Monte Carlo Calculations. VI. A Re-evaluation of the RRKM Theory of Unimolecular Reaction Rates

Bunker, Don L.; Pattengill, M. D.

doi:10.1063/1.1668710

Cited by 133 publications

(21 citation statements)

References 9 publications

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“…A statistical assumption of RRKM theory is that energy flow (that is, intramolecular vibrational energy redistribution) between the unimolecular reactant's vibrational modes is unrestricted and com~lete on the time scale of the unimolecular reaction (1 1). A transition state, which separates reactants from products, is assumed in RRKM theory and, according to variational RRKM theory (12)(13)(14), is placed at the minimum in the sum of states for the degrees of freedom orthogonal to the reaction coordinate as the system moves along the reaction path. If the unimolecular reaction has a well-defined potential energy barrier, this variational criterion typically places the transition state at or near this point.…”

Section: Statistical Theoriesmentioning

confidence: 99%

Simulations of Gas-Phase Chemical Reactions: Applications to S _N 2 Nucleophilic Substitution

Hase

1994

Science

299

300

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Computer simulations and animations of the motion of atoms as a chemical reaction proceeds give a detailed picture of how the reaction occurs at a microscopic level. This information is particularly useful for testing the accuracy of statistical models, which are used to calculate various attributes of chemical reactions. Such simulations and animations, in concert with experimental and ab initio studies, have begun to provide a microscopic picture of the intimate details of a particular class of gas-phase ion-molecule bimolecular reactions known as S(N)2 nucleophilic substitution. In these reactions, a nucleophile is displaced from a molecule by another nucleophile. The dynamical model of S(N)2 reactions that emerges from the computer studies, and its relation to statistical theories, is discussed here.

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Section: Statistical Theoriesmentioning

confidence: 99%

Simulations of Gas-Phase Chemical Reactions: Applications to S _N 2 Nucleophilic Substitution

Hase

1994

Science

299

300

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“…6 for two different total energies. For comparison, the quantum vibrator and flexible RRKM 148,149,152 as the largest center-of-mass separation attained by the ZPE constrained trajectories without dis-sociation occurring. Distributions of the latter are shown in Fig.…”

Section: ͑28͒mentioning

confidence: 99%

Comparison of zero-point energy constrained and quantum anharmonic Rice–Ramsperger–Kassel–Marcus and phase space theory rate constants for Al3 dissociation

Peslherbe

Hase

1996

The Journal of Chemical Physics

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A scrutiny of the premise of the Rice-Ramsperger-Kassel-Marcus theory in isomerization reaction of an Ar7type molecule Statistical anharmonic unimolecular rate constants for the dissociation of fluxional molecules: Application to aluminum clustersThe ZPE constrained trajectory model is found to retain the ergodicity and intrinsic Rice-Ramsperger-Kassel-Marcus ͑RRKM͒ behavior observed previously ͓J. Chem. Phys. 101, 8535 ͑1994͔͒ in unconstrained trajectories of Al 3 decomposition. Microcanonical unimolecular rate constants for Al 3 decomposition are calculated from the ZPE constrained trajectories and compared with the predictions of the vibrator and flexible transition state models of RRKM theory, phase space theory, and the orbiting transition state model of phase space theory ͑OTS/PST͒. Quantum anharmonic Al 3 vibrational densities of state, determined by a semiclassical approach, are used to calculate these statistical rate constants. Anharmonicity increases the density of states threefold for total energies 1-2 kcal/mol above the classical product asymptotic limit, but has a negligible effect on the Al 2 ---Al transition state sum of states. The ZPE constrained trajectory unimolecular rate constants are in poor agreement with the quantum anharmonic OTS/PST and flexible RRKM rate constants. This is because the ZPE constraint is too restrictive and some of the ZPE constrained trajectories are temporarily trapped in the ZPE forbidden region of phase space. The ZPE constrained trajectory rate constants are smaller than their purely classical counterparts, since Al 2 is not formed without its ZPE and thus the effective dissociation threshold is larger for the ZPE constrained trajectories. ZPE constrained sums and densities are calculated by including the ZPE constraint when solving the classical phase integral. RRKM rate constants calculated from these ZPE constrained sums and densities are in much better agreement with the quantum anharmonic OTS/PST and flexible RRKM rate constants, than are those calculated from the ZPE constrained trajectories. The difference between the ZPE constrained RRKM and quantum flexible RRKM rate constants becomes small and much less than the anharmonic correction, for energies slightly in excess of the Al 2 ϩAl classical asymptotic limit. This is because the number of real frequencies in the instantaneous normal mode analysis decreases as the total energy is increased, which makes the ZPE constrained RRKM rate constant more accurate. Product energy partitioning from the ZPE constrained trajectories is in good agreement with the predictions of quantum phase space theories, except that the product diatom is formed too rotationally excited. The ZPE constraint scheme retains a spurious frequency and zero-point energy for the Al 2 ---Al bending motion at large separations, which increases the Al 2 product rotational energy. The work reported here supports the proposal that a ZPE constraint model, based on an instantaneous normal mode analysis, may be a valid approach for including zero-poi...

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“…tribution P(t; E) is also exponential35,48,49,52,53,54 ; both gap and lifetime distributions for realistic molecular potentials have been of great interest since the earliest days of trajectory simulations of unimolecular decay, and many examples of non-exponential lifetime distributions have been found36,52,53,54,55,56,57,58,59 .III. MODEL DYNAMICS: DIVIDING SURFACES, FLUX, BREAKDOWN OF NORMAL HYPERBOLICITY, AND GAP TIME DISTRIBUTIONS…”

mentioning

confidence: 99%

Bifurcations of Normally Hyperbolic Invariant Manifolds in Analytically Tractable Models and Consequences for Reaction Dynamics

Mauguière

Collins

Ezra

et al. 2013

Int. J. Bifurcation Chaos

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In this paper we study the breakdown of normal hyperbolicity and its consequences for reaction dynamics; in particular, the dividing surface, the flux through the dividing surface (DS), and the gap time distribution. Our approach is to study these questions using simple, two degree-of-freedom Hamiltonian models where calculations for the different geometrical and dynamical quantities can be carried out exactly. For our examples, we show that resonances within the normally hyperbolic invariant manifold may, or may not, lead to a 'loss of normal hyperbolicity'. Moreover, we show that the onset of such resonances results in a change in topology of the dividing surface, but does not affect our ability to define a DS. The flux through the DS varies continuously with energy, even as the energy is varied in such a way that normal hyperbolicity is lost. For our examples the gap time distributions exhibit singularities at energies corresponding to the existence of homoclinic orbits in the DS, but these singularities are not associated with loss of normal hyperbolicity.

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Monte Carlo Calculations. VI. A Re-evaluation of the RRKM Theory of Unimolecular Reaction Rates

Cited by 133 publications

References 9 publications

Simulations of Gas-Phase Chemical Reactions: Applications to S _N 2 Nucleophilic Substitution

Simulations of Gas-Phase Chemical Reactions: Applications to S _N 2 Nucleophilic Substitution

Comparison of zero-point energy constrained and quantum anharmonic Rice–Ramsperger–Kassel–Marcus and phase space theory rate constants for Al3 dissociation

Bifurcations of Normally Hyperbolic Invariant Manifolds in Analytically Tractable Models and Consequences for Reaction Dynamics

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Monte Carlo Calculations. VI. A Re-evaluation of the RRKM Theory of Unimolecular Reaction Rates

Cited by 133 publications

References 9 publications

Simulations of Gas-Phase Chemical Reactions: Applications to S N 2 Nucleophilic Substitution

Simulations of Gas-Phase Chemical Reactions: Applications to S N 2 Nucleophilic Substitution

Comparison of zero-point energy constrained and quantum anharmonic Rice–Ramsperger–Kassel–Marcus and phase space theory rate constants for Al3 dissociation

Bifurcations of Normally Hyperbolic Invariant Manifolds in Analytically Tractable Models and Consequences for Reaction Dynamics

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Simulations of Gas-Phase Chemical Reactions: Applications to S _N 2 Nucleophilic Substitution

Simulations of Gas-Phase Chemical Reactions: Applications to S _N 2 Nucleophilic Substitution