Uniform description of non-Arrhenius temperature dependence of reaction rates, and a heuristic criterion for quantum tunneling vs classical non-extensive distribution

Ultralow-Friction at Cryogenic Temperature Induced by Hydrogen Correlated Quantum Effect

Temperature is one of the governing factors affecting friction of solids. Undesired high friction state has been generally reported at cryogenic temperatures due to the prohibition of thermally activated processes, following conventional Arrhenius equation. This has brought huge difficulties to lubrication at extremely low temperatures in industry. Here, the study uncovers a hydrogen-correlated sub-Arrhenius friction behavior in hydrogenated amorphous carbon (a-C:H) film at cryogenic temperatures, and a stable ultralow-friction over a wide temperature range (103-348 K) is achieved. This is attributed to hydrogen-transfer-induced mild structural ordering transformation, confirmed by machine-learning-based molecular dynamics simulations. The anomalous sub-Arrhenius temperature dependence of structural ordering transformation rate is well-described by a quantum mechanical tunneling (QMT) modified Arrhenius model, which is correlated with quantum delocalization of hydrogen in tribochemical reactions. This work reveals a hydrogen-correlated friction mechanism overcoming the Arrhenius temperature dependence and provides a new pathway for achieving ultralow friction under cryogenic conditions.

Energy Landscapes of Carbon Clusters from Tight-Binding Quantum Potentials

We calculate transformation pathways between fullerene and octahedral carbon clusters and between a buckyball and its bowl-shaped isomer. The energies and gradients are provided by efficient tight-binding potentials, which are interfaced to our Energy Landscape exploration software. From the global energy landscape, we extract the mechanistic and kinetic parameters as a function of temperature, and compare our results to selected density functional theory (DFT) (PBE/cc-pVTZ) benchmarks. Infrared spectra are calculated to provide data for experimental identification of the clusters and differentiation of their isomers. Our results suggest that the formation of buckyballs from a buckybowl will be suppressed at elevated temperatures (above around 5250 K) due to entropic effects, which may provide useful insight into the detection of cosmic fullerenes.

Current Understanding of Water Properties inside Carbon Nanotubes

Confined water inside carbon nanotubes (CNTs) has attracted a lot of attention in recent years, amassing as a result a very large number of dedicated studies, both theoretical and experimental. This exceptional scientific interest can be understood in terms of the exotic properties of nanoconfined water, as well as the vast array of possible applications of CNTs in a wide range of fields stretching from geology to medicine and biology. This review presents an overreaching narrative of the properties of water in CNTs, based mostly on results from systematic nuclear magnetic resonance (NMR) and molecular dynamics (MD) studies, which together allow the untangling and explanation of many seemingly contradictory results present in the literature. Further, we identify still-debatable issues and open problems, as well as avenues for future studies, both theoretical and experimental.

Depletion Induced Demixing and Crystallization in Binary Colloids Subjected to an External Potential Barrier

Depletion interaction plays an important role in determining the structural and dynamical properties of binary colloidal mixtures. We have investigated the effect of the attractive depletion interaction between an external potential barrier and larger species in the binary mixture on the phase behavior of a binary colloidal mixture using canonical-isokinetic ensemble molecular dynamics simulations. The demixing of the binary mixture due to this depletion interaction increases as the volume fraction increases, and a pure phase of larger particles forms in the region of the potential barrier. The local density of this pure phase is high enough that a face centered cubic crystalline domain is formed at this region. This crystalline phase diffuses perpendicular to the external potential barrier, indicating that moving crystals can be obtained in an equilibrium system. The temperature dependence of diffusivity of larger particles is non-Arrhenius and changes from sub-Arrhenius to super-Arrhenius as the volume fraction increases. This crossover from sub-Arrhenius to super-Arrhenius diffusion coincides with the crystalline formation near the potential barrier.

Non-Arrhenius kinetics and slowed-diffusion mechanism of molecular aggregation of a rhodamine dye on colloidal particles

The non-covalent association is important for many fields of science, including processes in living systems. This work elucidates the mechanism of rhodamine 123 molecular aggregation in dispersions of a layered silicate and explains the mystery of the slow kinetics of this process. Chemometric analysis of thousands of spectra recorded by stopped-flow visible spectroscopy identified two parallel diffusion processes described by a two-phase exponential function. The slow and fast processes followed the super-Arrhenius kinetics and were assigned to lateral (surface) diffusion and inter-particle diffusion of dye cations, respectively. This work, supported by a large amount of data and their in-depth analysis, provides the first evidence of how these processes coexist together and provides quantitative analysis of their dependence on the reaction conditions. The implications of this work can be crucial for understanding the mechanism of the non-covalent association of adsorbed molecules in nature.

Topography of the free energy landscape of Claisen-Schmidt condensation: solvent and temperature effects on the rate-controlling step

Recent studies have found that hydroxide elimination and the C[double bond, length as m-dash]C bond formation step in base-promoted aldol condensation have a strong influence on the overall rate of the reaction, in contrast to the well-accepted first enolization or C-C bond formation step. Here, applying theoretical models to the prototypical reaction of chalcone formation, the complete free energy profile of Claisen-Schmidt condensation is assessed, revealing how a protic solvent and a slight increase in temperature can induce the second enolization as the rate-controlling step (RCS). It is also observed: i) the nonexistence of a step with a much higher energetic barrier than the others, making the concept of RCS debatable; and ii) that the overall inverse kinetic isotopic effect does not exclude second enolization as a RCS in protic continuum medium. We expect that these results can expand the understanding of the decisive role of physicochemical factors on the choose of the RCS in the aldol condensation.

Super-Arrhenius diffusion in a binary colloidal mixture at low volume fraction: an effect of depletion interaction due to an asymmetric barrier

We report results from the molecular dynamics simulations of a binary colloidal mixture subjected to an external potential barrier along one of the spatial directions at low volume fraction, ϕ = 0.2. The variations in the asymmetry of the external potential barrier do not change the dynamics of the smaller particles, showing Arrhenius diffusion. However, the dynamics of the larger particles shows a crossover from sub-Arrhenius to super-Arrhenius diffusion with the asymmetry in the external potential at the low temperatures and low volume fraction. Super-Arrhenius diffusion is generally observed in the high density systems where the transient cages are present due to dense packing, e.g., supercooled liquids, jammed systems, diffusion through porous membranes, dynamics within the cellular environment, etc. This model can be applied to study the molecular transport across cell membranes, nano-, and micro-channels which are characterized by spatially asymmetric potentials.

Kinetics Study of the Hydrodeoxygenation of Xylitol over a ReOx-Pd/CeO2 Catalyst

In this study, we elucidate the reaction kinetics for the simultaneous hydrodeoxygenation of xylitol to 1,2-dideoxypentitol and 1,2,5-pentanetriol over a ReOx-Pd/CeO2 (2.0 weight% Re, 0.30 weight% Pd) catalyst. The reaction was determined to be a zero-order reaction with respect to xylitol. The activation energy was elucidated through an Arrhenius relationship as well as non-Arrhenius kinetics. The Arrhenius relationship was investigated at 150–170 °C and a constant H2 pressure of 10 bar resulting in an activation energy of 48.7 ± 10.5 kJ/mol. The investigation of non-Arrhenius kinetics was conducted at 120–170 °C and a sub-Arrhenius relation was elucidated with activation energy being dependent on temperature, and ranging from 10.2–51.8 kJ/mol in the temperature range investigated. Internal and external mass transfer were investigated through evaluating the Weisz–Prater criterion and the effect of varying stirring rate on the reaction rate, respectively. There were no internal or external mass transfer limitations present in the reaction.

Understanding the Dependence of Micropollutant Biotransformation Rates on Short-Term Temperature Shifts

Temperature is a key factor that influences chemical biotransformation potential and rates, on which exposure and fate models rely to predict the environmental (micro)pollutant fate. Arrhenius-based models are currently implemented in environmental exposure assessment to adapt biotransformation rates to actual temperatures, assuming validity in the 0-30 °C range. However, evidence on how temperature shifts affect the physicochemical and microbial features in biological systems is scarce, questioning the validity of the existing modeling approaches. In this work, laboratory-scale batch assays were designed to investigate how a mixed microbial community responds to short-term temperature shifts, and how this impacts its ability to biotransform a range of structurally diverse micropollutants. Our results revealed three distinct kinetic responses at temperatures above 20 °C, mostly deviating from the classic Arrhenius-type behavior. Micropollutants with similar temperature responses appeared to undergo mostly similar initial biotransformation reactions, with substitution-type reactions maintaining Arrhenius-type behavior up to higher temperatures than oxidation-type reactions. Above 20 °C, the microbial community also showed marked shifts in both composition and activity, which mostly correlated with the observed deviations from Arrhenius-type behavior, with compositional changes becoming a more relevant factor in biotransformations catalyzed by more specific enzymes (e.g., oxidation reactions). Our findings underline the need to re-examine and further develop current environmental fate models by integrating biological aspects, to improve accuracy in predicting the environmental fate of micropollutants.

Deciphering the Dynamics of Organic Nanoaggregates with AIEE Effect and Excited States: Lipophilic Benzothiadiazole Derivatives as Selective Cell Imaging Probes

An aggregation-induced emission enhancement (AIEE) effect in fluorescent lipophilic 2,1,3-benzothiadiazole (BTD) derivatives and their organic nanoaggregates were studied. A set of techniques such as single-crystal X-ray, dynamic light scattering (DLS), electron paramagnetic resonance (EPR), UV-vis, fluorescence, and density functional theory (DFT) calculations have been used to decipher the formation/break (kinetics), properties, and dynamics of the organic nanoaggregates of three BTD small organic molecules. An in-depth study of the excited-state also revealed the preferential relaxation emissive pathways for the BTD derivatives and the dynamics associated with it. The results described herein, for the first time, explain the formation of fluorescent BTD nanoaggregate derivatives and allow for the understanding of their dynamics in solution as well as the ruling forces of both aggregation and break processes along with the involved equilibrium. One of the developed dyes could be used at a nanomolar concentration to selectively stain lipid droplets emitting an intense and bright fluorescence at the red channel. The other two BTDs could also stain lipid droplets at very low concentrations and were visualized preferentially at the blue channel.

Non-Arrhenius behavior and fragile-to-strong transition of glass-forming liquids

Characterization of the non-Arrhenius behavior of glass-forming liquids is a broad avenue for research toward the understanding of the formation mechanisms of noncrystalline materials. In this context, this paper explores the main properties of the viscosity of glass-forming systems, considering super-Arrhenius diffusive processes. We establish the viscous activation energy as a function of the temperature, measure the degree of fragility of the system, and characterize the fragile-to-strong transition through the standard Angell's plot. Our results show that the non-Arrhenius behavior observed in fragile liquids can be understood through the non-Markovian dynamics that characterize the diffusive processes of these systems. Moreover, the fragile-to-strong transition corresponds to a change in the spatiotemporal range of correlations during the glass transition process.

From the Kinetic Theory of Gases to the Kinetics of Rate Processes: On the Verge of the Thermodynamic and Kinetic Limits

A variety of current experiments and molecular dynamics computations are expanding our understanding of rate processes occurring in extreme environments, especially at low temperatures, where deviations from linearity of Arrhenius plots are revealed. The thermodynamic behavior of molecular systems is determined at a specific temperature within conditions on large volume and number of particles at a given density (the thermodynamic limit): on the other side, kinetic features are intuitively perceived as defined in a range between the extreme temperatures, which limit the existence of each specific phase. In this paper, extending the statistical mechanics approach due to Fowler and collaborators, ensembles and partition functions are defined to evaluate initial state averages and activation energies involved in the kinetics of rate processes. A key step is delayed access to the thermodynamic limit when conditions on a large volume and number of particles are not fulfilled: the involved mathematical analysis requires consideration of the role of the succession for the exponential function due to Euler, precursor to the Poisson and Boltzmann classical distributions, recently discussed. Arguments are presented to demonstrate that a universal feature emerges: Convex Arrhenius plots (super-Arrhenius behavior) as temperature decreases are amply documented in progressively wider contexts, such as viscosity and glass transitions, biological processes, enzymatic catalysis, plasma catalysis, geochemical fluidity, and chemical reactions involving collective phenomena. The treatment expands the classical Tolman’s theorem formulated quantally by Fowler and Guggenheim: the activation energy of processes is related to the averages of microscopic energies. We previously introduced the concept of “transitivity”, a function that compactly accounts for the development of heuristic formulas and suggests the search for universal behavior. The velocity distribution function far from the thermodynamic limit is illustrated; the fraction of molecules with energy in excess of a certain threshold for the description of the kinetics of low-temperature transitions and of non-equilibrium reaction rates is derived. Uniform extension beyond the classical case to include quantum tunneling (leading to the concavity of plots, sub-Arrhenius behavior) and to Fermi and Bose statistics has been considered elsewhere. A companion paper presents a computational code permitting applications to a variety of phenomena and provides further examples.

Kinetics of Methyl Lactate Formation from the Transesterification of Polylactic Acid Catalyzed by Zn(II) Complexes

The kinetics of the transesterification of polylactic acid (PLA) with methanol to form methyl lactate catalyzed by Zn(II) complexes was studied experimentally and numerically. The complexes, Zn(1 ^Et )₂ and Zn(2 ^Pr )₂, were synthesized from ethylenediamine and propylenediamine Schiff bases, respectively. The temperature range covered was 313.2-383.2 K. An increase in the reaction rate with the increase in temperature was observed for the Zn(1 ^Et )₂-catalyzed reaction. The temperature relationship of the rate coefficients can be explained by a linear Arrhenius dependency with constant activation energy. The kinetics of Zn(2 ^Pr )₂, on the other hand, is only explained by non-Arrhenius kinetics with convex variable activation energy, resulting in faster methyl lactate production rates at 323.2 and 343.2 K. The formation of a new catalyst species, likely through reaction with protic reagents, appears to promote the formation of intermediate complexes, resulting in the nonlinear behavior. Stirring speed induced the stability of the intermediate complexes. Contrary to Zn(1 ^Et )₂, Zn(2 ^Pr )₂ was susceptible to the presence of air/moisture in solution. The kinetic parameters were obtained by fitting the experimental data to the mass and energy balance of a consecutive second step reversible reaction taking place in a jacketed stirred batch reactor. For the case of Zn(2 ^Pr )₂, the activation energy was fitted to a four-parameter equation. The kinetic parameters presented in this work are valuable for the design of processes involving the chemical recycling of PLA into green solvents.

Characterization of the non-Arrhenius behavior of supercooled liquids by modeling nonadditive stochastic systems

The characterization of the formation mechanisms of amorphous solids is a large avenue for research, since understanding its non-Arrhenius behavior is challenging to overcome. In this context, we present one path toward modeling the diffusive processes in supercooled liquids near glass transition through a class of nonhomogeneous continuity equations, providing a consistent theoretical basis for the physical interpretation of its non-Arrhenius behavior. More precisely, we obtain the generalized drag and diffusion coefficients that allow us to model a wide range of non-Arrhenius processes. This provides a reliable measurement of the degree of fragility of the system and an estimation of the fragile-to-strong transition in glass-forming liquids, as well as a generalized Stokes-Einstein equation, leading to a better understanding of the classical and quantum effects on the dynamics of nonadditive stochastic systems.

"Transitivity": A Code for Computing Kinetic and Related Parameters in Chemical Transformations and Transport Phenomena

The Transitivity function, defined in terms of the reciprocal of the apparent activation energy, measures the propensity for a reaction to proceed and can provide a tool for implementing phenomenological kinetic models. Applications to systems which deviate from the Arrhenius law at low temperature encouraged the development of a user-friendly graphical interface for estimating the kinetic and thermodynamic parameters of physical and chemical processes. Here, we document the Transitivity code, written in Python, a free open-source code compatible with Windows, Linux and macOS platforms. Procedures are made available to evaluate the phenomenology of the temperature dependence of rate constants for processes from the Arrhenius and Transitivity plots. Reaction rate constants can be calculated by the traditional Transition-State Theory using a set of one-dimensional tunneling corrections (Bell (1935), Bell (1958), Skodje and Truhlar and, in particular, the deformed ( d -TST) approach). To account for the solvent effect on reaction rate constant, implementation is given of the Kramers and of Collins-Kimball formulations. An input file generator is provided to run various molecular dynamics approaches in CPMD code. Examples are worked out and made available for testing. The novelty of this code is its general scope and particular exploit of d -formulations to cope with non-Arrhenius behavior at low temperatures, a topic which is the focus of recent intense investigations. We expect that this code serves as a quick and practical tool for data documentation from electronic structure calculations: It presents a very intuitive graphical interface which we believe to provide an excellent working tool for researchers and as courseware to teach statistical thermodynamics, thermochemistry, kinetics, and related areas.

Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity

Advances in the understanding of the dependence of reaction rates from temperature, as motivated from progress in experiments and theoretical tools (e. g., molecular dynamics), are needed for the modeling of extreme environmental conditions (e.g., in astrochemistry and in the chemistry of plasmas). While investigating statistical mechanics perspectives (Aquilanti et al., 2017b, 2018), the concept of transitivity was introduced as a measure for the propensity for a reaction to occur. The Transitivity plot is here defined as the reciprocal of the apparent activation energy vs. reciprocal absolute temperature. Since the transitivity function regulates transit in physicochemical transformations, not necessarily involving reference to transition-state hypothesis of Eyring, an extended version is here proposed to cope with general types of transformations. The transitivity plot permits a representation where deviations from Arrhenius behavior are given a geometrical meaning and make explicit a positive or negative linear dependence of transitivity for sub- and super-Arrhenius cases, respectively. To first-order in reciprocal temperature, the transitivity function models deviations from linearity in Arrhenius plots as originally proposed by Aquilanti and Mundim: when deviations are increasingly larger, other phenomenological formulas, such as Vogel-Fulcher-Tammann, Nakamura-Takayanagi-Sato, and Aquilanti-Sanches-Coutinho-Carvalho are here rediscussed from the transitivity concept perspective and with in a general context. Emphasized is the interest of introducing into this context modifications to a very successful tool of theoretical kinetics, Eyring's Transition-State Theory: considering the behavior of the transitivity function at low temperatures, in order to describe deviation from Arrhenius behavior under the quantum tunneling regime, a "d-TST" formulation was previously introduced (Carvalho-Silva et al., 2017). In this paper, a special attention is dedicated to a derivation of the temperature dependence of viscosity, making explicit reference to feature of the transitivity function, which in this case generally exhibits a super-Arrhenius behavior. This is of relevance also for advantages of using the transitivity function for diffusion-controlled phenomena.

Photoluminescence Quenching Probes Spin Conversion and Exciton Dynamics in Thermally Activated Delayed Fluorescence Materials

Fluorescent materials that efficiently convert triplet excitons into singlets through reverse intersystem crossing (RISC) rival the efficiencies of phosphorescent state-of-the-art organic light-emitting diodes. This upconversion process, a phenomenon known as thermally activated delayed fluorescence (TADF), is dictated by the rate of RISC, a material-dependent property that is challenging to determine experimentally. In this work, a new analytical model is developed which unambiguously determines the magnitude of RISC, as well as several other important photophysical parameters such as exciton diffusion coefficients and lengths, all from straightforward time-resolved photoluminescence measurements. From a detailed investigation of five TADF materials, important structure-property relationships are derived and a brominated derivative of 2,4,5,6-tetrakis(carbazol-9-yl)isophthalonitrile that has an exciton diffusion length of over 40 nm and whose excitons interconvert between the singlet and triplet states ≈36 times during one lifetime is identified.

Theoretical Investigation on H2O2-Ng (He, Ne, Ar, Kr, Xe, and Rn) Complexes Suitable for Stereodynamics: Interactions and Thermal Chiral Rate Consequences

Although molecular collisions of noble gases (Ng) can be theoretically used to distinguish between the enantiomers of hydrogen peroxide - H₂O₂ (HP), little is known about the effects of HP-Ng interactions on the chiral rate. In this work, the chiral rate as a function of temperature (CRT) between enantiomeric conformations of HP and Ng (Ng=He, Ne, Ar, Kr, Xe, and Rn) are presented at MP2(full)/aug-cc-pVTZ level of theory through a fully basis set superposition error (BSSE) corrected potential energy surface. The results show that: (a) the CRT is highly affected even at a small decrease in the height of trans-barrier; (b) its smallest values occur with Ne for all temperatures between 100 and 4,000 K; (c) that the decrease of CRT shows an inverse correlation with respect to the average valence electron energy of the Ng and (d) Ne and He may be the noble gases more suitable for study the oriented collision dynamics of HP. In addition to binding energies, the electron density ρ and its Laplacian ∇²ρ topological analyses were also performed within the atoms in molecules (AIM) theory in order to determine the nature of the HP-Ng interactions. The results of this work provide a more complete foundation on experiments to study HP's chirality using Ng in crossed molecular beams without a light source.

Kinetics of the OH+HCl→H2 O+Cl reaction: Rate determining roles of stereodynamics and roaming and of quantum tunneling

The OH + HCl → H₂ O + Cl reaction is one of the most studied four-body systems, extensively investigated by both experimental and theoretical approaches. Here, as a continuation of our previous work on the OH + HBr and OH + HI reactions, which manifest an anti-Arrhenius behavior that was explained by stereodynamic and roaming effects, we extend the strategy to understand the transition to the sub-Arrhenius behavior occurring for the HCl case. As previously, we perform first-principles on-the-fly Born-Oppenheimer molecular dynamics calculations, thermalized at four temperatures (50, 200, 350, and 500 K), but this time we also apply a high-level transition-state-theory, modified to account for tunneling conditions. We find that the theoretical rate constants calculated with Bell tunneling corrections are in good agreement with extensive experimental data available for this reaction in the ample temperature range: (i) simulations show that the roles of molecular orientation in promoting this reaction and of roaming in finding the favorable path are minor than in the HBr and HI cases, and (ii) dominating is the effect of quantum mechanical penetration through the energy barrier along the reaction path on the potential energy surface. The discussion of these results provides clarification of the origin on different non-Arrhenius mechanisms observed along this series of reactions. © 2018 Wiley Periodicals, Inc.

A novel assessment of the role of the methyl radical and water formation channel in the CH3OH + H reaction

A number of experimental and theoretical papers accounted almost exclusively for two channels in the reaction of atomic hydrogen with methanol: H-abstraction from the methyl (R1) and hydroxyl (R2) functional groups. Recently, several astrochemical studies claimed the importance of another channel for this reaction, which is crucial for kinetic simulations related to the abundance of molecular constituents in planetary atmospheres: methyl radical and water formation (R3 channel). Here, motivated by the lack of and uncertainties about the experimental and theoretical kinetic rate constants for the third channel, we developed first-principles Car-Parrinello molecular dynamics thermalized at two significant temperatures - 300 and 2500 K. Furthermore, the kinetic rate constant of all three channels was calculated using a high-level deformed-transition state theory (d-TST) at a benchmark electronic structure level. d-TST is shown to be suitable for describing the overall rate constant for the CH₃OH + H reaction (an archetype of the moderate tunnelling regime) with the precision required for practical applications. Considering the experimental ratios at 1000 K, k_R1/k_R2 ≈ 0.84 and k_R1/k_R3 ≈ 15-40, we provided a better estimate when compared with previous theoretical work: 7.47 and 637, respectively. The combination of these procedures explicitly demonstrates the role of the third channel in a significant range of temperatures and indicates its importance considering the thermodynamic control to estimate methyl radical and water formation. We expect that these results can help to shed new light on the fundamental kinetic rate equations for the CH₃OH + H reaction.

Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces

In this Introduction, we show the basic problems of non-statistical and non-equilibrium phenomena related to the papers collected in this themed issue. Over the past few years, significant advances in both computing power and development of theories have allowed the study of larger systems, increasing the time length of simulations and improving the quality of potential energy surfaces. In particular, the possibility of using quantum chemistry to calculate energies and forces 'on the fly' has paved the way to directly study chemical reactions. This has provided a valuable tool to explore molecular mechanisms at given temperatures and energies and to see whether these reactive trajectories follow statistical laws and/or minimum energy pathways. This themed issue collects different aspects of the problem and gives an overview of recent works and developments in different contexts, from the gas phase to the condensed phase to excited states.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions

This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d < 0, to those where d > 0, corresponding to the Pareto-Tsallis statistical weights: these generalize the Boltzmann-Gibbs weight, which is recovered for d = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d > 0 or for a negative binomial distribution if d < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super-Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub-Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti-Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Deformed transition-state theory: Deviation from Arrhenius behavior and application to bimolecular hydrogen transfer reaction rates in the tunneling regime

A formulation is presented for the application of tools from quantum chemistry and transition-state theory to phenomenologically cover cases where reaction rates deviate from Arrhenius law at low temperatures. A parameter d is introduced to describe the deviation for the systems from reaching the thermodynamic limit and is identified as the linearizing coefficient in the dependence of the inverse activation energy with inverse temperature. Its physical meaning is given and when deviation can be ascribed to quantum mechanical tunneling its value is calculated explicitly. Here, a new derivation is given of the previously established relationship of the parameter d with features of the barrier in the potential energy surface. The proposed variant of transition state theory permits comparison with experiments and tests against alternative formulations. Prescriptions are provided and implemented to three hydrogen transfer reactions: CH₄  + OH → CH₃  + H₂ O, CH₃ Cl + OH → CH₂ Cl + H₂ O and H₂  + CN → H + HCN, widely investigated both experimentally and theoretically. © 2016 Wiley Periodicals, Inc.

Investigation of the Abstraction and Dissociation Mechanism in the Nitrogen Trifluoride Channels: Combined Post-Hartree-Fock and Transition State Theory Approaches

The present paper concludes our series of kinetics studies on the reactions involved in the complex mechanism of nitrogen trifluoride decomposition. Two other related reactions that, along with this mechanism, take part in an efficient boron nitride growth process are also investigated. We report results concerning two abstraction reactions, namely NF2 + N ⇄ 2NF and NF3 + NF ⇄ 2NF2, and two dissociations, N2F4 ⇄ 2NF2 and N2F3 ⇄ NF2 + NF. State-of-the-art electronic structure calculations at the CCSD(T)/cc-pVTZ level of theory were considered to determine geometries and frequencies of reactants, products, and transition states. Extrapolation of the energies to the complete basis set limit was used to obtain energies of all the species. We applied transition state theory to compute thermal rate constants including Wigner, Eckart, Bell, and deformed theory corrections in order to take tunneling effects into account. The obtained results are in good agreement with the experimental data available in the literature and are expected to provide a better phenomenological understanding of the NF3 decomposition role in the boron nitride growth for a wide range of temperature values.

Stereodirectional Origin of anti-Arrhenius Kinetics for a Tetraatomic Hydrogen Exchange Reaction: Born-Oppenheimer Molecular Dynamics for OH + HBr

Among four-atom processes, the reaction OH + HBr → H2O + Br is one of the most studied experimentally: its kinetics has manifested an unusual anti-Arrhenius behavior, namely, a marked decrease of the rate constant as the temperature increases, which has intrigued theoreticians for a long time. Recently, salient features of the potential energy surface have been characterized and most kinetic aspects can be considered as satisfactorily reproduced by classical trajectory simulations. Motivation of the work reported in this paper is the investigation of the stereodirectional dynamics of this reaction as the prominent reason for the peculiar kinetics: we started in a previous Letter ( J. Phys. Chem. Lett. 2015 , 6 , 1553 - 1558 ) a first-principles Born-Oppenheimer "canonical" molecular dynamics approach. Trajectories are step-by-step generated on a potential energy surface quantum mechanically calculated on-the-fly and are thermostatically equilibrated to correspond to a specific temperature. Here, refinements of the method permitted a major increase of the number of trajectories and the consideration of four temperatures -50, +200, +350, and +500 K, for which the sampling of initial conditions allowed us to characterize the stereodynamical effect. The role is documented of the adjustment of the reactants' mutual orientation to encounter the entrance into the "cone of acceptance" for reactivity. The aperture angle of this cone is dictated by a range of directions of approach compatible with the formation of the specific HOH angle of the product water molecule; and consistently the adjustment is progressively less effective the higher the kinetic energy. Qualitatively, this emerging picture corroborates experiments on this reaction, involving collisions of aligned and oriented molecular beams, and covering a range of energies higher than the thermal ones. The extraction of thermal rate constants from this molecular dynamics approach is discussed and the systematic sampling of the canonical ensemble is indicated as needed for quantitative comparison with the kinetic experiments.

Stereodynamical Origin of Anti-Arrhenius Kinetics: Negative Activation Energy and Roaming for a Four-Atom Reaction

The OH + HBr → H2O + Br reaction, prototypical of halogen-atom liberating processes relevant to mechanisms for atmospheric ozone destruction, attracted frequent attention of experimental chemical kinetics: the nature of the unusual reactivity drop from low to high temperatures eluded a variety of theoretical efforts, ranking this one among the most studied four-atom reactions. Here, inspired by oriented molecular-beams experiments, we develop a first-principles stereodynamical approach. Thermalized sets of trajectories, evolving on a multidimensional potential energy surface quantum mechanically generated on-the-fly, provide a map of most visited regions at each temperature. Visualizations of rearrangements of bonds along trajectories and of the role of specific angles of reactants' mutual approach elucidate the mechanistic change from the low kinetic energy regime (where incident reactants reorient to find the propitious alignment leading to reaction) to high temperature (where speed hinders adjustment of directionality and roaming delays reactivity).

An alternative interpretation of the ultracold methylhydroxycarbene rearrangement mechanism: cooperative effects

Recent studies have reported surprising results related to the rearrangement of carbenes under ultracold conditions, through quantum tunnelling. Here, we demonstrate that a rearrangement of methylhydroxycarbene is possible through cooperative effects.

Alternative analytical forms to model diatomic systems based on the deformed exponential function

Using a deformed exponential function and the molecular-orbital theory for the simplest molecular ion, two new analytical functions are proposed to represent the potential energy of ground-state diatomic systems. The quality of these new forms was tested by fitting the ab initio electronic energies of the system LiH, LiNa, NaH, RbH, KH, H2, Li2, K2, H 2 (+) , BeH(+) and Li 2 (+) . From these fits, it was verified that these new proposals are able to adequately describe homonuclear, heteronuclear and cationic diatomic systems with good accuracy. Vibrational spectroscopic constant results obtained from these two proposals are in good agreement with experimental data.

Theoretical reaction kinetics astride the transition between moderate and deep tunneling regimes: the F + HD case

For the reaction between F and HD, giving HF + D and DF + H, the rate constants, obtained from rigorous quantum scattering calculations at temperatures ranging from 350 K down to 100 K, show deviations from the Arrhenius behavior that have been interpreted in terms of tunneling of either H or D atoms through a potential energy barrier. The interval of temperature investigated extends from above to below a crossover value Tc, a transition temperature separating the moderate and deep quantum tunneling regimes. Below Tc, the rate of the H or D exchange reaction is controlled by the prevalence of tunneling over the thermal activation mechanism. In this temperature range, Bell's early treatment of quantum tunneling, based on a semiclassical approximation for the barrier permeability, provides a reliable tool to quantitatively account for the contribution of the tunneling effect. This treatment is here applied for extracting from rate constants properties of the effective tunneling path, such as the activation barrier height and width. We show that this is a way of parametrizing the dependence of the apparent activation energy on temperature useful for both calculated and experimental rate constants in an ample interval of temperature, from above to below Tc, relevant for modelization of astrophysical and in general very low-temperature environments.