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

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.

Non-additive entropies and statistical mechanics at the edge of chaos: a bridge between natural and social sciences

The Boltzmann-Gibbs (BG) statistical mechanics constitutes one of the pillars of contemporary theoretical physics. It is constructed upon the other pillars-classical, quantum, relativistic mechanics and Maxwell equations for electromagnetism-and its foundations are grounded on the optimization of the BG (additive) entropic functional [Formula: see text]. Its use in the realm of classical mechanics is legitimate for vast classes of nonlinear dynamical systems under the assumption that the maximal Lyapunov exponent is positive (currently referred to as strong chaos), and its validity has been experimentally verified in countless situations. It fails however when the maximal Lyapunov exponent vanishes (referred to as weak chaos), which is virtually always the case with complex natural, artificial and social systems. To overcome this type of weakness of the BG theory, a generalization was proposed in 1988 grounded on the non-additive entropic functional [Formula: see text]. The index [Formula: see text] and related ones are to be calculated, whenever mathematically tractable, from first principles and reflect the specific class of weak chaos. We review here the basics of this generalization and illustrate its validity with selected examples aiming to bridge natural and social sciences. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)'.

Aqueous picloram degradation by hydroxyl radicals: Unveiling mechanism, kinetics, and ecotoxicity through experimental and theoretical approaches

Pesticides are chemical compounds widely used to combat pests in crops, and they thus play a key role in agricultural production. However, due to their persistence in aquatic environments, even at low concentrations, their use has been considered an environmental problem and caused concern regarding the adverse effects on human health. This paper reports, for the first time, the mechanisms, kinetics, and an evaluation of the toxicity of picloram degradation initiated by OH radicals in the aqueous environment using quantum chemistry and computational toxicology calculations. The rate constants are calculated using a combination of formulations derived from the Transition State Theory in a realistic temperature range (250-310 K). The results indicate that the two favorable pathways (R1 and R5) of OH -based reactions occur by addition to the pyridine ring. The calculated rate constant at 298 K is compared with the overall second-order reaction rate constant, quantified herein experimentally via the competition kinetics method and data available in the literature showing an excellent agreement. The toxicity assessment and a photolysis study provide important information: i) picloram and the majority of degradation products are estimated as harmful; however, ii) these compounds can suffer photolysis in sunlight. The results of the present study can help understand the mechanism of picloram, also providing important clues regarding risk assessment in aquatic environments as well as novel experimental information.

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.

Energetics and kinetics of various cyano radical hydrogen abstractions

The cyano radical (CN) is an abundant, open-shell molecule found in a variety of environments, including the atmosphere, the interstellar medium and combustion processes. In these environments, it often reacts with small, closed-shell molecules via hydrogen abstraction. Both carbon and nitrogen atoms of the cyano radical are reactive sites, however the carbon is more reactive with reaction barrier heights generally between 2-15 kcal mol^-1 lower than those of the analogous nitrogen. The CN + HX → HCN/HNC + X, with X = H, CH₃, NH₂, OH, F, SiH₃, PH₂, SH, Cl, C₂H, CN reactions have been studied at a high-level of theory, including CCSD(T)-F12a. Furthermore, kinetics were obtained over the 100-1000 K temperature range, showing excellent agreement with those rate constants that have been determined experimentally.

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.

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.

Nucleophilic substitution vs elimination reaction of bisulfide ions with substituted methanes: exploration of chiral selectivity by stereodirectional first-principles dynamics and transition state theory

Control of molecular orientation is emerging as crucial for the characterization of the stereodynamics of kinetics processes beyond structural stereochemistry. The special role played in chiral discrimination phenomena has been particularly emphasized by Aquilanti and collaborators after their extensive probes of experimental control of molecular alignment and orientation. In this work, the manifestation of the Aquilanti mechanism has been demonstrated for the first time in first-principles molecular dynamics simulations: stationary points characterized on potential energy surfaces have been calculated for the study of chemical reactions occurring between the bisulfide anion HS^- and oriented prototypical chiral molecules CHFXY (where X = CH₃ or CN and Y = Cl or I). The important reaction channels are those corresponding to bimolecular nucleophilic substitution (S_N2) and to bimolecular elimination (E2): their relative role has been assessed and alternative pathways due to the mirror forms of the oriented chiral molecule are revealed by the different reactivity of the two enantiomers of CHFCNI in S_N2 reaction.

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.

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.

Effects of multidimensional tunneling in the kinetics of hydrogen abstraction reactions of O (3 P) with CH3 OCHO

Quantum tunneling paths are important in reactions when there is a significant component of hydrogenic motion along the potential energy surface. In this study, variational transition state with multidimensional tunneling corrections are employed in the calculations of the thermal rate constants for hydrogen abstraction from the cis-CH₃ OCHO by O (³ P) giving CH₃ OCO + OH (R1) and CH₂ OCHO + OH (R2). The structures and electronic energies are computed with the M06-2X method. Benchmark calculations with the CBS_D-T approach give an enthalpy of reaction at 0 K for R1 (-2.8 kcal/mol) and R2 (-2.5 kcal/mol) which are in good agreement with the experiment, i.e. -2.61 and -1.81 kcal/mol. At the low and intermediate values of temperatures, small- and large-curvature tunneling dominate the kinetics of R1, which is the dominant path over the range of temperature from 250 to 1200 K. This study shows the importance of multidimensional tunneling corrections for both R1 and R2, for which the total rate constant at 298 K calculated with the CVT/μOMT method is 8.2 × 10^-15 cm³ molecule^-1 s^-1 which agrees well with experiment value of 9.3 × 10^-15 cm³ molecule^-1 s^-1 (Mori, Bull. Inst. Chem. Res. 1981, 59, 116). © 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.

A novel analytical potential function for dicationic diatomic molecular systems based on deformed exponential function

In this paper, we propose a new alternative analytical function aiming to better describe the potential energy curves of the doubly charged diatomic molecules. To achieve this goal, we modified an existing potential function in the literature to describe dicationic diatomic molecules using the deformed exponential function. We generated the potential energy curve of the testing group of dicationic diatomic molecules [Formula: see text], BH²⁺, [Formula: see text] and NH²⁺ by means of the CCSD(T)/aug-cc-pVQZ level of theory. To validate this new function, we also calculated the spectroscopic constants and the rovibrational spectra for the electronic state [Formula: see text]of the [Formula: see text] and [Formula: see text] systems using the Dunham and discrete variable representation methods. For BH²⁺ and NH²⁺ molecules, despite exhibiting a local minimum in the potential energy curve, no vibrational levels are supported, so the spectroscopic constants for these poorly bound systems are invalidated. The fitting accuracy had a better performance over the original potential for describing dicationic diatomic systems, considering that the discrete variable representation method resulted in a similar vibrational structure described in the literature. This fact can be explained due to the deformed function's flexibility.

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'.