Exact activation energies and phenomenological description of quantum tunneling for model potential energy surfaces. The F+H2 reaction at low temperature

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.

Torrefaction Thermogravimetric Analysis and Kinetics of Sorghum Distilled Residue for Sustainable Fuel Production

This study investigated the kinetics of isothermal torrefaction of sorghum distilled residue (SDR), the main byproduct of the sorghum liquor-making process. The samples chosen were torrefied isothermally at five different temperatures under a nitrogen atmosphere in a thermogravimetric analyzer. Afterward, two different kinetic methods, the traditional model-free approach, and a two-step parallel reaction (TPR) kinetic model, were used to obtain the torrefaction kinetics of SDR. With the acquired 92–97% fit quality, which is the degree of similarity between calculated and real torrefaction curves, the traditional method approached using the Arrhenius equation showed a poor ability on kinetics prediction, whereas the TPR kinetic model optimized by the particle swarm optimization (PSO) algorithm showed that all the fit qualities are as high as 99%. The results suggest that PSO can simulate the actual torrefaction kinetics more accurately than the traditional kinetics approach. Moreover, the PSO method can be further employed for simulating the weight changes of reaction intermediates throughout the process. This computational method could be used as a powerful tool for industrial design and optimization in the biochar manufacturing 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.

Benchmark Quantum Kinetics at Low Temperatures toward Absolute Zero and Role of Entrance Channel Wells on Tunneling, Virtual States, and Resonances: The F + HD Reaction

This paper reports a study of the quantum reaction dynamics and kinetics of the F + HD reaction at low and ultralow temperatures, focusing on the range from the Wigner limit up to 50 K. Close coupling time-independent quantum reactive scattering calculations for the production of HF and DF molecules have been carried out on two potential energy surfaces differing in the description of the reaction entrance channel. This case is computationally more demanding than the cases of F with H₂ and D₂ ( De Fazio et al. Frontiers in Chemistry 2019 , 7 , 328 ) but offers a wider phenomenology regarding the roles of quantum mechanical effects of tunneling, of virtual states, and of resonances. The results show that at the temperatures in the cold and ultracold regimes small changes in the entrance channel long-range interaction induce surprising near threshold features. The presence of a virtual state close to the reactive threshold gives rise to a marked anti-Arrhenius behavior of the rate constants below 100 mK. This effect enhances reaction rates by about 2 orders of magnitude, making them of the same order as those at room temperature and confining the onset of the Wigner regime in the microkelvin region.

"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.

Kinetics Of The H + CH2 → CH + H2 Reaction At Low Temperature

A quasiclassical trajectory study of the kinetics of the title astrochemical reaction in a range of temperatures varying from 5 to 1000 K (corresponding to both the outer and the inner regions of the protostar and the circumstellar envelopes) was carried out and a clear dependence of the rate coefficient on the temperature is given, in contrast with the constant value adopted in kinetics astrochemical databases. Levering the massive nature of the performed calculations and of the detailed dynamical investigation of the reactive process, a rationalization of the temperature dependence of the released translational energy and of the rovibrational population of the CH and H₂ diatomic products is also provided. Furthermore, the effect of the initial rovibrational energy of CH₂ on the state-specific rate coefficients and cross sections is analyzed in order to single out the role played by the different regions of the potential energy surface on the dynamical outcomes and on the modeling the temperature dependence of the reactive efficiency of the investigated process. This led to a parametrization of the computed rate in terms of the following double Arrhenius expression (in cm³ s^-1), k(T) = 2.50 × 10^-10 exp(- 1.67/T) + 5.98 × 10^-11 exp(- 280.5/T), alternative to the piecewise formulation into the three subintervals of temperature in which the overall 5-1000 K interval can be divided.

Quantum Dynamics and Kinetics of the F + H2 and F + D2 Reactions at Low and Ultra-Low Temperatures

Integral cross sections and rate constants for the prototypical chemical reactions of the fluorine atom with molecular hydrogen and deuterium have been calculated over a wide interval of collision energy and temperature ranging from the sub-thermal (50 K) down to the ultra-cold regimes (0.5 mK). Rigorous close coupling time-independent quantum reactive scattering calculations have been carried out on two potential energy surfaces, differing only at long-range in the reactants' channel. The results show that tunnel, resonance and virtual state effects enhance under-barrier reactivity giving rise to pronounced deviations from the Arrhenius law as temperature is lowered. Within the ultra-cold domain (below 1 mK), the reactivity is governed by virtual state effects and by tunneling through the reaction barrier; in the cold regime (1 mK–1 K), the shape resonances in the entrance channel of the potential energy surface make the quantum tunneling contribution larger so enhancing cross sections and rate constants by about one order of magnitude; at higher temperatures (above 10 K), the tunneling pathway enhanced by the constructive interference between two Feshbach resonances trapped in the reaction exit channel competes with the thermally activated mechanism, as the energy gets closer to the reaction barrier height. The results show that at low temperatures cross sections and rate constants are extremely sensitive to small changes in the long-range intermolecular interaction in the entrance channel of the potential energy surface, as well as to isotopic substitution.

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.

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'.

Steepest-entropy-ascent nonequilibrium quantum thermodynamic framework to model chemical reaction rates at an atomistic level

The steepest entropy ascent (SEA) dynamical principle provides a general framework for modeling the dynamics of nonequilibrium (NE) phenomena at any level of description, including the atomistic one. It has recently been shown to provide a precise implementation and meaning to the maximum entropy production principle and to encompass many well-established theories of nonequilibrium thermodynamics into a single unifying geometrical framework. Its original formulation in the framework of quantum thermodynamics (QT) assumes the simplest and most natural Fisher-Rao metric to geometrize from a dynamical standpoint the manifold of density operators, which represent the thermodynamic NE states of the system. This simplest SEAQT formulation is used here to develop a general mathematical framework for modeling the NE time evolution of the quantum state of a chemically reactive mixture at an atomistic level. The method is illustrated for a simple two-reaction kinetic scheme of the overall reaction F+H_{2}⇔HF+F in an isolated tank of fixed volume. However, the general formalism is developed for a reactive system subject to multiple reaction mechanisms. To explicitly implement the SEAQT nonlinear law of evolution for the density operator, both the energy and the particle number eigenvalue problems are set up and solved analytically under the dilute gas approximation. The system-level energy and particle number eigenvalues and eigenstates are used in the SEAQT equation of motion to determine the time evolution of the density operator, thus effectively describing the overall kinetics of the reacting system as it relaxes toward stable chemical equilibrium. The predicted time evolution in the near-equilibrium limit is compared to the reaction rates given by a standard detailed kinetic model so as to extract the single time constant needed by the present SEA model.

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.

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.

Complementarity between Quantum and Classical Mechanics in Chemical Modeling. The H + HeH+ → H2 + + He Reaction: A Rigourous Test for Reaction Dynamics Methods

In this work we present a dynamical study of the H + HeH+ → H2+ + He reaction in a collision energy range from 0.1 meV to 10 eV, suitable to be used in applicative models. The paper extends and complements a recent work [ Phys. Chem. Chem. Phys. 2014, 16, 11662] devoted to the characterization of the reactivity from the ultracold regime up to the three-body dissociation breakup. In particular, the accuracy of the quasi-classical trajectory method below the three-body dissociation threshold has been assessed by a detailed comparison with previous calculations performed with different reaction dynamics methods, whereas the reliability of the results in the high energy range has been checked by a direct comparison with the available experimental data. Integral cross sections for several HeH+ roto-vibrational states have been analyzed and used to understand the extent of quantum effects in the reaction dynamics. By using the quasi-classical trajectory method and quantum mechanical close coupling data, respectively, in the high and low collision energy ranges, we obtain highly accurate thermal rate costants until 15 000 K including all (178) the roto-vibrational bound and quasi-bound states of HeH+. The role of the collision-induced dissociation is also discussed and explicitly calculated for the ground roto-vibrational state of HeH+.

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).

The H + HeH(+) → He + H2(+) reaction from the ultra-cold regime to the three-body breakup: exact quantum mechanical integral cross sections and rate constants

In this work, we present a quantum mechanical scattering study of the title reaction from 1 mK to 2000 K. Total integral cross sections and thermal rate constants are compared with previous theoretical and experimental data and with simpler theoretical models to understand the range of validity of the approximations used in the previous studies. The obtained quantum reactive observables have been found to be nearly insensitive to the roto-vibrational energy of the reactants at high temperatures. More sensitive to the reactant's roto-vibrational energy are the data in the cold and ultra-cold regimes. The implications of the new data presented here in the early universe scenario are also discussed and analyzed.

Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F + HD → HF(v′ = 3) + D reaction

State-to-state reactive integral cross sections (ICSs) are often affected by quantum mechanical resonances, especially in the neighborhood of a reactive threshold.

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.

The He + H2+ → HeH+ + H reaction: ab initio studies of the potential energy surface, benchmark time-independent quantum dynamics in an extended energy range and comparison with experiments

In this work we critically revise several aspects of previous ab initio quantum chemistry studies [P. Palmieri et al., Mol. Phys. 98, 1835 (2000); C. N. Ramachandran et al., Chem. Phys. Lett. 469, 26 (2009)] of the HeH(2)(+) system. New diatomic curves for the H(2)(+) and HeH(+) molecular ions, which provide vibrational frequencies at a near spectroscopic level of accuracy, have been generated to test the quality of the diatomic terms employed in the previous analytical fittings. The reliability of the global potential energy surfaces has also been tested performing benchmark quantum scattering calculations within the time-independent approach in an extended interval of energies. In particular, the total integral cross sections have been calculated in the total collision energy range 0.955-2.400 eV for the scattering of the He atom by the ortho- and para-hydrogen molecular ion. The energy profiles of the total integral cross sections for selected vibro-rotational states of H(2)(+) (v = 0,...,5 and j = 1,...,7) show a strong rotational enhancement for the lower vibrational states which becomes weaker as the vibrational quantum number increases. Comparison with several available experimental data is presented and discussed.