Comparison of models for treating angular momentum in RRKM calculations with vibrator transition states. Pressure and temperature dependence of Cl + C2H2 association

Ling Zhu, Wei Chen, William L. Hase, E. W. Kaiser

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The RRKM expression for the microcanonical unimolecular rate constant depends on how the K rotational quantum number is treated. The limiting cases are to treat K as either adiabatic or active. The former occurs when K is a good quantum number for describing the vibrational/rotational energy levels. The latter case arises when coriolis coupling extensively mixes the (2J + 1) K levels. It is not necessary that K be simultaneously active or adiabatic for both the transition state and reactant molecule. Thus, four models which explicitly treat K with its proper limits, i.e. -J ≤ K ≤ J, can be formulated for the RRKM unimolecular rate constant. It is found that the calculated pressure- and temperature-dependent rate constant for Cl + C2H2 → C2H2Cl association is highly sensitive to the treatment of the K quantum number in RRKM theory. For example, to fit the association rate constant at low pressure using the model with K adiabatic in the transition state and active for the molecule requires a value for the collision efficiency βc twice the size needed when K is treated as active in both the molecule and transition state. These results indicate that until the proper model for treating K is identified it will be difficult to determine unambiguous values for βc by fitting experimental data. To assist in interpreting the experimental kinetics for the Cl + C2H2 → C2H2Cl system, ab initio calculations were performed to determine the structure, vibrational frequencies, and energy for C2H2Cl. The ab initio G2 value for the 0 K heat for Cl + C2H2 association is -16.855 kcal/mol, which agrees with semiempirical estimates of the heat of reaction. To fit the low-pressure experimental rate constants for Cl + C2H2 association in air requires values for βc which range from 0.4 to 1.0. However, none of the RRKM models for treating K provides an adequate fit to all the temperature- and pressure-dependent experimental rate constants. Possible explanations for this finding include an inadequate treatment of anharmonicity, non-RRKM rate constants for C2H2Cl dissociation, and imperfect extrapolations of the experimental rate constants to the high- and low-pressure asymptotic limits.

Original languageEnglish
Pages (from-to)311-322
Number of pages12
JournalJournal of physical chemistry
Issue number2
StatePublished - 1993


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