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Related Concept Videos

Electron Behavior01:09

Electron Behavior

Electrons are negatively charged subatomic particles attracted to and orbit around the positively-charged nucleus of an atom. They reside in spaces associated with energy levels called shells and are further organized into subshells and orbitals within each shell.
Electrons Orbit the Nucleus
Electrons are found in specific locations outside of the nucleus. The shell in which an electron resides indicates the general energy level of the electron: those closer to the nucleus have less energy,...
Electron Behavior00:54

Electron Behavior

Overview
Electrons are negatively charged subatomic particles that are attracted to an orbit around the positively-charged nucleus of an atom. They reside in locations that are associated with energy levels called shells and are further organized into sub-shells and orbitals within each shell.
Electrons Orbit the Nucleus
Electrons are found in specific locations outside of the nucleus. The shell in which an electron resides indicates the general energy level of the electron: those closer to the...
Electron Configurations02:46

Electron Configurations

Electron configurations and orbital diagrams can be determined by applying the Aufbau principle (each added electron occupies the subshell of lowest energy available), Pauli exclusion principle (no two electrons can have the same set of four quantum numbers), and Hund’s rule of maximum multiplicity (whenever possible, electrons retain unpaired spins in degenerate orbitals).
The relative energies of the subshells determine the order in which atomic orbitals are filled (1s, 2s, 2p, 3s, 3p, 4s,...
The Aufbau Principle and Hund's Rule03:02

The Aufbau Principle and Hund's Rule

To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the subshell of...
Electron Configuration of Multielectron Atoms03:26

Electron Configuration of Multielectron Atoms

The alkali metal sodium (atomic number 11) has one more electron than the neon atom. This electron must go into the lowest-energy subshell available, the 3s orbital, giving a 1s22s22p63s1 configuration. The electrons occupying the outermost shell orbital(s) (highest value of n) are called valence electrons, and those occupying the inner shell orbitals are called core electrons. Since the core electron shells correspond to noble gas electron configurations, we can abbreviate electron...
Electron Orbital Model01:18

Electron Orbital Model

Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...

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Photoelectron Imaging of Anions Illustrated by 310 Nm Detachment of F&#8722;
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Uniform electron gases. I. Electrons on a ring.

Pierre-François Loos1, Peter M W Gill

  • 1Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia. loos@rsc.anu.edu.au

The Journal of Chemical Physics
|May 3, 2013
PubMed
Summary

We present a new model for one-dimensional uniform electron gases (UEGs) confined to a ring. Our study provides analytical and numerical insights into their energy behavior across various densities and electron numbers.

Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Many-Body Physics

Background:

  • One-dimensional uniform electron gases (UEGs) are fundamental systems for understanding electron correlation.
  • Existing models often face limitations in describing UEGs across diverse density regimes.
  • A novel theoretical framework is needed to capture the behavior of UEGs confined in one dimension.

Purpose of the Study:

  • To introduce and analyze a new paradigm for one-dimensional uniform electron gases (UEGs) confined to a ring.
  • To investigate the ground-state energy of this system using perturbation theory and numerical methods.
  • To provide a comprehensive understanding of UEG behavior across a wide range of electron numbers and densities.

Main Methods:

  • Application of Rayleigh-Schrödinger perturbation theory for the high-density regime.

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  • Utilization of strong-coupling perturbation theory for the low-density regime.
  • Numerical studies employing Hylleraas-type and quantum Monte Carlo methods for electron numbers (n) from 2 to 10.

    • Main Results:

    • Derived explicit expressions for ground-state energy coefficients in both high-density (ε₀, ε₁, ε₂, ε₃) and low-density (η₀, η₁) regimes.
    • Determined the thermodynamic (large-n) limits for these energy coefficients.
    • Combined perturbative and numerical results to map the system's behavior across the full parameter space of n and Seitz radius (r(s)).

    Conclusions:

    • The proposed model offers a robust framework for studying one-dimensional uniform electron gases.
    • The analytical expressions and numerical data provide valuable benchmarks for future theoretical and experimental investigations.
    • This work elucidates the intricate interplay of electron correlation and dimensionality in confined quantum systems.