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Related Concept Videos

Fermi Level01:18

Fermi Level

The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
At absolute zero temperature, electrons fill all energy states up to the Fermi level, leaving upper states empty. As the temperature rises,...
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.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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...

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Related Experiment Video

Updated: Jun 23, 2026

Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures
08:53

Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures

Published on: October 9, 2012

Domain averaged Fermi hole analysis for open-shell systems.

Robert Ponec1, Ferran Feixas

  • 1Institute of Chemical Process Fundamentals of AS CR v.v.i., Prague 6, Suchdol 2, 165 02, Czech Republic. rponec@icpf.cas.cz

The Journal of Physical Chemistry. A
|April 24, 2009
PubMed
Summary
This summary is machine-generated.

This study extends the domain-averaged Fermi hole (DAFH) analysis to open-shell systems, enabling visualization of bonding interactions in radicals and molecules like NH3(+) and O2.

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Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures
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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Chemical Bonding Theory

Background:

  • The analysis of domain-averaged Fermi holes (DAFH) is a novel methodology for analyzing chemical bonding.
  • Existing DAFH methods are primarily suited for closed-shell systems.
  • Understanding bonding in open-shell systems is crucial in chemistry.

Purpose of the Study:

  • To generalize the DAFH methodology for the analysis of bonding in open-shell systems.
  • To provide a new computational tool for studying radical cations and open-shell molecules.
  • To visualize and interpret electronic structure in systems with unpaired electrons.

Main Methods:

  • Reformulation of the DAFH approach within unrestricted Hartree-Fock (UHF) and unrestricted Kohn-Sham (UKS) theories.
  • Application of the generalized DAFH method to analyze bonding in selected open-shell systems.
  • Utilizing computational chemistry techniques for electronic structure analysis.

Main Results:

  • Successful extension of the DAFH methodology to open-shell systems.
  • Detailed analysis of bonding in the doublet state of NH(3)(+) radical cation.
  • Visualization and interpretation of bonding in the triplet ground state of O(2) molecule.

Conclusions:

  • The generalized DAFH method provides an effective tool for studying bonding in open-shell systems.
  • This advancement allows for a deeper understanding of electronic structure in radical species.
  • The methodology offers new insights into the nature of chemical bonds in molecules with unpaired electrons.