Association of Cl with C2H2 by unified variable-reaction-coordinate and reaction-path variational transition-state theory

Significance A key issue in chemical kinetics is advancing the theoretical framework to handle reactions beyond the domain of textbook transition-state theory by including––for example––anharmonicity, barrierless transition states, transition states in series, and the effect of conformational flexibility on equilibrium constants. Other key issues are validating affordable electronic structure methods for direct dynamics and the direct calculation of high-pressure limiting rate constants, which are often obtainable experimentally only by extrapolation. The present article addresses all these issues for a prototype radical–molecule association reaction and thereby demonstrates how to combine improved theoretical methods to provide rate constants in cases where experimental data are uncertain or missing. Barrierless unimolecular association reactions are prominent in atmospheric and combustion mechanisms but are challenging for both experiment and kinetics theory. A key datum for understanding the pressure dependence of association and dissociation reactions is the high-pressure limit, but this is often available experimentally only by extrapolation. Here we calculate the high-pressure limit for the addition of a chlorine atom to acetylene molecule (Cl + C2H2→C2H2Cl). This reaction has outer and inner transition states in series; the outer transition state is barrierless, and it is necessary to use different theoretical frameworks to treat the two kinds of transition state. Here we study the reaction in the high-pressure limit using multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) at the outer transition state and reaction-path variational transition state theory (RP-VTST) at the inner turning point; then we combine the results with the canonical unified statistical (CUS) theory. The calculations are based on a density functional validated against the W3X-L method, which is based on coupled cluster theory with single, double, and triple excitations and a quasiperturbative treatment of connected quadruple excitations [CCSDT(Q)], and the computed rate constants are in good agreement with some of the experimental results. The chlorovinyl (C2H2Cl) adduct has two isomers that are equilibrium structures of a double-well C≡C–H bending potential. Two procedures are used to calculate the vibrational partition function of chlorovinyl; one treats the two isomers separately and the other solves the anharmonic energy levels of the double well. We use these results to calculate the standard-state free energy and equilibrium constant of the reaction.

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