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Related Concept Videos

Distribution of Molecular Speeds01:27

Distribution of Molecular Speeds

The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
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At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately 105 times per second. These two chair conformers are in equilibrium. The rapid ring flipping results in the interconversion of the axial proton to an equatorial proton and an equatorial to the axial proton. Such interconversions are too rapid and cannot be detected on the NMR timescale. Hence, the NMR spectrometer cannot distinguish between the...
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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...
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Updated: May 11, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Published on: April 8, 2020

Robust and efficient configurational molecular sampling via Langevin dynamics.

Benedict Leimkuhler1, Charles Matthews

  • 1School of Mathematics and Maxwell Institute of Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom.

The Journal of Chemical Physics
|May 10, 2013
PubMed
Summary

This study introduces an optimal numerical method for molecular dynamics simulations, significantly improving accuracy and efficiency. It reduces errors in configurational averages and enhances computational performance, especially for biomolecular modeling.

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Last Updated: May 11, 2026

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Area of Science:

  • Computational Chemistry
  • Molecular Dynamics Simulations
  • Numerical Analysis

Background:

  • Stochastic differential equations (SDEs) are central to molecular dynamics (MD).
  • Accurate and efficient numerical methods are crucial for reliable MD simulations.
  • Existing methods face challenges with stepsize-dependent bias and computational cost.

Purpose of the Study:

  • To evaluate and compare various numerical methods for solving SDEs in MD.
  • To identify an optimal method with minimal bias and high accuracy.
  • To assess the performance of the optimal method in biomolecular simulations.

Main Methods:

  • Application of deterministic impulses, drifts, and Brownian motions in numerical schemes.
  • Utilizing the Baker-Campbell-Hausdorff expansion to analyze stepsize-dependent bias.
  • Testing methods on harmonic oscillators and alanine dipeptide (solvated/unsolvated) simulations.

Main Results:

  • An optimal numerical scheme was identified with significantly lower bias than alternatives.
  • Harmonic oscillators showed exact configurational averaging for specific schemes.
  • Alanine dipeptide simulations demonstrated higher accuracy, improved efficiency (≥25%), and maintained conformational exploration rates.

Conclusions:

  • The identified optimal scheme offers superior performance for molecular sampling in MD.
  • This method allows for larger timesteps without compromising accuracy or efficiency.
  • Significant error reduction (≥10x) in configurational averages is achievable, particularly in solvated systems.