Reaction Rate Theory Research Articles

Plasticity of Metal-Organic Framework Crystals: Thermally Activated Collapse of Nanopores.

Unrecoverable deformation or plasticity can be generated in crystalline metal-organic frameworks (MOFs) by compressive loading with different rates in various applications. Herein, plastic behaviors of MOF HKUST-1 crystals are investigated by a series of in situ strain-rate-dependent compression tests. The yield strength is found to significantly increase with increasing strain rate, following a logarithmic dependence. Our reactive molecular dynamics simulations illustrate that the yielding of crystalline HKUST-1 is induced by the irreversible collapse of its nanopores, which can be accelerated by thermal activation at finite temperatures. Based on this mechanism together with the reaction rate theory, we derive an analytical expression relating the yield strength of MOFs and strain rate, which fits experimental findings well. Overall, this work can expand our current understanding of MOF plasticity, which is of importance for the mechanical shaping and various applications of MOF crystals.

Thermochemical and kinetic study of the recombination and dissociation reactions R + Br (+M) ⇄ RBr (+M) (R = CH3, CH2Cl, CHCl2, CHClBr, CH2Br and CHBr2)

The kinetics of the recombination and thermal dissociation reactions R + Br (+M) ⇄ RBr (+M) with R = CH3, CH2Cl, CHCl2, CHClBr, CH2Br and CHBr2 were theoretically studied over wide temperature and pressure ranges employing unimolecular reaction rate theory combined with potential energy surfaces derived at the ab initio G4//B3LYP/6-311++G(3df,3pd) level. The resulting rate constants are in good agreement with the available experimental information. Rate constant values for the reactions of CH2Cl, CHCl2, CHClBr, CH2Br and CHBr2 radicals with Br atoms are for a first time reported. Standard enthalpies of formation for the above and related molecules have been calculated.

Hydrogen diffusion and hydrogen embrittlement in iron (steel)

This article examines the diffusion of hydrogen (H-diffusion) and the temperature dependences of the diffusion coefficient of hydrogen (DH) in the metal (M)-hydrogen system. The metal used was iron and low-alloy steel. Taking into account experimental data on hydrogen diffusion in the Fe-H and steel-H systems, the main diffusion parameters were calculated and compared. It is shown that the temperature dependences of the hydrogen diffusion coefficient in metal samples in a one-stage reaction under isothermal conditions are described by the Arrhenius equation. For some M-H systems, experimental data show a deviation of the diffusion coefficient from the ideal one calculated using the Arrhenius equation. This discrepancy can be eliminated using the statistical theory of absolute reaction rates. For the temperature range 25–1250 oС, the pre-exponential coefficient and activation energy of hydrogen diffusion in a body-centered cubic (bcc) lattice of iron (α–Fe) were calculated using the Arrhenius equation. These parameters make it possible to describe the dependence of the rate of hydrogen diffusion in a metal on temperature and to predict the behavior of hydrogen diffusion when changing the conditions of the kinetic process (concentration of substances, pressure, structure, composition, etc.). Tabular values of the calculated pre-exponential factor and activation energy of hydrogen diffusion in previously studied iron-based samples are presented. The temperature dependences of the hydrogen diffusion coefficient in a lattice of iron α–Fe can be divided into low-temperature and high-temperature regions. The calculated diffusion parameters of hydrogen in the metal lattice for the low-temperature 25– 800 oC and high-temperature 800–1250 oC regions differ markedly from each other. In addition, these calculated values are significantly influenced by the structure and composition of the metal. We also studied the diffusion of hydrogen in α-iron using ab initio density functional calculations. Molecular dynamics calculations using transition state theory were used. The calculated diffusion coefficient of hydrogen in α-Fe is consistent with previously obtained experimental data. Hydrogen embrittlement (HE) is considered using internal pressure, hydrogen enhanced localized plasticity (HELP) and hydrogen enhanced decohesion embrittlement (HEDE) theories.

Cluster dynamics study on nano damage of RPV steels under proton irradiation at 290°C

Irradiation-induced defects such as dislocation loops, cavities or solute clusters and chemical composition segregation of reactor pressure vessel (RPV) steel are the root causes of irradiation embrittlement. Combining two nucleation mechanisms, namely, the uniform nucleation and non-uniform nucleation of solute clusters (such as Cu-rich phase), a cluster kinetic simulation was established based on the reaction rate theory, and the co-evolution of matrix damage and Cu-rich phase in low-copper RPV steel was simulated under irradiation. And the average size and number density of defective clusters and solute clusters were established with irradiation dose. Compared with the average size and number density of dislocation loops observed by transmission electron microscopy (TEM) of proton irradiated RPV steel at 290°C, the verification results show that the cluster dynamics model considering both the nucleation mechanism of interstitial dislocation loops and vacancy clusters can well simulate the irradiation damage behavior of materials.

A personal perspective of the present status and future challenges facing thermal reaction rate theory.

Reaction rate theory has been at the center of physical chemistry for well over one hundred years. The evolution of the theory is not only of historical interest. Reliable and accurate computation of reaction rates remains a challenge to this very day, especially in view of the development of quantum chemistry methods, which predict the relevant force fields. It is still not possible to compute the numerically exact rate on the fly when the system has more than at most a few dozen anharmonic degrees of freedom, so one must consider various approximate methods, not only from the practical point of view of constructing numerical algorithms but also on conceptual and formal levels. In this Perspective, I present some of the recent analytical results concerning leading order terms in an ℏ2m series expansion of the exact rate and their implications on various approximate theories. A second aspect has to do with the crossover temperature between tunneling and thermal activation. Using a uniform semiclassical transmission probability rather than the "primitive" semiclassical theory leads to the conclusion that there is no divergence problem associated with a "crossover temperature." If one defines a semiclassical crossover temperature as the point at which the tunneling energy of the instanton equals the barrier height, then it is a factor of two higher than its previous estimate based on the "primitive" semiclassical approximation. In the low temperature tunneling regime, the uniform semiclassical theory as well as the "primitive" semiclassical theory were based on the classical Euclidean action of a periodic orbit on the inverted potential. The uniform semiclassical theory wrongly predicts that the "half-point," which is the energy at which the transmission probability equals 1/2, for any barrier potential, is always the barrier energy. We describe here how augmenting the Euclidean action with constant terms of order ℏ2 can significantly improve the accuracy of the semiclassical theory and correct this deficiency. This also leads to a deep connection with and improvement of vibrational perturbation theory. The uniform semiclassical theory also enables an extension of the quantum version of Kramers' turnover theory to temperatures below the "crossover temperature." The implications of these recent advances on various approximate methods used to date are discussed at length, leading to the conclusion that reaction rate theory will continue to challenge us both on conceptual and practical levels for years to come.

ℏ2 Corrections to Semiclassical Transmission Coefficients.

The uniform semiclassical expression for the energy-dependent transmission probability through a barrier has been a staple of reaction rate theory for almost 90 years. Yet, when using the classical Euclidean action, the transmission probability is identical to 1/2 when the energy equals the barrier height since the Euclidean action vanishes at this energy. This result is generally incorrect. It also leads to an inaccurate estimate of the leading order term in an ℏ2n expansion of the thermal transmission coefficient. The central result of this paper is that adding an ℏ2 dependent correction to the uniform semiclassical expression, whether as a constant action or as a shift in the energy scale, not only corrects this inaccuracy but also leads to a theory that is more accurate than the previous one for almost any energy. Shifting the energy scale is a generalization of the vibrational perturbation theory 2 (VPT2) and is much more accurate than the "standard" VPT2 theory, especially when the potential is asymmetric. Shifting the action by a constant is a generalization of a result obtained by Yasumori and Fueki (YF) only for the Eckart barrier. The resulting modified VPT2 and YF semiclassical theories are applied to the symmetric and asymmetric Eckart barrier, a Gaussian barrier, and a tanh barrier. The one-dimensional theories are also generalized to many-dimensional systems. Their effect on the thermal instanton theory is discussed.

Ab Initio and Kinetic Modeling of β-d-Xylopyranose under Fast Pyrolysis Conditions.

Lignocellulosic biomass is an abundant renewable resource that can be upgraded to chemical and fuel products through a range of thermal conversion processes. Fast pyrolysis is a promising technology that uses high temperatures and fast heating rates to convert lignocellulose into bio-oils in high yields in the absence of oxygen. Hemicellulose is one of the three major components of lignocellulosic biomass and is a highly branched heteropolymer structure made of pentose, hexose sugars, and sugar acids. In this study, β-d-xylopyranose is proposed as a model structural motif for the essential chemical structure of hemicellulose. The gas-phase pyrolytic reactivity of β-d-xylopyranose is thoroughly investigated using computational strategies rooted in quantum chemistry. In particular, its thermal degradation potential energy surfaces are computed employing Minnesota global hybrid functional M06-2X in conjunction with the 6-311++G(d,p) Pople basis set. Electronic energies are further refined by performing DLPNO-CCSD(T)-F12 single-point calculations on top of M06-2X geometries using the cc-pVTZ-F12 basis set. Conformational analysis for minima and transition states is performed with state-of-the-art semiempirical quantum chemical methods coupled with metadynamics simulations. Key thermodynamic quantities (free energies, barrier heights, enthalpies of formation, and heat capacities) are computed. Rate coefficients for the initial steps of thermal decomposition are computed by means of reaction rate theory. For the first time, a detailed elementary reaction kinetic model for β-d-xylopyranose is developed by utilizing the thermodynamic and kinetic information acquired from the aforementioned calculations. This model specifically targets the initial stages of β-d-xylopyranose pyrolysis in the high-pressure limit, aiming to gain a deeper understanding of its reaction kinetics. This approach establishes a systematic strategy for exploring reactive pathways, evaluating competing parallel reactions, and selectively accepting or discarding pathways based on the analysis. The findings suggest that acyclic d-xylose plays a significant role as an intermediary in the production of key pyrolytic compounds during the pyrolysis of xylose. These compounds include furfural, anhydro-d-xylopyranose, glycolaldehyde, and dihydrofuran-3(2H)-one.

Reactions of gas phase amino acids with the prevailing radicals in biomass thermal treatments

AbstractAmino acids, N‐containing compounds, hold a significant importance in various field. Within the biomass energy sector, amino acids constitute a large fraction of the biomass's nitrogen content. As such, it is essential to comprehend their combustion chemistry; most specifically their biomolecular interactions with governing radicals in the pyrolytic and combustion media that prevail during thermal utilization of biomass. Herein, we have employed quantum chemical calculations and reaction rate theory to investigate reactions of a selected set of amino acids with H, CH3, NH2, OH, HO2, and HS radicals. Thermo‐kinetic calculations have been performed to determine the rates of hydrogen abstraction by these six radicals across all possible reaction channels for three specific amino acids: alanine, cysteine, and methionine. The investigation of other amino acids like glycine, threonine, and other models have been carried out for α‐C positions as the most probable abstractable sites. The study also examines the individual effects of different substituents (COOH, NH2, HS, and CH2) and uncovers significant insights. Notably, the presence of the COOH group introduces polar effects that counterintuitively deactivate the thermodynamically favored α‐abstraction pathway. Presented thermo‐kinetic values are anticipated to complement existing biomass kinetic models and to improve current understanding of chemical events that participate in the complex nitrogen transformation reactions in biomass.

Molecular Modeling of Supercritical Processes and the Lattice—Gas Model

The existing possibilities for modeling the kinetics of supercritical processes at the molecular level are considered from the point of view that the Second Law of thermodynamics must be fulfilled. The only approach that ensures the fulfillment of the Second Law of thermodynamics is the molecular theory based on the discrete–continuous lattice gas model. Expressions for the rates of the elementary stage on its basis give a self-consistent description of the equilibrium states of the mixtures under consideration. The common usage today of ideal kinetic models in SC processes in modeling industrial chemistry contradicts the non-ideal equation of states. The used molecular theory is the theory of absolute reaction rates for non-ideal reaction systems, which takes into account intermolecular interactions that change the effective activation energies of elementary stages. This allows the theory to describe the rates of elementary stages of chemical transformations and molecular transport at arbitrary temperatures and reagent densities in different phases. The application of this theory in a wide range of state parameters (pressure and temperature) is considered when calculating the rates of elementary bimolecular reactions and dissipative coefficients under supercritical conditions. Generalized dependencies are calculated within the framework of the law of the corresponding states for the coefficients of compressibility, shear viscosity, and thermal conductivity of pure substances, and for the coefficients of compressibility, self- and mutual diffusion, and shear viscosity of binary mixtures. The effect of density and temperature on the rates of elementary stages under supercritical conditions has been demonstrated for a reaction’s effective energies of activation, diffusion and share viscosity coefficients, and equilibrium constants of adsorption. Differences between models with effective parameters and the prospects for developing them by allowing for differences in size and contributions from the vibrational motions of components are described.

Recent Developments in Kramers' Theory of Reaction Rates.

In this short review, we provide an update of recent developments in Kramers' theory of reaction rates. After a brief introduction stressing the importance of this theory initially developed for chemical reactions, we briefly present the main theoretical formalism starting from the generalized Langevin equation and continue by showing the main points of the modern Pollak, Grabert and Hänggi theory. Kramers' theory is then sketched for quantum and classical surface diffusion. As an illustration the surface diffusion of Na atoms on a Cu(110) surface is discussed showing escape rates, jump distributions and diffusion coefficients as a function of reduced friction. Finally, some very recent applications of turnover theory to different fields such as nanoparticle levitation, microcavity polariton dynamics and simulation of reaction in liquids are presented. We end with several open problems and future challenges faced up by Kramers turnover theory.

Fast protein folding is governed by memory-dependent friction

When described by a low-dimensional reaction coordinate, the folding rates of most proteins are determined by a subtle interplay between free-energy barriers, which separate folded and unfolded states, and friction. While it is commonplace to extract free-energy profiles from molecular trajectories, a direct evaluation of friction is far more elusive and typically relies on fits of measured reaction rates to memoryless reaction-rate theories. Here, using memory-kernel extraction methods founded on a generalized Langevin equation (GLE) formalism, we directly calculate the time-dependent friction acting on the fraction of native contacts reaction coordinate Q, evaluated for eight fast-folding proteins, taken from a published set of large-scale molecular dynamics protein simulations. Our results reveal that, across the diverse range of proteins represented in this dataset, friction is more influential than free-energy barriers in determining protein folding rates. We also show that proteins fold in a regime where the finite decay time of friction significantly reduces the folding times, in some instances by as much as a factor of 10, compared to predictions based on memoryless friction.

Irradiation temperature and dose rate dependence of void swelling in RAFM steel during irradiation: Reaction rate theory analysis

Reaction rate theory analysis has performed to investigate the irradiation temperature and dose rate dependence of void swelling of RAFM steel under a wide range of irradiation temperatures and dose rates (250 to 620 °C and 10−7 to 10−3 dpa/s) with focusing on nucleation behavior of voids. In the rate theory analysis, an improved nucleation model is employed where the stable nucleus size of voids is estimated by the vacancy flux into/from voids which depends on irradiation condition and void size. The calculation says that the void swelling strongly depends on irradiation temperature and dose rate, and there is one unique peak temperature for each dose rate. As dose rate increases, the peak temperature shifts to higher temperatures and the peak swelling decreases; this results from the enhancement and suppression of void nucleation. The calculated stable nucleus size of voids remarkably depends on irradiation conditions and varies widely from 5 to about 50: the nucleus size drastically increases at higher temperatures, while it decreases at higher dose rates. For the dose rate dependence of the peak temperature of void swelling, the calculation provides a good agreement with the experiment more than a conventional model.

A comprehensive kinetic study of the combustion mechanismof methyl isocyanate

A detailed mechanism for the combustion of methyl isocyanate is proposed for the first time. Electronic structures were calculated at the CCSD(T)/cc-VTQ∞Z//B2PLYP-D3/6-311++G(3df,2pd) level of theory to investigate potential energy profiles and used in reaction rate theories to compute rate coefficients. The mechanism contains 130 reactions and was merged with the reaction base proposed by Glarborg et al.[1] for light hydrocarbons and nitrogen-containing species. Experimental data related to the pyrolysis of methyl isocyanate were simulated in a closed reactor and a good agreement was observed for all the species profiles reported. Similarly, the auto-ignition temperature (Tign) of methyl isocyanate was calculated based on the standard ASTME659-78 test, and led to a value close to the experimental value. Flow rate and sensitivity analysis were performed under pyrolysis and combustion conditions in order to highlight the main reaction pathways.

Expert Algorithm for Substance Identification Using Mass Spectrometry: Statistical Foundations in Unimolecular Reaction Rate Theory.

This study aims to resolve one of the longest-standing problems in mass spectrometry, which is how to accurately identify an organic substance from its mass spectrum when a spectrum of the suspected substance has not been analyzed contemporaneously on the same instrument. Part one of this two-part report describes how Rice-Ramsperger-Kassel-Marcus (RRKM) theory predicts that many branching ratios in replicate electron-ionization mass spectra will provide approximately linear correlations when analysis conditions change within or between instruments. Here, proof-of-concept general linear modeling is based on the 20 most abundant fragments in a database of 128 training spectra of cocaine collected over 6 months in an operational crime laboratory. The statistical validity of the approach is confirmed through both analysis of variance (ANOVA) of the regression models and assessment of the distributions of the residuals of the models. General linear modeling models typically explain more than 90% of the variance in normalized abundances. When the linear models from the training set are applied to 175 additional known positive cocaine spectra from more than 20 different laboratories, the linear models enabled ion abundances to be predicted with an accuracy of <2% relative to the base peak, even though the measured abundances vary by more than 30%. The same models were also applied to 716 known negative spectra, including the diastereomers of cocaine: allococaine, pseudococaine, and pseudoallococaine, and the residual errors were larger for the known negatives than for known positives. The second part of the manuscript describes how general linear regression modeling can serve as the basis for binary classification and reliable identification of cocaine from its diastereomers and all other known negatives.

Glass softening in the limit of high heating rates: Heterogeneous devitrification kinetics on nano, meso, and micrometer scale.

When heated rapidly, glasses often devitrify heterogeneously, i.e., by a softening front that originates at the surface of an amorphous film. Yet the fundamentals of this devitrification regime are not completely understood; depending on experimental conditions, the reported front propagation distances differ by an order of magnitude. Using a high-resolution fast scanning calorimetry technique, we have investigated the softening of glassy methylbenzene films with thicknesses between 30 and 1400nm. We confirm first that, in all films, the devitrification process begins with the formation of a softening front that propagates through the films over distances of ∼50nm and that the front propagation kinetics at this stage follow an Arrhenius law. However, we also show that, in films with thicknesses above 165nm, the front propagation does not terminate with the onset of bulk softening. Specifically, increasing the films' thicknesses above 165nm yields sharp, clearly discernible endotherms that precede the bulk softening endotherms and that are consistent with a two-fold increase in the enthalpic barrier to front propagation at a well-defined critical temperature. We term this phenomenon "Arrhenius discontinuity" and use reaction rate and continuum front dynamics theories to explain its origins and the physical nature of the resulting distinct heterogeneous devitrification processes. Finally, we discuss the findings in the context of recent theoretical, computational, and experimental studies of heterogeneous devitrification by other research groups.

Stochastic transitions: Paths over higher energy barriers can dominate in the early stages.

The time evolution of many physical, chemical, and biological systems can be modeled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two (or more) possible pathways that the system can take, the time available for the transition to occur is crucially important. The well-known results of the reaction rate theory for determining the rates of transitions apply in the long-time limit. However, at short times, the system can, instead, choose to pass over higher energy barriers with a much higher probability, as long as the distance to travel in phase space is shorter. We construct two simple models to illustrate this general phenomenon. We also apply a version of the geometric minimum action method algorithm of Vanden-Eijnden and Heymann [J. Chem. Phys. 128, 061103 (2008)] to determine the most likely path at both short and long times.

A first look at first-passage processes

These notes are based on the lectures that I gave (virtually) at the Bruneck Summer School in 2021 on first-passage processes and some applications of the basic theory. I begin by defining a first-passage process and presenting the connection between the first-passage probability and the familiar occupation probability. Some basic features of first passage on the semi-infinite line and a finite interval are then discussed, such as splitting probabilities and first-passage times. I also treat the fundamental connection between first passage and electrostatics. A number of applications of first-passage processes are then presented, including the hitting probability for a sphere in greater than two dimensions, reaction rate theory and its extension to receptors on a cell surface, first-passage inside an infinite absorbing wedge in two dimensions, stochastic hunting processes in one dimension, the survival of a diffusing particle in an expanding interval, and finally the dynamics of the classic birth–death process.

Extent of Inhibition of Malonic Acid on the Fermentation of Soursop Juice: A Thermodynamic Evaluation

The fermentation of soursop juice as substrate by Saccharomyces cerevisiae (yeast) was investigated to obtain certain useful thermodynamic parameters. This was achieved by the determination of the effects of temperature, substrate and inhibitor on the rate of carbon (IV) oxide (CO2) production. The extent of inhibition was examined by the addition of malonic acid inhibitor. The results indicate that the rate of fermentation of soursop juice increased in proportion with temperature (optimum 36oC), substrate (optimum 50%v/v) and malonic acid (optimum 30%v/v) up to a limit and decreased. This suggests that the reaction takes place in two steps (equilibrium and decomposition steps). The thermodynamic parameters determined are: enthalpy, ∆H* 151.14 kJmol-1; entropy of activation, ∆S* 275.359 Jmol-1k-1; Gibb’s free energy of activation, ∆G* -752.21 kJmol-1 and Equilibrium constant Keq, 1.33 respectively. The results show that the enthalpy value is positive indicating that the fermentation process is endothermic while the activation energy is same as the enthalpy. The entropy value is positive corroborating the positive enthalpy value. The fermentation process is spontaneous as shown by the negative change in free energy. These values were subsequently used to obtain by calculation Arrhenius constant A, 1.51x1023; orientation factor P, 1.41x10-34 and the collision frequency, Z, 1.07x1011 respectively. The calculated A and the P values obtained on the basis of collision theory and absolute reaction rate theory (or transition state theory), respectively show that the collision factor is of the order of 1011 min-1, about half that of gaseous molecules that can only be attained by an induced reduction in activation energy by a catalyst. The equilibrium constant value K suggests that the intermediate complex is rather interacting more with the substrate and also showing that only a limited amount of the substrate is converted to product. The equilibrium constant K is observed to be 1.33dm3mol-1 and not significantly far from unity implying that G* can be conveniently equated with the change in free energy at standard conditions. Finally, the type of inhibition was found to be uncompetitive from the extrapolated Lineweaver-Burk plots and did not bring about marked decrease in the rate of fermentation as expected.

Mechanism and Kinetics of The Degradation of Nitazoxanide and Hydroxychloroquine Drugs by Hydroxyl Radicals: Theoretical Approach to Ecotoxicity

The efforts of contrasting the effects caused by the Covid-19 (coronavirus disease 2019) pandemic increased the disposal of active pharmaceutical ingredients. This paper reports the mechanisms and kinetics of the degradation in aqueous environments induced by  OH of two drugs, among those most widely probed at the outbreak of coronavirus, nitazoxanide and hydroxychloroquine. The investigation exploits quantum chemistry techniques and a reaction rate theory combined with diffusion-controlled processes and quantum mechanical tunneling. The reaction rate constants are obtained in an environmentally relevant temperature range. The results show that (i) the deacetylation of nitazoxanide with formation of tizoxanide is kinetically the most favorable channel, in agreement with experimental work; (ii) for hydroxychloroquine, the present theoretical calculations show that the most favorable channel is the addition of  OH at the aromatic ring. The half-life time degradation products are for both cases in the range between 12 to 138 days. Both drugs presented toxicities between harmful and toxic as obtained by computational toxicology calculations: The toxicity is also calculated for the degradation products: (i) in the nitazoxanide degradation process, tizoxanide was characterized as more toxic, while (ii) in the case of hydroxychloroquine, the major degradation product showed a decrease in the toxicity.

Pair-Reaction Dynamics in Water: Competition of Memory, Potential Shape, and Inertial Effects.

When described by a one-dimensional reaction coordinate, pair-reaction rates in a solvent depend, in addition to the potential barrier height and the friction coefficient, on the potential shape, the effective mass, and the friction relaxation spectrum, but a rate theory that accurately accounts for all of these effects does not exist. After a review of classical reaction-rate theories, we show how to extract all parameters of the generalized Langevin equation (GLE) and, in particular, the friction memory function from molecular dynamics (MD) simulations of two prototypical pair reactions in water, the dissociation of NaCl and of two methane molecules. The memory exhibits multiple time scales and, for NaCl, pronounced oscillatory components. Simulations of the GLE by Markovian embedding techniques accurately reproduce the pair-reaction kinetics from MD simulations without any fitting parameters, which confirms the accuracy of the approximative form of the GLE and of the parameter extraction techniques. By modification of the GLE parameters, we investigate the relative importance of memory, mass, and potential shape effects. Neglect of memory slows down NaCl and methane dissociation by roughly a factor of 2; neglect of mass accelerates reactions by a similar factor, and the harmonic approximation of the potential shape gives rise to slight acceleration. This partial error cancellation explains why Kramers' theory, which neglects memory effects and treats the potential shape in harmonic approximation, describes reaction rates better than more sophisticated theories. In essence, all three effects, friction memory, inertia, and the potential shape nonharmonicity, are important to quantitatively describe pair-reaction kinetics in water.