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Related Concept Videos

Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

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 particular...
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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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Effective sample preparation is crucial for accurate and reliable laboratory analysis. During this process, two significant sources of error can arise: concentration bias from improper sample splitting and contamination caused by methods used to reduce particle size, such as grinding or homogenization. Identifying and minimizing these potential errors is crucial to ensuring the validity of the analysis.
Another key consideration is determining the appropriate number of samples required to...
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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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The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
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Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.Polar molecules have a partial positive charge on one end and a partial negative charge on the other end of the molecule,...

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Adapting Taylor Dispersion to Measure the Dispersion Coefficient of Electrolyte Solutions via an Accessible Microfluidic Setup
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Sensitivity analysis and uncertainty calculation for dispersion corrected density functional theory.

Felix Hanke1

  • 1Surface Science Research Centre, University of Liverpool, Liverpool, United Kingdom. hanke@liverpool.ac.uk

Journal of Computational Chemistry
|February 2, 2011
PubMed
Summary
This summary is machine-generated.

Dispersion-corrected density functional theory (DFT-D) calculations show uncertainties of several percent in binding energies and distances. Damping functions significantly impact binding geometries, especially for interlayer binding in graphite.

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Area of Science:

  • Computational chemistry
  • Materials science

Background:

  • Density functional theory (DFT) is a powerful tool for electronic structure calculations.
  • Dispersion corrections (DFT-D) are crucial for accurately describing van der Waals interactions.
  • Quantifying uncertainties in DFT-D is essential for reliable predictions.

Purpose of the Study:

  • To investigate the precision of binding energies and distances calculated using DFT-D.
  • To assess the impact of input parameters on dispersion corrections.
  • To provide methods for estimating error bars and result transferability.

Main Methods:

  • Propagation of uncertainties was used to determine relative uncertainties.
  • Sensitivity analysis was employed to evaluate parameter importance.
  • Interlayer binding of graphite was used as a detailed case study.

Main Results:

  • Relative uncertainties of several percent were found for binding energies and distances.
  • Damping functions significantly influence binding geometries, despite DFT-D's accuracy at large distances.
  • Geometry-dependent importance of input parameters for dispersion correction was quantified.

Conclusions:

  • The presented techniques enable rapid error bar computation for DFT-D results.
  • A posteriori estimates of result transferability can be obtained.
  • The findings can guide the development of improved dispersion corrections.