 2

P(r ) = e−(r − R / L)

(4)

Figure 1. (a) Population distribution (red) and potential well (black) of the simulation (see text). (b) Reactant population decay calculated for several values of the diffusion coefficient, shown on a semilogarithmic scale. B


Feature Article

The Journal of Physical Chemistry A where R = 25 Å and L = 10 Å is related to the potential well width. We assume that the reaction rate depends exponentially on the reaction coordinate and is given by k(r ) = k 0·e−a(r − R)

reaction window, and nondiffusing limits. They found that under certain conditions, the time dependence of the survival probability of the reactant is multiexponential rather than single exponential. At the beginning of the 1980s, experimental examples were reported4 in which the lifetime of excited-state intramolecular electron transfer, τexp, at room temperature roughly equals a constant-charge dielectric-relaxation time, τL:

(5) −1

−1

where k0 = 2 × 10 s and a = 0.5 Å . The exponential distance dependence of the rate coefficient is found in many of the electron and proton transfer reactions. In the Introduction, we emphasize the rapid equilibration of the population within the potential well as the key player to observe exponential kinetics and to obtain an independent rate coefficient. In simulating the equilibration process within the population distribution, P(r), we used a single parameter: a diffusion coefficient, D. We solved the Debye−Smoluchowski3 equation for the reacting population described above. Basically, a similar problem was first described in a seminal article by Agmon and Hopfield.4 The Agmon−Hopfield equation4 provides the time dependence of a population, p(x,t), that is governed by a diffusional motion along the reactive coordinate and a reaction rate that depends on the reactive coordinate. 8

∂p(x ,t ) ∂ 2p D ∂ ⎛⎜ ∂V ⎞⎟ =D 2 + · p − k(x)p ∂t kBT ∂x ⎝ ∂x ⎠ ∂x

τL = τD·ε0 /εs

(7)

where τD represents the constant-electric-field dielectricrelaxation time, εs is the static dielectric constant of the solvent, and ε0 is the high-frequency (optical) constant given asymptotically by the square of the refractive index. Because of the faster relaxation time of the vibrational motion, they assumed that the solvent coordinate, x, can define a rate constant at each value of x. Thus, k(x) is given by k(x) = νq exp[ − ΔG*(x)/kBT ]

(8)

where ΔG*(x) is given by eq 3.6 of ref 6 when the intramolecular q coordinate motion is treated classically. The reverse reaction is omitted for simplicity. The coordinate x diffuses under the influence of a potential V(x), which represents the free energy of the reactant’s surface (Scheme 2 or Figure 1 of ref 6). During the diffusion, the reactant becomes product with a probability rate constant of k(x) at each value of x. Then, the distribution function p(x;t) at the coordinate x and at time t satisfies the Agmon−Hopfield diffusion-assistedreaction equation (eq 6). Sumi and Marcus found an exact solution to the Agmon− Hopfield diffusion-assisted reaction shown in eq 6, for each of the four limiting cases given below. 1. Slow-Reaction Limit. In this limit the reaction that perturbs the thermal equilibrium distribution is very slow compared with the rate of reorientational fluctuation of the solvent molecules that attempts to restore the equilibrium distribution of x. In this slow-reaction limiting case, thermal equilibrium for x is maintained during the course of the reaction and hence p(x;t) is proportional to exp[−V(x)/kBT]. The probability, Q(t), of reactant survival should then show a single exponential decay with a rate constant independent of the relaxation time τL of the reorientational fluctuations. This thermally equilibrated reaction-rate constant, ke, is given by

(6)

In this expression, p(x,t) represents the probability density of finding the system at a given value (x) at time t. The decay of p(x,t) is affected both by random diffusion, which changes the distribution along the x-axis under an external potential V(x), and by the reaction rate coefficient k(x), which also affects the population by lowering the population. We solved the Agmon− Hopfield equation numerically for the problem mentioned above using the spherical-symmetric diffusion program (SSDP) of Krissinel’ and Agmon.5 Figure 1a shows the Gaussian population distribution and potential well of the simulation. Figure 1b shows the calculated overall population P(t) versus t on a semilogarithmic scale for several values of the diffusion coefficient. When D is rather small, D(x) < 10−8 cm2/s, then on a time scale of 10 ns, the reactant population along the reaction coordinate, x, is frozen. The reacting system is inhomogeneous. The reaction rate for each subpopulation P(x) depends on the coordinate x. The overall population decays nonexponentially as shown in the figure. For an intermediate diffusion coefficient 10−7−10−6 cm2/s, the amplitude of the short-time component of the nonexponential decay decreases the larger the value of D, and the decay time of the long-time component becomes shorter. When the diffusion coefficient is rather large (D > 10−5 cm2/s), the population equilibration time is shorter than the reaction rate and the decay rate is exponential. In this case, one can assign a time-independent rate coefficient. The model calculation displayed in Figure 1b, indeed shows that a timeindependent rate coefficient exists only when rapid equilibration occurs in a population distribution. The experimental results of examples of photoinduced processes described in the next section show that rapid equilibration does not exist in many photoinduced reacting systems. Sumi−Marcus Theory. Sumi and Marcus6 extended the Marcus electron-transfer theory to include the effect of both intramolecular-vibrational (q coordinate) and diffusive solventorientational motions (x coordinate) on the rate of electrontransfer reactions. Four limiting cases are considered for the two-electron-state problem: slow reaction, wide and narrow

−V (x)/ k T

B dx ∫ k(x)e ke = = v exp( − ΔG*/kBT ) −V (x)/ kBT dx ∫e

(9)

where v and ΔG* are given by

v = vq(λi /λ)1/2

(10)

and λ is the reorganization energy. λi and λo are the intramolecular and the “outer” contributions to the reorganization energy. ΔG* = (Δλ + ΔG°)2 /4λ

(11)

2. “Wide-Reaction-Window” Limit (λi/λo > 1). The reaction window has a large “width” in x space of (kBTλi/λo)1/2. In this limit the “window” is much wider than the thermal width (kBT)1/2, in x space. In this case, one can approximate the rate constant k(x) by a constant independent of x, which is given by the average of k(x) over the x distribution in V(x), written as ke in eq 9 as C


Feature Article

The Journal of Physical Chemistry A ⎡ (λ + ΔG°)2 ⎤ ⎥ k(x) ≅ ke ≅ vq exp⎢ i ⎣ 4λikBT ⎦

Kramers’ theory11 predicted that the reaction rate would continuously decrease, and asymptotically reach zero, as the friction or viscosity of the environment increased. GHT suggests that the passage of the reaction system over the top of a TS barrier and the role of any opposing environmental forces that induce recrossing should be limited to the very short time scales and space scales in the barrier neighborhood, before stabilization occurs in either the product or the reactant wells. GHT related this time scale to the inverse barrier frequency, which is proportional to the curvature of the barrier, so that the time scale can be very short if the barrier is high. The GHT theory suggests that slow motions of solvent molecules and large space scales should often be completely irrelevant for a solution rate constant. This is a result of SSP flux time correlation function rate constant expression, with the dynamics described not by the Langevin equation used by Kramers, but by the generalized Langevin equation. The end result is that the rate constant is given by its TST value multiplied by a transmission coefficient, κ. GHT provides a selfconsistent equation for κ, depending both on the barrier frequency and on the frequency component of the timedependent friction. The GHT predicts a transmission coefficient κ that is larger than that of Kramer’s theory, and in most cases, its value lies between 0.45 and 1. Thus, TST predicts, quite accurately, the reaction rate coefficient, whereas Kramer’s theory for viscous media fails to predict the reaction rate coefficient. Solvation Dynamics. For a polar solute in a strongly dipolar solvent, the time-dependent interactions between the electrostatic field of the charge distribution of the solute and the dipoles of the surrounding solvent provide the main source of solvation energy and provides the relaxation of an excitedstate transient spectrum. Solvation energy is a key parameter in the Marcus electron-transfer theory. The reorganization energy of an ionic reaction is inversely proportional to the static dielectric constant, εS. Molecular dynamics simulations have shown that the relaxation involved arises primarily from reorientational motions of solvent molecules, 12−17 The dynamics of polar solvation are therefore closely related to the dielectric response of the solvent, which arises from the fluid collective dipole reorientation. Theoretical studies on the effects of dynamic solvation on electronic spectra, began in the 1960s by Bakshiev, Mazurenko, and co-workers.18,19 Experimental work on the dynamics of polar solvation began about two decades later, because short-pulse-laser technology provided the time resolution needed for such measurements only in the 1990s. The method employed involved measuring the time-dependent emission spectrum of a fluorescence probe subsequent to ultrafast laser excitation. The laser-pulse excitation creates a new charge distribution in the solute, and the reequilibration of the solvent is monitored by measuring the time dependence of the emission-band peak position, ν(t). The spectral-response function

(12)

Because the reaction now occurs at each x with the same rate constant k, there should be a single exponential decay of Q(t), with a rate constant, ke, independent of the relaxation time τL of the reorientational fluctuation of the solvent molecules. 3. “Narrow-Reaction-Window” Limit (λi/λo < 1). This limit is just the opposite of the preceding one. In general, the reactant-survival probability Q(t) now displays a multiexponential decay, being composed of terms with different decay rates, which also depend on the relaxation time, τL, of the reorientational fluctuation of the solvent molecules. 4. Nondiffusing Limit. In this limit, the reaction from reactant to product proceeds so rapidly at the initial values of the slow coordinate, x, that the distribution of x is not restored by diffusion in the course of the reaction. Then, the reactant population, p(x;t), decreases independently of its initial value p(x;0) at each x with a rate constant, k(x). Thus, p(x ;t ) = p(x ;0)e−k(x)t

(13)

and Q(t) is given by Q (t ) =

∫ p(x ;0)e−k(x)t dx

(14)

which shows nonexponential decay. In this limit, the decay characteristics of Q(t) no longer depend on the relaxation time, τL, of the x coordinate Grote−Hynes Theory. Hynes and co-workers based the Grote−Hynes theory (GHT) on their stable-state picture (SSP) for reactions.7 Its basic idea was that transition-state theory (TST) focused on a reaction-dividing surface at the TS, usually a barrier top in free energy. However, reactions in fact involve the transition between stable reactants and stable products, which exist near the bottom of free-energy wells, usually far from the TS. Species immediately before and after the TS-dividing surface are not at all like the reactants and products. Although passage through a TS surface is of course necessary for successful reaction, it is more logical to define surfaces located away from the TS. SSP is successful (where other theories may fail) in computing low-barrier reactions.8−10 The SSP concept derives expressions, involving absorbingsurface boundary conditions, that allow definitions of clear fluxtime correlation function of rate constants. Several such ratecoefficient formulas were developed for various reaction types. The most well-known result is the Grote−Hynes theory (GHT) rate coefficient. k = kTST(λr /ω b)

(15)

where λr, the reactive frequency, is given by λr =

ω b2 λr + ζ (̂ λr)/μ

(16)

S(t ) ≡

Equations 15 and 16 are the key results of the GHT. They show that k is determined by λr and that the reactive frequency λr is determined both by the barrier frequency ωb and by the frequency component of the time-dependent friction ζ (̂ λr) =

∫0

∞

dt e

−λ r t

ζ (t )

ν(t ) − ν(∞) ν(0) − ν(∞)

(18)

provides the solvation-energy response that is also investigated in theory and simulation. Maroncelli and co-workers systematically studied the solvation dynamics by focusing on a single probe solute, coumarin 153 (C153).20 Although there is some variation of solvation times with this solute, C153 can be considered

(17)

at the reactive frequency λr. D


Feature Article

The Journal of Physical Chemistry A representative of large polyatomic solutes whose excitation does not involve important changes in specific solute−solvent interactions. The ground state of C153 is polar, with a measured dipole moment of ∼6.5 D. The S0 ↔ S1 transition displaces charge from the amino group to the coumarin ring system, which results in an S1 dipole moment of about 16.0 D, depending on the solvent (with no obvious trend with solvent polarity). Computational-chemistry calculations indicate that there is only a small change in the dipole direction (∼10°) between the two states. In their seminal paper,20 they presented the results of a systematic study of both the static and dynamic aspects of solvation of coumarin 153 in a variety of common roomtemperature solvents. Studies of the steady-state solvatochromism of C 153 show that this molecule provides an excellent probe of the energetics of solvation, uncomplicated by interference from either multiple excited states or specific solute−solvent interactions. On the basis of previous experiments and the interpretations provided by molecular-dynamics simulation and theory, the results of Maroncelli and co-workers provide the dynamics of nonspecific solvation of polyatomic molecules that undergo what is predominantly a dipolar perturbation. For such solutes in highly polar solvents, the observed dynamics can be semiquantitatively predicted from simple theories on the basis of the dielectric response of the pure solvent.

Figure 2. Fluorescence up-conversion signals of all-trans-β-carotene in n-octanol.

S0 → S2 to the S2(1B+u ) state rather than the S1 state. The excited molecule relaxes to the S1(2A−g ) state probably by conical intersection with a time constant of ∼220 fs. Because the S1(2A−g ) → S0 transition is forbidden, it exhibits a weak radiative transition to S0 that carries low oscillator strength. Therefore, the fluorescence of the S1(2A−g ) state is weak and does not contribute much to the total signal measured in the short-wavelength region where the S2 → S0 fluorescence rate is high. Figure 2 shows the fluorescence up-conversion signals, displayed on a semilogarithmic scale, of all-trans-β-carotene in n-octanol measured over the spectral range of 500−560 nm. As seen in the figure, the fluorescence decay is nearly exponential over a dynamic range of about 2 orders of magnitude. The decay time is almost independent of wavelength and τ ≈ 220 fs. The ultrafast decay is almost independent of the solvent used to dissolve the β-carotene. A fit to a single exponential function is also shown in the figure. An exponential decay is convoluted with the fluorescence upconversion system-response function. The ultrafast decay of the S2 excited state of β-carotene shown in Figure 2 and the limited response time of the experimental system prevents us from capturing in full detail the early times τ < 300 fs. We therefore cannot exclude that even this example also deviates from an exponential decay. As we will show in the following experimental results, exponential decay of molecules in the excited state is not the usual result when photochemistry takes place and the reaction takes place over a short time scale, which is the case of an excited-state reaction. Nonexponential Excited-State Proton Transfer (ESPT) in Green Fluorescent Protein. The green fluorescent protein (GFP) is a protein composed of 238 residues. When excited by blue light, it exhibits intense green fluorescence. The GFP has a typical β-barrel structure, consisting of 11 β-sheets with six α helices containing the covalently bonded chromophore 4-(phydroxybenzylidene) imidazolidin-5-one (HBI) located inside the center of the barrel. The GFP is an example of a biological system in which excited-state proton transfer (ESPT) probably plays a functional role in the mechanism of activity.21−25 Scheme 3 shows the chromophore and some amino-acid residues that are involved in the proton shuttle to the primary proton acceptor the glutamate 222. The proton wire consists of a water molecule (W22) and serine 205. Figure 3a shows the time-resolved emission of GFP in aqueous solution measured at 460 nm by the fluorescence upconversion technique over the time range 0−200 ps. The signals are multiplied by exp(t/τF) to compensate for the

■

EXPERIMENTAL SECTION In the studies presented in this article, the fluorescence upconversion technique was employed to measure the timeresolved emission spectra. The laser used for the fluorescence up-conversion was a cavity-dumped Ti:sapphire femtosecond laser (Mira, Coherent), which provides short, 150 fs, pulses at about 800 nm. The cavity dumper operated with a relatively low repetition rate of 800 kHz. The up-conversion system (FOG-100, CDP, Russia) operated at 800 kHz. The samples were excited by pulses of ∼8 mW on average at the 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 fwhm of the signal is 300 fs. Samples were placed in a rotating optical cell to avoid degradation. Measurements of time-correlated single-photon counting (TCSPC) were performed with the use of the same laser as a light source, and in the same setup. The TCSPC detection system was based on a Hamamatsu 3809U photomultiplier and an Edinburgh Instruments TCC 900 computer module for TCSPC. The overall instrument response was approximately 40 ps (fwhm) where the excitation pulse energy was reduced to about 10 pJ by neutral-density filters. The steady-state emission and absorption spectra were recorded by a Horiba Jobin Yvon FluoroMax-3 spectrofluorometer and a Cary 5000 spectrometer.

■

EXPERIMENTAL RESULTS Nonradiative Exponential Decay. As an exceptional case of a photoinduced process that leads to a nearly exponential decay, we show in Figure 2 the fluorescence decay of all-transβ-carotene, excited to the S2 electronic state. β-Carotene belongs to a large family of molecules with a long conjugated hydrocarbon chain. Because of symmetry considerations, the strong optical transition of these molecules is the E


Feature Article


transfers to other solvent molecules. Water is the best solvent for proton-transfer reactions. It can form four hydrogen bonds. Two of them are hydrogen-bond accepting, in which the lonepair electrons of the oxygen atoms of water are involved, and two are donating hydrogen bonds in which the two hydrogen atoms of water form hydrogen bonds with neighboring oxygen atoms of two water molecules. The ESPT rate constant spans a wide range of values. To enable observation of an ESPT process, the slow rate of weak photoacids should be about 1/10 or more of the radiative rate. Because the excited-state lifetime is about 10 ns or less, ESPT observable rates are larger than 107 s−1. In recent years, we studied a new class of very strong photoacids for which we found ESPT rates higher than 1012 s−1. Scheme 4 shows the molecular structures of quinone cyanine 7 (QCy7) and 9 (QCy9), which belong to this group of superphotoacids.28

Scheme 3. Suggested Proton Wires in the wt-GFP

Scheme 4. Molecular Structures of QCy7 and QCy9

radiative lifetime. The signals are displayed on a log−log plot to emphasize the nonexponential fluorescence decay over the short time scale of the first 200 ps of the ROH form of the chromophore. Figure 3b shows the fluorescence decay of the ROH form of the chromophore extended to a longer time, up to 10 ns, measured by the time-correlated single-photoncounting (TCSPC) technique. The full width at half-maximum (fwhm) of the instrument response of the up-conversion technique is shorter by a factor of more than a hundred than that of the TCSPC technique. Even though the TCSPC technique has a much larger dynamic range and much higher sensitivity than the up-conversion technique. As seen in the figure, both panels a and b show a nonexponential fluorescence decay that already starts at the shortest times before 1 ps. On the log−log plot the fluorescence tail decay of the signals is linear. This implies that the fluorescence decay acts according to a power law of t−α and α for short and long times is about 1 at short times and 3/2 at longer times. The power law of about −3/2 is valid in the GFP ROH-fluorescence tail from about 300 ps to about 10 ns, i.e., about 2 orders of magnitude. ESPT in Solution. Photoacids are weak acids in their ground state and much stronger in their first electronic excited state. Usually the photoacids are hydroxyl aryl compounds. 2Naphthol and its derivatives, like 2-naphthol-6,8-disulfonate, are examples of reversible photoacids.26,27 Upon photoexcitation the photoacids transfer a proton to the solvent. The protonated solvent can undergo further successive proton

These photoacids have pKa* values of −6.5 and −8.5 for QCy7 and QCy9, respectively. This is similar to strong mineral acids like HCl. The photoprotolytic cycle of photoacids is shown in Scheme 5. Scheme 5. Photoprotolytic Cycle

Excitation of a photoacid solution of pH lower than its ground-state pKa generates a vibrationally relaxed, electronically excited ROH molecule (denoted by ROH*) that initiates a photoprotolytic cycle. Proton dissociation, with an intrinsic rate constant, kPT, leads to the formation of an ion-pair RO−*··· H3O+ that subsequently forms an unpaired RO−* and a

Figure 3. (a) Fluorescence up-conversion signals of GFP in aqueous solution measured at 460 nm over the time range 0−200 ps. (b) TCSPC measurement of GFP in aqueous solution over the time range 0−10 ns. The signals are multiplied by exp(t/τF), where τF = 3.2 is the radiative rate, and are displayed on a log−log plot. F


Feature Article


Figure 4. Time-resolved emission of QCy7 ROH form on (a) a semilogarithmic plot and (b) a log−log plot.

proton diffusion in water, τHPT2O ∼ 2 ps and thus kPT ′ ∼ 5 × 1011 −1 s . From the above discussion, we estimate for QCy9 that the intrinsic proton-association rate constant, ka ≈ 106 s−1, which is rather small. As we will show in the figures below, the time-resolved emission of the ROH form of both QCy7 and QCy9 are nonexponential, even over the short time window of 1−10 ps. Over this time, and if we bear in mind a rather small intrinsic proton-association constant, the geminate-proton-recombination process should not strongly affect the decay of the ROH* form at short times of t < 5 ps. The experimental results show a rather unexpected large deviation from exponential decay of the ROH form of these two super photoacids. Figure 4a shows the time-resolved emission of the ROH form of QCy7 on a semilogarithmic plot. The fluorescence was acquired by the fluorescence upconversion technique. Figure 4b shows the same data on a log− log plot to emphasize the power-law decay of the long-time fluorescence of the ROH form of QCy7. To account for the finite radiative rate, the fluorescence-decay signal was multiplied by exp(t/τF) where the radiative lifetime in H2O τF = 120 ps, and the exponent α value is 1.4 ± 0.1. This unexpectedly large deviation from exponential decay at such an early time may arise from extensive proton recombination but could also serve as an example of nonexponential kinetics of fast reactions. The main reason for this is that the separation in time scales between the relaxation within the reactant potential well, τs and the reactive time τe, is not fulfilled. QCy9 ESPT. Figure 5 shows, on a semilog scale, the timeresolved fluorescence of the ROH form of QCy9 in D2O.

solvated proton, which diffuses into the bulk of the solvent. The proton and the RO−* may recombine via reversible (adiabatic) recombination with a rate constant of ka and re-form the excited acid, ROH*. In general,26,27,29 back-protonation may also proceed by an irreversible (nonadiabatic) pathway, involving fluorescence quenching of the RO−* by a proton with a rate constant of kq, forming the ground-state ROH. 1Naphthol and its derivatives are known to exhibit considerable fluorescence quenching of the deprotonated form, RO−*, in acidic aqueous solutions. Removal of an ion pair from the contact radius, a, to infinity is described by the transient numerical solution of the Debye− Smoluchowski equation (DSE).30,31 The motion of the transferred proton in water near the photoacid depends strongly on the electrical potential existing between it and the deprotonated form. The diffusion-assisted geminate recombination of the RO−* with the proton can be quantitatively described with the use of the numerical solution of the DSE under the initial and boundary conditions of the photoprotolytic process. In addition, the fluorescence lifetimes of all excited species are considered, with 1/kF = τROH for the acid, and 1/kF′ = τRO− for the conjugate base. Generally, kF′ and kF are much smaller than both the proton-reaction and diffusioncontrolled rate constants. The amplitude of the long-time fluorescence tail of ROH* depends on the intrinsic rate constants, ka and kPT, on the proton-diffusion constant, DH+, and on the electrical potential between RO−* and the proton. The diffusion-assisted proton-geminate-recombination process leads to the repopulation of the ROH* form of a reversible photoacid. The time-resolved fluorescence of the ROH form is bimodal. At short times the fluorescence decay follows the ESPT rate, whereas at longer times the proton-geminaterecombination process repopulates the ROH* and a long-time nonexponential fluorescence tail is formed. The fluorescence tail asymptotically follows a power-law decay, t−α, where α = d/ 2 and d is the diffusion space dimension. For very strong photoacids, the proton-recombination rate is rather small. We wish to evaluate the intrinsic association rate coefficient, ka (Scheme 5). If we ignore the diffusion-assisted formalism, the simple two-step kinetic model leads to Keq =

′ kPT·kPT ka·ka′

(19) 13 −1

For QCy9 pKa* ≈ −8 and Keq ≈ 10 and kPT ≈ 10 s . The proton-diffusion-controlled rate constant in water is 5 × 1010 M−1 s−1 because DH+ ≅ 10−4 cm2/s and the contact radius we assume to be a = 7 Å. kPT ′ can be also estimated from the rate of 8

Figure 5. Time-resolved fluorescence of the ROH form of QCy9 in D2O. G


Feature Article

The Journal of Physical Chemistry A The ESPT rate constant of QCy9 in H2O is 1013 s−1, whereas in D2O it is 5 × 1012 s−1 (τPT ∼ 200 fs). As seen in the figure, the fluorescence decay of the ROH form is nonexponential even at the shortest time scale, much before the protongeminate-recombination process takes place. We therefore conclude that the ESPT rate is nonexponential during the brief time shown in Figure 5. The ESPT rate of QCy9 is much higher than the average solvent-reorientation time, which was found to be ∼0.8 ps as measured by Rosenthal and Fleming.32 We previously suggested that the ESPT process of QCy9 belongs to the adiabatic regime.1,33−35 The expression for an adiabatic rate constant is given by ωQ, q + ≠ H kAD = exp[− (ΔGAD /kBT )] (20) 2π

derived by Rips and Jortner for the electron-transfer reaction.44 They derived a solvent controlled electron-transfer rate coefficient. AD kET = τs−1(ES /16πkT )1/2 exp[−(ΔG° − ES)2 /4ESkT ]

(21)

where τs is the average solvent characteristic time given by the average solvation correlation function ∼⟨S(t)⟩. Because τs−1 is an average of a nonexponential correlation function, one would expect to find nonexponential kinetics in the solvent-control regime. This is indeed the case for the ESPT of NM6HQ+. Parts a and b of Figure 6 show the time-resolved fluorescence signals of the ROH form of the N-methyl-6-hydroxyquinoline (NM6HQ+) photoacid in four alcohols: methanol, ethanol, propanol, and butanol. The fluorescence signals were measured by the fluorescence up-conversion technique. The signals were measured at 470 nm, the ROH steady-state fluorescence band peak. We used a biexponential and three exponential functions to fit the time-resolved emission signals of the ROH form. The fitting parameters are given in Table 1 along with the time constants of the exponents measured by Maroncelli and coworkers, Table 3 of ref 20, that summarizes the solvation dynamics of many common solvents. As seen in Figure 6, the emission signal at short times of up to 25 ps nicely fits the solvent-correlation-function parameters that were deduced by Maroncelli and co-workers for the solvation dynamics of Coumarin 153. At longer times (t ≥ 25 ps), proton geminate recombination takes place and increases the amplitude of the ROH long-time fluorescence tail. The ESPT rate of NM6HQ+ is a good example for showing that the reaction rate is nonexponential. This is so because the separation between time scales does not exist and the passage time, τe, of the reaction (see Introduction) is probably shorter than the fluctuation time, τs, of the reaction coordinate, x(t). Inhomogeneous Kinetics. p-Hydroxybenzylidene dimethylimidazolinone (P-HBDI), shown in Scheme 7, is a model compound of the GFP chromophore. The intense green fluorescence of the deprotonated form of GFP has a quantum yield of ∼0.83 whereas the fluorescence of denaturated GFP is less than 10−3. The low fluorescence quantum yield is also the case for HBDI in nonviscous solvents. Meech and co-workers45−47 found, by ultrafast techniques, that at high temperatures, the nonradiative decay is nonexponential but the rate depends only weakly on the polarity and viscosity of the solvent. This indicates that the ring rotation of the HBDI is not responsible for the internal conversion (IC) process. In a previous work we studied the time-resolved emission of HBDI in its deprotonated form in frozen water/glycerol mixtures at low temperatures48 for which we assume that ring rotation does not take place. Figure 7 shows the time-resolved emission of HBDI in glycerol/water mixtures containing 0.5 mol fraction of glycerol, at several temperatures. The fluorescence was acquired by the TCSPC technique and the plots are on a log−log scale. The fluorescence decay was multiplied by exp(t/τF) to account for the radiative rate (measured at low temperatures of 80 K, τF = 3.2 ns). As seen in the figure, the fluorescence of HBDI is nonexponential at all times and all temperatures. The important point we wish to make is that the viscosity of such mixtures is very large, >106 cP.49,50 We therefore excluded the possibility that ring rotation of HBDI is responsible for the large IC rate in these frozen mixtures.

If the activation energy ΔG≠AD is small, kAD is determined by ωQ,qH+/2π and for QCy9 in H2O it is 1013 s−1. This characteristic frequency, ωQ,qH+, is of the order of the intermolecular vibration found in water, both experimentally by Raman spectroscopy,36 νRaman = 170 cm−1, and by molecular-dynamics simulations.37 We therefore suggest that intermolecular vibration between the OH group of the QCy9 phenol and the oxygen atom of the nearby water molecule assisted the proton-tunneling process, the mechanism by which an ultrafast ESPT process proceeds. A theory explaining this is given by Goldanskii, Trakhtenberg, and Fleuorov38 and by Trakhtenberg et al.39 Solvent-Controlled ESPT Rate. The ESPT rate of strong photoacids (−6 < pKa* < −4) depends on the characteristic time of the solvent τ. The PT rate is limited by the solvent’s orientational motion, which minimizes the dipolar interaction energy of the solvent with the photoacid in both the ground and excited states and is defined by the generalized solvent coordinate, S. Its time dependence is characterized by the solvation correlation function S(t).20 The solvent surrounds both the reactant complex, ROH···OH2, and the product, RO−···H−OH2+. Pérez-Lustres, Kovalenko, Ernsting, and co-workers found, in their study,40 that the ESPT rate of N-methyl-6-hydroxyquinolinium (NM6HQ+), shown in Scheme 6, follows almost exactly the long-time components t > 0.3 ps of the solvation correlation function, S(t), of water, methanol, and ethanol. Scheme 6. Molecular Structure of NM6HQ+

The PT reaction rate is not exponential and follows the complex time dependence of S(t) of the solvent. The S(t) of linear alcohols is nonexponential and could be fitted by a fourexponential function.20 Their results are a good example of the concept that solvent orientational motion controls the high ESPT reaction rate of strong photoacids.40 The solvent reorientation of a dipolar solvent provides a large fraction of the solvent’s reorganization energy, ES, and therefore has a dominant role in the rate-determining step of the protontransfer reaction. This was also predicted for electron transfer41 and later also for the proton-transfer reaction.42,43 The theory explaining the role of the solvent on the rate constant was H


Feature Article


Figure 6. Time resolved fluorescence signals and fitting results of NM6HQ+ in four alcohols: methanol, ethanol, propanol, and butanol: (a) linear time scale up to 100 ps; (b) semilog time scale up to 25 ps.

kinetics occur but the solvent motion is relatively slow. In frozen liquids the solvent translation and rotation and also the intramolecular motion are too slow to participate in the dynamic process and thus influence the photoinduced relaxation of an excited molecule. The inhomogeneous model assumes a single floppy coordinate, x, governing the conformational state of the system. We consider a barrierless crossing to the ground state where the ground-state potential intersects the excited-state potential at its minimum. The Boltzmann equilibrium distribution, which presumably holds for harmonic groundstate potential V0(x) prior to excitation, is given by

Table 1. Fitting Parameters of Time-Resolved Emission of NM6HQ+ to Bi- or Triexponential Decay Functiona,b a2

τ2 (ps)

methanol ethanol propanol

0.05

0.3

butanol

0.25

5.0

a3

τ3 (ps)

a4

τ4 (ps)b

0.35 0.533a 0.35 0.266a 0.35 0.253a 0.45 0.467a

3.2

0.65 0.467a 0.65 0.734a 0.6

15.4

5.0 6.6 42.6

0.3 0.405a

29.6 47.8 133

a

Amplitude values taken from Table 3, ref 20. bLifetime values taken from Table 3 ref 20.

p(x) = Z exp[−V0(x)/kBT ] = Z exp[−(x − x0)2 ]

(22)

Z is the Gaussian normalization constant. This inhomogeneous distribution for the slow (here, frozen) coordinate is thus invariant of both temperature and time. The transitions from S1 to S0 can occur by two photophysical processes. The radiative process is homogeneous, with the same radiative lifetime, τF, for all conformations, whereas the nonradiative process is inhomogeneous. Thus, instead of dealing with a single nonradiative rate constant, knr, each conformation, x, decays back to the ground state with a rate constant, k(x), that depends on x. We assume that k(x) obeys an “energy-gap law”51,52

Scheme 7. Molecular Structure of p-Hydroxybenzylidene Dimethylimidazolinone (p-HBDI)

We used the inhomogeneous-kinetics concept to fit the fluorescence decay of HBDI in the frozen glycerol/water mixtures. The model is the asymptotic limit for which fast

k(x) = A exp( −γ ΔV (x)/kBT )

(23)

Figure 7. Time-resolved emission of HBDI in glycerol/water mixtures containing 0.5 mole fraction of glycerol at several temperatures: (a) on a semilog scale; (b) on a log−log scale. I


Feature Article

The Journal of Physical Chemistry A where A is a preexponential with units of 1/time and γ is a characteristic parameter. In the strong coupling regime ΔV = α1x2, where α1 is the excited state force constant of the parabolic shape potential as a function of x, setting b ≡ α1γ/kBT we derive k(x) = A exp( −bx 2)

Figure 8 shows, on a log−log plot, the nonradiative rate constant, knr, of AuO as a function of η, where η is the solvent

(24)

In the static limit, the fluorescence follows the population probability, P(t), that the excited state has not decayed by time t after excitation is given by p(t ) = exp( −t /τF)

∫0

∞

p(x) exp[−k(x)t ] dx

(25)

The first exponent accounts for the homogeneous radiativedecay process, whereas the integral of the second exponent represents the inhomogeneous nonradiative-decay kinetics, which is nonexponential. The solid lines in Figure 7 are the fit of the data with the use of the inhomogeneous kinetic model presented above. The temperature dependence of the fluorescence decay indeed shows that the parameter b has temperature dependence as the energy gap law predicts (eq 23). A model for nonradiative decay via nonadiabatic curvecrossing (a one-dimensional version of a conical intersection) was suggested by Bagchi, Fleming, and Oxtoby (BFO).53 At the intersection of the potential curves V1(x) and V0(x) and only there, rapid IC occurs. It is therefore described by a deltafunction “sink term”, short-range Gaussian, or Lorentzian shape sinks. After excitation to S1, the distribution p(x) has to diffuse to the intersection point to decay back to the ground state. This suggests that at low viscosities the decay should begin with a delay, which has not been observed experimentally. In highly viscous solvents no IC should occur, because the distribution cannot diffuse to the intersection point. This expectation contradicts the experimental observation54 of fast (nanosecond) multiexponential IC even in viscous solvents. Nonexponential Nonradiative Decay of Excited Molecular Rotors. The class of molecules that are named “molecular rotors” consists of molecules that have two aromatic or heterocyclic rings bridged by a central carbon atom or atoms chemically bonded to the two rings. This class of molecules is nearly nonfluorescent in low-viscosity solvents; however, when adsorbed on a surface, they are highly fluorescent and therefore serve as probe molecules for amyloid fibrils. The high sensitivity of the fluorescence quantum yield to the solvent viscosity is attributed to ring rotation that takes place in the excited state. When the twist angle between the aromatic rings is at 90°, the character of the excited state is that of a nonfluorescent chargetransfer state. In this subsection, we deal with two molecular rotors, thioflavin-T (ThT) and auramine O (AuO) shown in Scheme 8.

Figure 8. knr of auramine O versus the solvent viscosity on a log−log plot.

viscosity. The plot shows the linear dependence of the logarithm of knr as a function of the logarithm of solvent viscosity. knr is deduced from the inverse of the average fluorescence lifetime, τav−1, measured at the wavelength of the peak of the steady-state emission spectrum for the six solvents listed in the figure. The viscosities range from the nonviscous solvent acetonitrile (ACN), η = 0.375 cP, to the viscous solvent pentanol, η = 3.5 cP, and the slope is −1.1. The nonradiative rate for ACN is 2 × 1012 s−1 whereas for pentanol it is ∼1.1 × 1011 s−1. Quantum calculations of the excited-state potential as a function of the ring rotation show a parabolic well with a minimum at a twist angle of 90°, whereas the ground-state potential shows a double minimum and the minima are at angles of about 30° and 210°. A simple hydrodynamic friction model with a driving potential of 0.1 eV for 90° rotation of an aniline group predicts a rotation time of about 1 ps for 1 cP viscosity.55 This time scale is indeed observed for the average fluorescence lifetime of both ThT and AuO in ethanol (η = 1.1 cP). Figure 9 shows the normalized time-resolved emission of ThT measured at several wavelengths in three solvents. As seen in the figure, the fluorescence decay is nonexponential at all wavelengths and in all solvents. The shorter the wavelength the faster the average decay time. Modeling the Molecular-Rotor Nonradiative Rate. The model was first introduced by Glasbeek and co-workers for the nonradiative processes of auramine O.56,57 Auramine O, like ThT, has a nearly viscosity-dependent fluorescence quantum yield in many solvents. In this model, the first molecular electronically excited singlet state is expressed as a mixture of two separate states, an emissive (F) state and a dark (D) state. Following a short excitation pulse, the initial population distribution resides at short times after excitation in the F state and then diffuses by torsional motion of the two rings toward the D state at which the ring twist is at 90°. The two diabatic states, F and D, are adiabatically coupled as a function of the normalized twist coordinate z: 1 1 S1(z) = |F(z) + D(z)| − |F(z) + D(z)|2 + 4C 2 2 2

Scheme 8. Molecular Structure of Thioflavin-T (ThT) and Auramine O

(26)

and the time-dependent fluorescence Ifl(ν,t), at time t and frequency ν exhibits the following proportionality: J


Feature Article


Figure 9. Time-resolved emission of ThT over the wavelength range of 460−600 nm in (a) water, (b) propanol, and (c) acetonitrile.

Ifl(v ,t ) ∝

∫ dz {g(ν0(z),ν−ν0(z))|M(z)|2 p(z ,t )ν3}

Nonexponential Intramolecular Electron Transfer. FAD is an active electron carrier that serves as a prosthetic group in many Flavo-enzymes (Scheme 9).

(27)

where 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 and ground states and |M(z)|2 is the transition dipole moment that strongly depends on z. The population p(z,t) was obtained by solving the Debye− Smoluchowski equation (an equation similar to eq 26, but without the reactive term (third term) on the right-hand side). The Glasbeek model was also used by Meech and coworkers58 to quantify the torsional dynamics of auramine O. The change in the transition dipole moment of ThT as a function of the twist angle, z, was studied by quantummolecular calculations, while taking into account the solvent effect by a conductor-like screening model,59−63 where it was shown that the S1 → S0 transition dipole moment decreases by a factor of ∼100 as a function of the C−C dihedral angle. The time-dependent excited-state population p(z,t) appearing in eq 27 could be evaluated with the use of the Debye− Smoluchowski equation because the excited-state-potential curve as a function of z, the normalized twist angle, is known. The fitting results for ThT are shown in ref 55. The results are satisfactory only at longer times (t > 0.5 ps). The rate constant of the short-time fluorescence decay is greater than at longer times and must be treated separately. To summarize, the fluorescence decay of molecular rotors is another example of nonexponential decay arising from two excited states coupled by intramolecular ring rotation.

Scheme 9. FAD Molecular Structure

The chromophore moiety, the isoalloxazine ring of the FAD, is highly fluorescing in simple flavin compounds (riboflavin, FMN and lumiflavin), but in FAD its quantum yield is low,64 as a result of electron transfer from the adenine ring to the excited isoalloxazine moiety65 that causes fluorescence quenching of the excited state. In solution, the FAD assumes both open and folded conformations. In the folded state, the adenine base is close to the excited isoalloxazine ring with subsequent quenching of the excited state. Visser and co-workers66−68 K


Feature Article

The Journal of Physical Chemistry A have shown, by time-resolved fluorescence and molecular dynamics, that the folding of the open state into the closed configuration is responsible for the fast (τ ∼ 9 ps) decay of the excited open configuration of the FAD. Direct measurements of the vibrational spectroscopy of the excited FAD molecule, carried out by Kondo et al.,69 showed that the excited FAD molecule can relax directly to the ground state with a time constant, τ ∼ 15 ps. FAD in water prefers a folded structure that is stabilized by van der Waals interactions between the two heteroaromatic structures. The proximity of the adenine to the excited fluorophore leads to rapid quenching of the excited state by the electron-transfer process. Figure 10 shows the time-resolved emission of FAD, measured by the fluorescence up-conversion technique in

between the COMs of adenine and isoalloxazine is x, D is the one-dimensional diffusion coefficient describing the relative motion of the COMs one with respect to the other, V is the attracting potential well that restricts their motion, and k(x) is the rate constant of the electron-transfer-coupled quenching of the excited state of isoalloxazine. To reproduce the observed fluorescence-relaxation dynamics, one needs to determine the spatial distribution of the COMs and the dynamics of their motion. The simulation of the molecular dynamics generates a trajectory that provides the temporal fluctuations of the distance between COMs, from which one derives the shape of the potential well that regulates the motion of the COMs and the relative diffusivity along the distance axis.70 These two parameters are then introduced in the Agmon−Hopfield equation. Integration of eq 6 along the x coordinate provides the time-resolved emission signal, p(t). The variation of the distance between COMs was analyzed as a one-dimensional diffusion.70 Over the time window of 0.5−8 ps, the distance between the electron donor and acceptor has a constant slope that corresponds to D = 3 × 10−6 cm2 s−1. Over longer time intervals, the slope of the curve decreases and becomes independent of time at t > 50 ps. The structural fluctuation of the COMs, as analyzed for FAD in 10% methanol, yielded a larger diffusion coefficient of 4 × 10−6 cm2 s−1. Figure 10 shows the fit of the time-resolved fluorescence of FAD, with the use of the Agmon−Hopfield equation and the diffusion coefficients extracted from the molecular dynamic simulation. The average distance between the two ring systems is ∼4 Å. As seen from the figure, the fit is rather good and thus nonexponential kinetics are explained by population distribution and their adjustment as a function of time by diffusional motion.

Figure 10. Reconstruction of the midtime relaxation of FAD emission in water and in 10% methanol/water solution.

neat water and in a water-rich water/methanol mixture of 10% methanol by volume. The signal decay is bimodal. The first component is a short, nonexponential decay term with an amplitude of ∼0.8 attributed to the folded configuration. The second is a slow exponential decay with a radiative lifetime of ∼4.7 ns arising from the open configuration where electron transfer does not take place. We used the Agmon−Hopfield model4 described below to fit the short-time main component of the time-resolved emission of FAD shown in Figure 10. The long-decay-time component is assigned to the conformer. Modeling the ET Process in FAD. The model assumes that the rate of nonadiabatic electron transfer is an exponential function of the distance between the donor and acceptor.1 Equation 28 shows the connection between the rate constant (ket) and the separation between the donor and acceptor. The term (x − x0) is the deviation of the distance between the center of mass (COM) of the isoalloxazine from that of the adenine, (x), from its average value (x0). ket = k 0 exp[−β(x − x0)]

■

DISCUSSION Hierarchy of Time Scales of Fast Photoinduced Processes. After a molecule is photoexcited from the ground state to a higher electronic excited Franck−Condon state, several relaxation processes occur and these processes occur over different time scales. We list below the important and relevant processes that occur in the liquid phase. All these processes may affect the rate of a photoinduced reaction. Some of them may lead to nonexponential kinetics of a photoinduced reaction and thus are more relevant to the topic of this overview article. Relaxation Processes in Photoexcited Molecules. 1. Coherent Dephasing of Electronic and Vibrational Quantum States. The coherent dephasing of the ground and excited electronic states of large molecules in the condensed phase is rather rapid. It is estimated that the dephasing time is of the order of 20 fs. In this article we deal with nonexponential kinetics with smaller rates ≤1013 s−1 and thus the rapid electronic dephasing time does not affect these processes. The dephasing time of the wave packet of nuclear quantum states may take much longer and can be longer than 100 fs and thus may affect the rapid proton transfer of QCy9 in water (kPT ≈ 1013 s−1). 2. Intramolecular-Vibration Redistribution. When the photon energy is greater than the electronic energy gap between the ground and excited states, the excess energy excites vibrational state(s). If the excess photon energy is much greater than the energy gap (S0(0) → S1(0)), higher-energy vibrational

(28)

where k0 is the ET rate at the at the average distance, x0. Accordingly, the overall dynamics of the electron transfer, and the fluorescence relaxation dynamics, are a function of the distance distribution of the population and the diffusion coefficient between the various FAD configurations. The Agmon−Hopfield equation4 (eq 6) provides the time dependence of the FAD population, p(x,t). Both the relative diffusion motion of the isoalloxazine with respect to the adenine and the distance-dependent electron-transfer reaction, denoted by k(x) govern the change in the excited-state population. In the present case, the function p represents the probability of finding an excited FAD molecule, where the distance L


Feature Article


Plausible Origins of Nonexponential Kinetics. 1. LowBarrier Conditions. For a reaction with a rather low reactionenergy barrier separating the two potential wells, that of the reactant and that of the product, the energy fluctuation of the reactant may lead to a reaction on the time scale of τs, the characteristic time of the solute−solvent interaction. Because τs does not represent a true exponential decay time, but is an average of a broad spectrum of times, it is also expected that the reaction rate itself will show deviation from the exponential decay law. 2. Inseparable Equilibration Time τs and the Reactive Time. In the liquid phase, the solvent maintains all three degrees of molecular freedom, i.e., translation, rotation, and intra- and intermolecular vibrations. The solute−solvent interactions occur over a much longer time scale than the impact interactions of collisions in a dilute gas phase. These long-time interactions may lead to anomalous conditions in which τs and τe are not well separated, where τs includes all the characteristic times that lead to energy fluctuations of the reactant and τe is the characteristic time taken by the activated reactant to cross the barrier region and reach the potential well of the product. In fact, ultrafast electron- and proton-transfer reactions reach a rate that is controlled by the solvent−solute fluctuation times. This limit of reaction rate is termed the solvent control rate limit (eq 9). The characteristic time, τs, appears in the preexponential term and for very low activation energies it determines the reaction-rate coefficient. We contend in this article that τs exhibits rather nonexponential behavior and not true exponential decay in many cases in the liquid phase. If one assumes that a chemical reaction involves the active participation of the solvent, as in photoinduced electron or proton transfer to the solvent, then one should expect that some of the longer time solvent motions would strongly influence the energy landscape of reaction and the prerequisite time separation, τs ≪ τe, for an exponential reaction rate might not be fulfilled. In such a case, the decay of the reactant population, p(x,t), may not follow an exponential path and so an exponential rate coefficient cannot be determined from the decay of the reactant. 2. Recrossing. The recrossing of the activated product, P† (with excess energy), over the barrier (Scheme 2) to re-form an activated reactant, R†, is often neglected in theories of chemical reaction and also in the determination of the rate coefficient. In this article, we showed the results of a common excited-state proton-transfer-to-solvent reaction. In this type of reaction the excited state RO−* (product P) recombines with a proton in solution to re-form the excited state ROH* (reactant R). The geminate-recombination process is efficient and in some cases, all excited-state product molecules RO−* recombine with a proton within the lifetime of the excited state by a diffusionassisted reaction mechanism that leads to long-time nonexponential power-law (t−α) decay of the survival probability of the ROH* (reactant). By analogy, the neglected recrossing process at the barrier region may be efficient and should not be neglected in theories of chemical rate coefficients for ultrafast reactions. If the recrossing process occurs by a diffusion-assisted mechanism, the reactant-survival-probability decay is nonexponential, in a similar way as in the ESPT experiments. Loss of the excess energy of the activated product P† should also lead to product recrossing with a distribution of rates kr(E).

modes may be excited and the molecular system tends to redistribute the vibrational energy to excite the lower-energy modes of the molecule. This redistribution process is quite brief, and the relaxation time is about 100 fs. Thus, it will not affect the signal decay when the reaction kinetics is slower than k < 1012 s−1. 3. Intermolecular-Vibration Relaxation. In the liquid phase, this process is relatively slow, slower than the above processes. “Hot” molecules with excess vibrational energy (Eν > kBT) usually relax in a few picoseconds and this relaxation may take place for even longer times of about ten picoseconds. Thus, the reaction-rate coefficient of ultrafast photoinduced processes may be time dependent, because at t = 0 the molecule is hot and the reaction rate may depend on the excess vibrational energy. 4. Intramolecular Charge Rearrangement. Fayer and coworkers71 reported on slow charge rearrangement of several hydroxypyrene derivatives. The commonly used photoacid 8hydroxy-1,3,6-pyrenetrisulfonate (HPTS) shows a slow charge rearrangement of about 3 ps. They did not explain the mechanism of such slow charge rearrangement, but it is plausible that solute−solvent interaction in which a solute− solvent hydrogen bond is formed or solvation takes place, can promote slow charge rearrangements of the photoexcited molecule. 5. Solvation Dynamics. Solvation dynamics are observed when a ground-state molecule is electronically excited by a short laser pulse to a nonequilibrium solute−solvent configuration that places the initial population at a nonequilibrium position on the excited-state-potential curve. The nonequilibrium excited solute−solvent interaction leads the system to respond and the system reaches the minimum potential configuration at later times. The solvent correlation function S(t) (given in eq 18) describes this relaxation process. It is obtained by observing the fluorescence-band position as a function of time. It was found by Maroncelli and co-workers72 that for associative liquids, S(t) decays nonexponentially and could be fitted by a four-exponential function. The time window for S(t) decay is from about 100 fs to several tens of picoseconds for pentanol and other longer-chain linear alcohols. Solute−solvent interaction after photoexcitation leads to solvent reorganization to minimize these interactions. The main interactions are dipole−dipole and the making and breaking of hydrogen bonds. The hydrogen-bond processes occur over a time scale of 1−3 ps. Upon excitation, hydrogen bonds can strengthen or weaken, and these processes occur probably within 1 ps. In polar solvents, the dipolar solute−solvent interactions are very important in the stabilization of molecules in the excited state. Acetonitrile is a nonassociative solvent with a large dipole moment (μ = 3.92 D) and low viscosity. The dipolar reorganization energy in dipolar solvents is high, ∼0.3 eV for a large excited dipolar molecule with a dipole moment of μ ≈ 20 D. The average solvation time for acetonitrile is about 0.5 ps. For associative solvents like alcohols, the solvation dynamics occur over a much longer time window, from about 50 fs to a few tens of picoseconds in long-chain alcohols. The dielectric relaxation times, τD,, of pentanol and hexanol at room temperature are rather long (250 and 350 ps, respectively). Maroncelli and co-workers20 found that the solvation-dynamics reorganization time of model dye compounds like coumarin 153 is shorter by a factor of 5−10 than τD. M


Feature Article


(3) Smoluchowski, M. Brownian Molecular Movement Under the Action of External Forces and its Connection with the Generalized Diffusion Equation. Ann. Phys. (Leipzig) 1915, 48, 1103−1112. (4) Agmon, N.; Hopfield, J. Transient Kinetics of Chemical Reactions with Bounded Diffusion Perpendicular to the Reaction Coordinate: Intramolecular Processes with Slow Conformational Changes. J. Chem. Phys. 1983, 78, 6947−6959. (5) Krissinel’, E. B.; Agmon, N. Spherical Symmetric Diffusion Problem. J. Comput. Chem. 1996, 17, 1085−1098. (6) Sumi, H.; Marcus, R. Dynamical Effects in Electron Transfer Reactions. J. Chem. Phys. 1986, 84, 4894−4914. (7) Northrup, S. H.; Hynes, J. T. The Stable States Picture of Chemical Reactions. I. Formulation for Rate Constants and Initial Condition Effects. J. Chem. Phys. 1980, 73, 2700−2714. (8) Laage, D.; Hynes, J. T. On the Residence Time for Water in a Solute Hydration Shell: Application to Aqueous Halide Solutions. J. Phys. Chem. B 2008, 112, 7697−7701. (9) Laage, D.; Hynes, J. T. A Molecular Jump Mechanism of Water Reorientation. Science 2006, 311, 832−835. (10) Laage, D.; Hynes, J. T. On the Molecular Mechanism of Water Reorientation. J. Phys. Chem. B 2008, 112, 14230−14242. (11) Kramers, H. A. Brownian Motion in a Field of Force and the Diffusion Model of Chemical Reactions. Physica 1940, 7, 284−304. (12) Ladanyi, B. M.; Stratt, R. M. Short-Time Dynamics of Solvation: Relationship between Polar and Nonpolar Solvation. J. Phys. Chem. 1996, 100, 1266−1282. (13) Neria, E.; Nitzan, A. Simulations of Solvation Dynamics in Simple Polar Solvents. J. Chem. Phys. 1992, 96, 5433−5440. (14) Perera, L.; Berkowitz, M. L. Ultrafast Solvation Dynamics in a Stockmayer Fluid. J. Chem. Phys. 1992, 97, 5253−5254. (15) Muiño, P. L.; Callis, P. R. Hybrid Simulations of Solvation Effects on Electronic Spectra: Indoles in Water. J. Chem. Phys. 1994, 100, 4093−4109. (16) Kumar, P.; Maroncelli, M. Polar Solvation Dynamics of Polyatomic Solutes: Simulation Studies in Acetonitrile and Methanol. J. Chem. Phys. 1995, 103, 3038−3060. (17) Ladanyi, B. M.; Stratt, R. M. Short-Time Dynamics of Solvation: Linear Solvation Theory for Polar Solvents. J. Phys. Chem. 1995, 99, 2502−2511. (18) Mazurenko, Y. T.; Bakhshiev, N. Effect of Orientation Dipole Relaxation on Spectral, Time, and Polarization Characteristics of the Luminescence of Solutions. Opt. Spectrosc. 1970, 26, 490−494. (19) Bakshiev, N. Universal Intermolecular Interactions and their Effect on the Position of the Electronic Spectra of Molecules in Two Component Solutions. Opt. Spektrosk. 1964, 16, 821−832. (20) Horng, M.; Gardecki, J.; Papazyan, A.; Maroncelli, M. Subpicosecond Measurements of Polar Solvation Dynamics: Coumarin 153 Revisited. J. Phys. Chem. 1995, 99, 17311−17337. (21) Shu, X.; Leiderman, P.; Gepshtein, R.; Smith, N. R.; Kallio, K.; Huppert, D.; Remington, S. J. An Alternative Excited-State Proton Transfer Pathway in Green Fluorescent Protein Variant S205V. Protein Sci. 2007, 16, 2703−2710. (22) Tsien, R. Y. The Green Fluorescent Protein. Annu. Rev. Biochem. 1998, 67, 509−544. (23) Zimmer, M. Green Fluorescent Protein (GFP): Applications, Structure, and Related Photophysical Behavior. Chem. Rev. 2002, 102, 759−782. (24) Seward, H. E.; Bagshaw, C. R. The Photochemistry of Fluorescent Proteins: Implications for their Biological Applications. Chem. Soc. Rev. 2009, 38, 2842−2851. (25) Kennis, J. T.; Larsen, D. S.; van Stokkum, I. H.; Vengris, M.; van Thor, J. J.; van Grondelle, R. Uncovering the Hidden Ground State of Green Fluorescent Protein. Proc. Natl. Acad. Sci. U. S. A. 2004, 101, 17988−17993. (26) Pines, E.; Huppert, D.; Agmon, N. Geminate Recombination in excited-state proton-transfer Reactions: Numerical Solution of the Debye−Smoluchowski Equation with Backreaction and Comparison with Experimental Results. J. Chem. Phys. 1988, 88, 5620−5630.

3. Nonequilibrium Reactant Population Due to Photoexcitation. Photoexcitation of a reactant in the condensed phase leads to a Franck−Condon nonequilibrium state. The population at t = 0 after excitation undergoes various ultrafast relaxation processes that bring the excited molecule to a relaxed configuration. The slowest process is the transfer of excess energy to the surrounding solvent molecules. This process may take about 10 ps. Solvation dynamics is also a slow process in associative liquids that span short (femtoseconds) and long (tens of picoseconds) times. All of these relaxation processes may affect a fast photoinduced reaction rate and lead to nonexponential decay of the reactant-survival probability.

■

SUMMARY In the current article we focused on the nonexponential decay of many photoinduced reactions. These reactions seem not to obey the common textbook simple first-order kinetic rate law. We show several experimental examples that exhibit nonexponential kinetics of photoinduced processes. We provide semiquantitative models to explain the complex and nonexponential decay of the excited-state population. In the Discussion we address the issue of why ultrafast photoinduced reactions may not follow simple first-order rate equations.

■

AUTHOR INFORMATION

Corresponding Author

*Dan Huppert. E-mail: [email protected]. Phone: 972-36407012. Fax: 972-3-6407491. Notes

The authors declare no competing financial interest. Biographies Ron Simkovitch received a B.Sc. and M.Sc. in chemistry from the Tel Aviv University. He continues his studies under Prof Huppert as a Ph.D. student, focusing on excited-state proton transfer reactions in solutions, in a continuation of his studies as a M.Sc. student on super photoacids. Rinat Gepshtein received a B.Sc. and a Ph.D. (2008) in chemistry from the Tel Aviv University and studied the proton transfer reaction in the green fluorescent protein (GFP). She continues working under Prof. Huppert as an assistant. Dan Huppert received a B.Sc. and a Ph.D. (1974) in Chemistry from the Tel Aviv University and was a postdoctoral fellow at Bell Laboratories. Since 1977, he has been a faculty member of the Tel Aviv University, where he employs ultrafast spectroscopy to study excited state proton transfer reactions in solutions and in GFP proteins.

■

ACKNOWLEDGMENTS We thank professors Elli Pollak, Abraham Nitzan, Noam Agmon, Ehud Pines, and Menahem Gutman for many helpful discussions and for their contribution to this article. This work was supported by grants from the James-Franck German-Israeli Program in Laser-Matter Interaction, by the Israel Science Foundation, and by the United States-Israel Binational Science Foundation.

■

REFERENCES

(1) Nitzan, A. In Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems; Oxford University Press: New York, 2006. (2) Hänggi, P.; Talkner, P.; Borkovec, M. Reaction-Rate Theory: Fifty Years After Kramers. Rev. Mod. Phys. 1990, 62, 251−342. N


Feature Article

The Journal of Physical Chemistry A (27) Agmon, N.; Pines, E.; Huppert, D. Geminate Recombination in Proton-Transfer Reactions. II. Comparison of Diffusional and Kinetic Schemes. J. Chem. Phys. 1988, 88, 5631−5638. (28) Simkovitch, R.; Shomer, S.; Gepshtein, R.; Huppert, D. How Fast can a Proton-Transfer Reaction be Beyond the Solvent-Control Limit? J. Phys. Chem. B 2015, DOI: 10.1021/jp506011e. (29) Agmon, N. Elementary Steps in Excited-State Proton Transfer. J. Phys. Chem. A 2005, 109, 13−35. (30) Debye, P. Reaction Rates in Ionic Solutions. Trans. Electrochem. Soc. 1942, 82, 265−272. (31) Collins, F. C.; Kimball, G. E. Diffusion-Controlled Reaction Rates. J. Colloid Sci. 1949, 4, 425−437. (32) Vajda, Š.; Jimenez, R.; Rosenthal, S. J.; Fidler, V.; Fleming, G. R.; Castner, E. W. Femtosecond to Nanosecond Solvation Dynamics in Pure Water and Inside the γ-Cyclodextrin Cavity. J. Chem. Soc., Faraday Trans. 1995, 91, 867−873. (33) Borgis, D.; Hynes, J. T. Curve Crossing Formulation for Proton Transfer Reactions in Solution. J. Phys. Chem. 1996, 100, 1118−1128. (34) Kiefer, P. M.; Hynes, J. T. Nonlinear Free Energy Relations for Adiabatic Proton Transfer Reactions in a Polar Environment. I. Fixed Proton Donor-Acceptor Separation. J. Phys. Chem. A 2002, 106, 1834−1849. (35) Kiefer, P. M.; Hynes, J. T. Nonlinear Free Energy Relations for Adiabatic Proton Transfer Reactions in a Polar Environment. II. Inclusion of the Hydrogen Bond Vibration. J. Phys. Chem. A 2002, 106, 1850−1861. (36) Walrafen, G. E. Raman Spectral Studies of the Effects of Temperature on Water Structure. J. Chem. Phys. 1967, 47, 114−126. (37) Simkovitch, R.; Huppert, A.; Huppert, D.; Remington, S. J.; Miller, Y. Proton Transfer in Wild-Type GFP and S205V Mutant is Reduced by Conformational Changes of Residues in the Proton Wire. J. Phys. Chem. B 2013, 117, 11921−11931. (38) Gol’danskii, V. I.; Trakhtenberg, L. I.; Fleurov, V. N. In Tunneling phenomena in chemical physics; CRC Press: Boca Raton, FL, 1988. (39) Trakhtenberg, L.; Klochikhin, V. Effect of Pressure and Temperature on the H-Atom Tunneling in Solid Phase Chemical Reactions. The Acridine/Fluorene System. Chem. Phys. 1998, 232, 175−187. (40) Pérez-Lustres, J.; Rodriguez-Prieto, F.; Mosquera, M.; Senyushkina, T.; Ernsting, N.; Kovalenko, S. Ultrafast Proton Transfer to Solvent: Molecularity and Intermediates from Solvation-and Diffusion-Controlled Regimes. J. Am. Chem. Soc. 2007, 129, 5408− 5418. (41) Kosower, E. M.; Huppert, D. Solvent Motion Controls the Rate of Intramolecular Electron Transfer in Solution. Chem. Phys. Lett. 1983, 96, 433−435. (42) Carmeli, I.; Huppert, D.; Tolbert, L. M.; Haubrich, J. E. Ultrafast Excited-State Proton Transfer From Dicyano-naphthol. Chem. Phys. Lett. 1996, 260 (1), 109−114. (43) Cohen, B.; Huppert, D. Unusual Temperature Dependence of Excited State Proton Transfer Rates in Alcohols. J. Phys. Chem. A 2000, 104, 2663−2667. (44) Rips, I.; Jortner, J. Dynamic Solvent Effects on outer-sphere Electron Transfer. J. Chem. Phys. 1987, 87, 2090−2104. (45) Webber, N. M.; Litvinenko, K. L.; Meech, S. R. Radiationless Relaxation in a Synthetic Analogue of the Green Fluorescent Protein Chromophore. J. Phys. Chem. B 2001, 105, 8036−8039. (46) Litvinenko, K. L.; Webber, N. M.; Meech, S. R. Internal Conversion in the Chromophore of the Green Fluorescent Protein: Temperature Dependence and Isoviscosity Analysis. J. Phys. Chem. A 2003, 107, 2616−2623. (47) Mandal, D.; Tahara, T.; Meech, S. R. Excited-State Dynamics in the Green Fluorescent Protein Chromophore. J. Phys. Chem. B 2004, 108, 1102−1108. (48) Stavrov, S. S.; Solntsev, K. M.; Tolbert, L. M.; Huppert, D. Probing the Decay Coordinate of the Green Fluorescent Protein: Arrest of Cis-Trans Isomerization by the Protein significantly Narrows the Fluorescence Spectra. J. Am. Chem. Soc. 2006, 128, 1540−1546.

(49) Puzenko, A.; Hayashi, Y.; Ryabov, Y. E.; Balin, I.; Feldman, Y.; Kaatze, U.; Behrends, R. Relaxation Dynamics in Glycerol-Water Mixtures: I. Glycerol-Rich Mixtures. J. Phys. Chem. B 2005, 109, 6031− 6035. (50) Hayashi, Y.; Puzenko, A.; Balin, I.; Ryabov, Y. E.; Feldman, Y. Relaxation Dynamics in Glycerol-Water Mixtures. 2. Mesoscopic Feature in Water Rich Mixtures. J. Phys. Chem. B 2005, 109, 9174− 9177. (51) Siebrand, W. Radiationless Transitions in Polyatomic Molecules. I. Calculation of FranckCondon Factors. J. Chem. Phys. 1967, 46, 440−447. (52) Englman, R.; Jortner, J. The Energy Gap Law for Radiationless Transitions in Large Molecules. Mol. Phys. 1970, 18, 145−164. (53) Bagchi, B.; Fleming, G. R.; Oxtoby, D. W. Theory of Electronic Relaxation in Solution in the Absence of an Activation Barrier. J. Chem. Phys. 1983, 78, 7375−7385. (54) Kummer, A. D.; Kompa, C.; Niwa, H.; Hirano, T.; Kojima, S.; Michel-Beyerle, M. E. Viscosity-Dependent Fluorescence Decay of the GFP Chromophore in Solution due to Fast Internal Conversion. J. Phys. Chem. B 2002, 106, 7554−7559. (55) Amdursky, N.; Erez, Y.; Huppert, D. Molecular Rotors: What Lies Behind the High Sensitivity of the Thioflavin-T Fluorescent Marker. Acc. Chem. Res. 2012, 45, 1548−1557. (56) Van der Meer, M.; Zhang, H.; Glasbeek, M. Femtosecond Fluorescence Upconversion Studies of Barrierless Bond Twisting of Auramine in Solution. J. Chem. Phys. 2000, 112, 2878. (57) Glasbeek, M.; Zhang, H. Femtosecond Studies of Solvation and Intramolecular Configurational Dynamics of Fluorophores in Liquid Solution. Chem. Rev. 2004, 104, 1929−1954. (58) Heisler, I. A.; Kondo, M.; Meech, S. R. Reactive Dynamics in Confined Liquids: Ultrafast Torsional Dynamics of Auramine O in Nanoconfined Water in Aerosol OT Reverse Micelles. J. Phys. Chem. B 2009, 113, 1623−1631. (59) Stsiapura, V. I.; Maskevich, A. A.; Kuzmitsky, V. A.; Uversky, V. N.; Kuznetsova, I. M.; Turoverov, K. K. Thioflavin T as a Molecular Rotor: Fluorescent Properties of Thioflavin T in Solvents with Different Viscosity. J. Phys. Chem. B 2008, 112, 15893−15902. (60) Singh, P. K.; Kumbhakar, M.; Pal, H.; Nath, S. Viscosity Effect on the Ultrafast Bond Twisting Dynamics in an Amyloid Fibril Sensor: Thioflavin-T. J. Phys. Chem. B 2010, 114, 5920−5927. (61) Singh, P. K.; Kumbhakar, M.; Pal, H.; Nath, S. Ultrafast Bond Twisting Dynamics in Amyloid Fibril Sensor. J. Phys. Chem. B 2010, 114, 2541−2546. (62) Stsiapura, V. I.; Maskevich, A. A.; Kuzmitsky, V. A.; Turoverov, K. K.; Kuznetsova, I. M. Computational Study of Thioflavin T Torsional Relaxation in the Excited State. J. Phys. Chem. A 2007, 111, 4829−4835. (63) Erez, Y.; Liu, Y.; Amdursky, N.; Huppert, D. Modeling the Nonradiative Decay Rate of Electronically Excited Thioflavin T. J. Phys. Chem. A 2011, 115, 8479−8487. (64) Weber, G. Fluorescence of Riboflavin and Flavin-Adenine Dinucleotide. Biochem. J. 1950, 47, 114−121. (65) van den Berg, Petra A. W.; Feenstra, K. A.; Mark, A. E.; Berendsen, H. J.; Visser, A. J. Dynamic Conformations of Flavin Adenine Dinucleotide: Simulated Molecular Dynamics of the Flavin Cofactor Related to the Time-Resolved Fluorescence Characteristics. J. Phys. Chem. B 2002, 106, 8858−8869. (66) van den Berg, Petra A. W.; van Hoek, A.; Walentas, C. D.; Perham, R. N.; Visser, A. J. Flavin Fluorescence Dynamics and Photoinduced Electron Transfer in Escherichia coli Glutathione Reductase. Biophys. J. 1998, 74, 2046−2058. (67) van den Berg, Petra A. W.; Widengren, J.; Hink, M. A.; Rigler, R.; Visser, A. J. Fluorescence Correlation Spectroscopy of Flavins and Flavoenzymes: Photochemical and Photophysical Aspects. Spectrochim. Acta, Part A 2001, 57, 2135−2144. (68) Chosrowjan, H.; Taniguchi, S.; Mataga, N.; Tanaka, F.; Visser, A. J. The Stacked Flavin Adenine Dinucleotide Conformation in Water is Fluorescent on Picosecond Timescale. Chem. Phys. Lett. 2003, 378, 354−358. O


Feature Article

The Journal of Physical Chemistry A (69) Kondo, M.; Nappa, J.; Ronayne, K. L.; Stelling, A. L.; Tonge, P. J.; Meech, S. R. Ultrafast Vibrational Spectroscopy of the Flavin Chromophore. J. Phys. Chem. B 2006, 110, 20107−20110. (70) Radoszkowicz, L.; Presiado, I.; Erez, Y.; Nachliel, E.; Huppert, D.; Gutman, M. Time-Resolved Emission of Flavin Adenine Dinucleotide in Water and water−methanol Mixtures. Phys. Chem. Chem. Phys. 2011, 13, 12058−12066. (71) Spry, D. B.; Fayer, M. D. Charge Redistribution and Photoacidity: Neutral Versus Cationic Photoacids. J. Chem. Phys. 2008, 128, 084508−1−9. (72) Castner, E.; Bagchi, B.; Maroncelli, M.; Webb, S.; Ruggiero, A.; Fleming, G. The Dynamics of Polar Solvation. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 363−372.

P


Fast Photoinduced Reactions in the Condensed Phase Are

Recommend Documents