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Related Concept Videos

Reaction Mechanisms03:06

Reaction Mechanisms

Chemical reactions often occur in a stepwise fashion, involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs.
For instance, the decomposition of ozone appears to follow a mechanism with two steps:
Alkenes via Reductive Coupling of Aldehydes or Ketones: McMurry Reaction01:22

Alkenes via Reductive Coupling of Aldehydes or Ketones: McMurry Reaction

The radical dimerization of ketones or aldehydes gives vicinal diols through a pinacol coupling reaction. However, the behavior of titanium metals used for the reaction as a source of electrons is unusual. When the reaction is carried out in the presence of titanium, diols can be isolated at low temperatures. Else titanium further reacts with diols, forming alkenes through the McMurry reaction.
Reaction Mechanisms: Rate-limiting Step Approximation01:29

Reaction Mechanisms: Rate-limiting Step Approximation

The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
Radical Reactivity: Overview01:11

Radical Reactivity: Overview

Radicals, the highly reactive species, gain stability by undergoing three different reactions. The first reaction involves a radical-radical coupling, in which a radical combines with another radical, forming a spin‐paired molecule. The second reaction is between a radical and a spin‐paired molecule, generating a new radical and a new spin‐paired molecule. The third reaction is radical decomposition in a unimolecular reaction, forming a new radical and a spin‐paired molecule. These three...
Rate-Determining Steps03:08

Rate-Determining Steps

Relating Reaction Mechanisms
In a multistep reaction mechanism, one of the elementary steps progresses significantly slower than the others. This slowest step is called the rate-limiting step (or rate-determining step). A reaction cannot proceed faster than its slowest step, and hence, the rate-determining step limits the overall reaction rate.
The concept of rate-determining step can be understood from the analogy of a 4-lane freeway with a short-stretch of traffic-bottleneck caused due to...

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Dynamic Pore-scale Reservoir-condition Imaging of Reaction in Carbonates Using Synchrotron Fast Tomography
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Published on: February 21, 2017

Milestoning without a Reaction Coordinate.

Peter Májek1, Ron Elber

  • 1Department of Computer Science, Upson Hall 4130, Cornell University, Ithaca NY 14853-7501 pmajek@cs.cornell.edu.

Journal of Chemical Theory and Computation
|July 3, 2010
PubMed
Summary
This summary is machine-generated.

Directional Milestoning enhances molecular dynamics simulations for complex biomolecular processes. This new method accurately calculates kinetics and thermodynamics without needing a single reaction coordinate, improving efficiency and statistical stability.

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Area of Science:

  • Computational Chemistry
  • Biophysics
  • Molecular Dynamics Simulations

Background:

  • Milestoning is a computational method for calculating kinetics and thermodynamics of long time processes, often inaccessible to standard Molecular Dynamics (MD) simulations.
  • Traditional Milestoning relies on identifying a one-dimensional reaction coordinate, which is insufficient for biomolecular processes with multiple reaction channels or order parameters.
  • Existing methods may struggle with systems lacking a clear, single reaction coordinate.

Purpose of the Study:

  • To introduce Directional Milestoning, a novel variation of the Milestoning method that overcomes the limitations of single reaction coordinates.
  • To enable accurate calculation of kinetics and thermodynamics for complex biomolecular systems with multiple pathways.
  • To improve the efficiency and statistical stability of calculating mean first passage times (MFPTs).

Main Methods:

  • Developed Directional Milestoning, which utilizes higher-dimensional hypersurfaces to 'tag' trajectories, enabling efficient calculations.
  • Adapted Voronoi cell concepts to milestone systems without requiring a predefined order parameter.
  • Examined and relaxed assumptions in Milestoning calculations for MFPTs, using a more accurate distribution mimicking the first hitting point distribution.

Main Results:

  • Directional Milestoning successfully calculates kinetics and thermodynamics for systems without a single reaction coordinate.
  • The method demonstrates approximate satisfaction of assumptions required for exact MFPT calculations.
  • Applied to alanine dipeptide conformational transitions (in vacuum and solution), showing comparable correctness and improved efficiency/stability against exact MD and related methods.

Conclusions:

  • Directional Milestoning offers a robust and efficient approach for studying complex biomolecular dynamics.
  • The method expands the applicability of Milestoning to a wider range of challenging biological processes.
  • This advancement provides a more accurate and stable way to compute kinetic and thermodynamic properties from simulations.