Molecular models for recombination and disproportionation of radicals

Benson, Sidney W.

doi:10.1139/v83-158

Cited by 61 publications

(52 citation statements)

References 10 publications

(7 reference statements)

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“…͑The current experimental results indicate that insertion into the bond is less than Ͻ1% of the end-on attack.͒ As noted previously, the PST transition state utilized in these calculations is quite loose, and cannot correctly account for the well known [56][57][58][59][60][61][62][63][64][65][66][67][68] tightening of the transition state which typically occurs at higher energies, and thus at higher temperatures. At low pressure the recombination rate depends weakly on the transition state ͑via the effective energy barriers in the exit and entrance channels͒ and also on the density of states, of the ozone molecule and on the deactivation collision efficiency.…”

Section: Discussionmentioning

confidence: 99%

“…It is known that loose transition state theory, or phase space theory, does not agree with the negative temperature dependence so often seen in bimolecular association reactions. [56][57][58][59][60][61][62][63][64][65][66][67][68] Phase space theory, for example, gives Eq. ͑3.6͒ with its positive T 1/6 dependence ͑excluding the temperature dependence of the electronic partition function͒, instead of the stronger negative temperature dependence found, for example, in the exchange reactions at low pressure ͓which correspond to the high pressure recombination rates, e.g., as in Eq.…”

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confidence: 99%

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An intramolecular theory of the mass-independent isotope effect for ozone. II. Numerical implementation at low pressures using a loose transition state

Hathorn

Marcus

2000

The Journal of Chemical Physics

104

112

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A theory is described for the variation in the rate constants for formation of different ozone isotopomers from oxygen atoms and molecules at low pressures. The theory is implemented using a simplified description which treats the transition state as loose. The two principal features of the theory are a phase space partitioning of the transition states of the two exit channels after formation of the energetic molecule and a small ͑ca. 15%͒ decrease in the effective density of states, ͓a ''non-Rice-Ramsperger-Kassel-Marcus ͑RRKM͒ effect''͔, for the symmetric ozone isotopomers ͓B. C. Hathorn and R. A. Marcus, J. Chem. Phys. 111, 4087 ͑1999͔͒. This decrease is in addition to the usual statistical factor of 2 for symmetric molecules. Experimentally, the scrambled systems show a ''mass-independent'' effect for the enrichments ␦ ͑for trace͒ and E ͑for heavily͒ enriched systems, but the ratios of the individual isotopomeric rate constants for unscrambled systems show a strongly mass-dependent behavior. The contrasting behavior of scrambled and unscrambled systems is described theoretically using a ''phase space'' partitioning factor. In scrambled systems an energetic asymmetric ozone isotopomer is accessed from both entrance channels and, as shown in paper I, the partitioning factor becomes unity throughout. In unscrambled systems, access to an asymmetric ozone is only from one entrance channel, and differences in zero-point energies and other properties, such as the centrifugal potential, determine the relative contributions ͑the partitioning factors͒ of the two exit channels to the lifetime of the resulting energetic ozone molecule. They are responsible for the large differences in individual recombination rate constants at low pressures. While the decrease in for symmetric systems is attributed to a small non-RRKM effect , these calculated results are independent of the exact origin of the decrease. The calculated ''mass-independent'' enrichments, ␦ and E, in scrambled systems are relatively insensitive to the transition state ͑TS͒, because of the absence of the partitioning factor in their case ͑for a fixed non-RRKM ͒. They are compared with the data at room temperature. Calculated results for the ratios of individual isotopomeric rate constants for the strongly mass-independent behavior for unscrambled systems are quite sensitive to the nature of the TS because of the partitioning effect. The current data are available only at room temperature but the loose TS is valid only at low temperatures. Accordingly, the results calculated for the latter at 140 K represent a prediction, for any given . At present, a comparison of the 140 K results can be made only with room temperature data. They show the same trends as, and are in fortuitous agreement, with the data. Work is in progress on a description appropriate for room temperature.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

An intramolecular theory of the mass-independent isotope effect for ozone. II. Numerical implementation at low pressures using a loose transition state

Hathorn

Marcus

2000

The Journal of Chemical Physics

104

112

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“…For example, in the case of simple bond-fission reactions with loose transition states, the Gorin TS model gives a distinctly different temperature dependence for A ϱ and E ϱ than does the vibrational model. 12,34 Tight transition states, such as that required for Reaction ͑1͒, are generally well fitted using vibrational TS models and generally exhibit only a weak or negligible temperature dependence in A ϱ and E ϱ : The Arrhenius plots are nearly straight lines.…”

Section: Steady-state Unimolecular Reactionmentioning

confidence: 99%

Vibrational energy transfer in shock-heated norbornene

Barker

King

1995

The Journal of Chemical Physics

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Recently, Kiefer et al. ͓J. H. Kiefer, S. S. Kumaran, and S. Sundaram, J. Chem. Phys. 99, 3531 ͑1993͔͒ studied shock-heated norbornene ͑NB͒ in krypton bath gas using the laser-schlieren technique and observed vibrational relaxation, unimolecular dissociation ͑to 1,3-cyclopentadiene and ethylene͒, and dissociation incubation times. Other workers have obtained an extensive body of high-pressure limit unimolecular reaction rate data at lower temperatures using conventional static and flow reactors. In the present work, we have developed a vibrational energy transfer-unimolecular reaction model based on steady-state RRKM calculations and time-dependent master equation calculations to satisfactorily describe all of the NB data ͑incubation times, vibrational relaxation times, and unimolecular rate coefficients͒. The results cover the temperature range from ϳ300 to 1500 K and the excitation energy range from ϳ1 000 to 18 000 cm Ϫ1 . Three different models ͑based on the exponential step-size distribution͒ for the average downward energy transferred per collision, ͗⌬E͘ down were investigated. The experimental data are too limited to enable the identification of a preferred model and it was not possible to determine whether the average ͗⌬E͘ down is temperature dependent. However, all three ͗⌬E͘ down models depend linearly on vibrational energy and it is concluded that standard unimolecular reaction rate codes must be revised to include energy-dependent microcanonical energy transfer parameters. The choice of energy transfer model affects the deduced reaction critical energy by more than 2 kcal mol Ϫ1 , however, which shows the importance of energy transfer in determining thermochemistry from unimolecular reaction fall-off data. It is shown that a single set of Arrhenius parameters gives a good fit of all the low temperature data and the shock-tube data extrapolated to the high pressure limit, obviating the need to invoke a change in reaction mechanism from concerted to diradical for high temperature conditions. Some possible future experiments are suggested.

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“…The canonical coordinate pairs for the system are With this simplification, ell the derivatives in [3] can be evaluated analytically from [l] and [2] and the integration becomes straightforward. gy was required to within 6 X kcal mol-', which leads to the requirement of step lengths in the range 4 X 10-l6 to 3 X 10-l4 s; the total angular momentum, i.e.…”

Section: The Equations Of Motionmentioning

confidence: 99%

“…Thus, rather like a pair of dancers, they remain facing each other during the whole of the intimate encounter, regaining independent rotational motion only after they have receded beyond a critical value of the interparticle separation; however (to continue with the dancing analogy), collisions in which one radical "turns its back" on the other are not entirely excluded. These observations complicate attempts, such as those of Benson recently (3), to calculate disproportionation-recombination ratios by simple geometric arguments based on the spatial characteristics of the radicals.…”

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confidence: 99%

Oriented collisions in the recombination and disproportionation of free radicals

Cohen¹,

Pritchard²

1985

Can. J. Chem.

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, 2374 (1985). It is shown that there will be strong orienting effects in the collision of two radicals which will invalidate attempts to calculate disproportionation-recombination ratios by simple geometric arguments.L. K. COHEN et H. 0 . PRITCHARD. Can. J. Chem. 63, 2374 (1985). On dCmontre qu'il existe des effets directifs importants dans la collision de deux radicaux et que ces effets rendent invalides tous les essais de calculer les rapports de disproportionation-recombinaison par des arguments gtornCtriques simples.[Traduit par le journal]It is possible to take two extreme views of the disproportionation process which occurs between a pair of alkyl radicals, e.g.At one extreme, one can consider that the methyl radical abstracts a hydrogen atom from the difluoromethyl radical (1); at the other extreme, that the products are the "dissociated" species in a chemical activation process, with the recombined product (C2H4F2 in this case) being the "stabilised" fraction of the initial flux (2). It is the purpose of this note to throw some light on the mechanisms of these processes by performing trajectory calculations for the approach of two bodies under the influence of a strongly directional attractive potential, such as is characteristic of a p-orbital in an aliphatic free radical. We find that in such collisions, provided that the radicals are not rotating too strongly, there is a propensity for them to orient themselves so that they are "facing" each other. Thus, rather like a pair of dancers, they remain facing each other during the whole of the intimate encounter, regaining independent rotational motion only after they have receded beyond a critical value of the interparticle separation; however (to continue with the dancing analogy), collisions in which one radical "turns its back" on the other are not entirely excluded. These observations complicate attempts, such as those of Benson recently (3), to calculate disproportionation-recombination ratios by simple geometric arguments based on the spatial characteristics of the radicals.We are faced with a multitude of possible disproportionation reactions (4) and so, for our first examination of this problem, we restrict ourselves to a carefully chosen model of the collision between two methyl radicals which retains, we believe, sufficient physical reality to enable the salient physical effects to be discerned; extension to real reactive systems is then only a matter of detail and of computational complexity. The model and the potentialThe dominant interactions are the bonding attraction between the two radical centres, and the non-bonded repulsions between the valence-saturated atoms in the system. For the attractive potential we chose, simulating ethane, a Morse curve In order to test our conjecture that most, if not all, of the initial rotational angular momentum is converted into overall angular momentum during closest approach, it is not necessary to perform a full three-dimensional calculation with two radicals: the physical picture remains the same if on...

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Molecular models for recombination and disproportionation of radicals

Cited by 61 publications

References 10 publications

An intramolecular theory of the mass-independent isotope effect for ozone. II. Numerical implementation at low pressures using a loose transition state

An intramolecular theory of the mass-independent isotope effect for ozone. II. Numerical implementation at low pressures using a loose transition state

Vibrational energy transfer in shock-heated norbornene

Oriented collisions in the recombination and disproportionation of free radicals

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