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Related Concept Videos

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.
Thermodynamic Potentials01:26

Thermodynamic Potentials

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
Potential-Energy Criterion for Equilibrium01:16

Potential-Energy Criterion for Equilibrium

Potential energy or potential function plays an essential role in determining the stability of a mechanical system. If a system is subjected to both gravitational and elastic forces, the potential function of the system can be expressed as the algebraic sum of gravitational and elastic potential energy. If the system is in equilibrium and is displaced by a small amount, then the work done on the system equals the negative of the change in the system's potential energy from the initial to the...
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...
Standard Electrode Potentials03:02

Standard Electrode Potentials

On comparing the reactivity of silver and lead, it is observed that the two ionic species, Ag+ (aq) and Pb2+ (aq), show a difference in their redox reactivity towards copper: the silver ion undergoes spontaneous reduction, while the lead ion does not. This relative redox activity can be easily quantified in electrochemical cells by a property called cell potential. This property is commonly known as cell voltage in electrochemistry, and it is a measure of the energy which accompanies the charge...
Controlled-Potential Coulometry: Electrolytic Methods01:17

Controlled-Potential Coulometry: Electrolytic Methods

Controlled-potential coulometry, also known as potentiostatic coulometry, employs a three-electrode system in which the working electrode's potential is precisely regulated using a potentiostat. Platinum working electrodes are utilized for positive potentials, while mercury pool electrodes are favored for extremely negative potentials. The platinum counter electrode is separated from the analyte using a membrane or salt bridge to avoid interference in the analysis.
The chosen potential ensures...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Published on: April 8, 2020

A new practical scheme for the optimized effective potential method.

T Fukazawa1, H Akai

  • 1Department of Physics, Graduate School of Science, Osaka University, Japan.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 10, 2011
PubMed
Summary
This summary is machine-generated.

We present a new method to determine the optimized effective potential (OEP) for extended systems, resolving ambiguities in previous approaches. This advance facilitates broader application of OEP in density functional theory calculations.

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Area of Science:

  • Computational Physics
  • Quantum Chemistry
  • Materials Science

Background:

  • The optimized effective potential (OEP) method offers advantages over the local density approximation in density functional theory.
  • OEP has seen limited use in extended systems due to an ambiguous, ad hoc determined constant.
  • This ambiguity hinders accurate electronic structure calculations for materials.

Purpose of the Study:

  • To develop a practical and unambiguous scheme for determining the OEP in extended systems.
  • To overcome limitations of existing OEP methods for periodic materials.
  • To enable more accurate density functional theory calculations for condensed matter.

Main Methods:

  • A novel scheme is proposed to determine the indefinite constant in OEP.
  • The constant is determined by minimizing the total energy of the system.
  • An exchange-only version of the scheme was implemented.

Main Results:

  • The new scheme successfully determines the OEP without ambiguity.
  • The method was applied to crystalline alkali metals (Li, Na, K).
  • Applications included ferromagnetic Fe and antiferromagnetic MnO, demonstrating its versatility.

Conclusions:

  • The developed OEP scheme provides a robust and unambiguous approach for extended systems.
  • This method enhances the applicability of OEP in materials science and condensed matter physics.
  • Accurate electronic structure calculations for various materials are now more feasible.