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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...
Coulomb's Law01:30

Coulomb's Law

Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude of the force is linearly proportional to the net charge on each object and inversely proportional to the square of the distance between them. The direction of the force vector is along the imaginary line joining the two objects and is dictated by the signs of the charges involved.
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Calculations of Electric Potential I01:15

Calculations of Electric Potential I

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.
Coulomb's Law and The Principle of Superposition01:15

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Coulomb's Law describes the force experienced by two point charges under each other's presence. But what if there are more than two charges? For example, if there is a third charge, does it experience a force that is a simple combination of the individual forces due to the first two charges? Can it be described mathematically?
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Junction Potentials in Galvanic Cells01:21

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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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Application of Electrophysiology Measurement to Study the Activity of Electro-Neutral Transporters
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Universal correction for the Becke-Johnson exchange potential.

E Räsänen1, S Pittalis, C R Proetto

  • 1Department of Physics, Nanoscience Center, University of Jyväskylä, FI-40014 Jyvaskyla, Finland. erasanen@jyu.fi

The Journal of Chemical Physics
|February 2, 2010
PubMed
Summary
This summary is machine-generated.

This study corrects the Becke-Johnson exchange potential for improved accuracy in density-functional theory calculations. The enhanced potential accurately models systems with electric and magnetic fields, crucial for electronic structure studies.

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Area of Science:

  • Computational chemistry
  • Quantum mechanics
  • Materials science

Background:

  • The Becke-Johnson (BJ) exchange potential is widely used in density-functional theory (DFT) for electronic structure calculations.
  • The original BJ potential exhibits limitations in systems with non-Coulombic potentials or external fields.

Purpose of the Study:

  • To develop a system-independent correction to the Becke-Johnson exchange potential.
  • To enhance the potential's applicability to systems under external electric or magnetic fields and current-carrying states.

Main Methods:

  • The correction involves enforcing gauge-invariance of the potential.
  • The modified potential is made exact for single-electron systems.
  • The corrected potential's performance is evaluated through computational tests.

Main Results:

  • The corrected Becke-Johnson potential demonstrates improved accuracy for electronic structure calculations.
  • The enhanced potential accurately describes systems with external electric fields, such as a hydrogen chain.
  • The corrected potential performs well for systems in magnetic fields, exemplified by a four-electron harmonium.

Conclusions:

  • The developed correction significantly improves the Becke-Johnson exchange potential's reliability.
  • The gauge-invariant and single-electron exact potential is suitable for diverse electronic structure problems, including those with external fields.
  • This work provides a more robust tool for computational studies in chemistry and physics.