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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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Systematic Error: Methodological and Sampling Errors01:15

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In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According to the source, systematic errors can be divided into sampling, instrumental, methodological, and personal errors.
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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
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Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value. 
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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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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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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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在密度功能多体扩张中解开错误源.

Dustin R Broderick1, John M Herbert1

  • 1Department of Chemistry & Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States.

The journal of physical chemistry letters
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概括
此摘要是机器生成的。

在使用具有现代密度函数近似的标准网格时,多体扩张会放大电子结构计算中的错误. 这加剧了移位错误,需要更密集的网格来缓解计算化学中的问题.

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科学领域:

  • 计算化学是一种计算化学.
  • 电子结构理论 电子结构理论
  • 量子化学是一种量子化学.

背景情况:

  • 多体扩展是电子结构理论中数据驱动应用的强大工具,包括力场参数化和机器学习.
  • 现代密度函数近似 (DFA) 广泛使用,但可能对数值近似敏感.
  • 方格网对于电子结构计算中的数值集成至关重要.

研究的目的:

  • 在使用现代DFAs时,调查正方形格子错误对多体扩张的影响.
  • 为了证明标准的正方形网格如何放大错误,并加剧多体计算中的移位错误.
  • 探索减轻这些放大错误的策略.

主要方法:

  • 应用多体膨胀框架的应用.
  • 使用现代密度函数近似方法,包括SCAN,r2SCAN,oB97X-V和oB97M-V.
  • 在离子-水集群上进行计算.
  • 四边形网格密度的系统变化.

主要成果:

  • 标准的正方形网格在与多体扩展和现代DFAs一起使用时显著放大了错误.
  • 常规网格观察到失控错误积累,与标准密度函数计算不同.
  • 移位错误加剧,导致高估的非添加 n-body 相互作用.
  • 使用密集的正方形网格暴露了固有的自我交互错误.

结论:

  • 由于错误放大,将多体扩展和标准正方形网格与现代DFA相结合是有问题的.
  • 更密集的正方形格子是必要的,以获得可靠的结果,并暴露潜在的错误.
  • 一旦暴露在密集的网格中,可以有效地应用自我相互作用错误的缓解策略.