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

Abstract

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.

Physicochemical, antioxidant properties of carotenoids and its optoelectronic and interaction studies with chlorophyll pigments

“…Transitivity code 31 has been used to calculate the reaction rate constant with Transition-State Theory (TST) for reactions in gaseous phase. The graph Log K versus 1000/K were plotted for the fourteen carotenoid-chlorophyll complexes for the default temperature range 273.15 K to 4000.00 K. In this window, it is possible to estimate reaction rate constant with TST and several one-dimensional tunneling corrections, thermodynamic (∆ E , ∆ H and ∆ G ) and kinetic ( Eo , d, ν‡, and α from ST model) properties of the reaction.…”

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

“…A recent paper [3] also gives an account of how useful it is the introduction of representations of experimentally or numerically exact rate constant data; the first, of course, is the Arrhenius plane [5], whereby the apparent activation energy is interpreted according to the Tolman's theorem [79]; the second one is the transitivity plane. We sketched here and elaborated elsewhere [4] a further aspect justifying how the definition of the transitivity function that can provide an understanding of microscopic kinetic processes using alternative forms of scaling of the rate data, yielding naturally the conventional statistics used in rate process, from Maxwell-Boltzmann [34] to Tsallis statistics [62], and to the further popular Vogel-Fulcher-Tammann [80][81][82] distributions. From Figure 4, it is possible to perceive graphically the three limits in a 3D Arrhenius plot, lnk vs. d and β.…”

“…Aspects related to the foundations of the kinetics of rate processes were elaborated recently in previous papers [1][2][3][4]. In [1], fundamental concepts concerning statistical distributions and reaction rate theory were presented, including the definition of transitivity, a function of absolute temperature denoted as γ(T), based on extensive phenomenology that is being accumulated; a subsequent paper [2] considered the historical background of developments of chemical kinetics, leading to the basic foundations through analysis of key mathematical ingredients; in [3], the formulations based on the concept of transitivity were compacted and applied to the description of several phenomena on the temperature dependence of rate processes beyond Arrhenius and Eyring; and finally in paper [4], companion of this one in this topical issue, a computational code is described and provided to calculate kinetics and related parameters in chemical transformations and transport phenomena.…”

The Fuzziness in Molecular, Supramolecular, and Systems Chemistry

“…The transitivity function provides a tool for implementing phenomenological kinetic models. In reference [ 36 ], Machado, Sanches-Neto, Coutinho, Mundim, Palazzetti, and Carvalho-Silva document the general scope of a transitivity code that can estimate the kinetic and thermodynamic parameters of physicochemical processes and deal with non-Arrhenius behavior.…”