Reaction within the coulomb-cage; science in retrospect

The Coulomb-cage is defined as the space where the electrostatic interaction between two bodies is more intensive than the thermal energy (k_BT). For small molecule, the Coulomb-cage is a small sphere, extending only few water molecules towards the bulk and its radius is sensitive to the ionic strength of the solution. For charged proteins or membranal structures, the Coulomb-cage can engulf large fraction of the surface and provides a preferred pathway for ion propagation along the surface. Similarly, electrostatic potential at the inner space of a channel can form preferential trajectories passage for ions. The dynamics of ions inside the Coulomb-cage of ions was formulated by the studies of proton-anion recombination of excited photoacids. In the present article, we recount the study of intra- Coulomb-cage reaction taking place on the surface of macro-molecular bodies like micelles, membranes, proteins and intra-protein cavities. The study progressed stepwise, tracing the dynamics of a proton ejected from a photo-acid molecule located at defined sites (on membrane, inter-membrane space, active site of enzyme, inside Large Pore Channels etc.). Accumulation of experimental observations encouraged us to study of the reaction mechanism by molecular dynamics simulations of ions within the Coulomb-cage of proteins surface or inside large pores. The intra-Coulomb-cage proton transfer events follows closely the fine structure of the electrostatic field inside the cage and reflects the shape of nearby dielectric boundaries, the temporal ordering of the solvent molecules and the structural fluctuations of the charged side chains. The article sums some 40 years of research, which in retrospect clarifies the intra-Coulomb-cage reaction mechanism.

The Dual Use of the Pyranine (HPTS) Fluorescent Probe: A Ground-State pH Indicator and an Excited-State Proton Transfer Probe

Molecular fluorescent probes are an essential experimental tool in many fields, ranging from biology to chemistry and materials science, to study the localization and other environmental properties surrounding the fluorescent probe. Thousands of different molecular fluorescent probes can be grouped into different families according to their photophysical properties. This Account focuses on a unique class of fluorescent probes that distinguishes itself from all other probes. This class is termed photoacids, which are molecules exhibiting a change in their acid-base transition between the ground and excited states, resulting in a large change in their pKa values between these two states, which is thermodynamically described using the Förster cycle. While there are many different photoacids, we focus only on pyranine, which is the most used photoacid, with pKa values of ∼7.4 and ∼0.4 for its ground and excited states, respectively. Such a difference between the pKa values is the basis for the dual use of the pyranine fluorescent probe. Furthermore, the protonated and deprotonated states of pyranine absorb and emit at different wavelengths, making it easy to focus on a specific state. Pyranine has been used for decades as a fluorescent pH indicator for physiological pH values, which is based on its acid-base equilibrium in the ground state. While the unique excited-state proton transfer (ESPT) properties of photoacids have been explored for more than a half-century, it is only recently that photoacids and especially pyranine have been used as fluorescent probes for the local environment of the probe, especially the hydration layer surrounding it and related proton diffusion properties. Such use of photoacids is based on their capability for ESPT from the photoacid to a nearby proton acceptor, which is usually, but not necessarily, water. In this Account, we detail the photophysical properties of pyranine, distinguishing between the processes in the ground state and the ones in the excited state. We further review the different utilization of pyranine for probing different properties of the environment. Our main perspective is on the emerging use of the ESPT process for deciphering the hydration layer around the probe and other parameters related to proton diffusion taking place while the molecule is in the excited state, focusing primarily on bio-related materials. Special attention is given to how to perform the experiments and, most importantly, how to interpret their results. We also briefly discuss the breadth of possibilities in making pyranine derivatives and the use of pyranine for controlling dynamic reactions.

Space-time histories approach to fast stochastic simulation of bimolecular reactions

Computational models of reaction-diffusion systems involving low copy numbers or strongly heterogeneous molecular spatial distributions, such as those frequently found in cellular signaling pathways, require approaches that account for the stochastic dynamics of individual particles, as opposed to approaches representing them through their average concentrations. Efforts to remedy the high computational cost associated with particle-based stochastic approaches by taking advantage of Green's functions are hampered by the need to draw random numbers from complicated, and therefore costly, non-standard probability distributions to update particle positions. Here, we introduce an approach that permits the reconstruction of entire molecular trajectories, including bimolecular encounters, in retrospect, after a simulated time step, while avoiding inefficient draws from non-standard distributions. This means that highly accurate stochastic simulations can be performed for system sizes that would be prohibitively costly to simulate with conventional Green's function based methods. The algorithm applies equally well to one, two, and three dimensional systems and can be readily extended to include deterministic forces specified by an interaction potential, such as the Coulomb potential.

Reversible intermolecular-coupled-intramolecular (RICI) proton transfer occurring on the reaction-radius a of 2-naphthol-6,8-disulfonate photoacid

Steady-state and time-resolved fluorescence techniques were employed to study the excited-state proton transfer (ESPT) from a reversibly dissociating photoacid, 2-naphthol-6,8-disulfonate (2N68DS). The reaction was carried out in water and in acetonitrile-water solutions. We find by carefully analyzing the geminate recombination dynamics of the photobase-proton pair that follows the ESPT reaction that there are two targets for the proton back-recombination reaction: the original O^- dissociation site and the SO₃ ^- side group at the 8 position which is closest to the proton OH dissociation site. This observation is corroborated in acetonitrile-water mixtures of χ_water < 0.14, where a slow intramolecular ESPT occurs on a time scale of about 1 ns between the OH group and the SO₃ ^- group via H-bonding water. The proton-transferred R^*O^- fluorescence band in mixtures of χ_water < 0.14 where only intramolecular ESPT occurs is red shifted by about 2000 cm^-1 from the free R^*O^- band in neat water. As the water content in the mixture increases above χ_water = 0.14, the R^*O^- fluorescence band shifts noticeably to the blue region. For χ_water > 0.23 the band resembles the free anion band observed in pure water. Concomitantly, the ESPT rate increases when χ_water increases because the intermolecular ESPT to the solvent (bulk water) gradually prevails over the much slower intramolecular via the water-bridges ESPT process.

Exploring fast proton transfer events associated with lateral proton diffusion on the surface of membranes

Proton diffusion (PD) across biological membranes is a fundamental process in many biological systems, and much experimental and theoretical effort has been employed for deciphering it. Here, we report on a spectroscopic probe, which can be tightly tethered to the membrane, for following fast (nanosecond) proton transfer events on the surface of membranes. Our probe is composed of a photoacid that serves as our light-induced proton source for the initiation of the PD process. We use our probe to follow PD, and its pH dependence, on the surface of lipid vesicles composed of a zwitterionic headgroup, a negative headgroup, a headgroup that is composed only from the negative phosphate group, or a positive headgroup without the phosphate group. We reveal that the PD kinetic parameters are highly sensitive to the nature of the lipid headgroup, ranging from a fast lateral diffusion at some membranes to the escape of protons from surface to bulk (and vice versa) at others. By referring to existing theoretical models for membrane PD, we found that while some of our results confirm the quasi-equilibrium model, other results are in line with the nonequilibrium model.

Mutagenic induction of an ultra-fast water-chain proton wire

Replacement of the hydroxyl group of a hydrophilic sidechain by an H atom in the proton wire of GFP induces formation of a water-chain proton wire. Surprisingly, this "non-native" water chain functions as a proton wire with response times within 10 ps of the wild type protein. This remarkable rate retention is understood as a natural consequence of the well-known Grotthuss mechanism of proton transfer in water.

General Approach to Coupled Reactive Smoluchowski Equations: Integration and Application of Discrete Variable Representation and Generalized Coordinate Methods to Diffusive Problems

A new and more general approach to diffusion problems with the inclusion of reactivity among different coupled diffusional states is rationalized and presented. The integration of our previous developments in such a field [Phys. Chem. Chem. Phys., 2015, 17, 17362-17374; J. Chem. Theory Comput., 2016, 12, 3482-3490] are implemented in a software package tool allowing the generic user to set up and run diffusional calculations with very low efforts. We show the applicability of the whole framework to a generic diffusional case of chemical interest that is the study case of (N,N-dimethylamino)benzonitrile (DMABN) fluorescence, whose excited state undergoes twisted intramolecular charge transfer (TICT) relaxation. The population dynamics of the excited state coupled to the ground state is followed, and a fluorescence decay spectrum is calculated. The theoretical and numerical background here presented is robust and general enough to complement a wide number of diffusional problems of current interest.

Exploring the binding sites and proton diffusion on insulin amyloid fibril surfaces by naphthol-based photoacid fluorescence and molecular simulations

The diffusion of protons along biological surfaces and the interaction of biological structures with water are fundamental areas of interest in biology and chemistry. Here, we examine the surface of insulin amyloid fibrils and follow the binding of small molecules (photoacids) that differ according to the number and location of their sulfonic groups. We use transient fluorescence combined with a spherically-symmetric diffusion theory to show that the binding mode of different photoacids determines the efficiency of proton dissociation from the photoacid and the dimensionality of the proton’s diffusion. We use molecular dynamics simulations to examine the binding mode and mechanism of the photoacids and its influence on the unique kinetic rates and diffusion properties of the photoacid’s dissociated proton, where we also suggest a proton transfer process between one of the photoacids to proximal histidine residues. We show that the photoacids can be used as fluorescent markers for following the progression of amyloidogenic processes. The detailed characterisation of different binding modes to the surface of amyloid fibrils paves the way for better understanding of the binding mechanism of small molecules to amyloid fibrils.

Irradiation by blue light in the presence of a photoacid confers changes to colony morphology of the plant pathogen Colletotrichum gloeosporioides

We used the photoacid 8-hydroxy-1,3,6-pyrenetrisulfonate (HPTS) that converts blue photons to acidic protons in water, with an efficiency of close to 100%, and determined that this treatment conferred changes to colony morphology of the plant pathogen Colletotrichum gloeosporioides. The time elapsed until hyphal collapse is noticed depends on both the laser intensity in mW/cm², and the concentration of HPTS in the Agar hydrogel. The time elapsed until hyphal collapse is noticed varies by only ±8% at HPTS concentrations of 500μM and at lower concentrations of HPTS the variance increases as the inverse of the concentration. We found that the effect on C. gloeosporioides was photoacid concentration and irradiation dose dependent. In the presence of 500μM of HPTS within the agar hydrogel-based medium, hyphae collapsed after 37±3.5min of irradiation at 405nm at an intensity of 25mW/cm². We propose two mechanisms for such photo-alteration of C. gloeosporioides. One is based on the pH drop in the extracellular environment by the photo-protolytic process that the photoacid molecule undergoes. The second mechanism is based on an intracellular mechanism in which there is an uptake of HPTS into the interior of the fungus. We suggest that both mechanisms for photo-alteration which we found in this study may occur in plants during fungal infection.

Toward a General Yet Effective Computational Approach for Diffusive Problems: Variable Diffusion Tensor and DVR Solution of the Smoluchowski Equation along a General One-Dimensional Coordinate

A generalization to arbitrary large amplitude motions of a recent approach to the evaluation of diffusion tensors [ J. Comput. Chem. , 2009 , 30 , 2 - 13 ] is presented and implemented in a widely available package for electronic structure computations. A fully black-box tool is obtained, which, starting from the generation of geometric structures along different kinds of paths, proceeds toward the evaluation of an effective diffusion tensor and to the solution of one-dimensional Smoluchowski equations by a robust numerical approach rooted in the discrete variable representation (DVR). Application to a number of case studies shows that the results issuing from our approach are identical to those delivered by previous software (in particular DiTe) for rigid scans along a dihedral angle, but can be improved by employing relaxed scans (i.e., constrained geometry optimizations) or even more general large amplitude paths. The theoretical and numerical background is robust and general enough to allow quite straightforward extensions in several directions (e.g., inclusion of reactive paths, solution of Fokker-Planck or stochastic Liouville equations, multidimensional problems, free-energy rather than electronic-energy driven processes).

A slowing down of proton motion from HPTS to water adsorbed on the MCM-41 surface

We report on the steady-state and femtosecond-nanosecond (fs-ns) behaviour of 8-hydroxypyrene-1,3,6-trisulfonate (pyranine, HPTS) and its interaction with mesoporous silica based materials (MCM-41) in both solid-state and dichloromethane (DCM) suspensions in the absence and presence of water. In the absence of water, HPTS forms aggregates which are characterized by a broad emission spectrum and multiexponential behavior (τsolid-state/DCM = 120 ps, 600 ps, 2.2 ns). Upon interaction with MCM41, the aggregate population is found to be lower, leading to the formation of adsorbed monomers. In the presence of water (1%), HPTS with and without MCM41 materials in DCM suspensions undergoes an excited-state intermolecular proton-transfer (ESPT) reaction in the protonated form (ROH*) producing a deprotonated species (RO(-)*). The long-time emission decays of the ROH* in different systems in the presence of water are multiexponential, and are analysed using the diffusion-assisted geminate recombination model. The obtained proton-transfer and recombination rate constants for HPTS and HPTS/MCM41 complexes in DCM suspensions in the presence of water are kPT = 13 ns(-1), krec = 7.5 Å ns(-1), and kPT = 5.4 ns(-1), krec = 2.2 Å ns(-1), respectively, The slowing down of both processes in the latter case is explained in terms of specific interactions of the dye and of the water molecules with the silica surface. The ultrafast dynamics (fs-regime) of the HPTS/MCM41 complexes in DCM suspensions, without and with water, shows two components which are assigned to intramolecular vibrational-energy relaxation (IVR) (∼120 fs vs. ∼0.8 ps), and vibrational relaxation/cooling (VC), and charge transfer (CT) processes (∼2 ps without water and ∼5 ps with water) of the adsorbed ROH*. Our results provide new knowledge on the interactions and the proton-transfer reaction dynamics of HPTS adsorbed on mesoporous materials.

How Acidic Is Carbonic Acid?

Carbonic, lactic, and pyruvic acids have been generated in aqueous solution by the transient protonation of their corresponding conjugate bases by a tailor-made photoacid, the 6-hydroxy-1-sulfonate pyrene sodium salt molecule. A particular goal is to establish the pK(a) of carbonic acid H2CO3. The on-contact proton transfer (PT) reaction rate from the optically excited photoacid to the carboxylic bases was derived, with unprecedented precision, from time-correlated single-photon-counting measurements of the fluorescence lifetime of the photoacid in the presence of the proton acceptors. The time-dependent diffusion-assisted PT rate was analyzed using the Szabo-Collins-Kimball equation with a radiation boundary condition. The on-contact PT rates were found to follow the acidity order of the carboxylic acids: the stronger was the acid, the slower was the PT reaction to its conjugate base. The pK(a) of carbonic acid was found to be 3.49 ± 0.05 using both the Marcus and Kiefer-Hynes free energy correlations. This establishes H2CO3 as being 0.37 pK(a) units stronger and about 1 pK(a) unit weaker, respectively, than the physiologically important lactic and pyruvic acids. The considerable acid strength of intact carbonic acid indicates that it is an important protonation agent under physiological conditions.

Solvent dependence of excited-state proton transfer from pyranine-derived photoacids

Steady-state and time-resolved techniques were employed to study the excited-state proton-transfer (ESPT) rate of two newly synthesized 8-hydroxy-1,3,6-pyrenetrisulfonate (pyranine, HPTS) derived photoacids in three protic solvents, water, methanol and ethanol. The ESPT rate constant k(PT) of tris(1,1,1,3,3,3-hexafluoropropan-2-yl)-8-hydroxypyrene-1,3,6-trisulfonate, 1a, whose pK(a)* ~ -4, in water, methanol and ethanol is 3 × 10(11) s(-1), 8 × 10(9) s(-1) and 5 × 10(9) s(-1) respectively. (8-Hydroxy-N1,N3,N6-tris(2-hydroxyethyl)-N1,N3,N6-trimethylpyrene-1,3,6 trisulfonamide, 1b) is a weaker acid than 1a but still a strong photoacid with pK(a)* ~ -1 and the ESPT rate in water, methanol and ethanol is 7 × 10(10) s(-1), 4 × 10(8) s(-1) and 2 × 10(8) s(-1). We qualitatively explain our kinetic results by a Marcus-like free-energy correlation which was found to have a general form suitable for describing proton transfer reactions in both the proton-adiabatic and the proton-non-adiabatic limits.

Excited-state proton transfer of weak photoacids adsorbed on biomaterials: 8-hydroxy-1,3,6-pyrenetrisulfonate on chitin and cellulose

Time-resolved and steady-state florescence measurements were used to study the photoprotolytic process of an adsorbed photoacid on cellulose and chitin. For that purpose we used the 8-hydroxy-1,3,6-pyrenetrisulfonate (HPTS) photoacid which transfers a proton to water with a time constant of 100 ps, but is incapable of doing so in methanol or ethanol. We found that both biopolymers accept a proton from the electronically excited acidic ROH form of HPTS. The excited-state proton-transfer (ESPT) rate of HPTS adsorbed on chitin is greater than that on cellulose by a factor of 5. The ESPT on chitin also occurs in the presence of methanol or ethanol, but at a slower rate. The transferred protons can recombine efficiently with the conjugate excited base, the RO(-) form of HPTS.

Fast photoinduced reactions in the condensed phase are nonexponential

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 τ(s), the characteristic fast equilibration time of the population in the reactant potential well, and the longer time τ(e), the characteristic time to cross the energy barrier between the reactant and the product.

The area reactivity model of geminate recombination

We investigate the reversible diffusion-influenced reaction of an isolated pair in the context of the area reactivity model that describes the reversible binding of a single molecule in the presence of a binding site in terms of a generalized version of the Feynman-Kac equation in two dimensions. We compute the corresponding exact Green's function in the Laplace domain for both the initially unbound and bound molecule. We discuss convolution relations that facilitate the calculation of the binding and survival probabilities. Furthermore, we calculate an exact analytical expression for the Green's function in the time domain by inverting the Laplace transform via the Bromwich contour integral and derive expressions for the binding and survival probability in the time domain as well. We numerically confirm the accuracy of the obtained expressions by propagating the generalized Feynman-Kac equation in the time domain. Our results should be useful for comparing the area reactivity model with the contact reactivity model.

Synthesis and spectroscopic characterization of 1,8-naphthalimide derived "super" photoacids

The ground- and excited-state acid-base properties of three novel naphthalimide-based “super” photoacids were studied using steady-state and time-resolved spectroscopy. The compounds exhibit pKa = 8.8-8.0 and pKa* = -1.2 to -1.9. The decrease in both ground- and excited-state pKa is achieved by attachment of an electron withdrawing group (sulfonate) on the aromatic system. All compounds are deprotonated upon excitation in alcohols and DMSO. Good correlation is established between the pKa* and the ratio of the neutral and anion emission intensities in a certain solvent. The excited-state intermolecular proton transfer to solvent (H2O and DMSO) is explained by a two-step model. In the first step, short-range proton transfer takes place, resulting in the formation of a contact ion pair. Free ion pairs are formed in the diffusion controlled second step.

Effect of Ca²⁺ on the steady-state and time-resolved emission properties of the genetically encoded fluorescent sensor CatchER

We previously designed a calcium sensor CatchER (a GFP-based Calcium sensor for detecting high concentrations in the high calcium concentration environment such as ER) with a capability for monitoring calcium ion responses in various types of cells. Calcium binding to CatchER induces the ratiometric changes in the absorption spectra, as well as an increase in fluorescence emission at 510 nm upon excitation at both 395 and 488 nm. Here, we have applied the combination of the steady-state and time-resolved optical methods and Hydrogen/Deuterium isotope exchange to understand the origin of such calcium-induced optical property changes of CatchER. We first demonstrated that calcium binding results in a 44% mean fluorescence lifetime increase of the indirectly excited anionic chromophore. Thus, CatchER is the first protein-based calcium indicator with the single fluorescent moiety to show the direct correlation between the lifetime and calcium binding. Calcium exhibits a strong inhibition on the excited-state proton transfer nonadiabatic geminate recombination in protic (vs deuteric) medium. Analysis of CatchER crystal structures and the MD simulations reveal the proton transfer mechanism in which the disrupted proton migration path in CatchER is rescued by calcium binding. Our finding provides important insights for a strategy to design calcium sensors and suggests that CatchER could be a useful probe for FLIM imaging of calcium in situ.

Analytic solutions for some reaction-diffusion scenarios

Motivated currently by the problem of coalescence of receptor clusters in mast cells in the general subject of immune reactions, and formerly by the investigation of exciton trapping and sensitized luminescence in molecular systems and aggregates, we present analytic expressions for survival probabilities of moving entities undergoing diffusion and reaction on encounter. Results we provide cover several novel situations in simple 1-d systems as well as higher-dimensional counterparts along with a useful compendium of such expressions in chemical physics and allied fields. We also emphasize the importance of the relationship of discrete sink term analysis to continuum boundary condition studies.

Dissociation of a strong acid in neat solvents: diffusion is observed after reversible proton ejection inside the solvent shell

Strong-acid dissociation was studied in alcohols. Optical excitation of the cationic photoacid N-methyl-6-hydroxyquinolinium triggers proton transfer to the solvent, which was probed by spectral reconstruction of picosecond fluorescence traces. The process fulfills the classical Eigen-Weller mechanism in two stages: (a) solvent-controlled reversible dissociation inside the solvent shell and (b) barrierless splitting of the encounter complex. This can be appreciated only when fluorescence band integrals are used to monitor the time evolution of the reactant and product concentrations. Band integrals are insensitive to solvent dynamics and report relative concentrations directly. This was demonstrated by first measuring the fluorescence decay of the conjugate base across the full emission band, independently of the proton-transfer reaction. Multiexponential decay curves at single wavelengths result from a dynamic red shift of fluorescence in the course of solvent relaxation, whereas clean single exponential decays are obtained if the band integral is monitored instead. The extent of the shift is consistent with previously reported femtosecond transient absorption measurements, continuum theory of solvatochromism, and molecular properties derived from quantum chemical calculations. In turn, band integrals show clean biexponential decay of the photoacid and triexponential evolution of the conjugate base in the course of the proton transfer to solvent reaction. The dissociation step follows the slowest stage of solvation, which was measured here independently by picosecond fluorescence spectroscopy in five aliphatic alcohols. Also, the rate constant of the encounter-complex splitting stage is compatible with proton diffusion. Thus, for this photoacid, both stages reach the highest possible rates: solvation and diffusion control. Under these conditions, the concentration of the encounter complex is substantial during the earliest nanosecond.

Contrasting the excited state reaction pathways of phenol and para-methylthiophenol in the gas and liquid phases

To explore how the solvent influences primary aspects of bond breaking, the gas and solution phase photochemistries of phenol and ofpara-methylthiophenol are directly compared using, respectively, H (Rydberg) atom photofragment translation spectroscopy and femtosecond transient absorption spectroscopy. Approaches are demonstrated that allow explicit comparisons of the nascent product energy disposals and dissociation mechanisms in the two phases. It is found, at least for the case of the weakly perturbing cyclohexane environment, that most aspects of the primary reaction dynamics of the isolated molecule are reproduced in solution. Specifically, in the gas phase, both molecules can undergo fast X-H (X = O, S) bond dissociation upon excitation with short wavelengths (193 < lambda(pump) < 216 nm), following population of the dissociative S2 (1 1(pi sigma*)) state. Product electronic branching, vibrational and translational energy disposals are determined. Photolysis of phenol and para-methylthiophenol in solution at 200 nm results in formation of vibrationally excited radicals on a timescale shorter than 200 fs. Excitation of para-methylthiophenol at 267 nm reaches close to the S1 (1 1(pipi*))/S2 (11(pi sigma*)) conical intersection (CI): ultrafast dissociation is observed in both the isolated and solution systems-again indicating direct dissociation on the S2 potential energy surface. Comparing results for this precursor at different excitation energies, the extent of geminate recombination and the derived H-atom ejection lengths in the condensed phase photolyses are in qualitative agreement with the translational energy release measured in the gas phase studies. Conversely, excitation of phenol at 267 nm prepares the system in its S1 state at an energy well below its S1/S2 CI; the slow O-H bond fission inferred in the gas phase experiments is observed directly in the time-resolved studies in cyclohexane solution via the appearance of phenoxyl radical absorption after -1 ns, with only S1 excited state absorption discernible at earlier delay times. The slow O-H bond fission in solution provides additional evidence for a tunnelling dissociation mechanism, where the H atom tunnels beneath the lower diabats of the S2/S1 CI. Finally, the photodissociation of phenol clusters in solution is considered, where evidence is presented that the O-H dissociation coordinate is impeded in H-bonded dimers.

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.

Exact Green's function of the reversible diffusion-influenced reaction for an isolated pair in two dimensions

We derive an exact Green's function of the diffusion equation for a pair of disk-shaped interacting particles in two dimensions subject to a backreaction boundary condition. Furthermore, we use the obtained function to calculate exact expressions for the survival probability and the time-dependent rate coefficient for the initially unbound pair and the survival probability of the bound state. The derived expressions will be of particular utility for the description of reversible membrane-bound reactions in cell biology.

Photoinduced dynamics of oxyluciferin analogues: unusual enol "super"photoacidity and evidence for keto-enol isomerization

The first systematic pico-nanosecond time-resolved spectroscopic study of the firefly emitter oxyluciferin and two of its chemically modified analogues revealed that in the excited state the enol group is more acidic than the phenol group. The 6'-dehydroxylated derivative, in which only the 4-enolic hydroxyl proton is acidic, has an experimentally determined pK(a)* of 0.9 in dimethyl sulfoxide and an estimated pK(a)* of -0.3 in water. Moreover, this compound provided direct evidence that in a nonpolar, basic environment the keto form in the excited state can tautomerize into the enol, which subsequently undergoes excited-state proton transfer (ESPT) to produce enolate ion. This observation presents the first experimental evidence of excited-state keto-enol tautomerization of a firefly fluorophore, and it could be important in resolving the enol-keto conundrum related to the color-tuning mechanism of firefly bioluminescence. The 6'-dehydroxylated form of oxyluciferin adds a very rare case of a stable enol to the family of "super"photoacids.

Excited-state proton transfer in N-methyl-6-hydroxyquinolinium salts: solvent and temperature effects

The excited-state proton transfer (ESPT) reaction of the "super"photoacid N-methyl-6-hydroxyquinolinium (MHQ) was studied using both fluorescence upconversion and time-correlated single photon counting (TCSPC) techniques. The ultrafast ESPT kinetics were investigated in various alcohols and water and determined to be solvent-controlled. The ESPT temperature dependence of MHQ was also studied in various alcohols and compared to that observed for another "super"photoacid, 5,8-dicyano-2-naphthol (DCN2). A full set of kinetic and thermodynamic parameters describing the ESPT was obtained. The protolytic photodissociation rate constant for MHQ was higher than that for DCN2, while the ESPT activation energies of MHQ were smaller. These findings are attributed to the approximately 3 orders of magnitude differences in excited-state acidities of MHQ and DCN2.

Liquid water: from symmetry distortions to diffusive motion

Water deviates from tetrahedral symmetry on different scales, creating "defects" that are important for its dynamics. In this Account, I trace the manifestations of these distortions from the isolated molecule through gas-phase clusters to the liquid phase. Unlike the common depiction, an isolated water molecule has a nonsymmetric charge distribution: although its positive charge is localized at the hydrogens, the negative charge is smeared between the lone-pair sites. This creates a "negativity track" along which a positive charge may slide. Consequently, the most facile motion within the water dimer is a reorientation of the hydrogen-bond (HB) accepting molecule (known as an "acceptor switch"), such that the donor hydrogen switches from one lone pair to the other. Liquid water exhibits asymmetry between donor and acceptor HBs. Molecular dynamics simulations show that the water oxygens accepting HBs from the central molecule are spatially localized, whereas water hydrogens donating HBs to it are distributed along the negativity track. This asymmetry is manifested in a wider acceptor- versus donor-HB distribution. There is a higher probability for a water molecule to accept one (trigonal symmetry) or three HBs than to donate one or three HBs. A simple model can explain semiquantitatively how these distributions evolve by distorting perfectly tetrahedral water. Just two reactions are required: the dissociation of a HB between a double-donor donating to a double-acceptor, D(2)···A(2), followed by a switching reaction in which a HB donor rotates its hydrogen between two double-acceptor molecules. The preponderance of D(2)···A(2) dissociation events is in line with HB "anticooperativity", whereas positive cooperativity is exhibited by conditional HB distributions: a molecule with more acceptor bonds tends to have more donor bonds and vice versa. Quantum mechanically, such an effect arises from intermolecular charge transfer, but it is observed even for fixed-charge water models. Possibly, in the liquid state this is partly a collective effect, for example, a more ordered hydration shell that enhances the probability for both acceptor and donor HBs. The activation energy for liquid water self-diffusion is considerably larger than its HB strength, pointing to the involvement of collective dynamics. The remarkable agreement between the temperature dependence of the water self-diffusion coefficient and its Debye relaxation time suggests that both share the same mechanism, likely consisting of coupled rotation and translation with collective rearrangement of the environment. The auto-correlation function of a hydrogen-bonded water molecule pair is depicted quantitatively by the solution of the diffusion equation for reversible geminate recombination, up to long times where the ubiquitous t(-3/2) power law prevails. From the model, one obtains the HB dissociation and formation rate coefficients and their temperature dependence. Both have a similar activation enthalpy, suggesting rapid formation of HBs with alternate partners, perhaps by the HB switching reaction involving the trigonal site. A detailed picture of how small fluctuations evolve into large-scale molecular motions in water remains elusive. Nonetheless, our results demonstrate how the plasticity of water can be traced to its asymmetric charge distribution, with duality between tetrahedral and trigonal ligation states.

A Monte-Carlo step-by-step simulation code of the non-homogeneous chemistry of the radiolysis of water and aqueous solutions. Part I: theoretical framework and implementation

The importance of the radiolysis of water in irradiation of biological systems has motivated considerable theoretical and experimental work in the radiation chemistry of water and aqueous solutions. In particular, Monte-Carlo simulations of radiation track structure and non-homogeneous chemistry have greatly contributed to the understanding of experimental results in radiation chemistry of heavy ions. Actually, most simulations of the non-homogeneous chemistry are done using the Independent Reaction Time (IRT) method, a very fast technique. The main limitation of the IRT method is that the positions of the radiolytic species are not calculated as a function of time, which is needed to simulate the irradiation of more complex systems. Step-by-step (SBS) methods, which are able to provide such information, have been used only sparsely because these are time consuming in terms of calculation. Recent improvements in computer performance now allow the regular use of the SBS method in radiation chemistry. In the present paper, the first of a series of two, the SBS method is reviewed in detail. To these ends, simulation of diffusion of particles and chemical reactions in aqueous solutions is reviewed, and implementation of the program is discussed. Simulation of model systems is then performed to validate the adequacy of stepwise diffusion and reaction schemes. In the second paper, radiochemical yields of simulated radiation tracks calculated by the SBS program in different conditions of LET, pH, and temperature are compared with results from the IRT program and experimental data.

Diffusional effects on the reversible excited-state proton transfer. From experiments to Brownian dynamics simulations

We have studied an excited state proton transfer (ESPT) from the cationic "super" photoacid N-methyl 6-hydroxyquinolinium perfluorobutane sulfonate to non-aqueous solvents using picosecond and nanosecond time-resolved fluorescence spectroscopy. Upon the photoinduced adiabatic deprotonation from the hydroxyl moiety, a quinolinium zwitterion with a highly anisotropic charge distribution is formed. Due to the complexity of the resultant photodissociated system, the typical description of the reversible ESPT within the framework of the Spherically Symmetric Diffusion Problem (SSDP) is not possible. Additional complications are caused by the presence of a counteranion particle which affects the proton mobility. To better understand the ESPT process, we have performed extensive Brownian dynamics (BD) simulations of this three-body system as a tool to reveal the nature of the nonstationary interaction potentials and to elucidate the role of a counterion in the diffusion and reactive properties of the proton. Moreover, our results demonstrated that the anisotropy of the potential force can be taken into account after adapting this force for use in the SSDP. The results of both BD simulations and SSDP calculation with the adapted force field were used to fit the experimental kinetics of this three-body problem adequately.

Time-resolved emission of flavin adenine dinucleotide in water and water-methanol mixtures

Time-resolved fluorescence decay of flavin adenine dinucleotide (FAD) was studied at room temperature in water and water-methanol mixtures by a fluorescence upconversion technique. The observations were focused on the most initial decay phase (200 ps), before the residual fluorescence assumes a single exponential decay, typical for an extended conformation of the fluorophore. Within the first few picoseconds, where most of the electron transfer coupled quenching takes place, the emission decay curves could be fitted by a stretched exponent, compatible with the inhomogeneous distance dependent electron transfer model. This implies that the population of the excited FAD molecules exhibits a large number of non-identical states, each with its own separation between the donor (adenine) and acceptor (isoalloxazine) moieties, having its own rate of electron transfer. To evaluate the distribution of the separation between the donor-acceptor pair, we carried out molecular dynamics simulations of closed conformation of the FAD in water and water-methanol mixtures, sampling the structure at 10 fs intervals. The analysis of the dynamics reveals that within the 4 ps time frame, where most of the nonexponential fluorescence relaxation takes place, the relative motion of the donor-acceptor pair is consistent with a one-dimensional Brownian motion, where the diffusion coefficient and the shape of the confining potential well are solvent dependent. The presence of methanol enhances the diffusion constant and widens the width of the potential well. On the basis of these parameters, the relaxation dynamics was accurately reconstructed as an electron transfer reaction in an inhomogeneous system where the reactants are diffusing within the time frame of the observation.

Single molecule diffusion and the solution of the spherically symmetric residence time equation

The residence time of a single dye molecule diffusing within a laser spot is propotional to the total number of photons emitted by it. With this application in mind, we solve the spherically symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and the observation time. The solutions for initial conditions of potential experimental interest, starting in the center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1, 2, and 3 are obtained, which can be Laplace inverted analytically for d = 1 and 3. In addition, the analytic short- and long-time asymptotic behaviors of the MRT are derived and compared with the exact solutions for d = 1, 2, and 3. As a demonstration of the simplification afforded by the RTE, the Appendix obtains the residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work.