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Assumptions and Limitations in RRKM and TST

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RRKM Theory is a Microcanonical Version of TST
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RRKM Theory (Rice–Ramsperger–Kassel–Marcus Theory) is indeed often considered a microcanonical extension of Transition State Theory (TST). Both theories share foundational assumptions and are used to describe reaction rates, but they operate within different statistical frameworks:

  • TST typically operates within a canonical (constant temperature) ensemble, assuming that the system is in thermal equilibrium with a heat bath.
  • RRKM Theory extends TST to a microcanonical (constant energy) ensemble, allowing for the calculation of unimolecular reaction rates as a function of energy.

Common Assumptions in RRKM and TST
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  1. Born-Oppenheimer (BO) Approximation: Both theories assume the BO approximation, which separates electronic and nuclear motions due to the large difference in their masses. This allows the potential energy surface (PES) to be treated independently of electronic transitions during the reaction.

  2. Equilibrium Between Reactants and Activated Complex: Both theories assume that there is a rapid and reversible equilibrium between reactants and the activated (transition) complex. This implies that the population of the activated complex is determined by the equilibrium distribution.

  3. No Recrossing of the Transition State: Both theories assume that once the system crosses the transition state, it proceeds to form products without reverting to reactants. This idealization means that the transmission coefficient (κ) is assumed to be close to 1, indicating minimal or no recrossing.

  4. Separable Reaction Paths: The reaction path is assumed to be separable from the other degrees of freedom, allowing the reaction coordinate to be treated independently. This simplifies the analysis by focusing on the primary pathway of the reaction.

Limitations
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Given the assumptions outlined above, RRKM Theory and TST have several limitations that constrain their applicability:

  1. Single Reaction Surface:

    • Limitation: These theories are only applicable to reactions that proceed along a single, well-defined potential energy surface (PES) without significant contributions from multiple pathways or surfaces.
    • Implication: Reactions involving multiple competing pathways or surface crossings cannot be accurately described using RRKM or TST.

  2. Long Transition State Lifetimes Relative to IVR:

    • Limitation: Both theories require that the lifetime of the transition state is much longer than the timescale of Intramolecular Vibrational Redistribution (IVR).
    • Implication: If IVR is not sufficiently rapid, the energy within the activated complex may not be uniformly redistributed, violating the statistical energy distribution assumption and leading to inaccurate rate predictions.

  3. Transmission Coefficient Near 1:

    • Limitation: The assumption that the transmission coefficient (κ) is close to 1 implies negligible recrossing of the transition state.
    • Implication: In systems where recrossing is significant, the transmission coefficient deviates from 1, rendering the theories’ rate predictions unreliable.

  4. Inapplicability to Barrierless Reactions:

    • Limitation: Both RRKM and TST rely on the existence of a well-defined transition state with an associated energy barrier.
    • Implication: Barrierless reactions, which proceed without a significant energy barrier or distinct transition state, cannot be accurately described by these theories. Alternative models, such as direct dynamics simulations, are required for such reactions.

  5. Assumption of Separable Reaction Paths:

    • Limitation: The assumption that the reaction coordinate is separable from other degrees of freedom may not hold in systems where there is strong coupling between the reaction coordinate and other vibrational modes.
    • Implication: In such cases, the energy distribution cannot be treated independently, leading to potential inaccuracies in rate calculations.

  6. Neglect of Quantum Effects:

    • Limitation: Both theories primarily treat nuclear motion classically and may not account for quantum mechanical effects such as tunneling, especially significant in reactions involving light atoms like hydrogen.
    • Implication: For reactions where quantum effects play a crucial role, RRKM and TST may underestimate or misrepresent the actual reaction rates.

Summary
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  • RRKM Theory extends TST to a microcanonical framework, maintaining similar foundational assumptions.
  • Both theories assume the Born-Oppenheimer approximation, equilibrium between reactants and the activated complex, no recrossing, and separable reaction paths.
  • Limitations:
    • Applicable only to single reaction surfaces.
    • Require that the transition state lifetime is much longer than IVR.
    • Assume the transmission coefficient is near 1.
    • Not suitable for barrierless reactions.
    • Depend on the separability of reaction paths and often neglect quantum effects.