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Adiabatic Processes for an Ideal Gas01:18

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When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...
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Free expansion of a gas is an adiabatic process. However, there are few differences between free expansion and adiabatic expansion. During free expansion, no work is done, and there is no change in internal energy. But, for an adiabatic expansion, work is done, and there is a change in internal energy. During an adiabatic process, the relation between the pressure and volume is obtained from the condition for the adiabatic process, that is, 
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Exchange-only virial relation from the adiabatic connection.

Andre Laestadius1,2, Mihály A Csirik1,2, Markus Penz1,3

  • 1Department of Computer Science, Oslo Metropolitan University, 0130 Oslo, Norway.

The Journal of Chemical Physics
|February 29, 2024
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This study revisits the Levy-Perdew exchange-only virial relation. We introduce a new formulation using the adiabatic connection, defining exchange energy via a derivative, and prove a relation without needing an explicit local-exchange potential.

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Area of Science:

  • Quantum Chemistry
  • Density Functional Theory

Background:

  • The Levy-Perdew relation is fundamental in understanding exchange energy.
  • Existing formulations often rely on explicit local-exchange potentials.

Purpose of the Study:

  • To revisit and reformulate the exchange-only virial relation.
  • To develop a formulation independent of explicit local-exchange potentials.

Main Methods:

  • Utilizing the adiabatic connection method.
  • Defining exchange energy via the right-derivative of the universal density functional with respect to coupling strength at lambda=0.
  • Employing v-representability for a fixed density at varying coupling strength.

Main Results:

  • The exchange energy is expressed as a limit involving the exchange-correlation potential.
  • An exchange-only virial relation is proven without requiring an explicit local-exchange potential.
  • Demonstrated that a local-exchange potential is not necessarily warranted as such a limit.

Conclusions:

  • The reformulated exchange-only virial relation offers a new perspective.
  • This approach bypasses the need for explicit local-exchange potentials, simplifying theoretical treatments.
  • Highlights the importance of v-representability in deriving such relations.