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Related Concept Videos

Types of Errors: Detection and Minimization01:12

Types of Errors: Detection and Minimization

Error is the deviation of the obtained result from the true, expected value or the estimated central value. Errors are expressed in absolute or relative terms.
Absolute error in a measurement is the numerical difference from the true or central value. Relative error is the ratio between absolute error and the true or central value, expressed as a percentage.
Errors can be classified by source, magnitude, and sign. There are three types of errors: systematic, random, and gross.
Systematic or...
Contaminants and Errors01:16

Contaminants and Errors

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...
Crystal Density01:19

Crystal Density

The crystal lattice structure of a material allows us to determine how many molecules exist in its unit cell. With this information, alongside the unit-cell parameters - three distance parameters (a, b, c) and three angular parameters (α, β, γ).Density (ρ) = (Z × M) / (a × b × c × NA)where:Z is the number of formula units per unit cellM is the molar mass of the substancea, b, and c are the edge lengths of the unit cellNA is Avogadro’s numberFor a simple cubic lattice, atoms are located only at...
Systematic Error: Methodological and Sampling Errors01:15

Systematic Error: Methodological and Sampling Errors

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.
Sampling errors originate from improper sampling methods or the wrong sample population. These errors can be minimized by refining the sampling strategy. Defective instruments or faulty calibrations are the sources of instrumental...
Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections in Crystal Structure: Stoichiometric Point Defects

Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...

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Updated: May 8, 2026

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

Understanding and reducing errors in density functional calculations.

Min-Cheol Kim1, Eunji Sim, Kieron Burke

  • 1Department of Chemistry and Institute of Nano-Bio Molecular Assemblies, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul, Korea.

Physical Review Letters
|September 3, 2013
PubMed
Summary
This summary is machine-generated.

Density functional theory (DFT) calculations can have errors from approximate functionals or densities. In some cases, density errors dominate, and improving the density significantly reduces calculation errors, especially when orbital gaps are small.

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Last Updated: May 8, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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

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Thermochemical Studies of Ni(II) and Zn(II) Ternary Complexes Using Ion Mobility-Mass Spectrometry
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Thermochemical Studies of Ni(II) and Zn(II) Ternary Complexes Using Ion Mobility-Mass Spectrometry

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • Variational density functional theory (DFT) is a cornerstone of modern computational chemistry.
  • DFT calculations rely on approximations for both the exchange-correlation functional and the electron density.
  • Understanding the sources of error in DFT is crucial for accurate predictions.

Purpose of the Study:

  • To decompose the energy error in variational DFT calculations.
  • To identify conditions where errors arise predominantly from the approximate electron density.
  • To provide guidance on improving DFT accuracy in specific challenging cases.

Main Methods:

  • Decomposition of the total energy error into functional and density contributions.
  • Analysis of error sources in various chemical systems, including electron affinities and solvated ions/radicals.
  • Correlation of small orbital gaps with significant density-driven errors.

Main Results:

  • The energy error in DFT can be attributed to either the approximate functional or the approximate density.
  • While functional error typically dominates, density-driven error can be substantial in specific scenarios.
  • A small orbital gap is a key indicator of significant density-driven error.

Conclusions:

  • Improving the accuracy of the electron density can substantially reduce DFT errors in cases dominated by density-driven error.
  • The findings offer a pathway to enhance the reliability of DFT for challenging chemical problems.
  • Identifying systems with small orbital gaps can help predict and mitigate density-driven errors in computational studies.