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Related Concept Videos

The Uncertainty Principle04:08

The Uncertainty Principle

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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Uncertainty: Overview00:59

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Propagation of Uncertainty from Systematic Error01:10

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Uncertainty: Confidence Intervals00:54

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Updated: Nov 11, 2025

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
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Uncertainty quantification in classical molecular dynamics.

Shunzhou Wan1, Robert C Sinclair1, Peter V Coveney1,2

  • 1Centre for Computational Science, University College London, Gordon Street, London WC1H 0AJ, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|March 29, 2021
PubMed
Summary
This summary is machine-generated.

Molecular dynamics simulations need better error estimates for reliable predictions. Ensemble methods, running many simulations concurrently, provide these crucial uncertainty quantification measures for reproducible results in science and industry.

Keywords:
free energy calculationmolecular dynamics simulationuncertainty quantification

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Area of Science:

  • Computational science
  • Atomistic-scale simulations
  • Scientific reproducibility

Background:

  • Molecular dynamics (MD) simulations are widely used across science and engineering for atomistic-scale analysis.
  • MD has advanced from rationalizing experiments to making credible predictions in fields like materials science and drug discovery.
  • However, the reproducibility of MD simulations has not kept pace with their increasing adoption.

Purpose of the Study:

  • To address the need for better error estimates in molecular dynamics simulations.
  • To enhance the reliability and actionability of MD simulation results through uncertainty quantification.
  • To discuss and illustrate the application of ensemble methods for uncertainty quantification in MD.

Main Methods:

  • Utilizing ensemble methods for uncertainty quantification in molecular dynamics.
  • Running a sufficient number of simulation replicas concurrently to extract reliable statistics.
  • Applying standard uncertainty quantification techniques to MD simulations.

Main Results:

  • Ensemble methods provide a fundamental approach to handle the inherent chaotic nature of MD simulations.
  • Demonstrated the application of uncertainty quantification in diverse areas, including materials science.
  • Showcased the utility of the approach for ligand-protein binding free energy estimation.

Conclusions:

  • Uncertainty quantification using ensemble methods is essential for improving the reliability of molecular dynamics simulations.
  • This approach enables MD to provide actionable results, moving beyond mere rationalization of experimental data.
  • The findings support the broader theme of enhancing verification, validation, and uncertainty quantification in computational science.