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Related Concept Videos

Energy Associated With a Charge Distribution01:21

Energy Associated With a Charge Distribution

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The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
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Free Energy Changes for Nonstandard States

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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
 
where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient...
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Energy Diagrams - II01:10

Energy Diagrams - II

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Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the system.
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Energy Transfer in Chemical Reactions01:16

Energy Transfer in Chemical Reactions

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Chemical reactions require sufficient energy to cause the matter to collide with enough precision and force that old chemical bonds can be broken and new ones formed. In general, kinetic energy is the form of energy powering any type of matter in motion. Imagine a person building a brick wall. The energy it takes to lift and place one brick on top of another is the kinetic energy—the energy matter possesses because of its motion. Once the wall is in place, it stores potential energy.
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The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

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In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
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Arrhenius Plots02:34

Arrhenius Plots

39.0K
The Arrhenius equation relates the activation energy and the rate constant, k, for chemical reactions. In the Arrhenius equation, k = Ae−Ea/RT, R is the ideal gas constant, which has a value of 8.314 J/mol·K, T is the temperature on the kelvin scale, Ea is the activation energy in J/mole, e is the constant 2.7183, and A is a constant called the frequency factor, which is related to the frequency of collisions and the orientation of the reacting molecules.
The Arrhenius equation can be used...
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Exchange-Correlation Energy from Green's Functions.

Steven Crisostomo1, E K U Gross2, Kieron Burke1,3

  • 1Department of Physics and Astronomy, <a href="https://ror.org/04gyf1771">University of California, Irvine</a>, California 92697, USA.

Physical Review Letters
|September 6, 2024
PubMed
Summary
This summary is machine-generated.

We present a new method to calculate density-functional theory (DFT) exchange-correlation energies using Green's functions. This approach offers a spectral view, separating single-particle and many-particle effects in quantum systems.

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Area of Science:

  • Quantum many-body physics
  • Computational condensed matter physics

Background:

  • Density-functional theory (DFT) excels at ground-state properties.
  • Green's function methods, like GW, are standard for spectral functions.
  • A gap exists in directly linking DFT exchange-correlation to Green's functions.

Purpose of the Study:

  • To derive DFT exchange-correlation energy from Green's function formalism.
  • To establish a spectral representation for DFT exchange-correlation.
  • To provide an alternative to the fluctuation-dissipation theorem in DFT.

Main Methods:

  • Utilizing the Galitskii-Migdal formula.
  • Extracting exchange-correlation energy from Green's function.
  • Developing a spectral representation of exchange-correlation.

Main Results:

  • Successfully derived DFT exchange-correlation energy from Green's function.
  • Demonstrated a spectral representation revealing distinct single-particle and many-particle contributions.
  • Applied the method to the uniform electron gas and the two-site Hubbard model.

Conclusions:

  • The spectral approach offers a novel perspective on DFT exchange-correlation.
  • This method provides a bridge between Green's function techniques and DFT.
  • The findings are applicable to various quantum many-body systems.