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Related Concept Videos

Band Theory02:35

Band Theory

When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
The energy difference between these bands is known as the band gap.
Conductor, Semiconductor,...
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IR Absorption Frequency: Delocalization

Electron delocalization refers to the distribution of electrons across multiple atoms within a molecule rather than being confined to a single atom or bond. This phenomenon is common in systems with conjugated bonds—structures where alternating single and double bonds allow π-electrons to move freely across the network. The movement of electrons stabilizes the molecule and can affect various chemical properties, including vibrational frequencies observed in IR spectroscopy.
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Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
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Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections in Crystal Structure: Stoichiometric Point Defects

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Fermi Level Dynamics01:12

Fermi Level Dynamics

The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
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The work...
Energy Bands in Solids01:01

Energy Bands in Solids

Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
 Band Formation:
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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
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Localization and delocalization errors in density functional theory and implications for band-gap prediction.

Paula Mori-Sánchez1, Aron J Cohen, Weitao Yang

  • 1Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.

Physical Review Letters
|June 4, 2008
PubMed
Summary

Density functional theory (DFT) calculations often fail to accurately predict material band gaps. This study reveals that errors in total energy calculations for fractional charges cause delocalization and localization issues, hindering accurate band gap prediction.

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Area of Science:

  • Quantum Chemistry
  • Materials Science
  • Computational Physics

Background:

  • The band-gap problem is a persistent challenge in density functional theory (DFT), leading to systematic inaccuracies in predicting electronic properties.
  • Approximate exchange-correlation functionals often fail to capture the correct behavior of total energy for fractional electron charges.
  • These failures manifest as delocalization or localization errors, particularly in larger and bulk systems.

Purpose of the Study:

  • To explain the origins of the band-gap problem and other systematic failures in DFT.
  • To analyze the role of total energy calculations for fractional charges in these errors.
  • To identify the physical nature of errors that need correction for accurate band gap prediction.

Main Methods:

  • Analysis of total energy behavior for fractional charges in various systems.
  • Investigation of the convexity and concavity of exchange-correlation functionals.
  • Comparison of functional behavior in finite versus bulk system limits.

Main Results:

  • Deviation from linear energy behavior for fractional charges in finite systems causes delocalization and localization errors.
  • Convex functionals (e.g., LDA) exhibit incorrect apparent linearity in bulk due to delocalization error.
  • Concave functionals show incorrect apparent linearity in bulk calculations due to localization error and imposed symmetry.

Conclusions:

  • The study resolves the apparent paradox of functional behavior in different system sizes.
  • It identifies the physical origin of errors in DFT band gap predictions.
  • Addressing delocalization and localization errors related to fractional charges is crucial for improving DFT accuracy.