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Related Concept Videos

Transition State Theory01:25

Transition State Theory

Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Energy Diagrams, Transition States, and Intermediates02:13

Energy Diagrams, Transition States, and Intermediates

Free-energy diagrams, or reaction coordinate diagrams, are graphs showing the energy changes that occur during a chemical reaction. The reaction coordinate represented on the horizontal axis shows how far the reaction has progressed structurally. Positions along the x-axis close to the reactants have structures resembling the reactants, while positions close to the products resemble the products.  Peaks on the energy diagram represent stable structures with measurable lifetimes, while other...
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
Dynamic Equilibrium02:20

Dynamic Equilibrium

A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Chaotic dynamics in multidimensional transition states.

Ali Allahem1, Thomas Bartsch

  • 1Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom. a.allahem@lboro.ac.uk

The Journal of Chemical Physics
|December 13, 2012
PubMed
Summary
This summary is machine-generated.

The study reveals that transition state structures, crucial for chemical reactions, unexpectedly regain normal hyperbolicity despite increasing chaos. These essential phase space structures exist at most energies above the reaction threshold.

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Area of Science:

  • Chemical Dynamics
  • Physical Chemistry
  • Quantum Mechanics

Background:

  • Chemical reaction dynamics are governed by transition states, which are fleeting configurations.
  • Invariant geometric structures in phase space, like hyper-spheres and hyper-cylinders, mediate transition state crossing.
  • The stability of these structures depends on the normal hyperbolicity of the transition state dynamics.

Purpose of the Study:

  • To investigate the dynamics within the transition state for a hydrogen exchange reaction.
  • To determine how varying energy levels affect the chaoticity and normal hyperbolicity of the transition state.
  • To assess the persistence of key phase space structures in transition state theory.

Main Methods:

  • Studied the hydrogen exchange reaction in three degrees of freedom.
  • Analyzed the dynamics within the transition state region.
  • Examined the relationship between energy, chaos, and normal hyperbolicity.

Main Results:

  • Transition state dynamics become more chaotic as energy increases.
  • The transition state unexpectedly loses and then regains normal hyperbolicity.
  • Key phase space structures of transition state theory are found to exist at most energies above the threshold.

Conclusions:

  • The normal hyperbolicity of transition states is not monotonically dependent on energy.
  • Essential geometric structures for transition state theory are robust across a range of energies.
  • This finding has implications for understanding and predicting chemical reaction pathways.