Experimental evidence for a kinetic transition in reversible reactions

Modeling Excited-State Proton Transfer Using the Lindblad Equation: Quantification of Time-Resolved Spectroscopy with Mechanistic Insights

The quantum dynamics of excited-state intramolecular proton transfer (ESIPT) is studied using a multilevel vibronic Hamiltonian and the Lindblad master equation. We simulate time-resolved fluorescence spectroscopy of 2-(2'-hydroxyphenyl) benzothiazole (HBT) and 10-hydroxybenzo[h]quinoline (HBQ), which suggests that the underlying mechanism behind the initial ultrafast rise and decay in the spectra is electronic state population that evolves simultaneously with proton wave packet dynamics. The results predict that the initial rise and decay signals at different wavelengths vary significantly with system properties in terms of their shape, the time, and the intensity of the maximum. These findings provide clues for data interpretation, mechanism validation, and control of the dynamics, and the model serves as an attempt toward clarifying ESIPT by direct comparison to time-resolved spectroscopy.

Diffusional correlations among multiple active sites in a single enzyme

Simulations of the enzymatic dynamics of a model enzyme containing multiple substrate binding sites indicate the existence of diffusional correlations in the chemical reactivity of the active sites. A coarse-grain, particle-based, mesoscopic description of the system, comprising the enzyme, the substrate, the product and solvent, is constructed to study these effects. The reactive and non-reactive dynamics is followed using a hybrid scheme that combines molecular dynamics for the enzyme, substrate and product molecules with multiparticle collision dynamics for the solvent. It is found that the reactivity of an individual active site in the multiple-active-site enzyme is reduced substantially, and this effect is analyzed and attributed to diffusive competition for the substrate among the different active sites in the enzyme.

General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations

General matrix approach to the consideration of multistage geminate reactions of isolated pairs of reactants depending on reactant mobility is formulated on the basis of the concept of "effective" particles. Various elementary reactions (stages of multistage reaction including physicochemical processes of internal quantum state changes) proceeding with the participation of isolated pairs of reactants (or isolated reactants) are taken into account. Investigation has been made in terms of kinetic approach implying the derivation of general (matrix) kinetic equations for local and mean probabilities of finding any of the reaction species in the sample under study (or for local and mean concentrations). The recipes for the calculation of kinetic coefficients of the equations for mean quantities in terms of relative coordinates of reactants have been formulated in the general case of inhomogeneous reacting systems. Important specific case of homogeneous reacting systems is considered.

Green's function for reversible geminate reaction with volume reactivity

The kinetics of a diffusing particle near a reversible trap may be described by an extension of the Feynman-Kac equation to the case of reversible binding, which can occur within a finite reaction sphere. We obtain the Green's function solution for the Laplace transform of this equation when the particle is initially either bound or unbound. We study the solution in the time-domain by either inverting the Laplace transform numerically or propagating the partial differential equation in the time-domain. We show that integrals of this solution over the reaction sphere agree with previously obtained solutions.

Ultrafast photochemistry in liquids

Ultrafast photochemical processes can occur in parallel with the relaxation of the optically populated excited state toward equilibrium. The latter involves both intra- and intermolecular modes, namely vibrational and solvent coordinates, and takes place on timescales ranging from a few tens of femtoseconds to up to hundreds of picoseconds, depending on the system. As a consequence, the reaction dynamics can substantially differ from those usually measured with slower photoinduced processes occurring from equilibrated excited states. For example, the decay of the excited-state population may become strongly nonexponential and depend on the excitation wavelength, contrary to the Kasha and Vavilov rules. In this article, we first give a brief account of our current understanding of vibrational and solvent relaxation processes. We then present an overview of important classes of ultrafast photochemical reactions, namely electron and proton transfer as well as isomerization, and illustrate with several examples how nonequilibrium effects can affect their dynamics.

Distance-dependent diffusion-controlled reaction of •NO and O2•- at chemical equilibrium with ONOO-

The fast reaction of (•)NO and O(2)(•-) to give ONOO(-) has been extensively studied at irreversible conditions, but the reasons for the wide variations in observed forward rate constants (3.8 ≤ k(f) ≤ 20 × 10(9) M(-1) s(-1)) remain unexplained. We characterized the diffusion-dependent aqueous (pH > 12) chemical equilibrium of the form (•)NO + O(2)(•-) = ONOO(-) with respect to its dependence on temperature, viscosity, and [ONOO(-)](eq) by determining [ONOO(-)](eq) and [(•)NO](eq). The equilibrium forward reaction rate constant (k(f)(eq)) has negative activation energy, in contrast to that found under irreversible conditions. In contradiction to the law of mass action, we demonstrate that the equilibrium constant depends on ONOO(-) concentration. Therefore, a wide range of k(f)(eq) values could be derived (7.5-21 × 10(9) M(-1) s(-1)). Of general interest, the variations in k(f) can thus be explained by its dependence on the distance between ONOO(-) particles (sites of generation of (•)NO and O(2)(•-)).

Excited-state reversible geminate recombination in two dimensions

Excited-state reversible geminate recombination with two different lifetimes and quenching is investigated in two dimensions. From the exact Green function in the Laplace domain, analytic expressions of two-dimensional survival and binding probabilities are obtained at short and long times. We find that a new pattern of kinetic transition occurs in two dimensions. The long-time effective survival probabilities show a pattern of (ln t)(-1)-->constant-->e(t) depending on the rate constants while the effective binding probabilities show t(-1)(ln t)(-2)-->t(-1)-->e(t).

Excited-state proton transfer to solvent from phenol and cyanophenols in water

The excited-state proton transfer (ESPT) to solvent from phenol (PhOH) and cyanophenols (CNOHs) in water was studied by means of time-resolved fluorescence and photoacoustic spectroscopy. A characteristic property of PhOH and CNOHs is that the fluorescence quantum yields of the deprotonated forms are remarkably small (< or = 10(-3)) and the lifetimes are extremely short (< or = 30 ps). Time-resolved fluorescence measurements for PhOH, CNOHs, and their methoxy analogues at 298 K indicate that o- and m-cyanophenols (o- and m-CNOH) undergo rapid ESPT to the solvent water with rate constants of 6.6 x 10(10) and 2.6 x 10(10) s(-1), respectively, whereas the fluorescence properties of PhOH and p-CNOH does not exhibit clear evidence of the ESPT reaction. Photoacoustic measurements show that photoexcitation of o- and m-CNOH in water results in negative volume changes, supporting the occurrence of ESPT to produce a geminate ion pair. In contrast, the volume contractions for the PhOH and p-CNOH solutions are negligibly small, which indicates that, in these compounds, the yields of solvent-separated ion pairs resulting from the ESPT are very small. The volume change per absorbed Einstein (DeltaV(r)) for o-CNOH is obtained to be -5.0 mL Einstein(-1), which is much smaller than the estimated volume contraction per photoconverted mole (DeltaV(R)). This suggests that the geminate recombination between the ejected proton and the cyanophenolate anion occurs after rapid deactivation of the excited ion pair. In the temperature range between 275 and 323 K, the proton dissociation rates of o- and m-CNOH in H(2)O and D(2)O are slower than the solvent relaxation rates evaluated from the Debye dielectric relaxation time, indicating that the overall rate constant is determined mainly by the proton motion along the reaction coordinate.

Diffusion-influenced excited-state reversible geminate ABCD reaction in the presence of an external field

We obtained the exact Green functions, in the Laplace domain, for a diffusion-influenced excited-state reversible geminate ABCD reaction with two different lifetimes and quenching processes under a constant external field in one dimension. Analytic expressions for the survival probabilities of the initial and final states are obtained in the time domain at short and long times, respectively. The short-time approximations obtained in this work are valid for t</K/(-1), where K depends on several parameters of the system. The analysis of the long-time asymptotic behaviors reveals rather complex kinetic transitions dependent upon the field and lifetimes. We also find a destructive interplay leading to the reduction in the number of kinetic transitions similar to that found for the excited-state geminate ABC reaction with an external field in one dimension.

Diffusion-influenced reversible geminate ABCD reaction in the presence of an external field

We investigate a diffusion-influenced ground-state reversible geminate ABCD reaction in the presence of a constant external field in one dimension. In the Laplace domain, we first obtain the nonreactive Green function from which the reactive Green function is derived. Analytic asymptotic expressions of the survival probability are obtained in the time domain for both short and long time regions. There exist four regimes for the equilibrium survival probability according to the signs of the field intensities a1 and a2 that reactant and product states feel, respectively. Analysis of the long-time asymptotic behavior of the survival probability shows two regimes depending on the sign of a parameter K( identical with a(2)(2)D(2) -a(2)(1)D(1)), where D(1) and D(2) are the relative diffusion constants of corresponding states, respectively. Combining these two results, we predict a total of eight regimes for the long-time asymptotic behavior of the survival probability. We find that the long-time asymptotic behavior of the deviation of the effective survival probability shows the t(-3/2) power law when m( identical with min {a(2)(1)D(1), a(2)(2)D(2)}) not equal 0, whereas it shows t(-1/2) power law when m = 0. When one of the fields is turned off, the long-time asymptotic behavior of the survival probability shows a kinetic transition as the sign of the remaining field changes.

Biphasic Tautomerization Dynamics of Excited 7-Hydroxyquinoline in Reverse Micelles

The excited-state tautomerization dynamics of 7-hydroxyquinoline in the water pools of reverse micelles has been investigated by monitoring time-resolved fluorescence spectra and kinetics as well as static absorption and emission spectra with a variation of water content and isotopic fractionation. The normal and the tautomeric species are found to reside preferentially in the bound- and the free-water regions of the micelles, respectively. The excited-state tautomerization of the normal species in the bound-water layers is suggested to occur via two different channels, depending on rotamers at the moment of excitation. The cis tautomerizes via proton relay from the enol group to the imino group along a hydrogen-bonded water bridge, unusual in water but common in alcohols, whereas the trans tautomerizes via the stepwise individual acid-base reactions of two prototropic groups as found in bulk water. Proton relay can take place because water in the pools has substantially reduced polarity and disrupted hydrogen-bond networks compared with bulk water.

Excited-State Tautomerization Dynamics of 7-Hydroxyquinoline in β-Cyclodextrin

The excited-state tautomerization dynamics of 7-hydroxyquinoline encapsulated in beta-cyclodextrin is compared with that in pure water by measuring isotope-dependent fluorescence kinetics as well as absorption and emission spectra. The normal species tautomerizes stepwise via forming anionic intermediate species in both systems. However, the enol-deprotonation time (40 ps in water) becomes as large as 170 ps whereas the imine-protonation time of the anionic intermediate (160 ps in water) becomes as short as 85 ps in beta-cyclodextrin. The slow formation and the fast decay of the anionic species are attributed to the unstability of the charged species in hydrophobic cages. Encapsulation can be utilized to enhance fluorescence enormously and to accelerate selective reactions by retarding other processes.

Elementary Steps in Excited-State Proton Transfer

The absorption of a photon by a hydroxy-aromatic photoacid triggers a cascade of events contributing to the overall phenomenon of intermolecular excited-state proton transfer. The fundamental steps involved were studied over the last 20 years using a combination of theoretical and experimental techniques. They are surveyed in this sequel in sequential order, from fast to slow. The excitation triggers an intramolecular charge transfer to the ring system, which is more prominent for the anionic base than the acid. The charge redistribution, in turn, triggers changes in hydrogen-bond strengths that set the stage for the proton-transfer step itself. This step is strongly influenced by the solvent, resulting in unusual dependence of the dissociation rate coefficient on water content, temperature, and isotopic substitution. The photolyzed proton can diffuse in the aqueous solution in a mechanism that involves collective changes in hydrogen-bonding. On longer times, it may recombine adiabatically with the excited base or quench it. The theory for these diffusion-influenced geminate reactions has been developed, showing nice agreement with experiment. Finally, the effect of inert salts, bases, and acids on these reactions is analyzed.

Exact solution of the excited-state geminate A*+B⇄C*+D reaction with two different lifetimes and quenching

The authors obtain, in the Laplace transform space, the exact analytic solution for the Green function and survival probabilities for the excited-state diffusion-influenced reversible geminate reaction, A*+B <==> C*+D, with two different lifetimes and in the presence of an added quenching process. This extends a previous investigation by Popov and Agmon [J. Chem. Phys. 117, 5770 (2002)] of the ground-state reaction without quenching. The long-time asymptotic behavior of the survival probabilities is obtained in the time domain. It is found to be different from the equal-lifetime case. This paper also provides a useful short-time approximation for the kinetics.

Diffusion-influenced reversible geminate recombination in one dimension. III. Field effect on the excited-state reaction

We obtain exact analytic solutions of the diffusion-influenced excited-state reversible geminate recombination reaction, A* + B<-->(AB)*, with two different lifetimes and quenching under the influence of a constant external field in one dimension. These fundamental solutions generalize two previous results [Kim et al., J. Chem. Phys. 111, 3791 (1999); 114, 3905 (2001)] and provide us with the insight necessary to analyze their specific relations and asymptotic kinetic transition behaviors. We find that the number of kinetic transitions can be changed due to interplay between the field strength and lifetimes. Unlike the previous works, the number of lifetime dependent transitions is found to be one or zero. On the other hand, the number of the field dependent transitions becomes two, one, or zero. We find a new pattern of kinetic transition e(t)-->t(-1/2)-->e(t) when there is only one field dependent transition.

Excited-state proton transfer: from constrained systems to "super" photoacids to superfast proton transfer

We have used knowledge of the electronic structure of excited states of acids to design molecules that exhibit enhanced excited-state acidity. Such "super" photoacids are the strongest reversible photoacids known and allow the time evolution of proton transfer to be examined in a wide array of organic solvents. This includes breaking/formation of the hydrogen bonds in hundreds of femtoseconds, solvent reorientation and relaxation in picoseconds, proton dissociation, and, finally, diffusion and geminate recombination of the dissociated proton, observed in nanoseconds.