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Study of gas-phase reactions within the modified Marcus model. IV. Arrhenius equation for the reaction CH4 + CH3 → CH3 + CH4

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A Correction to this article was published on 07 September 2022

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Abstract

The results of a theoretical study (energy calculation level CCSD(T)/6–311++ G**//B3LYP/6–31 + G**) of methane with methyl radical gas-phase reaction kinetics [Comp. Theor. Chem. 1125 (2018), Comp. Theor. Chem.1179 (2020) 112,767] were used to analyze the Arrhenius equation in the temperatures range 2000–10 K. A discussion within the framework of the previously proposed (Russ. Bull. Int. Ed. 2008, 57, 1842–1849) model, which is a modification of the non-equilibrium Marcus model, is based on direct ab initio calculations of the structure and energy of the varied activated reaction complex in a wide range of distances between the reactants. The Arrhenius equation is analyzed in terms of the change with temperature parameters in the reaction rate constant equation. The results obtained make it possible to distinguish three temperature ranges (2000–900, 900–100 and 100–10 K), which are qualitatively different from each other in the nature and degree of influence of various variable factors on the Arrhenius plot.

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Notes

  1. The coordinate ρ in the Figs. 1 and 2 can formally be replaced by the coordinate q. It should be noted that the term "structural coordinate" is used here only in relation to the process of non-equilibrium reorganization of the system. In the general case, the reorganization of the system includes both non-equilibrium and equilibrium (when the system moves along the MEP) processes. In the TST limit, the reorganization of the system will proceed only according to the equilibrium mechanism and upon direct transition of the H-atom from the initial reagents to the final products (bypassing the movement along the MEP) the reorganization will be total non-equilibrium.

  2. In Marcus theory, the free-energy analogs of Eaeq and Eaneq energies are, respectively, the "working member" wr and the free activation energy in the collision complex, ΔG*.

  3. The description of the process of H-atom tunneling as a process of transition from the left to the right well of the potential V(r;ρ*,Q) forces, along with fixing the parameters Q and ρ*, to also fix the position of the H-atom in the left well (r01). The associated appearance of several imaginary frequencies is regarded as an artefact. It was found that taking these imaginary frequencies into account by replacing them with the corresponding real frequencies radically improves the agreement of the calculated values ​​of the H-atom transition rate constants with the available experimental data. Judging by the clearly overestimated values ​​of the KIE (kH/kD), there is no such agreement for the D (deuterium atom) transition. The reason for this may be the violation for D-atom the GFCP principle.22.

  4. Note, that for the saddle point on PES distance Q, QST = 2.69 A (this work).

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  1. Institut Himiceskoj Fiziki Imeni N N Semenova RAN RUSSIAN FEDERATION, Moscow, Russia

    Igor Romanskii

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Romanskii, I. Study of gas-phase reactions within the modified Marcus model. IV. Arrhenius equation for the reaction CH4 + CH3 → CH3 + CH4. Reac Kinet Mech Cat 135, 2401–2423 (2022). https://doi.org/10.1007/s11144-022-02245-3

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