Statistical theory for the kinetics and dynamics of roaming reactions

We present a statistical theory for the effect of roaming pathways on product branching fractions in both unimolecular and bimolecular reactions. The analysis employs a separation into three distinct steps: (i) the formation of weakly interacting fragments in the long-range/van der Waals region of the potential via either partial decomposition (for unimolecular reactants) or partial association (for bimolecular reactants), (ii) the roaming step, which involves the reorientation of the fragments from one region of the long-range potential to another, and (iii) the abstraction, addition, and/or decomposition from the long-range region to yield final products. The branching between the roaming induced channel(s) and other channels is obtained from a steady-state kinetic analysis for the two (or more) intermediates in the long-range region of the potential. This statistical theory for the roaming-induced product branching is illustrated through explicit comparisons with reduced dimension trajectory simulations for the decompositions of H(2)CO, CH(3)CHO, CH(3)OOH, and CH(3)CCH. These calculations employ high-accuracy analytic potentials obtained from fits to wide-ranging CASPT2 ab initio electronic structure calculations. The transition-state fluxes for the statistical theory calculations are obtained from generalizations of the variable reaction coordinate transition state theory approach. In each instance, at low energy the statistical analysis accurately reproduces the branching obtained from the trajectory simulations. At higher energies, e.g., above 1 kcal/mol, increasingly large discrepancies arise, apparently due to a dynamical biasing toward continued decomposition of the incipient molecular fragments (for unimolecular reactions). Overall, the statistical theory based kinetic analysis is found to provide a useful framework for interpreting the factors that determine the significance of roaming pathways in varying chemical environments.     

Interaction of 2-hydroxy-substituted Nile red fluorescent probe with organic nitrogen compounds

The fluorescent properties of 2-hydroxy Nile red dye (HONR) proved to be highly sensitive to the basicity of hydrogen bond acceptors. Fluorescence quantum yields and fluorescence decay profiles were measured as the function of the concentration of organic nitrogen compounds in solvents of various polarities. The detailed mechanism and the kinetics of the fluorescence quenching were revealed with the combined analysis of the steady-state and time-resolved spectroscopic data. The relative contribution of the competing reaction steps was found to be very sensitive to the basicity of the additive and to solvent polarity. The most profound change appeared in the unimolecular deactivation pathways of the excited hydrogen-bonded HONR, whereas the formation rate of this species varied to a lesser extent. The dissociation into excited HONR and ground-state base was able to compete with the energy dissipation only when 2,4,6-trimethylpyridine was used as hydrogen bond acceptor in toluene. The bimolecular quenching of the excited hydrogen-bonded complex played significant role in apolar solvents. Proton displacement along the hydrogen bond in the excited complex led to excited ion pairs in polar media.     

Anomalous features of the kinetics of subdiffusion-assisted bimolecular reactions

Some specific features of the kinetics of subdiffusion-assisted bimolecular reactions are analyzed in detail with the use of the non-Markovian stochastic Liouville equation (SLE) recently derived within the continuous time random walk approach. The SLE allows for describing important peculiarities of the reactions: Slow long time behavior of the kinetics, nonanalytical dependence of the reaction rate on the reactivity of particles, the onset of quasistatic regime independently of particle mobility in the case long-range reactivity, strong manifestation of fluctuation kinetics showing itself in very slow reaction kinetics at long times, etc.     

Fluorescence quenching of photoreaction products in the excited singlet state

The properties of steady-state spontaneous luminescence of a quantum system with a photoproduct with recordable fluorescence under the conditions of dynamic quenching of excited states by extraneous substances were considered. It was shown that the dependence of photoproduct fluorescence intensity and yield on quencher concentration was nontrivial and could not be conveniently used to determine the Stern-Volmer constant. At the same time, the initial form of the luminophore and its photoproduct produced in a kinetically controlled reaction are quenched in such a way that the ratio of their fluorescence intensities increases linearly as the quencher concentration grows. The corresponding equation was used to determine the constant of bimolecular quenching of reaction product excited states. The results were used in an analysis of the experimental fluorescence spectra of flavone (3-hydroxiflavone), whose fluorescence was excited under the conditions of dynamic quenching of the S ₁ state. Our analysis was shown to be applicable to a wide range of compounds with photoreactions accompanied by two-band fluorescence (charge transfer, proton transfer, phosphorescence, complex formation, etc.). It could be used to accurately determine bimolecular contact constants for excited states of photoreaction product molecules. Original Russian Text ? V.I. Tomin, 2009, published in Zhurnal Fizicheskoi Khimii, 2009, Vol. 83, No. 3, pp. 580–585.     

Slow manifold for a bimolecular association mechanism

Finding the slow manifold for two-variable ordinary differential equation (ODE) models of chemical reactions with a single equilibrium is generally simple. In such planar ODEs the slow manifold is the unique trajectory corresponding to the slow relaxation of the system as it moves towards the equilibrium point. One method of finding the slow manifold is to use direct iteration of a functional equation; another method is to obtain a series solution of the trajectory differential equation of the system. In some cases these two methods agree order-by-order in the singular perturbation parameter controlling the fast relaxation of the intermediate (complex). However, de la Llave has found a model ODE where the series method always diverges. Bimolecular association is an example of a chemical reaction where the series method for finding the slow manifold diverges but the iterative method converges. In this mechanism a complex is formed which can then undergo unimolecular decay, i.e., [reaction: see text]. The kinetics of this reaction are investigated and its properties compared with two other two-step mechanisms where series expansion and iteration methods are equivalent: the Michaelis-Menten mechanism for enzyme kinetics, and the Lindemann-Christiansen mechanism of unimolecular decay in gas kinetics.     

Quenching mechanism of Rose Bengal triplet state involved in photosensitization of oxygen in ethylene glycol

The quenching rate constants of the excited triplet state of Rose Bengal (RB) by oxygen (k(obs)) were measured in ethylene glycol (EG) at different temperatures using nanosecond laser flash photolysis. Although a plot of the quenching rate constant k(obs) for RB triplet state vs oxygen concentration is linear at 20 degrees C, the oxygen dependence of k(obs) does not exhibit linearity but upward curvature at high temperatures from 130 to 140 degrees C. The upward curvature at high temperatures is not well-described by a kinetic scheme first postulated by Gijzeman et al., which is characterized by exciplex formation and a unimolecular dissociation of the exciplex to products, but instead by a more comprehensive mechanism involving a bimolecular dissociation in addition to a unimolecular one. The measurements of the oxygen dependence of k(obs) for RB triplet state at different temperatures yielded a reaction enthalpy for the exciplex formation of 150 kJ mol(-1). Due to the large exothermic reaction enthalpy, equilibrium was obtained for the exciplex at 20 degrees C even at low oxygen concentration and the bimolecular quenching by oxygen became the major dissociation process. The equilibrium attainment and bimolecular dissociation provide a linear oxygen dependence of k(obs) to all outward appearances. Therefore, linearity does not always mean that exciplex dissociation proceeds solely through a unimolecular mechanism.     

Ab initio study of aluminum chemical vapor deposition from dimethylaluminum hydride: a gas phase reaction mechanism

The effect of preheating of dimethylaluminum hydride (DMAH) as a gas on the epitaxial growth in aluminum chemical vapor deposition (Al-CVD) is studied theoretically. The chemical changes of DMAH in the gas phase such as unimolecular decomposition reactions, bimolecular reactions and polymerizations are treated using ab initio molecular orbital method (MP2/6-31G**) and density functional theory (B3P86/LanL2DZ). The gas phase equilibrium composed of the previous reaction products under the usual experimental conditions for Al-CVD is also investigated in detail as the initial stage of the CVD process. From the energetics point of view, unimolecular decomposition reactions and bimolecular reactions hardly occur, however, polymerizations of DMAH take place readily at the low temperatures found in Al-CVD. A large amount of DMAH-dimer and a small amount of DMAH-monomer and trimer coexist in the equilibrium state.     

Pre-equilibrium approximation in chemical and photophysical kinetics

For most mechanisms of chemical reactions and molecular photophysical processes the time evolution of the concentration of the intervening species cannot be obtained analytically. The pre-equilibrium approximation is one of several useful approximation methods that allow the derivation of explicit solutions and simplify numerical solutions. In this work, a general view of the pre-equilibrium approximation is presented, along with the respective analytical solution. It is also shown that the kinetic behavior of systems subject to pre-equilibration can be obtained by the application of perturbation theory. Several photophysical systems are discussed, including excimer formation, thermally activated delayed fluorescence, and external-heavy atom quenching of luminescence.     

Steady-state master equation methods

This paper investigates the application of the steady-state master equation (SSME) to complex unimolecular reactions. It is shown how the steady-state approximation and the Boltzmann reservoir approximation can be applied, both together or separately, to improve the efficiency and the numerical robustness of simple master equation calculations. The case of a two-well isomerization is considered in detail, and two versions of the SSME are derived for it, one of which shows very clearly and analytically the relationship between the rate coefficients and the flux coefficients. It is shown for a reversible second order recombination reaction that the second order phenomenological equation can be regained in either version of the SSME. It is also shown how, under steady state conditions, the SSME may be used to determine rate coefficients for each reaction in a multiple well scheme.     

Thermolysis of polyethylene hydroperoxides in the melt, Part 12: Mechanisms and kinetics of thermolysis

The thermolysis of polyethylene hydroperoxides is attributed to the reaction of two hydroperoxide groups. This bimolecular reaction appears as a first-order reaction with the mean values of the hydroperoxide concentrations that can be used for the experimental verification of the kinetics. In low molecular mass liquids and solutions these findings would be irreconcilable. However, in polymer melts, this contradiction is more apparent than real. It is a consequence of the heterogeneous kinetics valid in polymer melts. The bimolecular reaction involves the decomposition of pairs of hydroperoxide groups that are relatively close in the elementary oxidation volumes. By diffusion these hydroperoxide groups can come close enough for reaction. From the chemical point of view the decomposition is a bimolecular reaction. However, from the kinetic point of view it is a first-order reaction of the hydroperoxide pairs. The dependency of the first-order rate on the initial hydroperoxide concentration is explained by the heterogeneous kinetics. The activation energy of the overall process can be related to the sum of the activation energies pertaining to the chemical reaction and to the diffusion process.     

A study of the accuracy of moment-closure approximations for stochastic chemical kinetics

Moment-closure approximations have in recent years become a popular means to estimate the mean concentrations and the variances and covariances of the concentration fluctuations of species involved in stochastic chemical reactions, such as those inside cells. The typical assumption behind these methods is that all cumulants of the probability distribution function solution of the chemical master equation which are higher than a certain order are negligibly small and hence can be set to zero. These approximations are ad hoc and hence the reliability of the predictions of these class of methods is presently unclear. In this article, we study the accuracy of the two moment approximation (2MA) (third and higher order cumulants are zero) and of the three moment approximation (3MA) (fourth and higher order cumulants are zero) for chemical systems which are monostable and composed of unimolecular and bimolecular reactions. We use the system-size expansion, a systematic method of solving the chemical master equation for monostable reaction systems, to calculate in the limit of large reaction volumes, the first- and second-order corrections to the mean concentration prediction of the rate equations and the first-order correction to the variance and covariance predictions of the linear-noise approximation. We also compute these corrections using the 2MA and the 3MA. Comparison of the latter results with those of the system-size expansion shows that: (i) the 2MA accurately captures the first-order correction to the rate equations but its first-order correction to the linear-noise approximation exhibits the wrong dependence on the rate constants. (ii) the 3MA accurately captures the first- and second-order corrections to the rate equation predictions and the first-order correction to the linear-noise approximation. Hence while both the 2MA and the 3MA are more accurate than the rate equations, only the 3MA is more accurate than the linear-noise approximation across all of parameter space. The analytical results are numerically validated for dimerization and enzyme-catalyzed reactions.     

Collision theory treatment of monomolecular and bimolecular gas reactions

An exact collision theory of unimolecular and bimolecular gas phase reactions is derived from a general quantum-mechanical formulation of reactions rates based on the assumption that the reactants are in thermal equilibrium. In this way the quantum corrections to the classical collision theory expressions are rigorously defined. Approximate formulas for these corrections make it possible to determine well the temperature ranges within which the classical and the semiclassical approximations are valid. A comparison is made between the collision and the transition state theory with emphasis on some conceptual difficulties of the latter in treating the simple decomposition and recombination reactions. It is shown that in the classical (high temperature) limit these theories are incompatible except when the reaction coordinate is entirely separable (i.e., when the transition state theory is no longer useful).     

High-temperature kinetics of thermal decomposition of acetic acid and its products

Kinetics of the thermal decomposition of acetic acid vapor dilute in argon have been studied over the temperature range of 1300–1950 K in a single-pulse shock tube. The acid was found to decompose homogeneously and molecularly via two competing firstorder reaction channels at nearly equal rates, to form methane and carbon dioxide on the one hand, and ketene and water on the other. Fall-off behavior has been taken into account and limiting high-pressure rate constants for both channels have been derived. Ketene was found to decompose both unimolecularly to methylene radicals and carbon monoxide and also by a radical reaction with CH₂ to form ethylene and carbon monoxide. The rate constant derived for the unimolecular reaction was found to be in good agreement with an earlier shock tube measurement by H. G. Wagner and F. Zabel [Ber. Bunsenges Phys. Chem., 75 , 114 (1971)]. The bimolecular reaction of ketene to produce allene and carbon dioxide, important in lower temperature reaction systems, has been found to be unimportant under the present conditions. A computer model for the decomposition kinetics involving 46 reactions of 21 species has been found to simulate the experimental yield data substantially. Sensitivity analyses have been used to identify reactions which make important contributions to the overall mechanism and yields of major products. Methylene radicals play important roles in determining yields of major species.     

The role of nucleophile--electrophile interactions in the unimolecular and bimolecular gas-phase ion chemistry of peptides and related systems

This account describes the experimental tools (multi-stage mass spectrometric experiments, isotopic and structural labelling, kinetics and theoretical modelling) and physical organic concepts (influence of charge, the intermediacy of ion-molecule complexes, etc.) that can be used to unravel the mechanisms of gas-phase unimolecular and bimolecular ionic reactions of peptides. The role that nucleophile-electrophile interactions play in charge-directed reactions is highlighted for both unimolecular fragmentations (examples are illustrated for protonated sulfur-containing amino acids and peptides) and bimolecular ion-molecule reactions which cleave peptide bonds.     

Photoinduced bimolecular electron transfer kinetics in small unilamellar vesicles

Photoinduced electron transfer (ET) from N,N-dimethylaniline to some coumarin derivatives has been studied in small unilamellar vesicles (SUVs) of the phospholipid, DL-alpha-dimyristoyl-phosphatidylcholine, using steady-state and time-resolved fluorescence quenching, both below and above the phase transition temperature of the vesicles. The primary interest was to examine whether Marcus inversion [H. Sumi and R. A. Marcus, J. Chem. Phys. 84, 4894 (1986)] could be observed for the present ET systems in these organized assemblies. The influence of the topology of SUVs on the photophysical properties of the reactants and consequently on their ET kinetics has also been investigated. Absorption and fluorescence spectral data of the coumarins in SUVs and the variation of their fluorescence decays with temperature indicate that the dyes are localized in the bilayer of the SUVs. Time-resolved area normalized emission spectra analysis, however, reveals that the dyes are distributed in two different microenvironments in the SUVs, which we attribute to the two leaflets of the bilayer, one toward bulk water and the other toward the inner water pool. The microenvironments in the two leaflets are, however, not indicated to be that significantly different. Time-resolved anisotropy decays were biexponential for all the dyes in SUVs, and this has been interpreted in terms of the compound motion model according to which the dye molecules can experience a fast wobbling-in-cone type of motion as well as a slow overall rotating motion of the cone containing the molecule. The expected bimolecular diffusion-controlled rates in SUVs, as estimated by comparing the microviscosities in SUVs (determined from rotational correlation times) and that in acetonitrile solution, are much slower than the observed fluorescence quenching rates, suggesting that reactant diffusion (translational) does not play any role in the quenching kinetics in the present systems. Accordingly, clear inversions are observed in the correlation of the fluorescence quenching rate constants k(q) with the free energy change, DeltaG(0) of the reactions. However, the coumarin dyes, C152 and C481 (cf. Scheme 1), show unusually high k(q) values and high activation barriers, which is not expected from Marcus ET theory. This unusual behavior is explained on the basis of participation of the twisted intramolecular charge transfer states of these two dyes in the ET kinetics.     

Theoretical Study of the Rate Coefficients for CH3NHNH2 + NO2 and Related Reactions

The kinetics and mechanisms of H atom abstraction reactions from CH₃NHNH₂ by NO₂ (R1) and related reactions have been investigated theoretically by using ωB97X‐D and CCSD(T)‐F12 quantum chemical calculations and the steady‐state unimolecular master equation analysis based on Rice–Ramsperger–Kassel–Marcus (RRKM) theory. For reaction (R1), both dissociation and isomerization steps between intermediate complexes were found to be important for the distribution of the dissociated bimolecular products. The dominant products of (R1) were found to be cis‐CH₃NHNH and HONO at lower temperature. The branching ratios for CH₃NNH₂ formation paths increased with increasing temperature. On the same reaction potential energy surface, six reactions including isomerization reactions between CH₃NNH₂ and cis‐/trans‐CH₃NHNH catalyzed by HONO were suggested to compete with the reverse reaction of (R1). The temperature‐ and pressure‐dependent rate expressions are proposed for kinetic modeling.     

Luminescence quenching by reversible ionization or exciplex formation/dissociation

The kinetics of fluorescence quenching by both charge transfer and exciplex formation is investigated, with an emphasis on the reversibility and nonstationarity of the reactions. The Weller elementary kinetic scheme of bimolecular geminate ionization and the Markovian rate theory are shown to lead to identical results, provided the rates of the forward and backward reactions account for the numerous recontacts during the reaction encounter. For excitation quenching by the reversible exciplex formation, the Stern-Volmer constant is specified in the framework of the integral encounter theory. The bulk recombination affecting the Stern-Volmer quenching constant makes it different for pulse excited and stationary luminescence. The theory approves that the free energy gap laws for ionization and exciplex formation are different and only the latter fits properly the available data (for lumiflavin quenching by aliphatic amines and aromatic donors) in the endergonic region.     

Two classes of quasi-steady-state model reductions for stochastic kinetics

The quasi-steady-state approximation (QSSA) is a model reduction technique used to remove highly reactive species from deterministic models of reaction mechanisms. In many reaction networks the highly reactive intermediates (QSSA species) have populations small enough to require a stochastic representation. In this work we apply singular perturbation analysis to remove the QSSA species from the chemical master equation for two classes of problems. The first class occurs in reaction networks where all the species have small populations and the QSSA species sample zero the majority of the time. The perturbation analysis provides a reduced master equation in which the highly reactive species can sample only zero, and are effectively removed from the model. The reduced master equation can be sampled with the Gillespie algorithm. This first stochastic QSSA reduction is applied to several example reaction mechanisms (including Michaelis-Menten kinetics) [Biochem. Z. 49, 333 (1913)]. A general framework for applying the first QSSA reduction technique to new reaction mechanisms is derived. The second class of QSSA model reductions is derived for reaction networks where non-QSSA species have large populations and QSSA species numbers are small and stochastic. We derive this second QSSA reduction from a combination of singular perturbation analysis and the Omega expansion. In some cases the reduced mechanisms and reaction rates from these two stochastic QSSA models and the classical deterministic QSSA reduction are equivalent; however, this is not usually the case.     

On the Coherent Description of Diffusion‐Influenced Fluorescence Quenching Experiments II: Early Events

In a previous article we showed how to perform and analyze steady‐state and nanosecond time‐resolved experiments on fluorescence quenching by electron transfer in a coherent manner. Now, by making use of a superior time resolution, we explore the first stages of this kind of reaction. The novel information gained enables us to merge the results on the viscosity and the driving‐force dependencies of the reaction rate. A unique set of parameters for a single reaction channel suffices to describe all the results in the frame of differential encounter theory for diffusion‐influenced, bimolecular, remote electron‐transfer reactions. The inclusion of the solvent structure is crucial for the understanding of the reaction kinetics. To the authors’ best knowledge, this is the first time that such a comprehensive set of data has been successfully and jointly explained in the field, with physically sound parameters for electron‐transfer reactions.