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Related Concept Videos

IR Absorption Frequency: Delocalization01:04

IR Absorption Frequency: Delocalization

940
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.
In IR...
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Energy Bands in Solids01:01

Energy Bands in Solids

1.3K
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:
When atoms are brought close together, as in a solid, these discrete energy levels begin to split due to the overlap of electron orbitals from adjacent atoms. This split occurs because of the Pauli exclusion principle, which states...
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Atomic Orbitals02:44

Atomic Orbitals

36.5K
An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
36.5K
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

48.0K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
48.0K
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

28.0K
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.
CFT focuses on...
28.0K
Electronic Structure of Atoms02:28

Electronic Structure of Atoms

24.6K

An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Localization and Delocalization in Solids from Electron Distribution Functions.

A Gallo-Bueno1, M Kohout2, E Francisco3

  • 1Center for Cooperative Research on Alternative Energies (CIC energiGUNE), Basque Research and Technology Alliance (BRTA), Álava Technology Park, Albert Einstein 48, 01510 Vitoria-Gasteiz, Spain.

Journal of Chemical Theory and Computation
|June 9, 2022
PubMed
Summary
This summary is machine-generated.

Electron distribution functions reveal electron behavior in materials. Most electrons delocalize, with conductivity distinguished by the decay rate of electron probability distributions.

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Area of Science:

  • Quantum Chemistry
  • Condensed Matter Physics
  • Materials Science

Background:

  • Electron localization and delocalization are key concepts in understanding molecular and condensed phases.
  • Existing localization descriptors often rely on orbital transformations and spatial partitioning.
  • Electron population fluctuations are linked to the conductive or insulating properties of systems.

Purpose of the Study:

  • To report electron distribution functions (EDFs) in periodic systems, analogous to Pauling resonance structures in molecules.
  • To investigate the relationship between EDFs and the degree of covalency in chemical compounds.
  • To explore electron delocalization patterns in metallic systems and differentiate conductors from insulators.

Main Methods:

  • Calculation and analysis of electron distribution functions (EDFs) in periodic systems.
  • Comparison of EDFs for ionic and covalent compounds.
  • Examination of electron delocalization in metallic systems like sodium.

Main Results:

  • EDFs in periodic systems show narrower distributions for ionic compounds, widening with increasing covalency.
  • Contrary to expectations, electrons exhibit significant delocalization even in metallic systems.
  • The decay rate of the electron probability distribution function effectively distinguishes between conductors and insulators.

Conclusions:

  • EDFs provide valuable insights into electron distribution and bonding in periodic systems.
  • Electron delocalization is prevalent, even in metals, challenging conventional interpretations.
  • The decay characteristics of electron distribution functions are crucial for classifying material conductivity.