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Related Concept Videos

Calculations of Electric Potential II01:27

Calculations of Electric Potential II

An electric dipole is a system of two equal but opposite charges, separated by a fixed distance. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, but only under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is equivalent to heat at the molecular level.
Consider a...
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The Quantum-Mechanical Model of an Atom

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. Schrödinger...
Force and Potential Energy in One Dimension01:13

Force and Potential Energy in One Dimension

Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
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Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
Calculations of Electric Potential I01:15

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Consider a ring of radius R with a uniform charge density λ. What will the electric potential be at point M, which is located on the axis of the ring at a distance x from the center of the ring?
The ring is divided into infinitesimal small arcs such that point M is equidistant from all the arcs. Here, the cylindrical coordinate system is used to calculate the electric potential at point M. A general element of the arc between angles θ and θ + dθ is of the length Rdθ and has a charge of λRdθ.
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Junction Potentials in Galvanic Cells

The Nernst equation, derived under the assumption of thermodynamic equilibrium, calculates the electromotive force (emf) as the sum of potential differences at phase boundaries in a reversible cell without a liquid junction. However, in irreversible cells such as the Daniell cell, an additional potential difference named the liquid-junction potential (EJ) arises across the interface of two electrolyte solutions due to different ion diffusion rates. This EJ represents the potential difference...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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The pseudopotential approximation in electronic structure theory.

Peter Schwerdtfeger1

  • 1Centre for Theoretical Chemistry and Physics (CTCP), The New Zealand Institute for Advanced Study (NZIAS), Massey University Auckland, Private Bag 102904, 0745 Auckland, New Zealand. peter.schwerdtfeger@gmail.com

Chemphyschem : a European Journal of Chemical Physics and Physical Chemistry
|August 3, 2011
PubMed
Summary
This summary is machine-generated.

The pseudopotential approximation, a key electronic structure theory, accurately models atoms, molecules, and solids. Relativistic quantum theory enhances its precision for heavy elements, making it widely used.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics

Background:

  • The pseudopotential approximation, introduced by Hellmann in 1934, is a cornerstone of electronic structure calculations.
  • Accurate modeling of atomic and molecular systems is crucial for understanding chemical and physical properties.

Purpose of the Study:

  • To review the pseudopotential approximation as a successful theory for electronic structure calculations.
  • To highlight recent advancements and applications, particularly for systems with heavy elements.

Main Methods:

  • Review of the pseudopotential approximation theory.
  • Incorporation of recent developments in relativistic quantum theory.
  • Adjustment of pseudopotential parameters to valence spectra.

Main Results:

  • Pseudopotential approximation yields results in excellent agreement with all-electron calculations when using a small-core definition.
  • Accurate adjustment of parameters to valence spectra is achievable with modern relativistic quantum theory.
  • The method is highly effective for properties of atoms, molecules, and the solid-state.

Conclusions:

  • The relativistic pseudopotential approximation is a highly accurate and efficient method for electronic structure calculations.
  • Its applicability is significantly enhanced for systems containing heavy elements.
  • This method is now the most widely applied approach for such systems.