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

"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.

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'.

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.